EUGENE ACKER MAN ]E3QQQQQQBBBBSOOE3E II El Marine Biological Laboratory Library D Woods Hole, Mass. H D C D B 8 ^ ! D II I Presented by \i a ii n ii t| Prentice-Hall, Inc. S | 1962, July k II II ^ R E8SQSQQQQQQQQQSE3E Biophysical Science EUGENE ACKERMAN Consultant, Section of Biophysics Mayo Clinic Associate Professor of Biophysics Mayo Foundation Rochester, Minnesota Biophysical Science PRENTICE-HALL, INC. Englewood Cliffs, N. J. 1962 ©-- 1962, PRENTICE-HALL, INC. Englewood Cliffs, X. J. All rights reserved. No part of this book may be reproduced in any form, by mimeo- graph or any other means, without per- mission in writing from the publisher. Library of Congress Catalog Card Number 62-1 1880 Printed in the United States of America 07715-C Preface This book presents an introduction to many of the topics which are presently considered part of biophysics. Biophysics deals with biological problems; accordingly, the various chapters have been grouped by the type of problem described rather than by the meth- odology employed. The mathematical level required has been limited, in most cases, to elementary calculus. As a separate discipline, biophysics is a recent addition to the sub-divisions of natural science. Until the mid-nineteenth century, it was quite common for investigators to be natural scientists con- tributing to many diverse fields. A well-known scientist who exem- plified this wide range of interest was Hermann von Helmholtz, who was trained as a medical doctor and practiced medicine. He not only conducted histological studies of the eye and ear, but also worked on theories of vision and hearing. In addition to being an excellent biologist, Helmholtz was an outstanding physicist. He developed acoustic instrumentation which he used for frequency analyses of speech and music. His contributions to thermodynamics are emphasized by the term Helmholtz free energy. His name is asso- ciated with a law in geometrical optics as well as with a differential equation for sinusoidal waves. With the growth of factual knowledge, it became more difficult for a person to do significant work in both the physical and biological sciences. Within each division of natural science, large numbers of subdivisions appeared; each small field had its own textbooks, its own theories, and its own part of human knowledge. However, there is a group of problems for which extreme speciali- zation is not desirable. Many of the problems of biophysics fall vi Preface into this category, and require a knowledge of several specialized fields. For example, a complete background for the study of vision must include geometrical optics, spectroscopy, quantum biochemistry, physiology, psychology, neurophysiology, and electronics. A certain group of research topics, all of which involve both biology and advanced physics, have come to be called biophysics. However, there is no general agreement concerning the topics properly belonging to this field. Those included here are the au- thor's choice and emphasize his interests. They do include most of the fields generally assigned to biophysics. Biophysics has become a field that is important for all physicists to study. For the prospective college teacher, it presents a variety of examples which can make general physics more interesting and of greater direct personal appeal. Accordingly, students from bio- logical and premedical curricula will learn more physics in a general course taught by an instructor well versed in biophysics. Similarly, the industrial physicist will find that a biophysics course will broaden his appreciation of the applications of physics. Biophysics is likewise a valuable course for seniors or graduate students majoring in biological sciences or medicine. Representing a different approach to topics they may study in other courses, biophysics can make an important contribution to a well-rounded training in biology. The premedical student will find that a bio- physics course will help him to understand normal and abnormal physiology and will make electromedical apparatus more useful to him. Another group for which a biophysics course may be useful is that of electrical engineers. The field of medical electronics has grown almost concurrently with the growth of biophysics. Each of these different types of readers will have different back- grounds and preparations, so background material from physics and biology is introduced at appropriate points. Such background material will give the reader an appreciation of the importance of both physics and biology. Biophysics is as unsuited to people who know no biology as to those who know no physics. In terms of the nature of the material covered, biophysics is cer- tainly closer to conventional biology than to traditional physics. Nonetheless, most physics majors can equip themselves, by extra reading, with sufficient biological knowledge to understand all the topics of biophysics. However, certain students majoring in the biological sciences must accept on faith the conclusions of many mathematical proofs. In terms of methodology, as opposed to content, biophysics is closer to physics than to biology. Preface vii To develop a branch of natural science as a logical structure, it is desirable to describe the behavior of highly organized systems in terms of the properties of simpler systems. This is not always feasible and in some cases cannot be followed at all. For example, in physics one discusses electric currents before attempting to present electronic conduction bands in metals. In this text we have tried to start from more general topics with which all varieties of readers will be intuitively familiar, and proceed to simpler but more abstract ideas. Thus, Part A on special sensory systems includes a chapter on vision and the eye; the neural aspects of vision are pre- sented in a chapter following discussion of nerve activity ; the molec- ular actions which convert light into nerve impulses form the basis of a chapter in Part D which deals with molecular biology; finally, the eye as a coding mechanism is discussed in a chapter on informa- tion theory located in Part E. Specialized physical instruments, necessary for these and other studies, are discussed in the last part of the text. All of the areas of the text taken together comprise biophysics. Within each area a careful selection has been made from a variety of topics all of which are part of biophysics. The topics included in this text were chosen not only for their relative importance, but also for their suitability for presentation in a one-year course for students with a variety of backgrounds. Other possible topics are included in the discussion questions at the end of each section of the text. It is the author's hope that the reader of this book will gain an insight into the nature of the topics included in biophysics, recog- nizing the attempt to quantify and develop biological problems in terms of physical models wherever this is practical. The reader should become acquainted both with the biological basis of the various areas of biophysics and also with the essential role of math- ematical analysis in most biophysical problems. The author wishes to thank his many students and friends, all of whom have had such a profound influence on the material in this text. It is not possible to name all who have helped, but special mention is made of those who contributed an extra amount of their time and ideas. They are: Dr. A. Anthony and Dr. G. K. Strother of the Pennsylvania State University; Dr. A. A. Benson of the Univer- sity of California; Dr. K. N. Ogle, Dr. A. L. Orvis, and Dr. C. M. Gambill of the Mayo Clinic; and Dr. A. S. Brill of Yale University. The permission of numerous publishers and authors to reprint their figures is also gratefully acknowledged. Without secretarial help, this text would never have been completed; special thanks are due viii Preface Miss Frances Fogle (Pennsylvania State University) and Miss Lorette Hentges (Mayo Clinic) for their part in making this text a reality. Eugene Ackerman Rochester, Minnesota Contents A. Special Sensory Systems I. Sound and the Ear 1. Hearing, 3; 2. Acoustics, 5; 3. Hearing Tests, 10; 4. Anatomy and Action of the Ear, 1 9 2. Light and the Eye 27 1. Vision, 27; 2. Optics, 29; 3. Anatomy of the Eye, 34; 4. Thresholds and Acuity, 43 3. Special Uses of Hearing and Vision 52 /. Introduction, 52 ; 2. Echo-Location in Bats, 53 ; 3. Echo- Location in Other Animals, 58 ; 4. Sense of Direction in Bees and Ants, 59 ; 5. Migration and Homing, 6 1 B. Nerve and Muscle 4. The Conduction of Impulses by Nerves 69 /. The Role of the Nervous System, 69 ; 2. A Brief Glance at Elec- tricity, 72; 3. Anatomy and Histology of Neurons, 74; 4. The Spike Potential, 78 ; 5. Synaptic Conduction, 83 IX 7! 16 j Contents 5. Electrical Potentials of the Brain 88 /. Electroencephalography, 88; 2. The Central Nervous System, 89 ; 3. Feedback Loops and the Nervous System, 92 ; 4. The Electro- encephalographic Patterns, 96; 5. Abnormal Electroencephalo- graphs Patterns, 100 ; 6. Summary, 1 02 6. Neural Mechanisms of Hearing 104 /. Place and Telephone Theories, 104; 2. Cochlear Mechanism of Neural Excitation, 108; 3. Arm Analogs and Neural Sharpen- ing, 111; 4. Cortical Representation, 113; 5. Summary of Hearing, 1 1 7 7. Neural Aspects of Vision 119 A Color Discrimination, 119; 2. Cellular Mechanisms, 124; 3. Direct Neural Measurements, 129; 4. Neural Sharpening and Analyses, 131; 5. Cortical Representation, 133; 6. Summary of Vision, 135 8. Muscles 137 1. Introduction, 137; 2. Anatomy, 138; 3. Physical Changes During Muscular Contraction, 141; 4. Muscle Chemistry, 147; 5. Electron-Microscope Studies of Muscles, 151; 6. Summary, 154 9. Mechanical and Electrical Character of the Heart Beat 157 1. Role of the Vertebrate Circulatory System, 157; 2. Blood Pressures and Velocities, 1 58 ; 3. The Vertebrate Heart, 161; 4. The Heart Sequence, 1 63 ; 5. Electrocardiography, 168 ; 5. Physics of Dipoles, 171; 7. F^c/or Electrocardiography, 1 75 ; 5. Summary, 177 C. Physical Microbiology 10. Cellular Events Produced by Ionizing Radiations 185 /. Ionizing Radiation as a Biological Tool, 1 85 ; 2. Dosage, 187; 3. Mitosis and Meiosis, 189; 4. Visible Cellular Effects, 191; 5. Genetic Effects, 1 96 ; 6. Evolution, Mutation and Fall-out, 200 ; 7. Summary, 20 1 Contents xi 11. The Absorption of Electromagnetic and Ultrasonic Energy 204 1. Role of Nonionizing Radiation, 204 ; 2. Electrical Imped- ances, 205 ; 3. Biological Impedance, 208 ; 4. Ultrasonics, 213; 5. Nondestructive Effects of Ultrasound, 214; 6. Dia- thermy, 217; 7. Summary, 2 1 8 12. Destructive Effects of High Intensity Ultrasound 220 /. High Intensity Ultrasound, 220 ; 2. Cavitation, 222 ; 3. Biological Cells and Cavitation, 224 ; 4. Cellular Fragilities and Resonances, 226 ; 5. Neurosurgery with Ultrasound, 230 13. Mechanical Resonances of Biological Cells 233 /. Experimental Basis, 233; 2. Inter facial-Tension Model, 236; 3. Gelatinous-Shell Model, 240; 4. More Exact Treatments, 242; 5. Summary, 244 14. Structure of Viruses 246 /. Introduction, 246; 2. Phage Studies Using Bacteriological Methods, 248 ; 3. Virus Studies Using Physical Methods, 25 1 ; 4. Physical Biochemistry of Viruses, 254; 5. Phage Genetics, 256; 6. Summary, 260 D. Molecular Biology 15. X-ray Analyses of Proteins and Nucleic Acids 267 /. Protoplasm, 267 ; 2. Proteins, 271 ; 3. Nucleic Acids, 277 ; 4. X-ray Diffraction, 280; 5. Protein Structure, 286; 6. Nu- cleic Acid Structure, 292 ; 7. Summary, 296 16. Molecular Action of Ionizing Radiations 299 /. Introduction, 299; 2. Polymers, Proteins, and DNA, 300; 3. Radiation Damage to Synthetic High Polymers, 302 ; 4. Target Theory, 305 ; 5. Inactivation of Dried Protein Films, 307 ; 6. Indirect Effects on Proteins and Nucleic Acids, 311; 7. Summary, 313 17. Enzyme Kinetics of Hydrolytic Reactions 315 /. Introduction, 31 5; 2. Enzymes, 318; 3. Michaelis-Menten Kinetics of Hydrolases, 320; 4. Action of Inhibitors, 327 XII Contents 18. Enzymes: Kinetics of Oxidations 332 /. Catalase, 332; 2. Peroxidase, 341 ; 3. Biological Oxidations, 344 ; 4. Oxidative Phosphorylation, 346 ; 5. Summary of En- zyme Kinetics, 349 19. Molecular Basis of Vision 351 /. Color Vision and Photopigments, 351; 2. Rhodopsin, 352; 3. Other Photopigments, 357; 4. The Origin of the Neural Spike, 358 20. Photosynthesis 360 1. Introduction, 360; 2. A Little Plant Histology, 361; 3. Basic Chemistry of Photosynthesis, 364 ; 4. The Path of Carbon in Photosynthesis, 368; 5. The Photosynthetic Pigments, 370; 6. The Light Reaction, 373; 7. Summary, ?>11 E. Thermodynamics and Transport Systems 21. Thermodynamics and Biology 385 1. The Role of Thermodynamics in Biology, 385 ; 2. The Laws of Thermodynamics, 386 ; 3. Other Thermodynamic Functions, 390 ; 4. Equilibrium Constants, 392 \ 5. Reactions of Catalase, 396 22. Thermodynamics of Enzyme Reactions 401 1. Collision Theory of Reactions, 401 ; 2. Collision Theory Ap- plied to Enzyme Reactions, 406 ; 3. Absolute Rate Theory, 408 ; 4. Denaturation Studies, 412; 5. Diffusion Studies ,415; 6. Summary, 417 23. Diffusion, Permeability and Active Transport 419 1. Introduction, 419; 2. Diffusion Equations, 42 1 ; 3. The Diffusion of Oxygen into Cells, 426 ; 4. Permeability of Red Blood Cells, 429 ; 5. Active Transport, 432 ; 6. Summary, 435 24. The Molecular Basis of Nerve Conduction 437 1. Donnan Membrane Potentials, 437 ; 2. Quasi-Static Analogs, 440 ; 3. Biochemical Extractions, 443 ; 4. Clamped Nerve Ex- periments, 446; 5. Summary, 457 Contents xlii 25. Information Theory and Biology 460 /. Languages, 460 ; 2. Information Theory — General Discus- sion, 46 1 ; 3. Information and Sensory Perception, 467 ; 4. In- formation Theory and Protein Structure, 47 1 ; 5. The Coding of Genetic Information, 474; 6. Summary, 475 F. Specialized Instrumentation 26. Absorption Spectrophotometry 481 /. Role of Absorption Spectrophotometry in Biology, 48 1 ; 2. Units and Symbols of Absorption, 484; 3. Spectrophotometers, 488; 4. Flow Systems, 495 ; 5. Split-Beam and Dual-Beam Spectro- photometers, 496 27. Quantum Mechanical Basis of Molecular Spectra 501 /. Introduction, 50 1 ; 2. An Elementary Approach to Quantum Mechanics, 502; 3. Molecular Spectra — Rotational and Vibra- tional Bands, 509 ; 4. Electronic Levels of Atoms and Molecules, 516 28. Magnetic Measurements 525 1. Magnetic Effects in Biology, 525 ; 2. Paramagnetism and Diamagnetism, 526 ; 3. Static Measurement Techniques, 528 ; 4. Resonance Measurements, 531; 5. Limitations and Applications of Magnetic Measurements, 534 29. Microscopy 537 /. Types of Microscopes, 537; 2. The Bright-Field Light Micro- scope, 538 ; 3. The Dark-Field Microscope, 542 ; 4. Phase- Contrast Microscopy, 544 ; 5. Interference-Contrast Microscopy, 545 ; 6. The Polarizing Microscope, 548 ; 7. Ultraviolet and X-ray Mi- croscopes, 550 ; 8. The Electron Microscope, 5o 1 30. Tracer Techniques 557 1. Introduction, 557 ; 2. Radioactive Tracers, 558 ; 3. C 14 , 563; 4. 7 131 , 565; 5. P 32 , 566; 6. Stable Isotopes, 567; 7. jV 15 , 568; 8. Summary, 570 XIV Contents 31. Electronic Computers 571 /. Need for High Speed Computation, 571; 2. Analog and Digital Computers, 572; 3. A Bone-Density Analog Computer, 573; 4. Curve Fitters, bll \ 5. Digital Computers, 580 Appendices A. Auditory Acoustics, 589 B. Geometrical Optics, 595 C. Electrical Terminology {Used in Chapters 4 through 7), 605 D. Ionizing Radiations, 610 Index 615 A Special Sensory Systems Introduction to Part A The first two chapters were chosen as biophysical topics, the ideas of which are intuitively familiar to a wide group of potential readers. These two chapters on "Sound and the Ear" and "Light and the Eye" emphasize basic concepts such as the physical nature of the stimuli and the anatomical character of the receptors. The ideas of Chapters 1 and 2 are extended in Chapter 3, "Special Uses of Sensory Systems," to unique applications of auditory and visual information by several animal species — uses which man can duplicate only with electronic equipment. Sensory systems form links between the central nervous system and the external world. Biophysicists study not only hearing and vision, but also other sensory systems such as taste, proprioception, and balance. However, the special senses of hearing and vision appear more appropriate for textbook material since they have been studied in greater detail. Ultimately, a discussion of hearing must involve such complex concepts as nerve mechanisms and information theory. These are presented in later chapters, following more general developments, namely, in Chapter 6, Part B, and Chapter 25, Part E. Likewise, additional topics in the field of vision are included in Chapter 7, Part B, Chapter 19, Part D, and Chapter 25, Part E. I Sound and the Ear I. Hearing The study of hearing is one of the oldest fields in biophysics. The reception and analysis of sound by the human ear has interested men who studied either physics or biology and has appealed especially to persons having a background in both the physical and biological sciences. The hearing mechanisms form one of the major sensory systems through which animals are stimulated by their environment. Vertebrates, in particular, have complicated sensory receptor systems which analyze incident sound waves for tone, quality, and loudness. Man relies on visual information when he wants accuracy such as is required in recording scientific data. However, in communicating daily with the people around him, man relies principally on hearing. As a result of this major role of hearing in social intercourse, persons with a hearing deficiency suffer more social disapproval than do those with visual deficiencies. Hearing is important not only for communicating with other persons, but also for avoiding many dangers such as being struck by an automobile. In addition, we learn to recognize certain living creatures and many types of events by their noises, for example, the cat's meow and the telephone's ring. Human emotions, too, are 3 4 Sound and the Ear /I : I influenced by the sense of hearing. Many of our forms of entertainment — concerts, theatre, movies, radio, and even television — depend upon our sense of hearing. Hearing can be studied from many different points of view. Physi- cists have learned how sound waves are generated and how they are transmitted. Anatomists have probed into the structure of the ear on a gross level and also on a microscopic level. They have traced the path- ways by which auditory nerve impulses travel from the ear to the brain. Psychologists, physiologists, and physicists all have studied the thresholds of sensitivity of the hearing system and the way in which we understand speech. Most of these groups, and especially biophysicists, have been interested in the manner in which the hearing organ operates, how sounds are analyzed, how they are converted into nervous impulses and then separated according to pitch, quality, and loudness. In this chapter and in Chapter 6, "Neural Mechanisms of Hearing," an attempt has been made to synthesize all of these different avenues of approach, while emphasizing those parts of each which have the greatest interest to the biophysicist. The first careful study of the ear and attempt to relate its structure to hearing was carried out by Helmholtz. Before that period, various theories of hearing existed, but few have had more significance than one which has survived in our colloquial speech. This was the idea that the ears were connected to a common hollow region within the head where the sound was somehow stored. If, so this theory went, we were not careful, the sound would go in one ear (through the storage chamber) and out the other. Since the middle of the last century, hearing has been the subject of many scientific investigations. The nature of these studies was radically altered around 1930 by the introduction of electronic techniques. These techniques have completely changed the study of hearing ; they have dramatically influenced the interpretation of all phases of hearing from pure acoustics to the final analyses of sounds within the brain. So complete is the dependence on electronic techniques today, that it is hard to remember that Helmholtz and Lord Rayleigh could do acoustic experiments successfully without electronic instrumentation. Hearing is the response to mechanical, vibratory stimuli. Not all such stimuli evoke the sensations of hearing. The sound must be loud enough to be heard and also be of a suitable pitch. The latter condition is physically equivalent to saying the vibration must be within the audible frequency range. Vibrations outside of this frequency range may be detected by human sensory systems other than hearing. At frequencies too low to be heard, vibrations are perceived through the sense of touch ; much greater amplitudes are needed for touch than are I : 2/ Sound and the Ear 5 needed for hearing. Frequencies higher than the audible range are not sensed until the energy becomes so great as to cause local heat and pain. Between these two extremes lie the frequencies to which the ear is sensitive. The exact frequency range depends on the person; it is influenced by his age and by the environment. All vertebrates have a hearing apparatus homologous to our ear, although the frequency ranges to which they respond are varied. Many other animals such as insects are sensitive to vibratory energy over a wide range of frequencies, but their receptors are different, and the mechan- isms involved in their response may be different. Even the single-celled animal, paramecium, can respond to vibratory energy in some fashion. Thus, there are many different types of sensory systems excited by vibratory mechanical energy. One of these, namely the human hearing apparatus, has been chosen for presentation in this chapter and in its sequel, Chapter 6, in Section B. 2. Acoustics The physical aspects of sound transmission and the vibration of the ear are a subdivision of acoustics. The latter, in turn, is a branch of physical mechanics. In order to read with understanding journal articles dealing with the ear and hearing, it is very helpful to be familiar with the terminology of acoustics and with the electro-acoustic analogs often used. The various acoustic terms useful in describing studies of hearing are defined and discussed briefly in Appendix A, entitled "Auditory Acoustics." In contrast, this section of this chapter contains only a few of the acoustic terms used most frequently in studies of the ear and hearing. Perhaps most familiar is the terra frequency which describes how many times a second the sound pattern is repeated. The simplest possible case is one in which the sound pressure, p, can be described by an equation such as p = po sin 2-nvt (1) where p Q is the acoustic pressure amplitude, / is the time, and v is the frequency. This is referred to as a pure tone. The latter term is applic- able since tone (or pitch) is the sensation associated with frequency. Most sounds consist of a mixture of frequencies which gives the sound its characteristic quality and timbre. A tuning fork comes close to pro- ducing a pure tone. One can come even closer by using an electronic oscillator and loudspeaker. Any complex tone can be represented as a sum of simpler pure tones. 6 Sound and the Ear /I : 2 This is known as a Fourier representation. In many cases, only a finite or a discrete set of frequencies is necessary; then, we refer to the repre- sentation as a Fourier series. Speech and the character of musical instruments are determined by the frequencies present and their relative amplitudes. In the most general case, the sound is represented by an amplitude distribution which is a continuous function of frequency. This amplitude function is called a Fourier transform. The amplitude distribution for a sound "ee" is shown in Figure 1. / \ * *•«=■>* * 7 — X 7 — _i L v i \ 1 \ *= — \- e C3 Co , C to ^£ C <*- 3 ° i5 0.2 0.5 1.0 Frequency (b) 2.0 5.0 10 kc Figure I. (a) Fourier Series. The complex wave form labeled "sum" can be formed by adding relative amounts of four pure tones shown, (b) Fourier transform (or spectrum). The spectrum of the sound "ee" has the general form shown. The Fourier transform is a complex number; only its absolute value is shown. A term closely related to frequency is wavelength, A. This is the distance between the two nearest wavefronts with the same displacement and particle velocity in a plane sound field. If one knows the frequency I : 2/ Sound and the Ear 7 and the velocity of sound propagation c, the wavelength may be deter- mined by the relationship X = - (2) The wavelength is important in discussing diffraction, a phenomenon common to all wave-motion. Diffraction patterns are significant when the wavelength is comparable to the object the sound wave encounters. At shorter wavelengths, specular reflection and shadows are produced, whereas at longer wavelengths, the wave is transmitted as though the object were not there. In air, a low tone of frequency 35 cps has a wavelength of about 10 m, which is comparable in size to a house. At the other end of the human audible range, a frequency of 9 x 10 3 cps (9 kc) has a wavelength of about 3 cm which is small compared to a person's head. Thus, the lowest audible frequencies will be diffracted around a house; in other words, the sound waves at these lowest frequencies will appear to bend around most obstacles. This makes it difficult to localize the source of the very low frequency tones below 100 cps. Conversely, the highest audible frequencies will form sharp shadows around small objects; the source of a 5-10 kc tone is easy to locate. At frequencies around 1 kc, the wavelength is comparable to the head. The diffraction pattern has the effect of increasing the amplitudes at the ear above those in the incident wave. This increased amplitude makes the sounds near 1 kc seem extra loud. 1 The loudness is not simply determined by the particle velocity v or the displacement in the incident wave. Rather, the loudness is most readily related to another physical characteristic, the sound pressure amplitude. The latter and not the particle velocity or displacement is actually measured in most acoustic experiments. The sound pressure p is defined as the difference between the average (or equilibrium) pressure P and the instantaneous total pressure, P; that is, P = P-Po (3) Diagrammatically, one may represent this as shown in Figure 2. The acoustic pressure p is a scalar which will vary with both position and time. Two waves of the same amplitude but traveling in opposite directions give rise to what is known as a standing wave pattern. Under some con- ditions, the wavelengths correspond to the characteristic dimensions of 1 Other effects discussed later in the chapter also contribute to the increased loudness of sounds at 1-3 kc. 8 Sound and the Ear /I : 2 a physical system, and the phenomenon of resonance arises. This is illustrated in Figures 3 and 4 for strings and organ pipes. Note that in each case a series of characteristic (eigen) frequencies exists. Vibrations at these fre- quencies are particularly easy to excite. The lowest possible frequency is called the funda- mental frequency or first harmonic. The next highest frequency is called the first overtone. If it is an integral multiple of the funda- mental, it is called a harmonic. For example, an overtone five times the fundamental is the fifth harmonic. The standing wave pattern in the outer ear is discussed further in Section 4. It was noted above that the loudness of a given pure tone is determined primarily by the sound pressure amplitude. Often, another physical term, intensity, is associated with loudness. Intensity is the energy transmitted across a unit area per unit time. In practice, intensity is difficult to measure and not too useful as a concept for studies of hearing. For a plane wave, the intensity T is related to the pressure by Time Figure 2. The dotted line shows the average pressure P and the solid line indicates the absolute pressure P. The difference between P and P is the acoustic pressure p. The maximum of p is A , the acoustic pressure amplitude. The figure is drawn for a pure tone showing simple har- monic dependence of p on time. In general, the form of p is more complex. An rms value of/) can be specified but not an amplitude for a com- plex wave form. T = I pc (4) where p is the root mean square (rms) acoustic pressure, p is the density of the air, and c is the wave velocity. For other wave shapes, the expression is more complex (although the term pc always appears). The intensity for a given value of p varies with the temperature, since pc also varies. Loudness depends only on p, not on the temperature. Instead of presenting data in terms of the rms sound pressure amplitudes, it is customary to use the sound pressure level L. This is defined by 201og © db (5) 2/ Sound and the Ear Fundamental 1 st Overtone v- ^^ -^ 2 nd Harmonic 2 nd Overtone 3 rd Overtone Fundamental 3 r Harmonic 4 Harmonic v n ft c 21 2c 21 3c 21 4c 21 ■in? sin^f sin^f sin*f Figure 3. Resonances of strings. The characteristic or reso- nant frequency is w n and the characteristic or eigenfunction is ip n . The displacement can be described by y = ZMn e±iw " where the A n 's are the amplitudes. The wave velocity where T is the tension and e is the mass per unit length. V) n Fundamental Fundamental Al 4r +n sing ^XT"^ ft Overtone 3 rd Harmonic fZ Jf sin 37TX 21 XX] 2 nd Overtone 5 th Harmonic fl ff sin 5 ^ 5 41 ^t Figure 4. Particle velocity for various overtones of a closed- end organ pipe. See Figure 3 for definition of the symbols. When the particle velocity has a node, the acoustic pressure has an anti-node, and conversely. The external ear canal re- sembles a closed-end organ pipe with a fundamental around 3 kc. 10 Sound and the Ear /I : 2 TABLE I Various Sound Pressure Levels Dynes/cm 2 SPL 160 db 10,000.00 Mechanical damage to human eardrum 100.00 0.01 140 Pain threshold Jet motor 120 Discomfort threshold Riveter (peak values) Damage to human hearing after prolonged exposure 100 Average factory Subway car Automobile 80 Class lecture 1.00 Loud radio 60 Typical office Conversational speech 40 Average living room 20 Very quiet room 0.0002 Threshold of hearing In air it is customary to use forp the arbitrary value 2 x 1 " 4 dynes/cm 2 . The 20 in the definition of decibels (db) arose out of historical reasons; from the properties of logarithms, one might equally well write this as I : 3/ Sound and the Ear II L = .0 log (g (6) or, for a plane wave, L = 10 log (J) (7) The latter is actually the original definition of a decibel. However, T depends on temperature, the medium, and the wave shape, so that the sound pressure level defined by Equation 5 is really a more con- venient quantity. The use of a logarithmic unit is helpful in plotting graphs, and to some extent loudness is proportional to the sound pressure level at fixed frequency. The logarithmic unit makes it possible to compare two sound pressure levels without knowing the absolute value of either. It also makes it appear as if many acoustic measurements were more precise than they actually are. The table on page 10 gives the sound pressure level of several common sounds, as well as the sound pressure amplitude p. In addition to decibels, persons working in psycho-acoustics have used many exotic units such as phons 2 and sones. 3 The purpose of these has been to bring the numbers measured into a closer correspondence with the psychological sensation of loudness. These units all depend on experiments on groups of people and are accordingly difficult to interpret either in terms of any direct physical significance or even in terms of their application to an individual. In this section, the physical quantities important in hearing have been introduced, and their application to a study of hearing has been indi- cated. The measurement of the typical values of these quantities, significant in human hearing, has given rise to a variety of types of tests. They are discussed in the following section. 3. Hearing Tests There are various ways of studying hearing. Tests on humans which do not involve any surgical techniques are discussed in this section. Clinically, the most widely employed tests measure the threshold of hearing. The observed thresholds are then compared with the normal threshold. The simplest of these tests uses pure tones. However, the 2 The loudness level of a sound measured in phons is defined as the sound pressure level of a 1 kc pure tone which sounds equally loud to the average observer. 3 The loudness of a sound may be measured in sones. A loudness of 1 sone is identical to a loudness level of 40 phons. The loudness of other sounds is measured in sones by subjective comparison to a 1 sone loudness. Ideally, the loudness in sones should be linearly related to the loudness level in phons. No such simple relationship exists. 12 Sound and the Ear /I : 3 exact sound pressure levels of the normal thresholds seem to be rather difficult to determine. The graph in Figure 5 shows the results of several investigations. These emphasize that the threshold depends to 0.01 I 0. 30cps 10 20 kc Frequency Figure 5. Pure tone thresholds. Note that the laboratory averages with trained, selected personnel are consistently lower than the mass survey averages. Recent studies at The Penn- sylvania State University by Professor J. Corso and his associ- ates gave mass survey values between the two curves shown. Notice that the threshold of feeling is not near the threshold of hearing at either 30 cps or 20 kc. The latter are limits of hearing in the sense that people can no longer distinguish tones outside of these limits. After J. G. R. Licklider, in Handbook of Experimental Psychology, S. S. Stevens, ed. (New York: John Wiley & Sons, Inc., 1951). some extent on who measures it. Notice that the ordinate is in decibels ; thus a difference of 20 db means a factor of 10 in the sound pressure. All the curves show the same general shape with a minimum threshold, that is maximum sensitivity, in the frequency range from 1-4 kc. When the tests are conducted under controlled laboratory conditions, with carefully screened young people, the thresholds are lower than those found in mass surveys. There exist various types of limits of hearing, none of which are very precise. These limits include a minimum pressure threshold and an upper pressure limit at each frequency, as well as a highest and a lowest I : 3/ Sound and the Ear 13 frequency limit at which one can hear. Of these, the threshold sound pressure level is most precise, but even it is a statistical limit. If an individual is presented with an acoustic pressure close to his threshold, he will hear the tone sometimes and not at other times. It is customary in tests of this nature to choose the halfway point where the subject hears the tone 50 per cent of the time as the limit of hearing. The upper limit of hearing is an even less clear concept. As the sound pressure level is raised towards 110 db, one becomes aware of feeling the sound in the external ear. At a still higher sound pressure level, perhaps 130 db, one begins to experience pain. If the sound pressure level is raised to 145 db, the pain becomes very severe. It has been shown in accidents due to carelessness that at sound pressure levels of about 155-160 db the human eardrum is ruptured. (The eardrum will eventually heal.) It is instructive to convert these sound pressure levels for eardrum rupture to actual sound pressures. Recall that the sound pressure level is defined by L = 20 log 10 (Plpo) where p = 0.0002 dynes/cm 2 If L = 160 db then log 10 p/p = 8 or pfp = 10 8 Hence p = 2 x 10 4 dynes/cm 2 This is the root mean square acoustic pressure. The acoustic pressure amplitude will be the V2 times greater for a pure tone. This gives an acoustic pressure amplitude A of A = 3 x 10 4 dynes/cm 2 The average atmospheric pressure is about 10 6 dynes/cm 2 , so that 160 db may also be written A = 0.03 atm The sound pressure level at which the eardrum is ruptured puts an upper limit on the loudness which one can hear. The low frequency limit to hearing is due to a different type of phenomenon. It used to be stated that the upper and the lower frequency limits of hearing were at the frequencies where the thresholds of pain and hearing crossed. At the low frequency end of the human hearing range, this does not seem to be the case. Rather, the limit at about 30 cps is due to the inability to identify tones or direction of frequency change. In the audible range, a person recognizes the direction in which a frequency change occurs, provided it is sufficiently great. For example, 14 Sound and the Ear /I : 3 if the frequency is lowered from, say, 1 ,000 cps to 500 cps, the listener hears a decrease in frequency of one octave. (A frequency ratio of 2 is called an octave in music.) Below about 30 cps, the listener cannot really distinguish tones or tell whether the frequency is being raised, lowered, or held constant. If the frequency is lowered to, say, 1 cps, the tone identified is not the applied sound frequency but rather some- thing in the neighborhood of 1,000 cps. Likewise, at high frequencies a point is reached above which a person can no longer distinguish tones. In addition, the threshold sound pressure rises very sharply. This latter effect limits experiments at the high frequency end of the spectrum. The exact frequency range in which this sharp rise occurs varies widely from individual to individual. For one graduate student who worked in the Pennsylvania State Uni- versity Acoustics Laboratory, this sharp rise occurred around 25 kc. He could tell that 23 kc was higher in pitch than 22 kc. The author's ears failed to respond to reasonable sound pressure levels if these were above 1 7 kc in frequency, whereas his wife did not hear above 6 kc. The highest frequency which normal humans hear varies by a factor of more than three. 4 This may seem large, but it is small compared to the variations in the pure tone thresholds. Variations from one individual to another may be as high as 40 db within the normal range of hearing. These numbers, when translated into actual acoustic pressures, represent a pressure ratio of a hundredfold, truly an enormous variation. In an ordinary room, the lowest sound pressure levels one can hear are limited by the ambient noise. In a very quiet room, where all the ambient noise is below the hearing threshold, the physiological noise level is approximately at the threshold of hearing. This physiological noise is due to a variety of causes: the pulse in the ear, the muscles contracting, breathing, and any motion of the joints. Physiological noise is effective only at those frequencies where the ear is most sensitive ; that is, the range 1-4 kc. Most sounds come to the ear from the air. Some, such as a few of the physiological noises, are transmitted by bone conduction. The entire structure of the middle and inner ear discriminates strongly in favor of airborne vibration as opposed to bone conduction. However, a suffi- ciently strong signal can be conducted by the bone. The bone con- duction threshold can be observed by blocking the ears 5 or by applying a vibrator directly to the head. The sound pressure levels necessary for hearing by bone conduction are about 40 db higher than by air conduction, and the threshold curve is much flatter. 4 Eight kc to higher than 25 kc. 5 This may raise the threshold. I : 3/ Sound and the Ear 15 The pure tone hearing threshold tests described above depend on the accuracy of the apparatus and the technique of the operator, as well as on the hearing of the person being tested. By suitable calibrating techniques, the equipment can be standardized so that the sound pressure levels are accurately known to within 1 db (that is, about ± 10 per cent in the actual sound pressure). It is difficult to improve on this by more than a factor of 2. The effect of the operator is harder to remove. He must present successively lower and then higher sound pressure levels to the subject. If he starts far above the threshold, the subject becomes familiar with the tone and will distinguish it at lower sound pressure levels than if the operator started below the threshold. The operator must cross and recross the threshold until, in his judgment, he has found a stable value. One very ingenious attempt to remove the effect of the operator was introduced by von Bekesy. His audiometer includes the person being tested as part of a feedback loop in an automatic control device designed to keep the sound pressure level at the ear close to the threshold. The system is illustrated in block diagram form in Figure 6. The output Ear Phone Z Oscillator z. Attenuator Motor Driving Chart and Oscillator Dial Record When depressed, motor increases attenuation. When re/eased, motor decreases attenuation. - Pen: Moves up and down indicating attenuation. Chart: Moves horizontally indicating frequency. Subject: Depresses switch when he hears sound. Releases switch when he does not. Figure 6. Block diagram of the Bekesy audiometer which records the threshold of hearing without influence of any operator other than the subject. of an oscillator is fed through a variable attenuator to the earphones. The subject is given a switch which he depresses when he hears the tone and releases when he does not. The switch is connected to a reversible motor which drives the variable attenuator in such a fashion that the 16 Sound and the Ear /I : 3 sound pressure level increases with the switch released and decreases with the switch depressed. The entire setup then hunts for the thresh- old, continuously crossing and recrossing it. A recording pen is attached to the variable attenuator. The pen writes on a calibrated chart, recording the instantaneous setting of the attenuator. Another motor drives both the chart and the oscillator so that a record is obtained of threshold level versus frequency. This level is recorded without any effect of the examiner. The Bekesy audiometer is very successful in limiting the role of any operator other than the subject. It also gives a continuous record of threshold versus frequency instead of values only at discrete points. It presents the threshold curve directly in a graphical form. However, it has several disadvantages. It is slower than an audiometer operated at discrete frequencies by an experienced technician. It is impossible with the Bekesy audiometer to distinguish between losses in a certain frequency range and apparent losses due to extraneous physiological noises such as swallowing. Using the discrete frequency audiometer, the operator crosses and recrosses the threshold, thereby eliminating the effect of extraneous physiological noises. Finally, the Bekesy audio- meter depends on the skill of the subject and his understanding of the instructions. Both of these will vary from person to person, introducing a nonhearing variable into the apparent threshold. An ideal compromise would be an instrument similar to the Bekesy audiometer but operating only at discrete frequencies. If the instru- ment could remain at one frequency until the threshold stays constant for, say, 15 seconds and then shift automatically to the next frequency, it would encompass most of the advantages of both the discrete frequency and the Bekesy audiometer. Unfortunately, this becomes so complex electronically that the author knows of only one audiometer of this type, and it takes a skilled electronic engineer to keep it running. The information obtained from a speech audiometer is different from that found by using a pure tone audiometer. In a speech audiometer various test words are presented at a constant sound pressure level. Some persons who have appreciable pure tone hearing losses at certain frequencies do not show any hearing loss for speech. Conversely, other people, with normal pure tone thresholds, have marked speech hearing deficiencies. The problem of recognition of speech is much more com- plex than hearing a pure tone. Understanding speech involves the function of several parts of the brain. Actually, speech can still be understood if any two continuous octaves of the audible spectrum are presented and the rest of the energy filtered out. The quality of the speech will be altered, but it is still understandable. (Even up to 50 per cent of every syllable or word can be removed. The remainder I : 3/ Sound and the Ear 17 when compressed to eliminate the blank times is still understandable.) The speech threshold measures a person's ability to participate in a conversation or listen to a lecture. It depends as much on the functional condition of the brain as it does on the action of the ear. In contrast, the pure tone threshold indicates to a greater extent the action of the ear itself. As people grow older, the pure tone thresholds are raised, particularly at higher frequencies. For people of all ages, these thresholds are raised by exposure to loud noises. The latter effect is reversible if only occa- sional exposures occur but is quite irreversible after years of continuous exposure. It is not worth while here to go into the details of current estimates on criteria for levels at which, say, 5 per cent of the persons will be appreciably deafened after years of exposure. The currently accepted levels are lower than those which exist in many factories today. The relationship of pleasure to audible frequency range is very complicated. In these days of high fidelity, stereophonic sound, and extended frequency ranges, one might guess that the greater the fre- quency range, the more pleasing. This does not seem to be the case. Older people find hearing aids which correct their high frequency losses make music sound harsh and unpleasant but that flat response ampli- fiers increase their satisfaction in listening to music. In other words, what the listener is used to hearing is enjoyable. Other types of information can be gleaned from experiments similar to those used to obtain the pure tone threshold curves. One test is to ask the subject to match in loudness tones of different frequencies. On the basis of these results, equal loudness curves can be drawn. They are illustrated in Figure 7. The lowest is the threshold curve itself. As the sound pressure level is raised, the equal loudness curves tend to flatten out, approaching straight lines by the time the sound pressure level at 1 kc has reached 100 db. Another test is to ask the subject to choose just noticeable differences in loudness. A change of this nature is sometimes referred to as a difference limen, abbreviated DL. When the sound pressure level is 60 db or more above the threshold of hearing the DL is of the order of 0.5 db 6 throughout most of the auditory range. At lower sound pressure levels, the DL's are greater. At 30 db above threshold they are about 1 db; they are as large as 6 db near threshold. Similarly, difference limens, or just noticeable differences, exist as the frequency is varied. At very low frequencies, a 0.5 cps change is detectable. In the middle frequency range (around 1 kc), the normal person can notice a 3 cps change. At the very high frequency end of the audible range, changes greater than 25 cps are necessary before a 6 That is to say, it is between 0.25 and 1.0 db. 18 Sound and the Ear /I : 3 change of pitch is noticed. These difference limens for frequency change are not independent of the sound pressure level. As the latter is lowered, the size of the difference limen for frequency changes increases. The presence of these finite steps, dignified by the term difference limens, resembles the phenomena well known in many phases of chemistry and physics, usually grouped under the classification quantum 20cps lOOcps .Okc Frequency Figure. 7. Equal loudness contours after the American Stand- ards Association (1936). There is no general agreement on the exact shape of these curves, but the general flattening at higher sound pressure levels is always observed. After J. C. R. Licklider, in Handbook of Experimental Psychology, S. S. Stevens, ed. (New York: John Wiley & Sons, Inc., 1951). mechanics. Similarly, pure tone thresholds measured on individuals at very low frequencies suggest some type of quantum effect. Quantum effects do occur in acoustics, but the physical quanta of sound energy, known as phonons, are far too small to associate them in any way with hearing. Just as does the photon, the phonon has an energy, E, such that E = hv where h is Planck's constant and v is the frequency. A straightforward calculation will show the reader that, even at the threshold of hearing, a huge number of phonons must be reaching the ear each second, or even each cycle. This number is so large that the phonon cannot be responsible for the quantization observed in hearing studies. The hearing tests described in this section give no direct clues to the I : 4/ Sound and the Ear 19 location of the organs responsible for the effects observed. These hearing tests are simple in that they do not necessitate surgery or putting electrodes into people. By contrast, the studies described in the next section and in Chapter 6 allow one to determine whether the effects are mechanical or nervous and to gain insight into the mechanism of hearing. 4. Anatomy and Action of the Ear The ear is the organ of hearing. Sound waves impinge on the ear which couples them to the endings of the sensory nerve associated with hearing. It is customary to divide the mammalian ear into three major divisions: the outer ear, the middle ear, and the inner ear. The outer and the middle ear are filled with air; their primary purpose seems to be to conduct sound to the inner ear. The inner ear consists of several parts, some of which are concerned with balance, and one of which is part of the hearing apparatus. Although anatomically the inner ear is one organ and is served by one cranial nerve, only the cochlear portion of the inner ear is associated with hearing. The incident sound waves in the air surrounding the head enter the outer ear first. This consists of three parts, an external auricle (or pinna), a narrow tube called the external auditory meatus, and the tympanic membrane (or eardrum). These are illustrated in Figure 8. The auricles are almost vestigial in humans and play a very minor role in the phenomenon of hearing. In most mam- mals, the pinnae are large and can be raised, lowered, and rotated. In this way they can be used to help locate the origin of a given sound. In rodents, and some other mammals also, the auricle is at times laid down across the opening to the meatus to give some protection against very loud sounds. In humans, the external auditory meatus (or ear canal) is somewhat cir- cular in cross section and more or less a straight tube. In an average adult, it is about 1 .04 ml in volume and about 2.7 cm long. As in many other biological Pinna or Auricle Part of Middle Ear r^y showing Malleus Tympanic Membrane or Ear Drum External Auditory Meatus or Ear Canal Figure 8. The outer ear. After A. J. Carlson and V. Johnson, The Machinery of the Body (Chicago: The University of Chicago Press, 1941). 20 Sound and the Ear /I : 4 measurements, variations of ± 10 per cent from the mean are quite usual but variations as great as ± 20 per cent are rare. The meatus is terminated by a thick fibrous membrane called the tympanum or tym- panic membrane. Along the edges of the membrane are glands which secrete a waxlike substance called cerumen. This forms a protective coating. In cases of irritation, an excess of this wax is secreted, often causing a temporary loss of hearing. The external auditory meatus may be thought of somewhat as a closed-end organ pipe. The tympanum at the end of the meatus is relatively stiff. Here, the particle velocity should be a minimum and the acoustic pressure a maximum. The opening to the air should be just the opposite, a pressure node and particle velocity antinode. The diagram in Figure 4 shows that the external auditory meatus at reson- ance is a quarter wavelength long. At this frequency, about 3 kc, there will be a maximum acoustic pressure delivered to the inner ear for a given incident pressure. This resonance corresponds to the minimum in the pure tone threshold curve. Studies with probe tubes attached to microphones show that the maximum pressure amplification in the ear canal is about 10 db. This is not sufficient to account for the threshold minimum from 1-4 kc but definitely contributes to it. At the base of the external auditory meatus is the tympanic membrane. In humans it is oval in shape, about 66 mm 2 in area and about 0.1 mm thick. It couples the vibration of the air molecules in the outer ear to the small bones of the middle ear. At extreme intensities the tym- panic membrane is a nonlinear device; that is, it produces harmonics and subharmonics of the frequencies exciting it. These nonlinear effects however are only important at very high sound pressure levels. In some mammalian species, the tympanum vibrates as an elastic mem- brane. In other species including the human, the motion of the tym- panum is more like that of a rotating piston. The mode of vibration of the tympanum was studied in detail by von Bekesy. Various techniques have been used to observe the motion of the tympanum. The simplest is to glue a long light stick to the tympanum and observe the motion of the end of the stick. Most of these techniques are useful only at low frequencies; the results can be extended only by extrapolation. Tests of this type show that the particle velocity of the tympanum is of the same order of magnitude as that in a plane wave in air. Applying this result to db, the approximate threshold at 1 kc, one finds for the particle velocity v P v = — pc v = 5 x 10 ~ 6 cm/sec I : 4/ Sound and the Ear 21 or for the displacement £ 27TV = 10" 9 cm o.i A This displacement is smaller than an atomic radius! The tympanic membrane forms the outer boundary of the middle ear. The latter is an air-filled space in the temporal bone ; this space is referred to as the tympanic cavity. It has a volume of about 1 ml and an irregular shape. Within this cavity are three small bones or ossicles, which are Vestibular Portion of Inner Ear , Tensor Tympani Malleus Tympanic Membrane 'Eustachian to Pharynx' Stapes Presses on Oval Window to Inner Ear Figure 9. The middle ear which is filled with air is connected by two membranes called windows to the fluid-filled canals of the inner ear. The eustachian tube connecting it with the pharynx is even smaller in diameter than is indicated here. Modified from Life : An Introduction to Biology by G. G. Simpson, G. S. P. Hendrigh, and L. H. Tiffany, © 1957, by Harcourt, Brace & World, Inc. named according to their shapes. These are the malleus (hammer), the incus (anvil), and the stapes (stirrup). They are illustrated in Figure 9. The general purpose of these bones seems to be to help match acoustic properties of the air and the inner ear. The ossicles act as a mechanical transformer and increase the fraction of the incident energy available to excite the mechanisms of the inner ear. The bones of the middle ear are so pivoted that they are particularly insensitive to vibrations of the head and to bone-conducted sound waves. One action of the ossicles is to amplify the acoustic pressure of vibrations transmitted from the air via the tympanum, while at the same time 22 Sound and the Ear /I : 4 discriminating against vibrations reaching them via the skull. This insensitivity of the ossicles to bone conduction, as well as the symmetry of the vocal cords, restricts most of the hearing of one's own voice to sound transmitted in the air from the mouth around to the ears. (This can be demonstrated by covering one's ears while talking and noting the changes in loudness and quality.) The ossicles are believed to have an additional function besides impedance matching. This is to decrease the amount of energy fed into the inner ear at high sound levels. Part of this is thought to be accom- plished by changes in the tension of the tensor tympani and stapedius muscles which hold the ossicles in place. The action may be compared to the automatic volume control in a superheterodyne radio. In both cases, when a large signal enters the system and is detected, the amplifica- tion of an earlier portion of the system is decreased. These are specific examples of so-called "feedback systems" or "automatic control," as this type of phenomenon is called by physicists and engineers. (Physiol- ogists usually call this type of effect a "homeostatic mechanism.") In the case of the middle ear, one may describe this action in teleological terms as trying to maintain a constant sound level incident to the inner ear. Although this response is too slow to protect the ear from damage due to sudden noises, it is of the proper nature to explain the flattening of the equal loudness contours at high intensities. High signal transmissions are also limited by a shift in the mode of vibration of the stapes. In one of its two possible modes of vibration, the stapes pushes uniformly on the oval window. In the other it rocks in such a fashion that it causes a negligible net displacement of the oval window. The latter type of motion is believed more important at higher intensities. Both the variable coupling and the two possible modes of vibration are nonlinear effects. Both contribute to harmonic generation as well as to amplitude distortion. In physical form the outermost ossicle, the malleus, is pressed against the tympanic membrane. The innermost one, the stapes, pushes against a membrane called the oval window which separates the air-filled middle ear from the liquid-filled channels of the inner ear. The oval window forms one end of one of these channels, the scala vestibuli. Another channel, the scala tympani, also ends in a membrane separating it from the middle ear. This second membrane is called the round window. The effective area of the tympanum in a human is about 0.66 cm 2 of which perhaps 0.55 cm 2 is in contact with the malleus. The force F m on the malleus, due to the acoustic wave, equals the product of the pressure, p t , on the tympanum times the area of contact. That is, F m = 0.55 p t I : 4/ Sound and the Ear 23 Models indicate that the ossicles have a theoretical mechanical advan- tage of 1.3. Therefore, the force on the stapes F s would be given by F = 1 3F if friction were absent. Likewise, the pressure p w , exerted by the stapes on the oval window, which it contacts for 0.032 cm 2 , can be computed from p w = FJ0.032 Solving for the pressure amplification, A=^ Pt one finds a theoretical value, in the absence of friction, of twenty- two-fold. Actual measurements carried out by von Bekesy have shown that the correct value is A = \lx The latter number is a 25 db gain in acoustic pressure. This value is believed valid throughout most of the auditory range although it is based on extrapolations from low frequencies and high sound pressures. Since the middle ear is filled with air, any difference in pressure on the two sides of the tympanic membrane will tend to displace the membrane. Small differences in pressure at frequencies to which the cochlea responds cause the vibrations of the tympanic membrane during normal hearing. In contrast, large slow changes in pressure, due to atmospheric variations or altitude changes, could distort the shape and position of the tympanic membrane. To avoid this distortion, a con- nection is necessary between the middle ear and the ambient air; but this connection must be unable to transmit changes that take place in less than a tenth of a second. A small narrow tube will do exactly this. Such a tube does connect the middle ear with the pharynx; it is called the eustachian tube. The soft walls of the eustachian tube are easily collapsed by an excess pressure outside the tube. This leads to a very unpleasant feeling often experienced when descending in an airplane. Swallowing, chewing gum, or attempting to blow with the mouth and nose held shut, all open the eustachian tube permitting the equalization of the pressure outside and within the middle ear. The outer and the middle ear together produce a maximum pressure amplification of about 35 db. They tend to reduce the hearing of sounds that are conducted through the bones, to make one insensitive to one's own voice except inasmuch as it is heard through air conduction outside the head, and also to act as an automatic control unit. None of 24 Sound and the Ear /I : 4 these are essential for hearing, although all are desired effects. It is possible to hear without a tympanic membrane and without ossicles. There is a hearing loss under these conditions, but this loss is com- parable to the variations in the normal range of hearing thresholds. However, the two windows to the inner ear, one of which is driven much more than the other by the incident wave, are necessary for hearing. The inner ear consists of several portions all having two common fluids, and all served by the eighth cranial nerve. Only the cochlear portion of the inner ear is associated with hearing. Grossly, the cochlea is a Tectorial Membrane (a) r wmnnnir Membrane - : -' ; ^wfi& tympanic . ■.--,: z-yMf Auditory Nerve (b) Figure 1 0. (a) The cochlea or inner ear removed from the bone. (b) Cross section through one turn of the cochlea. The tym- panic and vestibular canals are filled with perilymph and the cochlear canal with endolymph. After A. J. Carlson and V. Johnson, The Machinery of the Body (Chicago: The University of Chicago Press, 1941). spiral; in the human there are two and a half complete turns. Around this spiral run three parallel, fluid-filled ducts. These are illustrated in Figures 10 and 11. The fluid in the tympanic and vestibular ducts is called the perilymph. These two ducts (or scalae) are connected at the apex of the spiral through a small duct called the helicotrema. Somewhat sandwiched between these two ducts is the cochlear duct (or scala media). It is filled with a fluid, similar to that of the other two, called the endolymph. The endolymph and perilymph are anatomically and electrically separated from each other. Between the cochlear duct and the vestibular duct is a very thin fibrous membrane known as Reisner's membrane. Between the cochlear duct and the tympanic duct is a thicker membrane called the basilar membrane. The basilar membrane gets I : 4/ Sound and the Ear 25 progressively broader and thicker as one proceeds toward the apex of the spiral. The basilar membrane is the seat of the organ qfCorti, shown in detail in Figure 11. This organ contains the nerve endings. Thus one may think of the organ of Corti as a neuromechanical transducer. (A trans- ducer is a device which converts one form of energy to another form.) Outer Hair Cell Tectorial Membrane Vestibular Lip Outer Tunnel Spiral Ll * amenf Claudius C ^of Hensen Phalangeal Vas Phalangeal Q e ll s Spiralis Cells Tympanic Lip Auditory Nerse Figure II. Histology of the organ of Corti. After A. A. Maximow and W. Bloom, Textbook of Histology (Philadelphia: W. B. Saunders Company, 1957). Histologists have studied the organ of Corti in great detail. It seems as if almost every cell has its own name. The diagram in Figure 1 1 shows many of these. It includes Claudine cells, Hensen cells, inner and outer hair cells, and the tectorial membrane. It is believed that the bending of the hair cells in some way excites the nerve endings which are located in the organ of Corti. The action of the inner ear intimately involves the nervous system. The details are deferred to Chapter 6 which follows chapters on the conduction of impulses by nerves and the electrical potentials of the central nervous system. REFERENCES 1. Hunter, J. L., Acoustics (Englewood Cliffs, New Jersey: Prentice-Hall, Inc., 1957). 26 Sound and the Ear 2. Beranek, L. L., Acoustic Measurements (New York: John Wiley & Sons, Inc., 1949). 3. Wever, E. G., and Merle Lawrence, Physiological Acoustics (Princeton, New Jersey: Princeton University Press, 1954). 4. Stevens, S. S., ed., Handbook of Experimental Psychology (New York: John Wiley & Sons, Inc., 1951). a. von Bekesy, Georg, and W. A. Rosenblith, "The Mechanical Pro- perties of the Ear," pp. 1075-1115. b. Licklider, J. C. R., "Basic Correlates of the Auditory Stimulus," pp. 985-1039. 5. Stuhlman, Jr., Otto, An Introduction to Biophysics (New York: John Wiley &; Sons, Inc., 1943). 6. Corso, J. F., "Age and Sex Differences in Pure-Tone Thresholds," J. Acous. Soc. Am., 31, 498-507 (April 1959). Detailed anatomical drawings can be found in the following book: 7. Polyak, S. L., Gladys McHugh, and D. K. Judd, The Human Ear in Ana- tomical Transparencies (Published under auspices of Sonotone Corporation, Elmsford, New York, 1946, distributed by T. H. McKenna, New York, New York). 2 Light and the Eye I. Vision In many aspects of human life, vision is far more important than any other sensation. History, legal agreements, and knowledge of the uni- verse are all recorded in a written form. Without vision these would be of little value. In most measurements in physics, it is customary to base sensitive, precise observations on visual data. In mechanics, the position of a pointer on a balance, length on a meter stick, and pressure are all measured visually. Even in acoustics, precise data are usually based on the readings of electrical meters. This latter is the direct result of the prominent role played by electronics in acoustics. (Similar statements can be made about all other branches of physics.) In chemistry and in the biological sciences, electronic tools have also come to be widely used measuring devices. Today, in almost all of natural science, the reading of electrical meters is an important means of gathering data. However, even before the advent of electronics, the data of the biologist and the chemist, just as those of the physicist, were based primarily on what he could measure by visual means. Vision plays other roles in life besides data gathering. Many of our aesthetic pleasures come from objects which are viewed. The pre- 27 28 Light and the Eye /2 : I liminary part of the mating procedure in humans is based on visual stimulation. Furthermore, vision acts to protect man from many dangers such as those which beset him in crossing a street, driving a car, or climbing the stairs. For other types of activity, vision is not necessary but nonetheless plays an important role in normal human beings ; most outstanding of these is the sense of balance. Finally, it should be noted that human beings use visual cues more frequently than any other type of sensory information. . Vision depends on light. During most of the evolutionary develop- ment of animals, light came primarily from the sun. It is only in recent times that artificial lighting has been used. Since, in their development, all animals were exposed to similar physical light stimuli, it is not sur- prising that all animals have similar visual ranges. This uniformity contrasts sharply with the spread of the frequency ranges of hearing which vary by more than an order of magnitude from one species to another. It is necessary to understand something about the physical character of visible light to have an appreciation of the phenomena of vision. Light may be discussed, depending on the problem under consideration, from three different avenues of approach. The first of these, and historically the oldest, is called geometrical optics. It applies to many problems in optics which can be solved by treating light as if it were propagated as bundles of rays, each normal to the wave front. Most of geometrical optics dealing with lenses can be discussed from this point of view. The optical properties of the eye as a focusing lens system are most simply described by geometrical optics. The second approach to the study of light places its emphasis on wave aspects. Light waves are electromagnetic in character; the pro- perties of the waves are used to describe the transmission of light through a medium. In particular, the wave theories are useful in discussing such phenomena as diffraction, interference, polarization, and resolving power. The wave theories are also useful in discussions of visual acuity and color vision. From the point of view of physics, the most basic approach to a study of light is that of quantum mechanics. It is used in problems dealing with the emission or absorption of light. In the quantum theory, light is considered to be made of packets (or quanta) of energy called photons. The probability of finding a photon at a given place can be described by a mathematical form called a wave function. This quantum view of light is necessary for studies of visual thresholds described in this chapter and for the discussions in Chapter 19 of the absorption of light on a molecular scale. The next section of this chapter presents several of the physical 2 : 2/ Light and the Eye 29 phenomena of light which apply directly to vision. These include the three avenues of approach outlined above, namely, geometrical optics, electromagnetic waves, and the quantum theory of light. This is followed by Section 3, on the anatomy of the human eye. The optical properties of the eye considered as a thick lens, as well as visual defects, are included in that section. Biophysicists have also been interested in visual thresholds and in measurements of visual acuity ; these are dis- cussed in the final section of this chapter. Many aspects of vision will be deferred to later chapters. For example, color vision and the neural mechanisms making vision possible are described in Chapter 7 which follows other chapters on the operation of the nervous system. The properties of the retinal pigments which absorb light are easier to understand following a study of enzymes. The visual pigments are discussed in Chapter 19, Part D. Finally, Chapter 25, on information theory, contains a section which includes visual information. 2. Optics A. Geometrical Optics Many properties of lens and mirror systems can be treated by regarding light as bundles of rays each of which moves at right angles to the wave- front. This approach is utilized in this section in the discussion of the properties of thick lenses. These properties are applied to the eye in subsection B of Section 3. From the point of view of geometrical optics, the most important property of a medium is the velocity at which light is propagated. In free space, the velocity of light is usually designated by the symbol c, and in cgs units, it has the value c = 3 x 10 10 cm/sec It is customary to specify the velocity v in any other medium by the index of refraction, n. This is a dimensionless number defined by the ratio * = - (1) v (Strictly speaking, n is always the index of refraction referred to the velocity of light in free space. However, one may also use the relative index of refraction n 12 between any two media, where n 12 is defined by ■u = ?) (2) 30 Light and the Eye \1 : 2 The use of geometrical optics to describe the properties of thick lenses is outlined in Appendix B. The details will not be pursued here. Rather, it is hoped that readers interested in geometrical optics will turn to this appendix where the behavior of light at surfaces of refraction (lenses) is discussed. In the eye, the luminous energy passes through a series of curved surfaces of refraction. All of these surfaces may be approximated by sections of spheres whose centers lie on a common line. This general case has been shown to be mathematically equivalent to a single thick lens, which separates two media of different indices of refraction. It is not possible to relate the image and object distances by as simple an expression as that for a thin lens, such as Equation 10 of Appendix B. Object Image Figure I. A thick lens immersed in different media on its two sides. F x and F 2 are focal points. Note that F x does not equal F 2 . The principal points are H ± and H 2 , and the nodal points are N x and N 2 . Rays a, b, and c are drawn as in Fig- ures B-6 and B-7 of Appendix B. However, six cardinal points completely specify the lens action. These consist of two focal points, two principal points, and two nodal points. This general case is illustrated in Figure 1. The cardinal points are denned in Figure 1 ; they will be used in the next section to describe the eye. The strength of a lens (or its power), L, is defined as the reciprocal of the focal length / measured from the corresponding principal plane ; that is 'V (3) When /is measured in meters, L will be expressed in diopters. A lens with a shorter focal length can produce a real image for closer objects than a lens with a longer focal length. Thus, the lens produces a greater algebraic change in curvature of an incident light front. In this sense, a lens of shorter focal length is indeed stronger. In any case, increasing the radius of curvature of a converging surface will increase 2 : 2/ Light and the Eye 31 the focal length and decrease the lens strength. In a system of a series of spherical surfaces, such as is found in the eye, the forward and back- ward focal lengths will be different. B. Light as an Electromagnetic Wave Although many actions of lens systems may be adequately described by geometrical optics, others cannot be. In the last chapter, reference was made to the phenomena of diffraction and interference. Diffraction refers to the fact that a wave will not behave as a bundle of rays, especially Resolvable as Two Images "Limit of Resolution ' Not Resolvable as Two Images According to Rayleigh Criterion Figure 2. Dual Diffraction Patterns. in the neighborhood of objects comparable in linear dimensions to the wavelengths of the light. (See Chapter 1 for a definition of wavelength.) In discussing sound, it was noted that the wavelengths of many audible sounds were comparable to the sizes of rooms and buildings. Thus, speech sound waves are diffracted by (or bent around) the furniture and other objects. The wavelength of visible light is much smaller than most common objects; hence, diffraction effects are not a usual part of everyday experience. However, experiments with slits, fine wires, small spheres, and so forth show that diffraction effects do occur. For similar reasons, interference effects in the form of standing waves are familiar in sound experiments but demand special equipment in order to be demonstrated for light. These and many other experiments make 32 Light and the Eye \1 : 2 it impossible to avoid the conclusion that light is a wave motion repre- sented to a sufficient approximation by rays only in limited circum- stances. The limitations are sufficiently broad to allow the use of geometrical optics in many visual problems. The wave nature of light has two very important consequences for the sensation of vision. The first is that there is a theoretical limit to the resolution of any lens system, including the eye; that is, there is a mini- mum separation of two points whose images are resolvable. Figure 2 shows the diffraction patterns of the light originating from two point light sources. If one computes the dimensions of the diffraction patterns of the light originating at the two points and asks that the central maximum of one coincide with the first minimum of the second, one finds that the angular separation of the lines from the lens center to the two points is given by 9-1™ ' (4) a where A is the wavelength of the light and a is the radius of the aperture of the lens. It is often assumed that this is about the minimum separation at which two points can be distinguished. The reciprocal of 6 in minutes of arc is called the resolving power. Actually, trained microscopists and spectroscopists resolve slightly smaller angles than the one computed by the formula above. (This formula was first developed by Lord Rayleigh; it is often called the Rayleigh criterion.) In addition to its use in predicting resolving power, the wave nature of light is necessary to discuss color vision. If light of a narrow wave- length band is present, it is said to be monochromatic; that is, it gives the sensation of a single color. Only about one octave (that is, a factor of two in the frequency) is visible to humans. In wavelength terms, the visible spectrum runs from about 760 mfi (red) down to about 380 OT/u, (violet), although the exact limits quoted by different experi- menters vary. One octave seems a narrow band when compared with the sense of hearing where musical tones are audible in at least nine octaves. The resolution of different wavelengths by the eye is much poorer than the sharp tone discrimination of the ear. Combinations of different wavelengths of light produce complex color sensations because the eye does not analyze frequencies in any fashion analogous to that of the ear. Light waves are not elastic disturbances. A number of different types of experiments have left no doubt that light waves are electro- magnetic waves. Two of these experiments will be mentioned here. First, one can compute on theoretical grounds that an electromagnetic wave should be transverse and have a velocity which can be determined 2 : 2/ Light and the Eye 33 by electrostatic and magnetic measurements. Polarization experiments confirm that light waves are transverse. Optically determined values of the velocity of light, c, agree with those predicted for electromagnetic waves to better than one part in a million. Further evidence that light consists of electromagnetic waves is its continuity with radiation produced by other methods. Using tech- niques which overlap at their wavelength limits, one may produce radio waves, microwaves (radar), heat waves (infrared), light waves, ultraviolet rays, X rays, and y rays. Thus, all of these are part of the same basic phenomenon: electromagnetic waves. No explicit use will be made of the electromagnetic properties of light waves in the chapters on the eye or on vision in this text. C. Light as Photons The electromagnetic wave theory correctly describes the transmission of light, but a number of other effects are impossible to understand without the quantum theory. These include the characteristic spectra of atoms, the absorption spectra of atoms and molecules, the photo- electric effect, black-body radiation, and the failure of the equipartition of energy for electrons in a metal and for the vibrations of diatomic gases at room temperatures. All of these and many other phenomena have been explained only in the terms of quantum mechanics. Quantum mechanics teaches that energy comes in packets or quanta. The probability of finding the packet at a given place is determined by the square of the amplitude of a wave function. In particular, for electro- magnetic waves, the quantum theory states that energy E comes in photons each having the energy he E = j (5) where h is Planck's constant, which is about 6.6 x 10 ~ 27 erg -sec, c is the velocity of light, and A is the wavelength. The relative probability of finding a photon at a given place is essentially identical to the intensity computed on the basis of the electromagnetic wave theory. Strictly speaking, a measured quantity has been specified by a probability, but experimentally these two are indistinguishable. The photon nature of light is important in describing the threshold of vision. It is likewise necessary, in Chapter 19, where vision is dis- cussed on the molecular level. In the latter case one may ask: How many photons react with a molecule; how do the photons change the sensitive molecules; and how are the resulting small bursts of energy transduced to neural impulses ? Unfortunately, it will appear that one cannot give a complete answer. Nonetheless, the language of photons 34 Light and the Eye /2 : 3 and of quantum mechanics is the only one in which these topics are discussed. The reader with a background in biology, or even an undergraduate physics major, may feel that this topic of quantum mechanics has been introduced too lightly, but only the concepts of quantum mechanics which are needed for a discussion of vision have been included above. Quantum mechanics is necessary for an understanding of character- istic spectra. Accordingly, quantum theory is discussed more thoroughly in Chapter 27. Even there, the author must make several statements which are foreign to everyday experience and certainly are not proved in this text. It is hoped that, in spite of this, the reader will at least gain a feeling of what quantum mechanics is and how it is used, even though he may be completely unable to manipulate it. 3. Anatomy of the Eye A. Gross Anatomy The gross anatomies of all the vertebrate eyes are very similar. For simplicity, numerical values will be given only for the human eye. The human eyeball is roughly a sphere approximately 2.4 cm in diameter. It is supported in a special socket in the cranium. The orientation of the eyeball is controlled by six sets of muscles. These rotate the eyeball quite freely because the socket is well lubricated. The muscles are con- trolled by three pairs of nerves. The relative tensions in the muscles are signals which might be used by the brain to determine the location of the object viewed. 1 Many binocular judgments of distance, size, and orientation could be "computed" by the central nervous system from data on the relative tensions of these muscles. The external covering of the eyeball is made up of three spherical layers, as shown in Figure 3. The outermost is the sclera. It is a white fibrous coat commonly called the "white of the eye." At the very front portion of the eye, the sclera leads into the cornea, a clear transparent structure which admits light into the eye. The human cornea is about 12 mm in diameter and has a radius of curvature of about 8 mm. A major part of the refractive power occurs at the cornea. On top of the sclera is another thin layer called the choroid layer. It contains the blood vessels and a pigmented substance. The choroid layer does not continue all the way around to the cornea, as is shown in Figure 3. 1 The evidence as to whether or not this information is actually used by humans is quite controversial. 2 : 3/ Light and the Eye 35 The third and innermost layer of the eyeball is the retina. The active photoreceptors, called rods and cones, are located in the retina. It is convenient to divide the retina into ten layers. Light must pass through Visual Axis Cornea Ciliary Muscle Optical Axis Anterior Chamber Iris Posterior Chamber \ Retina Choroid Layer Sclera Optic Nerve Fovea Figure 3. The eye. After A. A. Maximow and W. Bloom, Textbook of Histology (Philadelphia: W. B. Saunders Company, 1957). eight of these before reaching the rods and cones located in the ninth layer. Slightly displaced from the intersection of the optic axis of the eye with the retina is a yellow spot known as the fovea centralis (the macula lutea) . It is a slight depression on the surface of the retina. The active elements in the fovea are all cones; they are very closely packed. For maximum acuity, the eye is directed so that the image falls on the fovea. Somewhat on the nasal side of the fovea is the optic disk. Here the optic nerve pierces through the sclera, the choroid layer, and the retina ; in the center of the optic nerve are a vein and an artery. From this disk, nerve fibers and blood vessels branch out over the surface of the retina. Objects focused on this disk cannot be seen since there are no rods or cones in it. Thus, this disk is referred to as the blind spot. One may put two marks on a piece of paper as indicated in Figure 4, cover one eye, and fixate one of the marks. If one then alternately moves his head toward and away from the paper, the other mark will 36 Light and the Eye /2 : 3 disappear when its image falls on the blind spot. In Figure 4, the x , the . , and the : disappear at different distances. Within the eye there are additional, optically important structures. One of these is the iris, which acts as a light diaphragm. In bright light, the iris has a min- imum opening. This is desirable for several reasons. A smaller opening means fewer light photons enter the eye, thereby decreasing the "overloading" of the retinal system. In addi- tion, it improves the validity of the approxi- mation which is made in the discussion of spherical lenses, namely, that just a small section of a sphere is used. 2 Thus, a small iris opening limits such distortions as spherical aberration, field curvature, and coma asso- ciated with finite sections of spheres. Finally, a small iris opening increases the depth of focus. The reason for this can be seen from a simple ray diagram, such as is shown in Figure 5. At night, maximum acuity and depth of focus are less important than maxi- mum sensitivity. At this time the iris is opened to its widest. Another optically significant structure within the eye is the crystalline lens. In spite of its name, this is actually a cellular structure. The rear face is curved more sharply than the front. The eye accommodates to objects at different distances by changing the cur- vature of the front face of this lens. When the object is farther away, a weaker lens is needed to focus the image on the retina than when the object is closer. Hence, for more distant objects, the lens must be flatter, whereas, for closer objects, it must become more curved. The shape of the crystalline lens is controlled by a ring of muscles surrounding the lens. These are called the ciliary muscles. Most physiologists believe that the lens is normally held in a strained position by the ciliary fibers. These fibers hold the lens in a flattened condition suitable for viewing distant objects. When the ciliary muscle contracts, it moves the base of the fibers forward permitting the lens to relax into a more curved shape. When the muscle relaxes, the lens is again placed under tension. The space between the lens and the retina is filled with the vitreous humor, a jelly-like mass of material traversed by fibrils. Staining Figure 4. Pattern to ob- serve the blind spot in the eye. Fixate the right eye on the large dot and bring the face very close to the figure. Now slowly move the face away while keep- ing the right eye fixated on the large dot. The other symbols will disappear and then reappear as their images cross the blind spot on the retina. 2 See Appendix B. 2 : 3/ Light and the Eye 37 techniques indicate that the vitreous humor does contain some sort of structure. Optically, the vitreous humor is indistinguishable from the Wide Aperture Light rays proceeding so as to focus to a point at q iris Diaphragm (a) Retina Light rays as above Narrow Aperture (b) Iris Diaphragm Retina Figure 5. Effect of aperture on depth of focus. A point focused at q will appear as a circle of diameter 8 on the retina, As shown in (a), if the aperture of the iris diaphragm is wide, the diameter of 8 will be large; hence, one image will blur into the next unless q is very close to the retina. Thus, increasing the aperture decreases the depth of focus. As shown in (b), a narrower aperture increases the depth of focus but decreases the luminous energy reaching the retina. aqueous humor which fills the space in the eyeball between the cornea and the crystalline lens. The aqueous humor, as its name implies, is a water-like solution containing the normal solutes of a body fluid. B. Geometrical Optics of the Eye Light enters the eye through the transparent cornea. It then passes through the aqueous humor, through the crystalline lens, and into the vitreous humor. It is received on the photosensitive retina, where there must be an image in focus if the object is to be seen clearly. The dimensions, radii of curvatures, distances apart, and positions of the six cardinal points are shown in Figure 6 for a schematic eye. The greatest part of the refractive power of the eye occurs at the 38 Light and the Eye \1 : 3 cornea. Individuals lacking a lens can still see, but their vision is much less sharp than that of a normal person because the image on the retina is out of focus. By changing the exact shape of the lens, the eye can accommodate for objects at different distances. The young person with normal vision can accommodate for objects nearer than 250 mm. An Cornea Anterior Focal Point Crystalline Lens 10 17.10 Vitreous n v = 1.336 ri a = 1.336 (a) Retina Principal Focal Point Retina Figure 6. Optical properties of the eye. All distances shown are mm. The values are averages and will vary from indivi- dual to individual. These drawings, not to scale, show Ogle's modification of Gullstrand's schematic eye. Notice that although the lens of the eye appears to be strong in air, it is much weaker in situ since the difference in index of refraction between the lens and the surrounding media is much smaller. After K. N. Ogle, Optics, An Introduction for Ophthalmologists (Springfield, 111.: G. C. Thomas, 1961). object distance of 250 mm corresponds to about 16 focal lengths. Accordingly, to compensate for the change in image distance as the object is moved from about 16 focal lengths to infinity, the effective posterior focal length of the eye must change about 6 per cent. In terms of the radius of curvature of the crystalline lens, this corresponds to a change of around 20 per cent. The posterior focal length of the 2 : 3/ Light and the Eye 39 average human eye from the second principal point H' to the posterior focal point +F is 2.2 cm. Thus, the eye has a strength of about 48 diopters. If the eye is stronger than this, images of distant objects will be focused in front of the retina. Such an eye is called near-sighted or myopic because near objects will be focused on the retina. This ocular defect can be corrected by placing a negative (diverging) lens in front of the eye. "Normal" vision is the ability to focus on the retina images of objects more than 25 cm away. If the refractive power of the eye is too weak, the image will be formed behind the retina, and positive lenses are needed for correction. Such eyes are called hyperopic or far-sighted. By and large, it is not possible to design a corrective positive lens for objects at all distances and so bifocals or trifocals are necessary. Another frequent defect, which can be corrected by glasses, is called astigmatism. This defect consists of having different focal lengths for lines in different directions. A so-called normal person would see all the lines of a fan chart, Figure 7, as equally black, whereas one with astigmatism will see lines in one meridian darker than those in the meridian at right angles. Astigmatism is due to the fact that some of the refractive surfaces of the eye, especially the cornea, are not spherical but have different curvatures in two meridians. To recapitulate, the eye lends itself to a description in the terms of geometrical optics. The eye is a system of spherical surfaces separated by media of different indices of refraction. Optically, it can be des- cribed in terms of six cardinal points. The common defects easily corrected by glasses can also be described in the language of geometrical optics. Figure 7. Pattern for observ- ing astigmatism. C. Histology of the Eye Each gross structure of the eye can be described on a microscopic scale. This is the role of histology. The evidence from histology, in turn, forms part of the basis of the biophysics of vision. Without a knowledge of the histology of the retina, there can be no neural interpretation of vision, such as is discussed in Chapter 7. Likewise, the parts of the eye, referred to in subsection B, can be described in terms of their histological structures. 40 Light and the Eye \1 : 3 Light enters the eye through the cornea, whose microscopic structure is shown in Figure 8. First, the light passes through an outer layer of epithelial cells. These cells are separated by a thin membrane from an inner fibrous layer which in thickness comprises most of the cornea. These fibers are very similar to the fibers in the sclera. Those in the cornea are unique in that they are arranged in an orderly fashion. It appears that it is this orderliness of the fibers of the cornea that is responsible for its transparency as contrasted with the opacity of the sclera. Inside the fibrous layer of the cornea is another very thin limiting membrane and finally a lining of cells called endothelial cells. Epithelium ^T Bowman's Membrane Substantia Propria {Fibers) Membrane of Descemet Corneal Endothelium Figure 8. Histology of the cornea. After Schaffer, in A. A. Maximow and W. Bloom, Textbook of Histology (Philadelphia: W. B. Saunders Company, 1957). As noted previously, the shape of the cornea is responsible for the major refraction of the eye. Any large irregularities or abrasions would reduce the acuity of vision. The usefulness of the eye depends on keeping the cornea clear and transparent. If a large object approaches the cornea, the eyelids are closed by a reflex action. Smaller particles are removed by blinking and through tear formation. The outer epithelial layer of the cornea is very highly innervated ; the nerves terminate in bare nerve endings. Any slight disturbance stimulates these endings, resulting eventually in the blinking reflex. All persons normally blink quite frequently; this cleans and moistens the outer surface of the cornea which otherwise would become dehydrated and lose its transparency. It always appears surprising when one first encounters the idea that 2 : 3/ Light and the Eye 41 light can pass through several layers of cells and fibers and still retain its original form. If these layers are arranged in a sufficiently orderly fashion, there is relatively little scattering or absorption of light as it passes through the tissue. The so-called "crystalline lens" is also a cellular structure. The cells are long hexagonal columns. Most of the cell nuclei are grouped in a restricted region of the lens which is not active in vision. A typical cross section of a lens is shown schematically in Figure 9. (a) (b) Capsule Nuclear Zone of Lens Vitreous Humor Figure 9. Histology of the lens, (a) Frontal section through the equator of the lens showing the regular arrangement of the cells, (b) Transverse section through the lens. After Schaffer, in A. A. Maximow and W. Bloom, Textbook of Histology (Philadelphia: W. B. Saunders Company, 1957). The last cellular structure of the eye, through which incoming light must pass, is the retina. Here, the active photoreceptors are located. There are two types of receptors, called rods and cones. Although not customary, it is technically correct to refer to these rods and cones as transducers. These transducers convert light energy into electrical impulses which travel along the nerve fibers. As noted earlier, the retina may be divided into 10 layers. These are diagrammed in Figure 10. Starting from the outermost layer, away from the light, one can list the layers shown in Table I. 42 Light and the Eye \1 : 3 Layer TABLE I Layers of the Retina Function or Structure bo O A -t-> 1. Pigmented epithelium 2. Rods and cones 3. Outer limiting membrane 4. Outer nuclear layer 5. Outer plexiform layer 6. Inner nuclear layer 7. Inner plexiform layer 8. Layer of ganglion cells 9. Optic nerve fibers 10. Inner limiting membrane absorbs light, limits reflection the photoreceptors cell bodies of rods and cones synapses between processes from rods and cones and cells of layer 6 neuron cell bodies synapses between processes from cells of layers 6 and 8 neuron cell bodies also some blood vessels, connective tissue, and so forth The neurons in the retina are similar to those in other parts of the nervous system. Their detailed form and action are discussed in 1. Pigment Epithe/ium_ 2. Rods and Cones 3. Outer Limiting Membrane 4. Cell Bodies of Rods and Cones 5. Outer Plexiform Layer (Synapses) o 6. Inner Nuclear Layer (Neuron Cell Bodies) 7. Inner Plexiform Layer (Synapses) _ 8. Gang/ion Cell Layer (Neuron Cell Bodies) 9. Optic Nerve Fibers 10. Inner Limiting Membrane Figure 10. Histology of the retina. After A. A. Maximow and W. Bloom, Textbook of Histology (Philadelphia: W. B. Saunders Company, 1957). 2 : 4/ Light and the Eye 43 Chapter 4. For the purposes of this chapter, one should note that the neurons are the functional units of the nervous system. Each consists essentially of a cell body, a long process called an axon, and shorter processes called dendrites. The rod and cone cell bodies are similar to neuron cell bodies except that they are attached to photoreceptors in lieu of axons. It should be emphasized that light goes through layers 10, 9, 8, 7, 6, 5, 4, 3 before being useful for vision in layer 2. The arrangement of two layers of neuron cell bodies, with their connections to the rod and cone cell bodies, as well as almost innumerable connections between neuron cell bodies, is indeed complex. To those who have looked behind the front panels of an electronic digital computer, the retinal structure suggests strongly that the output of the rods and cones is analyzed in a computerlike fashion by these layers of nerve cell bodies. And indeed, it will be shown in Chapter 7 that electrophysiological evidence supports this suggestion. Within the layers of nerve cell bodies, a number of different types of cells have been discovered. In discussing the mechanism of color vision, it is important to include these different types. A discussion of their forms will be deferred until Chapter 7. 4. Thresholds and Acuity In this section, three different types of measures of the sensitivity of the eye are discussed. The first is the quantum threshold, that is, the minimum number of photons necessary to elicit a sensory response. The second is the relative sensitivity of the eye to light of varying wavelengths. The last measure, the acuity, represents the keenness of vision and is measured by the minimum separation of two objects that can just be discriminated as two and not one. A. Quantum Thresholds Vision occurs when light is absorbed by the photosensitive rods and cones. At the threshold of vision, only a minimum of light is necessary. The absorption of light is best described in terms of quantum theory. A natural question then is: How many photons must be absorbed by a visual receptor (rod or cone) for the subject to see a flash of light? This problem was first investigated in detail by the biophysicist S. Hecht. His first approach was to use light of wavelengths to which the eye was most sensitive and to expose the eye to short flashes. The eyes were dark-adapted to make their sensitivity a maximum. The number of photons striking the cornea for a just noticeable flash was measured. 44 Light and the Eye \1 : 4 The number was reduced by the fraction (about f) which he found to be absorbed in the eye. The final number, then, should be the minimum or number of photons necessary for threshold vision. At least it would be if this number were much larger than one, in which case all pulses could be considered as having equal numbers of photons. Otherwise, the entire data would have to receive a probability-type interpretation. Early estimates based on this method indicated that about 150 photons were necessary at the cornea, and about 30 of these reached the retina for a just visible flash. As this number was redetermined during the 1920's and 1930's, it decreased steadily from 30 down to one or two. This small number violates the original basis of the determinations because the number of photons in a light pulse, the number absorbed along the way, and even the fraction absorbed in the retina of those which get there, are subject to probability considerations. In general, one cannot measure these probabilities separately. However, the average number of photons b absorbed by a single receptor of the retina will be proportional to the intensity /, provided the eye does not move ; that is, b = kl (6) The proportionality constant k will vary with many factors including the size of the test patch, the pupil opening, the wavelength, and the length of the flash. It is clearly desirable to carry out an experiment to measure the threshold number of photons independently of k. The following mathematical manipulations indicate how to design an experiment which satisfies this criterion. The number of photons absorbed by a photoreceptor in the retina during a given flash is an integer. It may have any positive value, or it may be zero. However, the average number of photons need not be an integer but will have a definite value b. The probability P that m photons will be absorbed during a flash by the photoreceptor will be given by the Poisson probability distribution, namely: P(m) = e —L. (7) ml Vision will occur if some given integral number n or more photons are absorbed during the exposure. The probability P n that n or more photons will be absorbed in a flash is given by P n = § P(m) = 1-2 nm) (8) m = n Now, one may plot computed values for P n against log b, giving curves such as those shown in Figure 11. Notice that each of these has a different slope. Although the value of b is not known, the value of the 2 : 4/ Light and the Eye 45 intensity / can be measured. Therefore, a plot of the fraction of number of correct responses when the light was perceived by the subject against the log / should have the same shape as one of the curves shown in Figure 11. By adding an arbitrary constant to log/, it should be possible to show that the experimental points correspond best to one value of n. This experiment satisfies the criterion of not needing to measure the constant k in Equation 6 and gives unique data for the determination for any individual value of the integer n in Equation 8. The value for this constant for some human subjects indicates that n is as high as eight. For other subjects, consistent values as low as one or two have 05 Figure I I . P n versus log b for quantum threshold calculation. In this graph, P n is the Poisson distribution probability for n or more events occurring, and b is the average number of events occurring. been found for the number of photons necessary to elicit a visual response. In spite of these individual variations, the human data support the idea that the quantum threshold n is a very low number. Most of these measurements are for rod vision, but there is nothing to indicate that the threshold number of photons absorbed is different for cones. For the human eye, it is impossible to determine whether the response measured is that of a single receptor. It is possible in experiments using invertebrate eyes, such as those of the king crab, limulus. These eyes have only rod-like receptors called ornmatidia. There is one receptor per nerve fiber. For threshold experiments, the eye, with the optic nerve attached, is removed from the animal. The nerve is then dissected until only one nerve fiber remains intact. It then becomes possible to 46 Light and the Eye \1 : 4 measure electrically the response of only one receptor. Such experiments indicate either one or two photons are necessary to initiate an electrical response in the nerve fiber. Most investigators today use the number one; that is, one photon absorbed in the receptor, one response. (Note that this is very different from the statement, one photon reaching the receptor, one response.) This quantum threshold seems surprisingly small since one photon has so little energy. It is instructive to compute the size of a photon of visible light. Applying Equation 5 to the energy £ of a photon of green light, wavelength about 5,000 A, one finds that E = 4 x 10 " 12 ergs In terms of a mole of photons (often called an einstein) , this becomes kcal £ = 40 mole Readers familiar with chemical thermodynamics will recognize that these numbers imply that a photon of green light can break only a small number of molecular bonds when it is absorbed. It is indeed impressive that such a small change can alter the electrical state of the photo- receptor in such a fashion as to initiate a nervous pulse which results in the sensation of vision. B. Luminosity Thresholds The above-mentioned sensitivity is based on the number of photons absorbed. This absorption is the result of the action of certain photo- sensitive pigments found in the rods and cones of the retina. The relative fraction of light that reaches the rods and cones and is absorbed varies markedly with wavelength. It is convenient to separate the effect of wavelength from the numerous other factors altering threshold intensities. To do this, a set of threshold data is taken, varying only the wavelength. The entire set is multiplied by a normalizing constant chosen to reduce the minimum threshold to an arbitrary value. The reciprocal of the normalized threshold is known as the relative luminosity. Relative luminosity curves have been measured both for dark-adapted eyes and for light-adapted eyes. Vision under conditions of dark adaptation is called scotopic, whereas vision with light-adapted eyes is called photopic. In either case, one may interpret the thresholds as the intensity at which a response is obtained 50 per cent of the time. For short flashes, less than 10 milliseconds, the product of the intensity and exposure length determines the observed threshold, whereas for long exposures, 2 : 4/ Light and the Eye 47 say more than 50 milliseconds, only the intensity is important. The exact size of the test patch used becomes very important if it is two minutes of arc or less. With very small test patches, the exact location of the test patch very markedly affects the shape of the relative luminosity versus wavelength curve. For larger test patches, threshold curves are obtained which do not depend specifically on the particular area on the retina which is illuminated. The general shape of the relative luminosity curves for photopic and scotopic vision is shown in Figure 12. Owing to the definition of 1.0 0.8 ^0.6 o c 6 3 0.4 0.2 V \ f \ 400 500 600 Wavelength (m\t) 700 Figure 12. Relative luminosity curves. The curve for the dark-adapted eye is labeled b and for the light-adapted eye, a. After Committee on Colorimetry, The Optical Society of America, The Science of Color (New York: Thomas Y. Crowell Company, 1953), p. 225. relative luminosity, the absolute height of the curves does not have any significance. Much greater intensities are needed for photopic vision than for scotopic vision. (This difference is part of everyday experience. After the lights are turned off at night a room looks totally dark, but gradually one can see more and more objects in it.) Luminosity thresh- old measurements are not easy to perform. More than half an hour is necessary for dark adaptation. Care must be taken to illuminate the same area of the retina, and many other precautions must be observed as well. However, the relative luminosity curves do lead to reproducible results. The separation of the maximum points of the scotopic and the photopic 48 Light and the Eye /2 : 4 curves can be interpreted as an indication that luminosity depends on at least two types of receptors. The simplest interpretation might be to assign scotopic vision to the rods and photopic vision to the cones. This choice would be indicated by the fact that the scotopic sensitivity is greater in the periphery where there are more rods, whereas the photopic response is greatest in the fovea where there are no rods. However, this separation of function is definitely oversimplified; the rods appear to be active in both dark-adapted and light-adapted eyes, whereas the cones are active only in light-adapted eyes. C. Acuity Studies of the acuity of vision also indicate that the rods are the active elements in the dark-adapted eye. The acuity of the eye adapted to scotopic vision is a minimum at the fovea where there are no rods. Thus, the rods seem to be the active elements in scotopic vision. The acuity of scotopic vision shows a maximum for light at the retinal region where the rod density is highest, namely, about 20° from the fovea. Acuity under scotopic conditions is lower than under photopic con- ditions in any region of the retina. The neural basis for this is discussed in Chapter 7. However, in photopic vision there is a sharp maximum in the ability to resolve two spots of light when the images fall on the fovea. The acuity in the foveal region is much greater than in the remainder of the retina. The acuity of vision may be expressed in terms of the minimum angular separation of two equidistant points of light which can just be resolved. The angular separation 6 between two points, when expressed in radians, is approximately equal to the distance between the points divided by the distance from the eye, provided 6 is less than 0.1. The angle 6 will also be equal to the separation of the two images on the retina divided by the distance from the second nodal point. From Equation 4, one can calculate a minimum value of 6, according to the Rayleigh criterion, for green light (A — 5 x 10 ~ 5 cm) and an iris diameter of about 0.5 cm. Rounding off to one significant figure, the limit, according to this criterion, would be d R == I x 10~ 4 radians == 0.03 minutes of arc This is a theoretical lower limit for the resolution of two points of light. Experiments have shown that most people cannot resolve two points of light if their separation is as small as 5 x 10 ~ 4 radians. Persons with the most acute vision can resolve an angular separation of about 2 x 10 ~ 4 radians under optimum conditions. Because this is higher than the Rayleigh criterion, it seems that visual resolution must be 2 : 4/ Light and the Eye 49 limited by other factors such as scattering, spherical aberration, and the separation of the receptors in the retina. In the center of the fovea where the resolution is greatest, the cones are separated by about two microns from center to center. In order to resolve two points of light as separate images, it must be necessary to excite at least two cones while leaving one in between unexcited. Thus, the images on the retina would have to be separated at least four microns from center to center. If it were necessary to have two cones unexcited between the images of the two spots, this number would be increased to six microns. The maximum resolution observed of 2 x 1 ~ 4 radians corresponds to a separation between the image centers on the retina of five microns. In other words, the discrete structure of the retinal receptors could be responsible for the lower limit of resolution for persons with the most acute vision. The psychophysical processes of recognizing shapes are very complex. However, a minimum requirement for small objects is that the angular separation of their different parts be larger than the limit of resolution. At 25 cm from the eye, an angle of 5 x 10 ~ 4 radians would correspond to about 100 microns. This is about the length of a Paramecium caudatum which should accordingly be recognized as having a rod shape at that distance. In contrast, the smaller species, Paramecium aurelia, would have to be brought closer to the eye before its shape could be recognized by the unaided eye, even under ideal conditions of lighting. In a camera, resolution in white light is often limited by chromatic aberration, that is, the different wavelengths focus at different planes. The resolution can be improved to some extent by using a system of positive and negative lenses made of different types of glass. 3 The index of refraction of each will vary in a different fashion with wavelength. By a proper choice, a combination can be made which has a positive focal length that is almost independent of wavelength throughout the visible region. Chromatic aberration in the eye is minimized by limiting the wave- lengths of light to which the eye will respond. A bare retina from which the vitreous humor has been removed will respond far into the ultra- violet. However, in the intact eye, the cornea absorbs most energy at wavelengths shorter than 3,000 A. Accordingly, energy at these wave- lengths does not contribute to vision although it can produce corneal damage. The crystalline lens has a very sharp cutoff at about 3,800 A. Persons without this lens cannot accommodate to different object distances, lack acuity, but can see objects using ultraviolet radiations only. They have 3 These are called achromatic lenses. 50 Light and the Eye \1 : 4 a sensation of violet when viewing ultraviolet. Persons with a lens do not receive any appreciable energy at the retina at wavelengths shorter than about 3,800 A. Thus, the lens (and cornea) limit the photons reaching the retina to wavelengths greater than 3,800 A. On the long wavelength side, the water molecules in the cornea and aqueous humor eventually absorb most of the energy at wavelengths longer than 12,000 A. However, the eye pigments become very insensitive to light above 7,000 A, and are almost unresponsive above 8,000 A. Technically, to find the long wavelength limit, one should go to such high intensities that the eye is heated but not badly burned ; this experiment is rarely performed. Thus, the filter action of the lens and cornea, plus the response characteristic of the optically active pigments in the photoreceptors tend to restrict the wavelength band, thereby reducing chromatic aberration. In addition, the greatest acuity occurs in photopic vision at the fovea. In this region, there are only cones which probably do not respond to blue light. In this region also is a yellow pigment believed by many to further eliminate the blue end of the spectrum. Accordingly, the acuity at the fovea is greatest not only for objects viewed with monochromatic green light, but also for those seen in white light. REFERENCES 1. Stuhlman, Otto, Jr., Introduction to Biophysics (New York: John Wiley & Sons, Inc., 1943). 2. Stevens, S. S., ed., Handbook of Experimental Psychology (New York: John Wiley & Sons, Inc., 1951). a. Judd, D. B., "Basic Correlates of the Visual Stimulus," pp. 811-867. b. Graham, C. H., "Visual Perception," pp. 868-920. 3. Glasser, Otto, ed., Medical Physics (Chicago, Illinois: Year Book Publishers, Inc., 1944) Vol. 1. a. Luckiesh, Matthew, and F. K. Moss, "Light, Vision, and Seeing," pp. 672-684. b. Sheard, Charles, "Optics: Ophthalmic, With Applications to Physio- logic Optics," pp. 830-869. For a more thorough discussion of optics at an intermediate physics level, see: 4. Robertson, J. K., Introduction to Physical Optics. 2nd ed. (New York: D. Van Nostrand, 1935). Light and the Eye 51 For a more complete discussion of histology of the eye, see: 5. Maximow, A. A., and William Bloom, Textbook of Histology (Philadelphia: W. B. Saunders Company), any recent edition. For a presentation from the point of view of medical physiology, see: 6. Best, C. H., and N. B. Taylor, Physiological Basis of Medical Practice. 7th ed. (Baltimore: Williams & Wilkins Company, 1961). 7. Ogle, K. N., Optics: An Introduction for Ophthalmologists (Springfield, Illinois: Charles C. Thomas, 1961). 3 Special Uses of Hearing and Vision I. introduction Biophysicists have, in one fashion or another, been interested in many sensory systems including hearing, vision, olfaction, taste, touch, tempera- ture, pain, proprioception, and time. All are contained in the human body. There is no reason to suppose that some living organisms could not be sensitive to types of stimuli other than those to which humans respond, such as magnetic fields or even neutron beams. All experi- ments to date, however, tend to confirm that the types of sensory mechan- isms active in humans are the only important ones in other living organisms. The differences which do exist involve quantitative aspects such as the frequency range of hearing, the wavelength band of vision, and the particular chemicals to which an organism responds. It is conceivable, nonetheless, that the failure to find other sensory systems may reflect our ignorance rather than their nonexistence. In spite of our inability to detect basically different systems, there are many novel ways in which the known sensations are used. For example, 52 3 : 2/ Special Uses of Hearing and Vision 53 certain types of plants "compute" the average length of sunlight per day to find out when to flower, or when to shed their leaves. Others use the length of night, and still others the average light-to-darkness ratio. Another example is the sense of time, which is poor in most humans. Certain animals, for example, cockroaches, have a much more highly developed sense of time than man does. In some phenomena, such as bird homing, it is not well understood just what sensory cues or information the animal does use. In others, particularly echo-location, an understanding was developed only after physical analogs had been constructed. Before this, it was beyond human conception to design the proper experiments, even though these experiments could have been readily carried out. To put it in a some- what different fashion, human intuition is often a poor guide to experi- mental design. Someone must not only develop the proper ideas but also be persuasive enough to interest his peers. In the following section, the ability of bats to use echo-location in flight, in capturing prey, and in avoiding obstacles is set forth. Many years ago a few persons, perhaps by chance, hit on the correct solution to how a bat senses its surroundings, but these solutions were discarded by their contemporaries as absurd. Pasteur said that chance favors the mind prepared by study and experimentation. We might add, it also favors the man who lives in an age in which his contemporaries are like- wise prepared. Besides bats, other mammals and some birds use echo-location. These are also discussed in this chapter. Bees use sensory information for direction-finding and homing; this involves time and orientation senses, and also perhaps the ability to detect polarized light. Making a beeline for home is discussed in Section 4. The concluding section of this chapter deals with bird navigation and homing. 2. Echo-Location in Bats In many families of bats, the sense of vision is poorly developed, hence the colloquial expression, "blind as a bat." It has been shown by direct experimentation that bats fly, hunt, and avoid obstacles, as well when blindfolded as when their eyes are open. Anatomically, the visual portion of the bat brain is very poorly developed, whereas the acoustic or auditory portion makes up a major part of the brain. This suggests that they sense their surroundings through auditory stimuli. Indeed, deafened bats, or ones with their ears covered over, cannot fly well, avoid obstacles, or hunt in the same fashion as normal bats. Covering the bat's mouth (and nose) also interferes in a like manner with its 54 Special Uses of Hearing and Vision /3 : 2 flight. Many experiments have shown that bats navigate, sense their surroundings, and hunt by a process known as echo-location. Echo-location has been used for many years to determine the depth of the ocean. During World War II, two practical applications of echo- location were developed. Systems using electromagnetic echoes are called radar, whereas those employing acoustic echoes are named sonar. In either case, a pulse of energy is sent out, reflected from an object, and the returning echo is detected. By measuring the time for the echo to return, one can compute the object distance. For radar, if the object is at a distance d of 60 km, the pulse will return in the time t necessary to travel 2d or. 120 km. That is , 2d 120 km _ . .... t = — = r-^-j : — = 0.4 millisecond c i x 10 s km/sec The echo will be weaker than the original pulse emitted. To detect the echo, the original pulse must have stopped before the echo returns. Thus, very short pulses are necessary. To aid in distinguishing the echo from noise, among other reasons, the original pulse is emitted at a carrier frequency which is high compared to the reciprocal of the pulse length. For radar, frequencies of 10 9 to 3 x 10 10 cps are used. An echo-location system like that described above will determine distance but not shape. To find the latter, it is necessary to emit many pulses, each one in a slightly different direction. These echoes must all occur before the object has moved very far. Thus, a high pulse- repetition rate is needed to find detail. By contrast, a low rate is needed to find distant objects. Finally, to be useful for determining distance and shape, there must be some way of rapidly displaying the echoes as a function of direction and time of return because there is not time to do a paper-and-pencil calculation for most uses of echo-location. A similar rapid sensing of shape and motion occurs when watching the wheel of a moving car. One does not see that each point on the wheel describes a curve of complex form and then figure out that the wheel is turning; rather, one perceives this directly. Therefore, any successful echo-location system must reveal directly the shape, size, and distance of the objects. Human brains do not do this with echoes. Therefore, radar and sonar equip- ment display their results after electronic computation. The bat brain apparently makes a similar calculation directly. Radar works well in air but is useless under water since the electro- magnetic waves are rapidly absorbed. Sonar, although less effective than radar in air, can be used to locate objects under water. The speed of sound in water is only 1.5 km/sec, so much longer pulses can be used 3 : 2/ Special Uses of Hearing and Vision 55 for sonar; to limit sound absorption, much lower frequencies are em- ployed, usually around 3 x 10 4 cps. Griffin and Galambos showed in 1941 that bats use a sonar type of echo-location. Since then, Griffin and his associates have studied echo- location in bats in great detail. The bats emit and detect airborne sound pulses; these travel at the speed of sound, 0.34 km/sec. A bat can use comparatively long pulse lengths and still recognize close objects. The pulse lengths used by an individual bat may vary from around 1 millisecond to 5 milliseconds. The lower limit allows a bat to dis- tinguish echoes from objects as close as 15 cm (6 inches). Other species of bats with poorer acoustic orientation use pulses of 10 to 100 milli- seconds. To be effective, the wavelength of the sounds in the bat's pulse must be of the order of the linear size of the smallest objects the bat chases. The wavelength A is equal to the velocity of sound divided by the fre- quency. The latter is easier to measure electronically. The frequency of the sound which the bat emits varies during the pulse by a factor of close to two. The highest frequency in some species is around 100 kc, where the wavelength A of sound in air is about 0.3 cm. Appreciable echoes should occur until the diameter of the object is about A/2, in this case, about 0.05 cm (20 mils). Behavioral experiments with wire grids show that such bats are extremely successful in avoiding wires 0.3 cm in diameter but cannot detect wires 0.025 cm in diameter. The shape of the pulse is shown in Figure 1 . The role of the frequency changes during the sound pulse is not known. One possibility is that it is used to indicate size, the lower frequencies being reflected less by small objects than the higher ones. The directivity pattern of the sound emitted by the bat also changes during the pulse in such a manner as to support this hypothesis. The higher frequencies are concentrated into a narrower beam, favoring their reflection from smaller objects directly ahead of the bat. Another possibility is that the bat uses its own particular frequency variations to distinguish its echoes from those of other bats close by or from surrounding noises. Bats must be very skillfull at distinguishing their own pulses from others because they navigate well in the presence of thousands of other bats in dark caves with hard reflecting walls. They are also able to detect their own pulses from loud noises. Attempts at "jamming" bat sonar, with broad-band noise, have so far failed. The sound pressure level (see Chapter 1) near the bat's mouth is about 120 db, that is, about 175 dynes/cm 2 . Even broad-band noise signals at these sound pressure levels in the bat's frequency range have failed to jam the bat's sonar, although the echoes are very weak compared to the over-all noise levels. 56 Special Uses of Hearing and Vision /3 : 2 It is interesting to compare the physical characteristics of a bat with radar and sonar equipment. The table on page 57 lists some data for radar and sonar systems of World War II, and the insectivorous bat, Eptesicus fuscus. It is clear that the bat compares favorably with the sonar and radar systems. 2 I I 2 MYOTIS LUCIFUGUS 2 I 2 L EPTESICUS FUSCUS Figure I. Photographs of oscilloscope traces of the sound pressure pulses emitted by two different species of bats. The time markers are in milliseconds. After D. R. Griffin, Listen- ing in the Dark (New Haven, Connecticut: Yale University Press, 1958). The bat is superior to the radar and sonar systems in some respects. When the insect-hunting bat is far above the ground it emits only long pulses at a comparatively slow repetition rate, that is, 50 millisecond pulses, five times per second. As it approaches its prey, the pulse length shortens to two milliseconds and the repetition rate increases to 200 per second. This makes maximum use of its available facilities. 3 : 2/ Special Uses of Hearing and Vision 57 TABLE I Echo-Location Comparisons Radar Systems SCR-268 AN/AB-10 Sonar Bat (ground- (air- System (Eptesicus based) borne) QCS/T fuscus) Wavelength (cm) 150 3.2 5-13 0.4-2 Approximate total weight (kg) 13,000 58 about 100 0.014 Peak power output (watts) 75,000 10,000 600 io- 4 Minimum detectable echo power (watts) io- 13 io- 13 ? 10- 16 to io- 14 Target detected Airplanes Airplanes Submarines Insects Size of target (m 2 ) 3-5 3-5 10 io- 4 Working range for target (km) 150 80 2.5 io- 1 Length of emitted pulse ' {2d) (meters) 1,800 240 100-300 1-5 The bat is far inferior to radar and sonar in other respects, particu- larly in its ability to distinguish shapes. Bats apparently could not dis- tinguish solid objects in the shape of a cross from others in the shape of a circle, although all were large compared to the minimum sizes the bat detected. Furthermore, insectivorous bats will chase pebbles thrown into the air just as readily as they pursue moths. Various families of bats differ in their anatomy and their use of echo- location. There is no simple relationship between the range of hearing and the pulses used. All bats can hear from 30 cps to 100 kc or higher according to electrophysiological data. However, the largest bats depend on visual information and lack a "sonar" system. Certain Central American bats emit very high frequency pulses; these are pure tone pulses, in the range of 80-120 kc, and of comparatively low intensity. Other bats use pulses whose frequencies decrease to as low as 20 kc. One species, Rousettus aegyptiens, the Egyptian tomb bat, emits a pulse whose frequency goes from 100 kc to 6.5 kc each pulse. Some types of bats emit their pulses through their mouths, others through their nostrils, and still others can use either. Many species of bats have specially shaped external ears which act as directional receiving horns, and others have bizarre nose forms which act as horns for the emitted signal. Figure 2 shows an insectivorous bat. Before the development of radar and sonar, it was hard to guess how 58 Special Uses of Hearing and Vision /3 : 3 bats navigated. The present knowledge followed the construction of these physical analogs. Moreover, the pulses of the bats can be detected, analyzed, and displayed only by modern acoustic and electronic techniques. In order to discover the details of bat navigation, Griffin and his associates had to be pre- pared to apply modern physical techniques. 3. Echo-Location in Other Animals Because bats use echo-location, one might wonder if other animals can also use this type of information. The answer is a strong affirmative ; the number of animals known to use echo-location has grown rapidly since 1945. The list includes birds that live in dark caves, marine animals, and, to a limited extent, humans. It is not inconceivable that certain deep-sea fish also use some form of echo-location. Among birds, two types have been shown to use auditory clues when flying in dark caves. One of these is the oilbird of the valley of Caripe, in Venezuela, named Steatornis caripensis. These birds, when flying in the light, use their visual system to sense their sur- roundings. In the dark, either at night or far within their caves, they emit clicks of 1 to 1.5 millisecond duration with frequencies in the neigh- borhood of 7 kc. This is lower than most bat sound pulses. How- ever, bird hearing is, in general, limited to the same range as human hearing, in contrast to small mammals most of which can hear frequencies as high as 100 kc. Thus, it is physiologically reasonable that the oil- birds should use lower frequencies than the bats. It seems physically reasonable also because the oilbird, being much larger, is concerned Figu re 2. Photograph of a flying bat, after Edgerton. After Griffin, D. R. , Listening in the Dark (New Haven, Connecticut: Yale University Press, 1958). 3 : 4/ Special Uses of Hearing and Vision 59 with larger objects (and therefore does not need short wavelengths). Certain swiftlets {Collecalic brevirostris unicolor) also live in caves. Although studied in less detail than the oilbird, it has been found that the cave-dwelling swiftlets emit sharp clicks when flying in the dark. The ability of the swiftlet to fly in the light is only slightly impaired if either its eyes or ears are covered. It becomes quite helpless when both are masked. No studies have been made of the frequencies of its clicks. Marine mammals, such as porpoises and small whales, have hearing ranges which extend well above 100 kc. Their hearing has been shown by conditioning experiments to be extremely sensitive. All of this group of animals emit short sound pulses. Only the pulses from por- poises have been studied in detail. They emit more and shorter pulses when hunting for fish. Experiments have shown that porpoises use these pulses for echo-location both in navigating and in locating food. Other animals are thought to use echo-location, although the evidence is less certain. For example, deep-sea fish emit light flashes and certain electrical fish send out weak electrical impulses. It is quite possible that both of these are also used for echo-location of some type. 1 There is also some evidence that blind humans use the echoes of their footsteps to sense their closeness to objects. Attempts have been made to extend this sense electronically to give details of size, shape, and hardness. These have all failed because the added information gained was less than that lost by wearing earphones or interfering with the normal hearing of sound. 4. Sense of Direction in Bees and Ants Besides echo-location, other sensory information is used in ways which are unique to limited groups of animals. In this section, the sense of direction in bees and ants is briefly considered. Humans possess a sense of direction and use many different types of clues as guides such as knowledge of the terrain, the stars, the compass, road signs, and mile posts. Most of these are unavailable to bees and ants; nonetheless, they proceed straight from their homes to a food source and back again. This is the biological source of the colloquial expression "made a bee- line." There is no doubt that, when ants follow the trails of other ants, they use olfactory senses as a guide to direction. Likewise, they also can use 1 Many of these electrical fish can detect electrical impulses with sensory receptors, known as the lateral line organs. To some degree, these electrical receptors represent a type of sensory system not found in humans. Although all sensory receptors respond to electrical stimulation, humans have none that are specialized for this type of stimulus. 60 Special Uses of Hearing and Vision /3 : 4 some sort of kinesthetic sense. However, if the trail is completely obliterated, the ants still proceed directly to their homes. The ants apparently can sense the angle of the sun's rays and use this information to determine directions. If ants are imprisoned while returning to their nests and kept for a period of hours in a darkened container, they start off in the wrong direction when released. The direction chosen makes the same angle with the rays of the sun as did the correct path at the time of their initial imprisonment. Feeding Place Bee Displaced \in Covered \ Container \Bee Displaced I in Covered Container Hive (a) (b) (d) Normal Confined in Dark until Time, t y Figure 3. Flight patterns of bees returning to their hive from a feeding place. Sketch (a) shows the normal flight pattern. The flight patterns of bees displaced from their feeding places are diagrammed in sketches (b) and (c). The change in pattern when the bee is confined is illustrated in sketch (d). Similar experiments have been conducted with bees. They, too, will proceed in the wrong direction after release following imprisonment in the dark. After flying in the wrong direction the distance to where their hives should have been, they "recognize an error" and fly in a random fashion over a very small area. Finally using some other sense, perhaps memory of the surroundings, they fly straight to their hives. This is illustrated in Figure 3a. If a bee is moved in a darkened container from its feeding place and 3 : 5/ Special Uses of Hearing and Vision 61 released shortly thereafter, it makes a beeline in the direction its hive would have been had it not been moved. Arriving at the wrong site, it circles and eventually travels in a fairly straight line to its hive. This is diagrammed in Figure 3b. Not only can bees find their way to the hive by the angle with the rays of the sun, but they also communicate to other bees the location of a new source of food in terms of this angle. When a bee finds such a source, it goes through a complicated dance pattern on the side of the hive. The amplitude of the pattern communicates the time of flight and the predominant angle with the vertical reveals the angle between the flight path and the sun's rays. Bees and other insects have vision extending into the ultraviolet; this portion of the sun's spectrum is useful to insects but not to mammals. There are reports that bees can sense not only the direction of the sun's rays but also their polarization. Other reports indicate that the apparent ability to sense polarization is misleading. (It should be noted there is a small polarization effect in human vision which can be just barely demonstrated by psychophysical tests.) Whether or not the bees use the angle of polarization, their precision in comparing their flight path with the angle of the sun's rays is far beyond anything humans can do without the help of physical instrumentation. 5. Migration and Homing Although insects use the angle of the sun's rays to return to their homes, they have other sensory information which allows them to "home" if their angle computations have led them astray. Other animals such as bats, fish, turtles, and pigeons also exhibit homing tendencies. It is most likely that bats do not use any form of visual clues. Some evidence indicates that fish and turtles, as do insects, use the sun in homing. One type offish, the bass, probably has an internal clock and avoids the errors made by ants and bees when imprisoned in the dark. Certain pigeons have been selected and bred for their ability to home. These birds may be taken hundreds of miles from their nests in containers which are completely covered so that they cannot see the surroundings. Even though the pigeons have never been in that location before, many are able to follow a very straight line to their nest. (However, they must be trained over increasingly large distances starting with about 25 miles, before the longest flights are possible.) Various theories have attempted to relate the pigeon's homing to a combination of hypothetical senses. One of these postulated an extreme ability to detect the angle of the sun and combine it with a very precise 62 Special Uses of Hearing and Vision /3 : 5 internal "clock" to find direction. Another, based on the behavior of untrained birds in new territories, ascribed homing to flying in random circles until some feature of the terrain was recognized. A third theory assigned homing to an ability to detect the vertical component of the earth's magnetic field and the Coriolis force (experienced by bodies moving at an angle to the earth's axis of rotation). None of these has ever been conclusively disproved. However, experiments to verify any of these theories have all been inconclusive. It is the author's guess that pigeons use strictly visual clues of a very ordinary kind in homing. If this is true, pigeons must be unique in their ability to see a limited number of features of the skyline from a long distance. Not only must they be able to see these features, but they must also possess the ability to learn these features well enough to orient themselves, even if released at a long distance from their origin. This guess has been strongly conditioned by experiments on bird migration. Birds migrate as far as 15,000 km over territory they have never seen before and yet manage to return to their own nesting areas of a kilometer or so in radius. They thus have a tremendous precision of migration. It is possible that most are led on their initial flights by other birds who have flown the "course" before, but nonetheless they must either be born with or acquire a tremendous store of visual memory with which to compare their surroundings. This visual memory must be very precise to keep them on course for 8,000 miles. At the same time, it cannot be too precise or rigid, lest the birds be confused by changes in the terrain which occur from year to year. The large number of birds killed by flying into radio towers and monuments for many years after their con- struction attest to the fact that birds only observe a limited number of features of their terrain and discard other information. Likewise, the ability of various species to migrate at night indicates that the position of the sun is at best only one of the visual clues used during migration. Man is born with comparatively little information inherited at a con- scious level. By analogy, one might suspect, therefore, that birds had to acquire their knowledge of the terrain on the first migration or two. However, very few people could learn so many landmarks so quickly; by analogy again, this type of learning would also seem unlikely for birds. Perhaps a better comparison than a human is a self-controlled (that is, internal radar controlled) airplane which can fly from the west coast of the United States to the east coast and land on the proper runway with only a few feet margin of error. Such planes have been built with a radar memory of the terrain imprinted on their magnetic tapes. The same problems of precision while ignoring fine details affect the self- controlled plane and the migrating bird. 3 : 5/ Special Uses of Hearing and Vision 63 At least one European plover, hatched from its egg in isolation from all other birds, developed with a memory of the terrain over which its species migrated. This bird, at the start of the fall season, became extremely restless in captivity but made no consistent attempt to fly in any given direction. When it was placed in the Paris Planetarium with the proper skyline and the proper orientation of stars for that time of year, the bird attempted to fly along the migration course characteristic of its species. It simulated flight southward to the Mediterranean shore, then turned eastward and simulated flight around the Mediterranean to Africa. By simulated day it used the skyline to navigate, and on simu- lated clear nights it used the position of the stars. A built-in "clock" (time sense) enabled the bird to "compute" the proper position of the stars at that time of night for the Mediterranean shore at that season of year. There is nothing to indicate that similar built-in, inherited memories exist in all migratory birds. Nor is there any reason to guess whether or not some inherit their memories and others acquire them on their first flights. (Migration experiments do give one reason to doubt the carry-over of learning experiments from birds to man.) Birds use their visual sensations in migrating in a very special way which man is not adapted to emulate, except through his artifacts such as the "migrating" airplane. REFERENCES A large portion of the material in this chapter was based on the experimental work of D. R. Griffin and his co-workers. A pleasant review of this work, on a high, technical level, but written in an entertaining fashion, is his book: 1. Griffin, D. R., Listening in the Dark : The Acoustic Orientation of Bats and Men (New Haven, Connecticut: Yale University Press, 1958). This book contains 386 pages of text as well as 467 references, which are pertinent to the present chapter. Two shorter articles are in Scientific American: 2. Griffin, D. R., "Bird Sonar" 190: 78-83 (March 1954). 3. Griffin, D. R., "More About Bat 'Radar'" 199: 40-44 (Jan. 1958). The homing of bees and ants is discussed in : 4. Fraenkel, G. S., and D. L. Gunn, Orientation of Animals : Kinesis, Taxes and Compass Reactions (New York, N.Y. : Oxford University Press, 1940). 5. von Frisch, Karl, Dancing Bees: An Account of the Life and Senses of the Honey Bee. Translated by Dora Use (London, England: Methuen and Com- pany, Ltd., 1954). 64 Special Uses of Hearing and Vision 6. Baylor, E. R., and F. E. Smith, Polarized Light and Bees (Unpublished data). 7. de Vries, Hessel, and J. W. Kuiper, "Optics of the Insect Eye," Ann. New York Acad. Sc. 74: 196-203 (1958). The homing and navigation of birds are discussed in : 8. Matthews, G. V. T., Bird Navigation (New York: Cambridge University Press, 1955). 9. Griffin, D. R., and C. G. Gross, book review of G. V. T. Matthews' Bird Navigation. Quart. Rev. Biol. 32: 278-279 (1957). 10. Yeagley, Henry L., "A Preliminary Study of a Physical Basis of Bird Navigation," J. Appl. Physiol. 18: 1035-1063 (Dec. 1947). 11. Sauer, E. G. F., "Celestial Navigation by Birds," Scientific Am. 199: 42-47 (Aug. 1958). Homing in fish is discussed by: 12. Hasler, A. D., et al., "Sun Orientation and Homing in Fishes," Limnology Oceanography 3: 353-361 (1958). The following two articles also deal with subjects related to those in this chapter. Both are in Reviews of Modern Physics, Vol. 31 (1959). 13. Schmitt, O. H., "Biological Transducers and Coding," pp. 492-503. 14. Bullock, T. H., "Initiation of Nerve Impulses in Receptor and Central Neurons," pp. 504-514. Discussion Questions — Part A 65 DISCUSSION QUESTIONS— PART A The following topics are suitable for student reports, term papers, or library examinations in connection with Part A of this text. It is assumed the student will answer the questions with the help of adequate library facilities. 1. Besides vision and hearing, biophysicists have been active in studies of taste and olfaction. What is the present state of knowledge in these fields? 2. Insects as well as mammals sense vibrations and sound. Describe the receptor organs, the threshold versus frequency curves, and the equipment necessary to measure vibration and sound thresholds for insects. 3. Invertebrates respond to light when it falls upon special sensory organs. Describe briefly the simple and compound eyes of insects and the "eye-spot" of Euglena. How is visual acuity possible in the compound eye? 4. Discuss the evidence concerning any possible role of polarized light in the vision of man, vertebrates, and insects. 5. At various times, it has been reported that animals could in some way sense or respond to magnetic fields. Review critically the evidence for such a magnetic sense. 6. Ants communicate and sense direction, in part, by the odor of certain specific chemical compounds which they secrete. These compounds are referred to by various names as pheromones, ectohormones, and chemical releasers. Describe the evidence for such compounds. 7. Describe in detail the methods for observing the motion of the eardrum (tympanic membrane) and of the ossicles of the middle ear. 8. Develop the mathematical theory of the Helmholz resonator. How was this type of resonator used to analyze speech ? 9. Bekesy audiometers are discussed in Chapter 1. Draw up ideal speci- fications for such an audiometer and compare them with those of a com- mercially available model. 10. The theory of lenses discussed in Chapter 2 uses the infinitesimal approximation of small angles sin 6 = 6 Derive third order equivalent formulas and discuss in terms of these formulas : spherical aberration, coma, field curvature, astigmatism, and image distortion. What is the importance of these various effects for the eye ? 11. Compare the pulses emitted by several species of bats in terms of sound pressure level, sound frequency, pulse length, and repetition rate. Relate these to the physical structure of the ears, nose, and mouth of the particular species and to their feeding habits. 12. Describe in considerable detail the experiments indicating that bees can sense the angle of the sun's rays. B Nerve and Muscle Introduction to Part B The following six chapters are' devoted to biophysical studies of nerves and muscles and to the interpretation of other phenomena in terms of the properties of these two tissues. The first chapter of this part (Chapter 4) con- tains a discussion of the conduction of information by nerve fibers in the form of electrical impulses. Several concepts of basic electrical theory, needed in various chapters throughout the text, are summarized in Appendix C ; it is hoped that readers unfamiliar with these terms will read that appendix. In Chapter 5, "Electrical Potentials of the Brain," the so-called "electroencephalographic waves" are described. Their interpretation and relationship to nerve impulse conduction is also discussed. Chapters 6 and 7 discuss the neural mechanisms associated with hearing and vision, respectively. The ideas presented in Chapters 1 through 5 are used in these two chapters about the neural aspects of hearing and vision. The physical and chemical nature of muscular con- traction forms the basis for Chapter 8. Some biochemical concepts, presented more fully in later chapters, are intro- duced in order to restrict the discussion of muscles to Chapter 8. Finally, the last chapter in Part B, "Mechanical and Electrical Character of the Heart Beat," applies many of the ideas presented in Chapters 4 and 8 to the mammalian heart. The molecular description of the action of nerve axons is deferred to Chapter 24 following discussions of thermo- dynamics and active transport. 67 4 The Conduction of Impulses by Nerves I. The Role of the Nervous System The nervous system is composed of units called neurons which transmit information in the form of electrical pulses from one place within the organism to another. This action is essential for the rapid responses of animals to external stimuli. Animals respond more rapidly than plants do to conditions outside themselves. For instance, certain plants have flowers which are open only in bright sunlight, and deciduous trees shed their leaves during the fall season. However, these are comparatively slow responses involving time intervals from minutes to days. In con- trast, the responses of a motorist to a red light or of a fly to an approach- ing swatter are both very much quicker. These rapid responses of animals timed in milliseconds or, at most, seconds are mediated by the nervous system. The rapid coordinations and responses of animals strongly suggest that the nervous system must transmit information in an electrical or magnetic form. One might reach this conclusion without detailed 69 70 The Conduction of Impulses by Nerves /4 : I knowledge of the structure and properties of the neurons. Studies of nerves have shown that they consist of bundles of long processes called axons or nerve fibers. The axons are each a part of an individual neuron. Along the nerve fiber, the information is coded and transmitted in the form of an "all-or-none" or "on-off" electrical pulse called an action potential or spike potential. On a teleological basis, the problems of the nervous system are similar to those of transmitting telephone messages over long distances. Either there must be many parallel low frequency channels, or fewer high frequency channels, each modulated by many separate signals. The living organisms which respond rapidly to external stimuli (that is, animals) have varying numbers of parallel low frequency electrical channels. The number of channels increases with the complexity of the animal. Along each of these channels (nerve fibers), information is transmitted by electrical pulses, referred to as action (or spike) potentials. The individual channel, with its energy supply and its connections, is called a neuron. 1 Its distinguishing features involve the biological generation and transmission of electrical potentials. The earliest experiments which could be called bioelectrical occurred toward the end of the eighteenth century. Galvani put two dissimilar metals into a frog's leg muscle and observed a twitch. He correctly associated the response with electricity but assumed that the electricity was generated within the muscle by a vital process. Volta proved that Galvani's electricity was not of biological origin; the existence of true biological potential generators was not discovered for almost another century. Today, it is known that all nerve fibers, in fact, probably all cell membranes, are charged electrically. The membrane charges, as well as the spike potentials, are so small that they could not be observed with the instrumentation of Galvani and Volta. The field of bio- electricity is a fertile one for the application of electronic gadgeteering and physical instrumentation; it has attracted many persons with a background in physics who welcomed a challenging biological problem to which they could apply their previous training. A major application of bioelectricity is the study of the conduction of .impulses by nerves. Animals possess other mechanisms, besides the bioelectrical properties of the nervous system, for transmitting information from one part to another. These other systems are called endocrine; they involve the internal secretion of certain chemicals called hormones. The hormones alter metabolic rates, dilation of blood vessels, and secretory rates at 1 Some giant invertebrate fibers are fusion products of several embryonic neurons. 4:1/ The Conduction of Impulses by Nerves 71 specific target organs. Similarly, when information is transmitted from one neuron to another, there is often a chemical intermediate. The process differs from the endocrine system only in the length of time involved. The hormones act, in general, over a period of hours or days, whereas the transmission from one neuron to the next takes only milliseconds. Some hormones act faster so that there is no sharp dividing line between the hormones and the neuro-chemical transmitters. Plants also possess chemical transmitters. The distinguishing feature of higher animals is their nervous system, which transmits information far more rapidly than the endocrine systems do. Biophysicists have studied both the nervous and the endocrine systems. Both lend themselves to the application of complex physical techniques, and both can be analyzed by the type of reasoning common to physics and electronics. This is particularly true of the interactions between groups of neurons, of interactions between groups of endocrine glands, and also of the neuron-endocrine interactions. In all of these, "feed- back" loops exist in which the effect produced alters the behavior of the neurons or endocrine glands producing these effects. Physicists and electrical engineers refer to these types of control mechanisms as "nega- tive feedback"; physiologists have called many of them "homeostatic" mechanisms because they tend to keep the state of the organism constant. In this text, only the actions of the nervous system are discussed. It is the aim of this chapter to present, in so far as possible, a picture of the physical properties of nervous tissues and a description of how nerve fibers conduct spike potentials. Because each reader will have a different background, an attempt has been made first to present the fundamentals of electricity. A more detailed discussion of electrical terminology can be found in Appendix C. The electricity section of this chapter is followed by a brief description of certain salient features of the vertebrate neuron. Details of the physical characteristics of the action potential are then presented. The final section of this chapter deals with con- duction from one neuron to the next, called synaptic transmission. Many aspects of the nervous system are discussed in other chapters. Chapter 5 describes the electrical potentials of the brain and contains a discussion of feedback mechanisms. Chapters 6 and 7 deal with the neural aspects of vision and hearing. Chapter 8 includes the stimulation of muscles by nerves, and Chapter 9 the neural control of the heart rate. Perhaps most important of all, from the point of view of the biophysicist, the molecular basis of the action potential is discussed in Chapter 24. A knowledge of the material in Part D (molecular biology) and the other chapters of Part E (thermodynamics and transport systems), makes that chapter much easier to understand. 72 The Conduction of Impulses by Nerves /4 : 2 2. A Brief Glance at Electricity Physicists consider all matter to be made up of neutral atoms, which, in turn, are made up of positively and negatively charged particles. Although large chunks of matter are electrically neutral, on a subatomic scale, many particles have a net charge. In a liquid or a crystal, there are often ions or groups of atoms which are likewise charged. For instance, NaCl splits into Na + and CI - ions in a water solution. In an NaCl crystal, the sites are occupied by Na + and Cl~ ions. Even water has measurable H + and OH" concentrations. Thus, on an atomic or molecular scale, charges frequently do not balance out even though a volume containing many molecules is approximately electrically neutral. Likewise, when a metal is placed in a liquid, or when two dissimilar metals are placed in contact, the two faces of the surfaces of discontinuity become charged. The "dry" cell and storage battery are examples of two metals in a liquid. Unlike charges are separated at the metal- liquid interfaces. If two dissimilar metals are used, the charge separa- tion will be unequal; charges will flow when these two metals are connected by an external conductor. The thermocouple is an example of a practical use of the charge separation at the junction of two metals. If charge is not allowed to flow after equilibrium has been established, the actual charge separation is very small in each of the cases above ; the net charge separation is negligible compared to a coulomb. This leads one to suspect that although matter is approximately neutral, in no case do the charges balance out to the last electron. Biological cells and parts of cells are not exceptions. The net charge on any cell measured in coulombs is infinitesimal, but measured in the units of the charge on an electron e, it is appreciable. The neurons are distinguished from most other cells in that they are specialized to transmit changes in their surface potential rapidly. (Muscle fibers are similar to neurons in this respect.) The flow of electrical charge is known as electrical current. Currents are measured in units called amperes. Early investigators of bioelectrical phenomena regarded the current as the fundamental event in the con- duction of impulses by neurons. Hence, they referred to these as action currents. Considerable experimental evidence, however, supports the electrical potential changes as being uniquely a property of the neuron membrane. In any case, the potential is the parameter actually measured in most experiments. The electrical potential difference between two points is defined in elementary physics as the energy received by a unit charge when it is carried between these two points. Thus, it is a potential energy per unit charge. Electrical potential is usually measured in volts. 4 : 2/ The Conduction of Impulses by Nerves 73 Qualitatively, one may think of the potential as similar to an electrical pressure or force driving positive charges to regions of lower potential (and negative ones in the opposite direction). The ratio of the potential difference to the current flowing through a conductor is called the resistance R. For many substances, R is a constant independent of the current. In these cases, one can easily analyze direct-current circuits, such as those shown in Figure 1 . r = internal resistance of battery % — emf of battery R — load resistance V = potential difference across R I = current through R (a) (b) ^C C = capacitator Charge flows only while capacitator is becoming charged (c) Figure I. (a) Direct current circuit, (b) Direct current circuit with capacitor, (c) Simplified circuit representing a resting axon (see Chapter 24). Most bioelectrical phenomena involve changes which occur quite rapidly in time. As stated in the first chapter, events with complex time dependence can be analyzed in terms of simple harmonic changes (alternations) at one frequency. In electricity, a-c circuits are more complex than d-c inasmuch as elements other than resistances can impede the flow of an alternating current. In an a-c circuit of fixed frequency, the ratio of the potential to the current is called the impedance. The ratio of the component of the potential in phase with the current, to the current, is called the resistance, whereas the ratio of the out-of- phase component of the potential to the current is the reactance. React- ances arise due to capacitors, C, which do not pass direct current, and 74 The Conduction of Impulses by Nerves /4 : 3 ,---!/, = — I- *~*# M (~) V 2 =jwL I V-* = RI inductors, L, which do not impede a direct current. An a-c circuit is illustrated in Figure 2. Inductors are not as frequently encountered in biological systems as are cap- acitors. Most biological mem- branes act as capacitors in an equivalent electrical circuit. As such, they may be charged, maintaining a fixed potential difference between their two sides, or they may conduct a rapid change in potential. These ideas are applied directly to neurons in Section 4 of this chapter. In addition, most membranes can generate a potential differ- ence between their two sides, thereby expending chemical energy. Such a generator is called an electromotive force or emf. These generator pro- perties of neuron and muscle membranes are discussed in this chapter and in Chapter 8, as well as in Chapters 23 and 24. / V" Figure 2. An a-c series circuit. Note in the symbolism used that in Figure 1(c). The hollow §hdl j g fiUed wkh Qne conducting medium (cytoplasm) and immersed in another (intercellular fluid). This picture applies to all axons except the thickly myelinated ones, which will be discussed further later in this section. The existence of these potentials across the extremely thin axon membrane indicates the ability of these membranes to withstand very high electrical field strengths. Dry air breaks down at 3 x 10 6 v/m. Many insulators (including corrosion on spark plugs) raise the field strength necessary for breakdown of air as high as 10 8 v/m. At the surfaces of many biological cells, including neurons, it appears that high field strengths of about 10 8 v/m occur. These are in such small regions that numbers for air prove misleading. The cell membranes are more nearly analogous to the junctions between two dissimilar metals. At the latter, field strengths as high as 5 x 10 9 v/m are known 4 : 4/ The Conduction of Impulses by Nerves 79 without sparking or breakdown of any sort. Thus, it is not too surprising that the neuron membrane can withstand field strengths at which dry air breaks down. When the axon is stimulated, its surface potential changes in a characteristic fashion to an action potential or a spike potential. (The latter name arose from the appearance of these impulses on the screen of a cathode ray oscilloscope.) Axons may be stimulated by any of a wide variety of means. Electrical pulses of various shapes, heat, cold, chemical changes, and mechanical pressures all lead to the same V t = Inside Potential V - Outside Potential Positive After Potential Refractory Period Figure 5. Diagrammatic representation of the time course of the spike potential at a fixed point along the axon. During the refractory period, another impulse cannot be started. The threshold for stimulation is lowered during the negative after potential and raised during the positive after potential. The magnitude and duration of these effects is characteristic of the particular nerve fiber. phenomena. The local membrane polarization disappears, reverses in polarity very quickly, then returns to normal over a series of "bumps." The spike potential formed in this fashion travels down the axon in both directions from the point of stimulation. (Owing to the nature of the synapses, only one of these directions is usually effective when an intact nerve is stimulated.) The time dependence of the potential at one spot is shown in Figure 5. The corresponding distributions of charges along the axon cylinder at a given time are shown in Figure 6. In laboratory experiments, spike potentials are usually excited by electrical stimuli because they are easier to control in time, space, and strength than are any other type of stimuli. For very weak stimuli, a local response occurs which is similar to, but smaller than, the spike potential. As the stimulus is increased, a certain threshold is reached 80 The Conduction of Impulses by Nerves /4 : 4 where a transmitted spike potential is generated. The spike potential then travels along the axon at a characteristic velocity. The spike potential is an all-or-none response. Either there is a transmitted spike or there is not. If the spike is present, its height and shape are independent of the stimulus strength. The neuron acts in a similar manner to a flip-flop electronic circuit such as used in counters and in digital computers. That is to say, the neuron is either in the conducting or nonconducting state; nothing is transmitted in between. This analogy seems so strong that it is hard to avoid describing the computer in anthropomorphic terms and the nervous system in terms of a digital computer. Positive Negative After After Resting Potential Potential Spike Before + + + + +++++ + + + + - + + + + + + + + + +++ + +++ + + - + + + + + Figure 6. Space distribution of charges along an axon con- ducting a spike potential. Arrow shows direction in which spike is moving. If an axon is cut, and the two pieces insulated electrically, no impulse travels from one part to the other. However, if the two are connected by a metallic conductor, or a salt bridge, the spike potential crosses readily from one part of the axon to the other. This emphasizes the essentially electrical nature of the action potential. These spike poten- tials occur in tissues, which are fluid-like media. Currents in fluids are carried by ions, therefore it is appropriate to consider the resting potential as well as the spike potential as due to ionic distributions. While the spike potential is present at the axon, another one cannot be started. By contrast, several subthreshold stimuli may be summed to give a response if they come close enough together in time. During the positive after-potential, the threshold is increased. The lengths of time for these potentials and the rate of conduction of the spike potentials led to the classification of vertebrate axons presented in the table on page 81. Particular attention should be called to the giant squid axon. From 4 : 4/ The Conduction of Impulses by Nerves 81 c G =3 O O S-l CO LU _J CO < a> U -O c rt c o X < o a> G — ' S-, a o Oh o q g ^ o _r o o CM o _ CN 2 co m CO — c CM I q CM m cm co 7 - CO O V •s. 3.6 S u JO > c _o o 3 G O O _o 'C u a* o u - V V C G o o -o 2 2 £ o m co 1 o o o 10 ~-r o co o m —• | CD O O co None None 1.5-4.0 00-300 90 O ^?o2 O © °> •-< V ■&, c«-i o G V U O fc « > > CO u (U a, as J3 U be c o c V o Ph u V V N CO g u he C •— < rt J* a rt -4— ' u a. CO G G aj c *j H o a.sp J5* Oh — u ,° 03 bec t^ !t! u — c < co + G Q Resti: Spike * 82 The Conduction of Impulses by Nerves /4 : 4 a comparative point of view, it is a huge axon. It is possible to shove all sorts of electrodes and shafts inside this axon. Experiments with squid axons confirm that the resting potential and the spike potential depend only on the membrane, not on the bulk of the axoplasm. This is in accord with the charge distribution shown in Figures 2 and 4. Similar experiments have % shown that this pattern is valid also for all other axons, for muscle fibers, and for many long algal cells. The local response has the same form as the spike potential shown in Figures 4 and 7a. A small depolarization applied externally results in a flow of ions, so that a greater depolarization of the membrane occurs. Subthreshold Stimulus Produces Local Response Two Subthreshold Stimuli Add to Trigger Conducted Spike Potential Second Response Inhibited by First for Greater Time Between Figure 7. Temporal summation of subthreshold responses. Figure 7b shows a second subthreshold stimulus following closely after a first one. These add and give rise to a conducted spike potential. Figure 7c illustrates two stimuli slightly further apart in time. In this case, the first local response inhibits the second one. Both the local responses and the conducted spike potential involve a flow of ions. In the initial or resting condition, the K + concentration inside the fiber is greater than that outside and the Na + less than that outside. The ions are maintained with this distribution at the expense of metabolic energy. The spike potential does not merely result in a depolarization of the axon membrane, since the potential actually reverses in sign. Rather, measurements of the Cv ">lex impedance Z, per unit surface area, have shown that ionic condui tion increases both during the regenerative phase of the spike and agai.x during the recovery. Tracer experiments and others described in Chapter 24 have shown that Na + flows into the axon during the regenerative phase and K + flows out during the recovery phase. This may be summarized by the 4 : 5/ The Conduction of Impulses by Nerves 83 diagram shown in Figure 8. This entire process is an active one, so that the spike potential is not attenuated as it travels along the axon but, rather, is built up anew at each spot along the way. The velocity at which a spike potential travels along a fiber is limited by the diameter of the fiber. Larger diameters correspond to larger velocities. In the large "myelinated" vertebrate fibers, the spike travels at a rate in excess of that predicted from the axon diameter. It Spike Resting A/o + Intercellular Fluid Na* Membrane Metabolism Ax op I asm .. Regenerative Na* — Phase Recovery Phase Figure 8. Ion movements across axon surface. After A. L. Hodgkin and R. D. Keynes, "Active Transport in Nerve," J. Physiol. 128: 28 (1955). is believed that the regenerative and recovery phases described above occur only at the nodes. In between, the spike is simply conducted, the entire segment acting as a single conductor. The spike potential thus is attenuated between the nodes and restored to its characteristic height at the nodes. The myelin sheaths of the "nonmyelinated" axons may act primarily as electrical insulation between fibers. This limits the probability that a spike potential along one axon will stimulate its neighbor. Muscle fibers have similar spike potentials but lack myelin insulation. In the muscle, unlike the nerve, it may be desirable for one fiber to stimulate other parallel ones, although this has never been demonstrated to occur. 5. Synaptic Conduction Along the axon, the information is transmitted as an electrical spike potential. This transmitted spike is maintained at a constant height by renewal and amplification, either continuously or at certain nodes. There are thus tw6 symbols for coding transmitted information: either a spike or its absence. In other words, all neural information is coded as binary digits. (See Chapter 25.) The axon transmits equally well in either direction, but in the intact 84 The Conduction of Impulses by Nerves /4 : 5 animal it is only used in one direction. This limitation is imposed by the synapses between neurons and by their junctions with the sensory receptors. 4 Similar limitations exist for muscle fibers which conduct spike potentials in either direction along the fiber but are only stimulated in life at the junction between the nerve terminals and the muscle. At Synapse Presynaptic Fiber Vesicle Containing Transmitter Molecules Postsynaptic Fiber Sensitive Area (a) Figure 9. (a) Chemical transmission. The incoming spike re- leases packets of molecules which diffuse across synapse to produce local excitation at sensitive areas. Diagrammatic representation, (b) Electrical transmission. With suitable geometry, a large field strength can be created in synapse by a spike potential on fiber A, thereby exciting B. The geometry and synaptic rectification prohibits conduction in the other direction. Diagrammatic representation. this point, the muscle fiber has a special structure called an end plate. The neuromuscular junction is homologous to the synapses between neurons ; much of our knowledge of neural synaptic conduction is based on studies of the neuromuscular junction. Accordingly, the term 4 Synapses are probably not polarized in some invertebrates. 4 : 5/ The Conduction of Impulses by Nerves 85 "synaptic conduction" is interpreted in this section to include the trans- mission of spike potentials from nerve to muscle. Two different modes of synaptic conduction occur: electrical and chemical. These are illustrated in Figure 9. The electrical conduction may be very rare; it has been demonstrated positively only for the "giant synapse" in the crayfish. At this synapse, impulses travel electrically from one axon to another with negligible time delay. Conduction can occur only in one direction. Similar giant synapses in the squid, however, exhibit appreciable time delay and no electrical transfer of charge. Conduction across the squid giant synapses, just as across all vertebrate synapses studied, is mediated by a specific chemical. There is no reason to believe that the same chemical is involved at all the synapses lacking direct electrical transfer. On the contrary, there is considerable evidence to indicate that different substances act at different synapses. Most nerve fiber terminals are so small that it is impossible to make direct observations and hence, determine the trans- mitter substance. As a result of the small size, only very small amounts of the transmitting chemicals are necessary. At the neuromuscular junction in vertebrates about 10" 18 moles of acetylcholine (ACh) produce a spike potential. ACh is the only synaptic transmitter substance which has been definitely confirmed. In chemical transmission, the substance, as ACh, is released when a spike potential reaches the appropriate nerve fiber terminal. It then diffuses across the synapse. This distance is of the order of a micron or two, and diffusion can occur in a millisecond or two. The diffusing substance is then absorbed at the receiving terminal or motor end plate, where it changes the ionic permeability of the membrane. Finally, the absorbed molecules are enzymatically destroyed. Experiments with vertebrate motor end plates have shown that the area sensitive to ACh is extremely small ; it is confined specifically to the outer surface of the motor end plate nearest to the nerve endings. This outer surface may be regarded as a chemoreceptor. Furthermore, these studies showed that ACh does not produce a depolarization of the membrane but increases its permeability to all small cations such as Li + , Na + , and K + . Finally, the ACh is destroyed by a specific protein catalyst, acetylcholinesterase, located in the end plate. The response across the synapse is a local response. The spike potential may originate near there as in the case of vertebrate muscle fibers and giant synapses in squid. In contrast, in sensory neurons (whose axon runs towards the cell body) the spike is formed at the distal end of the axon where several fiber terminals join together. In motor neurons, where the local response occurs in dendrites, the transmitted spike potential is formed at or past the nerve cell body. 86 The Conduction of Impulses by Nerves /4 : 5 One spike potential on a presynaptic fiber may excite one spike potential on the postsynaptic fiber. In some cases, a spike on any one of several different presynaptic fibers may excite a spike on a given postsynaptic fiber. At other synapses, one spike on a presynaptic fiber will produce only a local subthreshold response. In this case, there exists the possibility of adding subthreshold responses from several synapses to produce a spike potential. Thus, the neuron can act as an adder. Likewise, two, three, or more local responses in a short time at one synapse may be necessary to produce a transmitted impulse. Then the synapse is acting as a "divider." If several terminals from one neuron cell synapse with differing time delays at the same second neuron, then the original spike could be "multiplied." Neurons can likewise subtract. This is possible because not all post- synaptic membranes are similar. For instance, ACh produces a spike potential at motor end plates but inhibits heart muscles. (This inhibi- tory effect of the ACh secreted by the vagus nerve endings in the heart led to its original discovery.) At inhibitory junctions, the transmitter substance increases the permeability to K + and larger cations but does not alter the Na + or Li + permeability. The net result is a change in the transmembrane potential and an increase in the local response necessary at other synapses to start a transmitted spike. This produces, effectively, subtraction of the impulses from two different incoming neurons. At the synapses, then, the arithmetic processes of addition, subtraction, multiplication, and division can occur. Because the local responses exhibit a complex time pattern, the calculus operations of integration and differentiation can also be produced. However, the neurons are not as simple as electronic circuits, and the various numerical processes are also much more complex. This situation may be described in mathematical terms by saying the system is nonlinear. For example, a dividing synapse, if presented with three impulses, may transmit one ; but seven will be necessary for two transmitted spikes and 14 or more will be needed for three transmitted spikes. In addition, the synaptic conduction is altered by slow potential fluctuations which are small compared to the membrane potentials and by changes in the ionic content of the intracellular fluid. Aside from the direct effects of K + and Na + , the Ca + + and Mg + + and particularly their ratio alter the synaptic conduction. At the neuromuscular junction, it has been shown that ACh is released in packets of the order of 1,000 molecules from small vesicles in the nerve endings. The probability of a given packet entering the intercellular fluid is a function of the Ca ++ /Mg ++ ratio. To summarize this section, transsynaptic conduction usually occurs in one direction. It may be mediated by electrical charge conduction or 4 : 5/ The Conduction of Impulses by Nerves 87 special chemical transmitters. The latter alter the permeability of the surface of the second neuron (or the muscle fiber) at specific receptor spots. Depending on the receptor, and perhaps on the chemical nature of the transmitter, this may result in stimulation or inhibition. All manner of arithmetic and calculus operations can occur at synapses between neurons. The behavior is similar to that in digital computers but far more complex. REFERENCES 1. Maximow, A. A., and William Bloom, A Textbook of Histology 4th ed. (Philadelphia: W. B. Saunders Company, 1942). 2. Glasser, Otto, ed., Medical Physics (Chicago, Illinois: Year Book Publishers, Inc.). a. Beutner, R., "Bioelectricity," (1944) Vol. I, pp. 35-88. b. Curtis, H. J., and K. S. Cole, "Nervous System: Excitation and Propagation of Nerve," (1950) Vol. II, pp. 584-595. c. Rashevsky, N., "Nervous System: Mathematical Theory of Its Functions," (1950) Vol. II, pp. 595-603. 3. Barron, E. S. G., ed., Modern Trends in Physiology and Biochemistry (New York: Academic Press, Inc., 1952). a. Grundfest, H., "Mechanisms and Properties of Biological Potentials," pp. 193-228. 4. Stevens, S. S., ed., Handbook of Experimental Psychology (New York: John Wiley & Sons, Inc., 1951). a. Brink, Frank, Jr., "Excitation and Conduction in the Neuron," pp. 50-93. b. "Synaptic Mechanisms," pp. 94-120. 5. Reviews of Modern Physics, Vol. 31 (1959). a. Schmitt, F. O., "Molecular Organization of the Nerve Fiber," pp. 455-465. b. Katz, Bernard, "Nature of the Nerve Impulse," pp. 466-474. c. "Mechanisms of Synaptic Transmission," pp. 524-531. 5 Electrical Potentials of the Brain I. Electroencephalography Electroencephalography is a study (or graphing) of the electrical poten- tials on the surface of the head. In terms of its derivation, electro- encephalography (electro + encephalon + ography) could refer to any electrical potentials of the head. Actually, it is restricted to those potentials, other than neuron spikes, that are associated with the brain's action. At the outer surface of the scalp, these electroencephalographic (eeg) x potentials are small compared to the potentials due to the heart- beat and are comparable to the potentials associated with the motion of the muscles controlling the eye, jaw, neck, and so on. The small 1 Throughout this chapter, the abbreviation "eeg" will be used as an adjective or noun as appropriate, to refer either to these potentials, to the recording appara- tus, or to the graphic record of these potentials as a function of time. The eeg potentials arise from the action of nervous tissue. The student will find it profit- able to have read thoroughly the preceding chapter before starting this one. A knowledge of that material is presupposed in this chapter. 88 5 : 2/ Electrical Potentials of the Brain 89 eeg potentials can be observed only with electronic amplifiers which discriminate both against other potentials of physiological origin and against electrical noise. The characteristic form of the eeg pattern has been used clinically and experimentally. Various types of epilepsy have typical eeg patterns which are useful for diagnosis and occasionally in treatment. Brain tumors likewise may be located from an eeg if the tumor is sufficiently close to the brain's surface. Many brain injuries can be diagnosed from alterations in the patterns of the potentials near the injury. Behavioral experiments use eeg patterns to indicate alarm reactions, sensory res- ponses, and so forth. From the viewpoint of this text, the more significant application of these so-called "brain waves" is that they may indicate the operation of the central nervous system. Many theories have been proposed, based on the form of these brain potentials. To date, none of these theories has been altogether successful. The eeg potentials are a building block which may eventually lead to an undejstanding of the function of the brain. The potentials associated with brain activity may be as large as 100 microvolts on the human scalp; these can be observed electronically. In laboratory animals, it is more difficult, if not impossible, to measure eeg potentials outside the skull. Small electrodes inserted through the skull onto the surface of the brain indicate potentials similar to those found on the human scalp. In other studies, electrodes are inserted into the interior of the brain. Potentials measured within the brain, with electrodes so large (diameter 0.01 mm or greater) that they respond to some type of average of the activity of many cells, are also referred to as eeg potentials. The instrument used to record the potentials is called an electroencephalograph and the record an electroencephalogram. 2. The Central Nervous System The eeg potentials result from the action of the central nervous system. To aid in discussing these brain potentials, an outline of the anatomy of the central nervous system is given in this section. In Section 3 of this chapter, some of the actions of the central nervous system are inter- preted by analogy with electronic feedback networks. The central nervous system, as is the case with all other nervous tissue, is made up of neurons. Some carry information into the central nervous system; these are sensory or afferent neurons. Others carry spike potentials out of the central nervous system and are called motor 90 Electrical Potentials of the Brain /5 : 2 or efferent neurons. The great majority of the units within the central nervous system start and end there ; these are called interneurons. Thus, many neurons form links between other neurons. As was pointed out in the last chapter, one neuron may receive impulses from several neurons, and it may excite or inhibit more than one other neuron. Each neuron follows an all-or-none law; that is, it either is or is not conducting a spike potential. This assemblage of neurons connecting with other neurons is very similar in form to a complex digital computer whose units are in one of two possible states. In addition to the spike potentials, there are also more diffuse changes in electrical potential in various areas of the brain. These may also play an important role in the central nervous system function, for example, by altering the synaptic transmission from one neuron to the next. These diffuse, slower potential changes are analogous to what one might expect to find in an analog computer. They indicate the diffi- culty of trying to use any electronic model for the central nervous system. The vertebrate central nervous system is easily divided into two major parts: the brain and the spinal cord. Both are surrounded by three membranes, or meninges, which serve to protect the central nervous system from injury. Between the various meninges are layers of cerebro- spinal fluid which cushion the central nervous system from shock. There are also fluid-filled chambers within the central nervous system itself: four ventricles in the brain and the central canal in the spinal cord. All four ventricles and the spinal canal are interconnected. Various nerves leave (or enter) the central nervous system. Along the spinal cord, a pair of nerves passes between each pair of vertebrae. These supply sensory, motor, and autonomic fibers to all parts of the body other than the head. In addition, 12 pairs of nerves originate in the brain itself. The spinal cord and brain consist of white matter and gray matter. The white color is due to the myelin around the large nerve fibers; the white matter is made up of fiber tracts. The gray matter contains most of the cell bodies. Some of these are arranged in compact volumes referred to as nuclei. Many nuclei can be associated with specific functions or actions, such as control of respiration, or conducting impulses from muscular proprioceptors, and so forth. However, the over-all action of the nervous system, particularly with respect to subjective phenomena as thinking or memory, is still in the realm of specula- don. Figure 1 shows the structure of a medial section through the human brain. The portion of the brain joining the spinal column is called the brain stem. In lower vertebrates, as fishes, there are two small bumps 5 : 2/ Electrical Potentials of the Brain 91 A.C. Anterior Commissure A.P.S. Anterior Parolfactory Sulcus C. Cuneus Ca.F. Calcarine Fissure C.F. Body of Fornix C.P. Cerebral Peduncle C.P.V.3 Choroid Plexus of 3rd Ven- tricle Co.F. Column of Fornix D.F.H. Dentate Fascia of Hippo- campus F.G. Fusiform Gyrus F.I. Interpeduncular Fossa G.C. Gyrus Cinguli G.C.C. Genu of Corpus Callosum H.G. Hippocampal Gyrus I.T.G. Inferior Temporal Gyrus L.G. Lingual Gyrus L.Q. Lamina Quadrigemina M.I. Massa Intermedia M.B. Mammillary Body O.C. Optic Chiasm O.R. Optic Recess P.A. Parolfactory Area Figure I. Medial aspects of the human brain. Copyright The CIBA Collection of Medical Illustrations by Frank H. Netter, M.D., Vol. 1, "The Nervous System," 1953. P.C. Precuneus P-C. Posterior Commissure P.O.S. Parieto-occipital Fissure P-C.L. Paracentral Lobe Pi. Pineal Body Pit. Pituitary Gland P.P.S. Posterior Parolfactory Sulcus R.C.C. Rostrum of Corpus Cal- losum S.C Sulcus Cinguli S.C.(P.F.) Sulcus Cinguli (Pars Frontalis) S.C.(P.M.) Sulcus Cinguli (Pars Marginalis) S.C.C. Splenium of Corpus Cal- losum SC.G. Subcallosal Gyrus S..F.G. Superior Frontal Gyrus T.C.C. Trunk of Corpus Callosum Th. Thalamus T.P. Temporal Pole U. Uncus 92 Electrical Potentials of the Brain /5 : 3 called the cerebral hemispheres near the olfactory area. In mammals, and to the greatest extent in man, these cerebral hemispheres are a major part of the brain. The cerebral cortex which covers the hemispheres is so folded around and over the brain stem in mammals that the eeg potentials on the skull are related to the cerebral cortex only, and probably only to the outermost layers of the cerebral cortex. (By placing electrodes within the brain, eeg potentials can be measured as a function of the part of the brain nearest the electrodes, rather than of the outer layers of the cortex.) The portion of the brain stem connected directly to the cerebral cortex is called the thalamus. The sensory pathways all have synapses in the thalamus. Certain thalamic regions are believed associated with emotional responses. Thus, if an electrode is placed in the appropriate spot in a rat's thalamus, it will pull a lever to shock itself in preference to eating food. Other areas in the thalamus produce just the opposite effect when stimulated. It appears proper to consider all mammals, and possibly all vertebrates, as having emotions homologous to ours and represented by thalamic centers. Thought, memory, conscious sensations, and conscious motor activity are all associated with the cerebral cortex. The cerebrum is attached to the thalamus. In the relative size and complexity of his cerebral cortex, man is unique among the animals. As illustrated in Figure 2, certain areas can be associated with specific functions. However, the role of many areas of the cerebral cortex is not known, nor is it known how man analyzes, or thinks, or remembers. Because it reflects, in some sense, the activity of this part of the brain, the eeg has attracted the interest of many investigators. However, if the cerebral cortex is removed, similar eeg patterns remain. Even fishes, whose cerebral cortices are negligible, possess typical eeg patterns similar to man's. The eeg is a vertebrate pheno- menon; insect ganglia do not exhibit comparable potentials. The eeg must, in some way, be related to the structure and function of the verte- brate central nervous system. 3. Feedback Loops and the Nervous System It is possible that the eeg potentials reflect, in some manner, feedback loops within the central nervous system. Whether or not this is the case is a moot point, but there is no doubt that feedback loops are important in all coordinated animals and, in particular, in the over-all action of the nervous system. The basic elements of a feedback loop are shown in Figure 3. They consist of (a) a quantity being controlled, such as the 5 : 3/ Electrical Potentials of the Brain 93 temperature of a room ; (b) a method of sensing this quantity such as a thermostat; and (c) an active mechanism whose rate can be varied by the sensing element to effect the control (in this example, an oil furnace). If the control opposes changes, the loop is said to have a negative feed- back. Similar negative feedback loops are common in electronics. One such frequent use is to keep an amplifier's gain constant in spite of changes in supply voltages and tube characteristics. Feedback loops can also Pre -motor Suppressor Suppressor Biological Intelligence Somato-mofor Somato- sensory -Suppressor Bodily Awareness Writing __ Speech Understanding Visuo-sensory Visuo-psychic Suppressor Biological ^ j^ \ Intelligence '• $.-'„' Reading (Visual Speech) Audito- / I Suppressor psychic Audito-sensory Somato -motor Somato -sensory Stressor . ;; ^^ [i!; ^ ! ^^^ ^Suppressor Pre -motor ~ ^^f ^ssl^ ,|!p''! ■ sUP"^*^ Suppressor Visuo-psychic Visuo-sensory Suppressor Olfactory Figure 2. Functions of the human cerebral cortex. Copy- right The CIBA Collection of Medical Illustrations by Frank H. Netter, M.D., Vol. 1, "The Nervous System," 1953. maintain the output of a power supply at a constant voltage or vary an amplifier's gain to keep its output constant. The latter is illustrated in Figure 3b. Instead of just one room, it is sometimes desired to regulate indepen- dently the temperature of several rooms. Individual thermostats may control dampers in the hot air lines to their respective rooms and a complex system must coordinate the results of the various thermostats to control the furnace. Complex, interlocking loops also occur in the nervous system. 94 Electrical Potentials of the Brain /5 : 3 The thermostat operates only in an on-off, that is, all-or-none, manner. If, instead of the thermostat, one uses a thermocouple, or External Influences Sensing Element Comparator Reference Control Device (a) (b) Heat Loss to Outside Room \ Dial Setting (Reference)^ Temperature J Thermosrar ^ \ -g* Mt **\ f~K-^fr~^ 1-3 fi< * V j i jv mi i r i j. 7-9 WwvvwkvwW Vw, W'^^vMvi%Vw/A^ — ~ -**V-~W ~->T\WV*yW\*'*-*•*-* — rA^wywMwwvvwws I sec l50y,v Figure 6. Normal eeg patterns illustrating abolition of the a-rhythm with eyes open. If eyes remained open for longer period of time, the a-rhythm would build up again. Original figure of R. G. Bickford, M.D., Mayo Clinic. many normal adults completely lack a-waves both on the scalp and on the cortex. Besides the a-rhythm, there are so-called "/?- waves" in the frequency range of 14-50 cps. They are always present in normal adults. The /3-waves are smaller in amplitude than the a-waves and are usually spindle shaped. In some adults, there are large voltage (50-100 /xv), slow ( |-4 cps) S-waves, as well as slightly faster #-waves in the frequency range 5-7 cps. Both the 8- and the 0-waves are often associated with abnormalities. Although the eeg patterns are not the same for all normal adults, they do vary with the activity of the central nervous system. The most studied example is the a-rhythm, which occurs predominantly in the 5 : 4/ Electrical Potentials of the Brain 99 occipital region where vision is projected on the surface of the cortex. If the eye is suddenly focused on a bright image, the a-rhythm is abolished leaving only higher frequency, low voltage waves in the eeg pattern. With continued concentration, the a-rhythm returns. The a-rhythm is also altered by blinking. With the eyes closed, it is slower than with the eyes open. Similarly, the eeg pattern is altered by anesthesia and by sleep. With anesthesia, the a-rhythm tends to build up and then later to disappear. As one falls asleep the eeg pattern changes dramatically. During the drifting-off stage, the a-rhythm tends to disappear. (In individuals lacking an a-rhythm when awake, one appears during the drifting-off stage.) As the a-rhythm disappears, 4-6 cps waves appear. In the next stage, 14-16 cps spikes with the spindle shape of /3-waves appear; this is the "dream" stage. With full sleep, very slow \- 3 cps waves predominate. A sudden stimulus produces an 8-14 cps (a-wave) burst superimposed on the slow waves. Eeg patterns not only are dependent on the state of awareness and optical activity, but they also vary considerably during development. On the scalp of a year-old baby, there appear the first orderly eeg rhythms. These are occasional bursts of 4-8 cps, especially in the occipital area. By four years of age, 7-8 cps appear. At nine years of age, the frontal and parietal waves are slower than in adults, and 9-10 cps rhythms are more common in the occipital region. Even at 14 years of age, when people in many parts of the world are supporting themselves and reproducing, childish forms are found in the eeg. By 19, however, all the records are adult in form. There can be no question that the eeg provides real clues as to the mental state and activity. It varies with age, with sleep, and anesthesia, and with shutting the eyelids. Eeg changes associated with certain abnormal states are well known and used clinically. They are discussed in Section 5. Likewise, eeg records are used routinely in behavioral experiments to indicate alarm reactions, conditioning, and so forth. None of these answer the fundamental question of the function and origin of the eeg potentials. In spite of many experiments, the role of the eeg potentials is still obscure. The simplest hypothesis would seem to be that they represent some type of scanning by the brain of impulses coming in on the sensory neurons and of information within the brain. This hypothesis is simplest to one who has worked with large digital computers. The experimental data either supporting or refuting this hypothesis are very weak. Perhaps the place to start studying the role of the eeg potentials is in discovering their origin. Here, the experimental data are conflicting. 100 Electrical Potentials of the Brain /5 : 5 Some people have found that a small part of the cortex, when isolated from the remainder of the brain, will continue to produce eeg rhythms. Others have claimed, on the basis of their experiments, that large areas or all of the cortex must remain intact to produce normal eeg rhythms. Still others believe, again on the basis of experiments, that the eeg patterns involve closed neuron circuits which include both the cerebral cortex and the thalamus. The scanning hypothesis cannot explain how some normal persons can lack the a-rhythm which is so predominant in most others. Further- more, there is no simple explanation of the variation of the spatial distribution from one head to another. Again, the speed or frequency of the a-rhythm does not relate to any known sensory, motor, or thought process of the majority of normal persons. (See, however, the dis- cussion of epilepsy in the next section.) The theories that include the thalamus as part of the feedback loop are difficult to reconcile with the absence of changes of the eeg on the scalp of persons with thalamic tumors. The lack of any definite cellular knowledge regarding the origin of the eeg makes it extremely hard to interpret. 5. Abnormal Electroencephalographic Patterns Clinically, abnormal eeg patterns are used to localize brain tumors and to study epilepsy. Although various investigators have reported a relationship between psychological disturbances and eeg patterns, these seem so uncertain that they will not be discussed further here. Both the tumor and epilepsy patterns have been intensively studied, and the results not only are clinically useful but they serve to emphasize our inability to directly relate brain activity and eeg patterns. The most reliable method of detecting brain tumors is the so-called "pneumoencephalograph." In this method, the fluid spaces of the brain and spinal cord are drained, the fluid being replaced with air. X-ray photographs are then taken. The contrast in X-ray opacity between the brain and air is large (although between brain and fluid it is negligible) . A tumor is discovered from a distortion of the ventricles. This method of diagnosis has a definite mortality rate, it is extremely painful, and it fails to reveal small tumors. By contrast, the eeg can show a brain tumor two years before the pneumoencephalograph does, is not painful, and has a zero mortality rate. Its use is limited by its complexity and the volumes of records which must be analyzed, and by its failure to show tumors below the surface of the cerebral cortex. Using 24 electrodes, as shown in Figure 5, there are 276 possible pairs. If eight pairs are recorded at one time, for 5 : 5/ Electrical Potentials of the Brain 101 five minutes per set, a total of about four hours is necessary. By making judicious choices, this time can be reduced to an hour, but a great many paper recordings must be closely scrutinized. On analyzing these records, four types of abnormalities associated with brain tumors are found. These are: a S-rhythm; a 0-rhythm; high voltage single spikes or multiple spikes at 10-20 cps; and episodic or continuously enhanced a-rhythms. None of these abnormal rhythms are due to tumor tissue which is always silent, but the abnormalities are most pronounced in the part of the brain nearest the tumor. The eeg changes are most useful in localizing abnormal growths along the surface of the cerebral cortex, but there are no major changes in the eeg pattern E.E.G. Patterns Normal Eyes Open Nonspecific Dysrhythmia Spike and Wave Multiple Spike and Wave Slow Spike Delta I sec Figure 7. The various abnormal eeg patterns each have specific clinical implications. For example, the "spike and wave" is characteristic of petit mal seizures. Original figure of R. G. Bickford, M.D., Mayo Clinic. on the scalp because of tumors along the brain stem. Bilateral differences in the eeg patterns also help locate cerebral tumors. Another clinical use of eeg patterns is for studies of epilepsy. In general terms, an epileptic seizure is an uncontrolled hyperexcitability and spontaneous discharge of part of the central nervous system. If the discharge occurs in motor areas of the cerebral cortex, the person has a 102 Electrical Potentials of the Brain /5 : 6 violent seizure with muscular spasms followed by unconsciousness. This is called a grand mal seizure. In other persons, the sensory areas of the cortex are hyperexcited, producing sensory illusions such as buzzing in the ear, spots of light, or nausea, followed by unconsciousness. Illusions followed by unconsciousness are called petit mal seizures. Another type of epileptic seizure is called psychomotor, an attack in which the person has sensory illusions followed by inappropriate automatic actions and then amnesia. All three types have characteristic eeg patterns, such as those shown in Figure 7. For a given patient, these eeg abnormalities are more constant than the exact nature of the seizure. All are characterized by large, low frequency waves. One might be tempted to conclude that the size of the eeg indicated the degree of nervous activity. However, there are also electrically silent seizures in which the normal potentials are markedly decreased. The eeg is nonetheless useful in determining the type of epilepsy, choosing the treatment, and following the patient's progress. 6. Summary The eeg patterns are tantalizing in that they seem to be intimately associated with the over-all action of the brain. They are useful for clinical purposes, just as a patient's temperature may be of interest to a physician with no knowledge of temperature control mechanisms on the cellular level. The fundamental question of interest to the biophysicist is : In what way are the eeg patterns related to the actions of the neurons of the brain ? This question has not been answered. It may be that extending measurements to lower frequencies, small regions of the brain, and so forth, may provide more clues. It seems more probable that what is needed are new ideas concerning the inter- pretation of the data and the planning of additional experiments. REFERENCES The form and action of the central nervous system are described in many texts. The following were used in writing this chapter. 1. Best, C. H., and N. B. Taylor, The Physiological Basis of Medical Practice, 7th ed., 1 96 1 (Baltimore, Maryland: Williams & Wilkins Company). 2. Ranson, S. W., and S. L. Clark, The Anatomy of the Nervous System: Its Development and Function, 10th ed., 1959 (Philadelphia: W. B. Saunders Company) . Electrical Potentials of the Brain 103 3. Netter, F. H., Nervous System CIBA Collection of Medical Illustrations, CIBA Pharmaceutical Products, Inc. (Summit, New Jersey, 1953) A popular book describing electroencephalography is : 4. Walter, W. G., The Living Brain (New York: W. W. Norton & Company, Inc., 1953). Somewhat more technical discussions can be found in: 5. Gibbs, F. A., "Electro-encephalography," Medical Physics, Otto Glasser, ed. (Chicago, Illinois: Year Book Publishers, Inc., 1944) Vol. 1, pp. 361-371. 6. Kaada, B. R., "Electrical Activity of the Brain," Ann. Rev. Physiol. 15: 39-62 (1953). (This includes 265 references.) Clinical uses are discussed in the text edited by: 7. Shedlovsky, Theodore, ed., Electrochemistry in Biology and Medicine (New York: John Wiley & Sons, Inc., 1955). a. Bagchi, B. K., "Preoperative Electroencephalographic Localization of Brain Tumors," pp. 331-351. b. Jasper, H. H., "Electrical Signs of Epileptic Discharge," pp. 352-359. Journal References: Biophysical experiments using brain potentials can be found in many recent journals including the J. Acoustical Soc. Am., Am. J. Physiol., Biophysics (USSR). 6 Neural Mechanisms of Hearing I. Place and Telephone Theories Hearing may be approached from various viewpoints. Some of these have been so completely studied it is unlikely that in 50 years our con- cepts will have changed appreciably. These aspects of hearing were presented in Chapter 1. They included the nature of sound trans- mission through the atmosphere, and the gross anatomy and the histology of the ear. Similarly, the role of the outer and middle portions of the ear as pressure amplifiers and mechanical transformers is quite well established. As was discussed in Chapter 1, a maximum amplification of about 35 db can be obtained. Other aspects of hearing are far less well understood. Specifically, the conversion of acoustic energy to neural spikes in the inner ear and the analysis of these spikes in the central nervous system are current areas of research. They are discussed in the present chapter. It is assumed that the reader is familiar with the material in Chapter 1 on "Sound and the Ear," as well as in Chapters 4 and 5 on the "Conduction of Impulses by Nerves," and the "Electrical Potentials of the Brain." The physicist regards the inner ear as a transducer, that is, as a device which converts one form of energy into another. The inner ear converts 104 6:1/ Neural Mechanisms of Hearing 105 mechanical energy into electrical spikes on nerve fibers. It was only in the 1940's that a reasonable understanding of this action was developed. Before considering the modern studies, the ideas firmly believed not very many years ago will be briefly examined. Two general types of theories were developed: the resonator theory, and the telephone theory. Al- though neither can be supported any longer, the theories were both very successful in one sense. Each correlated many of the known facts and inspired scientists to carry out further experiments. Then, additional studies showed that neither theory was correct and led to the present concepts of cochlear action. The resonator theory was developed by Helmholtz. He had studied musical instruments and found that they all resonated. Moreover, he Figure I. Helmholtz resonators. The exact shape and sym- metry are not important. The resonant frequency depends on the volume of the cavity and the cross sectional area and length of the neck. Some glass Christmas tree ornaments make excellent Helmholtz resonators. carried out frequency analyses of sound with specially built resonators. They are still known as Helmholtz resonators. Their form is shown in Figure 1. The resonant frequency depended on the geometrical pro- perties of the resonator. By using a series of these, Helmholtz could analyze the harmonics (that is, overtones) in a piano note and could even analyze some of the frequency components of speech. Helmholtz resonators were widely used until the advent of electronic analyzers. The latter are more convenient and much more precise but in all cases depend on an electrical resonant circuit. Helmholtz knew only mechanical resonators and so he looked for these in the cochlea. The most promising structure seemed to be the basilar membrane. This membrane separates the central cochlear duct from the tympanic duct. The basilar membrane supports the organ of Corti with its histologically complex structure and many nerve endings. The basilar membrane has a fiber-like character, and it gets broader and thicker as it proceeds along the spiral to the apex. This resembles the general form of a piano, a collection of strings going from short, thin 106 Neural Mechanisms of Hearing /6 : I strings at the high end to thick, long strings at the low end. Accordingly, the resonator theory postulated that the basilar membrane was made up of resonant fibers held under tension as piano wires. These fibers were very sharply tuned and resulted in a mechanical analysis of incoming sounds in much the same fashion as the Helmholtz resonators. Each fiber of the basilar membrane was supposed to activate a nerve fiber. Thus, pitch would be detected by the particular fiber most strongly activated, loudness (or sound pressure level) by the amplitude of the fiber motion, and quality by the relative amplitudes of various fibers. The resonator theory can be disproved in a number of ways. One objection, not too serious, is that a sharply tuned resonator is hard to excite; also it continues to vibrate long after the excitation has ceased. It is impossible to design mechanical resonators whose sharpness would permit the pitch discrimination possessed by many people and which would also permit the time resolution necessary to understand speech. If pitch discrimination is partly a function of the nervous system, then the resonators need not be so sharp. However, this inclusion of the central nervous system destroys the beautiful simplicity of the resonator theory. The most direct tests of the resonator theory were carried out by Bekesy. He measured the width of the basilar membrane of human ears and found it changed only by a factor of a hundredfold, whereas the thickness varied by a factor much less than 100. If this membrane were made up of resonant fibers similar to piano wires, the frequency of resonance f T should be given by the expression where T is the tension, p x is the mass per unit length, and L is the length. Because audible frequencies vary from 30 to 20,000 cps, that is, by a factor of almost 10 3 , Tjp-^L 2 would have to vary by 5 x 10 5 . Bekesy's measurements of tensions showed that 5 x 10 5 was at least a factor of 20 too great. His measurements depended on modern tech- nology and could not have been made at a much earlier date. With this knowledge that the resonator theory is clearly wrong, it is possible to find other pieces of information also tending to contradict the resonator idea. For instance, no one has ever actually found fibers in the basilar membrane which were independent of and ran directly across the membrane. An alternative hypothesis of hearing was the telephone theory. Rayleigh and many other scientists of his day were very impressed with the telephone, which acted as a transducer changing sound energy into electrical energy and then back to sound energy at another point. They 6 : 1/ Neural Mechanisms of Hearing 107 also knew that the cochlea acted as a transducer changing sound energy to electrical energy, but, without electronic gadgets, they knew nothing of the form of this electrical energy. They reasoned that the cochlea acted as a microphone, transmitting along the nerve fibers a signal whose form was that of the incoming pressure wave. In one of its variations, the theory suggested that only the nerve fibers nearest the windows to the middle ear were stimulated by weak sounds but that the entire cochlea was activated by loud sounds. If the proponents of this theory had had more electronic instruments available, they might have found additional evidence which could have been misinterpreted to support the telephone theory. In one experi- ment an electrode is placed at or near the cochlea. Definite electrical potentials are discovered which do reproduce the form of the applied pressure wave. These potentials are called cochlear potentials or cochlear microphonics; they are small in magnitude, perhaps no bigger than 100 /xv, but they definitely exist in the cochlea and not in the measuring equipment. These cochlea'r microphonics were discovered in the 1930's by Wever and Bray. Another experiment follows the auditory pathways into the brain stem. If an electrode is placed in these areas, a signal is picked up which is an integrated response of many nerve fibers. This electrical potential reproduces the form of the applied sound pressure, provided the frequency is below 3-4 kc. (Above 4 kc a submultiple of the applied frequency is usually present.) Several lines of evidence show that the telephone theory cannot be valid over most of the audible range. The most unequivocal of these is that an individual nerve fiber cannot conduct more than 1,000 spikes per second. This limitation occurs because there is a period of 1 milli- second or more following a spike during which time another cannot be generated. The occurrence of 1.000 spikes per second would not allow the nerve fiber to reproduce a sound wave of 1,000 cps. As shown in Figure 2, many spikes are necessary per cycle. Thus, the telephone theory cannot be valid above about 60 cps. Moreover, whereas the integrated spikes in the fiber tracts in the brain stem do reproduce the form of the pressure wave, the potentials on the surface of the cerebral cortex fail to follow above 200 cps. In addition to the impossibility of individual axons acting as telephone lines, the telephone theory is refuted by a large body of experimental evidence favoring a place theory of hearing. In other words, different frequencies are represented at different places along the basilar membrane of the cochlea, albeit not analyzed by a resonator mechanism. For instance, lesions can often be observed in the inner ears of deafened persons. (In order to observe this, the person's hearing had to be tested in the hospital immediately before death. Then the ear had to be 108 Neural Mechanisms of Hearing /6 : 2 removed within an hour after death.) In cases in which specific frequencies were missing in the person's hearing, lesions occurred at corresponding regions along the basilar membrane (as predicted by the resonator theory!). The cochlear microphonics show maxima along the basilar membrane (again at the place indicated by the resonator theory!). Finally, if the basilar membrane of an experimental animal is destroyed Acoustic Pressure Spikes Axon Spikes Time Figure 2. This illustrates that to reproduce a sine wave many spikes per cycle are necessary. Even the 1 5 per cycle illustrated integrates at best to a crude sine wave. in a narrow region, it is found by both behavioral and electrical studies that the animal cannot hear in the corresponding frequency region. Thus, neither the resonator theory nor the telephone theory can be maintained in the light of present knowledge of the ear and the nervous system. Although the resonator theory is anatomically unsound, a spatial localization of frequencies along the basilar membrane does occur. Likewise, although the telephone theory per se cannot be maintained, its prediction of the form of the integrated nerve potentials in the brain stem is reasonably accurate. 2. Cochlear Mechanism of Neural Excitation Present theories incorporate all of the positive evidence presented in the last section. Needless to say, these theories are somewhat more complex. At least 12 different variations exist around the basic hydrodynamic theory proposed originally by Bekesy. He showed that, in addition to the compressional waves traditionally treated in acoustics, there could also exist certain slow hydrodynamic waves in a structure such as the cochlea. These waves bear certain similarities to surface waves on a large body of water or interfacial tension waves at an oil-water interface. (Note, "bear certain similarities" does not mean "identical to!") These hydrodynamic waves are in a dispersive medium, that is, one in 6 : 2/ Neural Mechanisms of Hearing 109 which the wave velocity is a function of the frequency. In such a medium, one may have a piling up of the waves to maxima in certain regions. This phenomenon can be observed in the build up and decrease of surface waves on the ocean. It is also a familiar idea used repeatedly in quantum theory. The various mathematical analyses of the cochlea, using this type of model, are beyond the scope of this text but should be studied by readers with sufficient mathematical preparation. Bekesy demonstrated s Dental Dam £v\\y.v (a) Window Analoq v/ ".'.' ' • "::." '.'.'.■, Analog of Apex of Spiral (Helicotrema) Vibrator (b) Analog of Apex Dental Dam (c) Figure 3. Bekesy's hydrodynamic analog of cochlea, (a) Transverse cross section. This shows two channels separated by dental dam. (b) Longitudinal cross section. This shows increase in width from "window" to "apex." (c) Perspective view. The two end windows as well as the partition are of dental dam. that these hydrodynamic waves existed not only in the cochlea but also in simple models which are satisfying substitutes for a mathematical analysis. For the simplest model, he used two rigid walls (microscope slides) resting on a solid surface and covered with dental dam (rubber sheet). A slightly more refined system is shown in Figure 3, where two channels and two windows are included. At low frequencies, the actual motion of the dental dam can be observed. There is a maximum region for each frequency ; this maximum is more or less independent of the shape of the channels and varies only slightly for major changes of the thickness or tension of the elastic membrane or of the dimensions of the channel. It is important that one window be driven and the other free. The model emphasizes the biological utility of the hydrodynamic waves whose maxima do not depend on exact physical dimensions. There is a maximum shearing force across the membrane at the maximum in 110 Neural Mechanisms of Hearing/ 6 : 2 amplitude. The general shape of these maxima is shown in Figure 4. Experiments with intact and excised ears in humans and laboratory rodents, at low frequency and high intensity, showed similar maxima. For a given sound pressure level, the lower the frequency, the greater is the displacement. These measurements, when extrapolated to the limit of audibility at 1 ,000 cps, show that the maximum displacements of the basilar membrane may be smaller than a nuclear radius, 10 ~ 12 cm. Both the theoretical analyses and the model experiments agree that all that is essential for the maxima of hydrodynamic waves, separated according to frequency, are rigid walls, two parallel tubes separated by an elastic membrane, and two windows, one driven and the other "open" High Frequency Maximum Low Frequency Maximum Figure 4. Maxima of the displacement of the rubber dam for the model in Figure 3. Lower frequencies have maxima nearer the windows. to the air of the middle ear. The maxima of these hydrodynamic waves give only a crude place localization of different tones. The maxima are narrow enough to account for the experiments with lesions and cochlear potentials but are far too broad to explain pitch discrimination by themselves. One must invoke a neural mechanism for the extremely sharp pitch discrimination which the human ear can perform. This pattern is discussed further in Section 3. The over-all action of the cochlea is, then, to convert (transduce) a hydrodynamic wave into electrical spikes on nerve axons. In an attempt to find the details of how this occurred, Bekesy and his co-workers studied the electrical properties of the cochlea. Although the over-all goal of describing the cochlear mechanism of neural excitation is still incomplete, many interesting facts have been uncovered. They have shown that in the intact animal the tympanic and vestibular ducts act as an electrical shield around the cochlear duct. The fluid in the tympanic and vestibular ducts is a good conductor. It is, however, electrically insulated from the cochlear duct by the basilar membrane and Reisner's membrane. Thus, the basilar membrane plays an import- ant role both as the elastic membrane for mechanical vibrations and also as an electrical insulator. In a phonograph cable, it is necessary to surround the inner conductor with an insulator, which in turn is covered by a second conductor. The outer conductor is called a shield and is 6 : 3/ Neural Mechanisms of Hearing 1 1 1 maintained at ground potential. It greatly reduces the pick-up of unwanted signals by the central conductor. In a similar manner, the fluid in the vestibular and tympanic ducts is at body potential and shields the central conductor. With sufficiently sensitive equipment, it can be shown that many shielded cables have a d-c potential between the inner conductor and the shield. A similar d-c potential exists across the basilar membrane. It can also be shown that any shielded cable acts as a microphone con- verting alternating pressures into electrical signals. Many people believe the cochlear potentials are of a similar nature, that is, unwanted electrical signals resulting from mechanical vibrations. These are called microphonics when they occur in an electronic circuit. By analogy, the cochlear potentials are referred to as microphonics. Whether the cochlear potential plays any role other than that of a microphonic is not known. The cochlear potential is absent in some deaf cats which lack hair cells ; it may be associated with the hair cells in some fashion. Most investigators feel that the hair cells are inti- mately associated with initiating the nerve potential. Similar hair cells are found at the nerve endings in the inner ear associated with balance and acceleration. The exact manner in which the electrical impulses in the nerve fibers are initiated is not known. (Nor, for that matter, is it known for most sensory nerve endings.) The description to this point includes most of the outstanding features of the known actions of the cochlear portion of the inner ear. It appears necessary to assign to the nervous system both the acuity of tonal dis- crimination and also the reconstitution of the individual nerve impulses, to have the integrated form of the original pressure wave. 3. Arm Analogs and Neural Sharpening The exact mechanism by which the nervous system carries out an extremely sharp frequency analysis is not known. However, it is a familiar fact that the nervous system does sharpen many types of stimuli. Thus, when a bright spot is focused on the retina, the sensi- tivity of the eye to surrounding areas is decreased. In bright light, this has the advantage of eliminating the effect of stray light. Simi- larly, if two compass points are pressed against the skin of the forearm at distances greater than about 2.5 cm apart, two sensations are received. At around 2.5 cm the two sensations weaken each other, whereas, at still closer distances, the two sensations add to each other. In the latter case, the person feels the stimulus midway between the two actual compass points. This is illustrated in Figure 5. 112 Neural Mechanisms of Hearing /6 : 3 Another interesting case is the location of two click-like stimuli on opposite sides of the finger. For long time delays between the two, separate clicks are felt. If the time delay is decreased, the second click Forearm 3cm 2.5 cm m 2 cm (a) Stimulus @ Sensation (b) (c) Figure 5. Neural sharpening and funnelling when two com- pass points are pressed on the arm. For large separation, separate sensations result. Medium separation sensations tend to suppress each other. Small separation sensations add and are located in a "sharpened" area. is no longer felt. As the time interval approaches zero, a single sensation is felt which approaches midway between the two stimuli and has a larger apparent area. The results of an experiment of this nature are shown in Figure 6. This same type of phenomenon occurs when one locates a sound by the difference in the times of its arrival at the two ears. This addition of more than one stimulus into a single, stronger sensation is called "funnelling" by Bekesy and his co-workers. Mallet. Large Time Separation Small Time Separation Simultaneous (c) Figure 6. Neural funnelling when the forefinger is struck with two small mallets (clicks), (a) With large time separation, both "clicks" are sensed, (b) With small time separation, only the first is sensed, (c) Simultaneous clicks add to com- mon larger sensation half way between the two stimuli. These sharpening and locating effects which occur in the senses of touch and sight as well as hearing are very interesting. They emphasize that the nervous system does act as a complex computer with a great deal 6:4/ Neural Mechanisms of Hearing ||3 of feedback. They also emphasize that many of the types of neural action essential for hearing also occur in other senses. It has indeed been possible for Bekesy to make an enlarged cochlear model, using the forearm for a sensing organ. Most of the phenomena of hearing are reproduced by this model. The model consists of a series of resonant vibrators of varying fre- quency running along the arm. When these are electrically driven, several neighboring ones respond, the central one most strongly. The person senses the resonant frequency at a much more sharply located spot than is indicated by the behavior of the vibrators. Phenomena of masking, beats, harmonic distortion, and sharp frequency and intensity discrimination are all shown by this "analog" of the ear. Thus, there can be no doubt that the nervous system, in some fashion, does sharpen neural impulses. Likewise, funnelling can be demonstrated for the arm analog. Just how the nervous system goes about sharpening and funnelling is not known. The arm models of the ear demonstrate that nonlinear and harmonic distortion occurs in the nervous system, as well as in the tympanic membrane and middle ear. It is quite probable that a similar distortion also occurs within the inner ear. This is indicated by the cochlear potentials. However, because the cochlear and neural potentials are so difficult to separate, it is not certain whether distortion actually occurs within the cochlea. The arm models strongly support the idea that pitch discrimination is, to a large degree, a function of the central nervous system. The details of this action are not known yet. Nonetheless, many experiments with vertebrates, and even invertebrates, have shown that the central nervous system can carry out complex actions such as "sensation sharpening," "amplitude analysis," and "funnelling." Anatomical and electrical studies of the central nervous system emphasize the possibilities of such computerlike actions. 4. Cortical Representation The spike potentials generated in the basilar membrane of the cochlea travel along the fibers of the acoustic nerve. As has been stated, most sensory nerve cell bodies are located in compact groups called ganglia. The acoustic nerve, however, has a diffuse set of cell bodies spread out along its path through the spiral bony partition which supports the cochlea. These nerve cell bodies are called the spiral ganglion. The pulses in the second set of axons in the acoustic nerve enter the brain. The acoustic nerve is the eighth one (counting from the front end) to 114 Neural Mechanisms of Hearing/ 6 : 4 enter the brain; it is often called the eighth cranial nerve. As shown in Figure 7, several additional synapses occur within the brain stem. Some of the pulses cross over to the opposite half of the brain stem so Medial Geniculate Body Ihferior- Colliculus Midbrain- Level Nuclei of Lateral Lemnisci Medulla, Level Vestibular Membrane .Cochlear Duct .Sea la Tympani Olivary Complex Cochlear Nerve Inner \ ' Outer Pillar \ Pillar Basilar Membrane Phalangeal Cells Figure 7. Auditory pathways of the central nervous system. Copyright The CIBA Collection of Medical Illustrations, by Frank H. Netter, M.D., Vol. I, "The Nervous System," 1953. that those starting at either ear are represented in both halves of the brain. Finally, at least in unconscious animals, the pulses are con- ducted to specific areas on the surface of the temporal lobes of the cerebral hemisphere. This latter projection is believed to be necessary for conscious hearing. In humans and other primates, this auditory area on the temporal 6 : 4/ Neural Mechanisms of Hearing 1 15 lobe of the cerebral cortex is buried deep in one of the folds of the cortex and is hard to study. In other mammals, the cerebral projection is on or nearer the exposed portions of the cortex. In these latter animals, there are always two and, in some animals, three areas where responses appear (in the unconscious animal) when the ear is stimulated. Each of these areas is connected to both ears. Within each cerebral projection area, specific smaller areas correspond to specific spots along the basilar membrane. A detailed examination of the acoustic pathway shows that several neurons are involved. The first is located in the spiral ganglion within the inner ear. The nerve fibers leaving this ganglion join those from the vestibular portion of the ear to form the eighth cranial nerve. Within the brain, the vestibular and auditory fibers separate. Those from the cochlea go to one of two nuclei in the lower brain stem known as the dorsal and ventral cochlear nuclei. Some fibers leaving these have synapses with other neurons associated with reflex actions and balance. Others go to synapses in another nucleus in -the lower brain stem called the superior olivary complex. Some fibers synapse in the superior olivary complex on the same side, others on the opposite side of the brain, and still others pass through without interruption, joining fibers from the superior olivary complexes and passing up the brain stem. In the nuclei of the lateral lemniscus farther along the brain stem, some of the auditory fibers end, and others pass through uninterrupted. In the midbrain level, some of the auditory fibers end at synapses in the inferior colliculus. From here, some fibers cross over to synapses in the opposite inferior colliculus. All of the fibers of the auditory tract have synapses in another nucleus of the midbrain, the medial geniculate body. Fibers of these neurons finally reach the auditory areas of the cerebral cortex. The groups of nerve fibers in the brain stem "fire" in such a fashion as to reconstitute the original sound wave, or at least almost do so. Where this synchronization starts is not known. Wever has proposed that it occurs in the cochlea, that in some fashion the nerve fibers fire in volleys to reproduce the over-all form of the incident pressure wave. The manner in which this could occur is shown in Figure 8, for 15 nerve fibers. Observe that none fires too often, but that there is a certain over-all synchrony. This effect need not occur in the cochlea. It could just as well originate at the first or even second synapse. This semisynchronous action is called the volley theory. It states, in its simplest form, that below some frequency, say 100 cps, the number of nerve fibers excited varies with the instantaneous pressure. From 300 to 3,000 cps, the volley-type effect reproduces the form of the incident sound wave, whereas above 3,000 cps it cannot follow, but reproduces 116 Neural Mechanisms of Hearing /6 : 4 submultiples of the stimulus frequency. Somehow the brain is thought to carry out a frequency analysis on the over-all electrical signal. In other words, the ear carries out a crude frequency analysis in terms of exciting preferentially certain nerve fibers. The central nervous system then carries out a finer frequency analysis. Acoustic Pressure Axon # I 2 3 4 5 6 7 8 9 10 II 12 13 14 15 All I Spikes in Axon * I 2 3 4 5 6 7 8 9 10 II 12 13 14 15 minimi mm iiiiiiiiiii i i lllllllllll I I I I Integrated Figure 8. Illustration of the volley principle which allows axons to fire once per cycle and still reproduce the shape of the sound wave. Although it is clear that the detailed frequency analysis occurs by sharpening within the central nervous system, it is by no means under- stood exactly how or where this takes place. Part of the difficulty is in distinguishing neural impulses from cochlear potentials. For example, if a click is presented to the ear, two types of electrical potentials result. The first, essentially simultaneous with the click, is the cochlear potential. It remains even if the acoustic nerve is destroyed. The second is the true nerve potential; it occurs after a slight time delay and is abolished if the acoustic nerve is not functioning. For acoustic signals other than clicks, it is difficult to distinguish between these two types of potentials. Accordingly, most studies of the neural responses have been carried out past the first synapse in the diffuse spiral ganglion and usually have been restricted to the central nervous system. This has made it impossible to determine at what level detailed frequency analysis occurs. 6:5/ Neural Mechanisms of Hearing 1 17 5. Summary of Hearing Biophysical approaches to the sensation of hearing have been discussed in Chapters 1 and 3 as well as in this one. The material in Chapter 1 dealt with the physical parameters of sound important for hearing and with the anatomical characteristics of the ear, both on a gross level and also as revealed by histology. All of these are very important parts of man's knowledge of hearing. These topics in Chapter 1 are all well known and have been firmly established for many years. Although detailed studies may slightly modify them, the contents of Chapter 1 probably will not be dramatically altered. Certain peripheral studies, such as those of the mechanical behavior of the eardrum and ossicles at higher sound pressure levels, will undoubtedly supplement the present picture of the physical properties of the anatomical structure of the ear. The ideas presented in Chapter 3 on the uses of pulses of sound for echo-location by bats, porpoises, and birds are of more recent origin. The first significant studies in this direction date back only to 1940. Nonetheless, the ideas presented there are all so well supported by experimental evidence that it appears unlikely that they will be signifi- cantly altered in the near future. It does seem more probable that echo-location will be recognized as an important factor in other species. The material in this chapter deals with the most important bio- physical aspects of hearing, namely the conversion of sound waves to neural impulses and their analysis within the central nervous system. Although these topics are central to the biophysics of hearing, large gaps still remain in our understanding. Basically, the uncertainties are similar to those discussed in Chapter 5. It is in this general area that significant, major advances may be anticipated. REFERENCES 1. Wever, E. G., and Merle Lawrence, Physiological Acoustics (Princeton, New Jersey: Princeton University Press, 1954). 2. von Bekesy, Georg, and W. A. Rosenblith, "The Mechanical Properties of the Ear," in Handbook of Experimental Psychology, S. S. Stevens, ed., (New York: John Wiley & Sons, Inc., 1951) pp. 1075-1115. 3. Articles in J. Acous. Soc. Am. by Georg von Bekesy pertinent to this chapter include : a. 1949, 21, pp. 233-245. "The Vibration of the Cochlear Partition in Anatomical Preparations and in Models of the Inner Ear." b. 1949, 21, pp. 245-254. "On the Resonance Curve and Decay Period at Various Points on the Cochlear Partition." c. 1953, 25, 770-785. "Description of Some Mechanical Properties of the Organ of Corti." 118 Neural Mechanisms of Hearing d. 1953, 25, pp. 786-790. "Shearing Microphonics Produced by Vibrations Near the Inner and Outer Hair Cells." e. 1957, 29, pp. 489-501. "Sensations on the Skin Similar to Direc- tional Hearing, Beats, and Harmonics in the Ear." f. 1958, 30, pp. 399-412. "Funnelling in the Nervous System and Its Role in Loudness and Sensation Intensity on the Skin." g. 1959, 31, pp. 338-349. "Synchronism of Neural Discharges and Their Demultiplication in Pitch Perception on the Skin and in Hearing." 4. Other articles in J. Acous. Soc. Am. : a. 1951, 23, pp. 637-645. Fletcher, Harvey, " On the Dynamics of the Cochlea." b. 1959, 31, pp. 356-364. Goldstein, M. H., Jr., N. Y-S. Kiang, and R. M. Brown, "Responses of the Auditory Cortex to Repetitive Acoustic Stimuli." 7 Neural Aspects of Vision I. Color Discrimination The anatomical and physical features of the eye were described in Chapter 2. That chapter was terminated without a discussion of color discrimination because the latter depends on the action of nerve cells and the central nervous system. In this chapter, the neural mechanisms necessary for vision will be examined in more detail. To review briefly, the retina acts as a "photoneural" transducer converting incoming electromagnetic energy to spike potentials on nerve fibers. The potentials travel along the optic nerve, enter the central nervous system, and eventually reach specific areas of the cerebral cortex. The information is "analyzed" at a series of synapses, both within the retina and within the central nervous system proper. Out of this analysis there are, in some way, created the sensations of color, acuity, brightness, shape, and so forth. (It is assumed that the reader will be familiar with the ideas of Chapters 2, 4, and 5 before studying this one.) One step in the over-all process of vision, the photomolecular reactions in the rod and cone cells of the retina, is of extreme importance to an understanding of vision. At the same time, it is not necessary to understand these reactions before discussing the neural aspects of vision. 119 120 Neural Aspects of Vision \1 : I Accordingly, the molecular reactions are deferred to Chapter 19. A fundamental test of any theory of the neural aspects of vision is the explanation of color discrimination. The subjective sensations of color are familiar to most humans. However, at the lowest intensities where objects are barely visible to the dark-adapted eye, there is no sensation of color. At light intensities which are just slightly greater than this, colors begin to be sensed. The sensation of color is a complex function of the wavelengths of light reaching the eye. Just how complex this function is has been emphasized by a set of experiments referred to at the end of Section 4. However, when a large patch of light of the same wavelength is presented to the eye, it is identified as a single color. A light consisting of a very narrow wavelength band is called mono- chromatic. The other extreme, equal intensities at all wavelengths, is called white. The sensation of white can be evoked by many compositions simpler than uniform intensity throughout the visible spectrum. Certain pairs of colored lights, such as blue and yellow, appear white when mixed in equal proportions. The pairs of colors producing white are called complementary. Sets of three colors, such as red, green, and blue, as well as sets of four or more colors, also give a sensation of white. Likewise, varied groups of colored lights can produce any given color sensation. Psychophysicists distinguish several different qualities of sensations associated with color vision. These include luminosity (or luminous intensity), hue, and saturation. Luminosity 1 is defined as a "measure of the flux of luminous energy per unit solid angle emitted by a source." The luminous energy is in turn "an evaluation of radiant energy in terms of its ability to produce brightness." A colored light, as well as a given luminosity or brightness, will always have a certain hue 2 which is defined as " the quality of a sensation according to which an observer is aware of differences of wavelength of radiant energy." A given colored light may not be a pure hue but may be mixed with white light. This is measured by the saturation 3 which is the "quality of sensation by which an observer is aware of different purities of any one dominant wavelength." For example, pink repre- sents a mixture of red and white ; it is said to be less saturated than a pure red color. Hue and saturation taken together constitute chroma- ticity. It has been known for many years that sets of three stimuli existed, 1 Quoted from: Committee on Colorimetry, The Optical Society of America, The Science of Color. (New York: Thomas Y. Crowell Company, 1953.) 2 Ibid. 3 Ibid. 7:1/ Neural Aspects of Vision 121 so that by choosing the proper amounts of these, one could match the chromaticity of a given light in terms of the sensation it evoked in the average observer. If the amounts of each of the three standards are indicated by x, y, and z respectively, then one may represent symboli- cally a light A, by A = x A + y A + z A and a light B, by B = x B + y B + z B If one now adds equal amounts of A and B to form a new light C, which may be represented as C = x c + y c + z c then it is found that x A + x B = x c y A + y B = y c and z A + z B = z c In general, any algebraic combination pf colored lights is matched by the corresponding algebraic combination of the amounts of the standards matching these lights. 4> 400 500 600 700 Wavelength (m|x) 400 500 600 700 Wavelength (mnJ "3 400 500 600 700 Wavelength [myt) Figure I. Standard CLE. tristimulus values of unit energy for indicated wavelengths. After Committee on Colorimetry, The Optical Society of America, The Science of Color (New York: Thomas Y. Crowell Company, 1953) pp. 242-243. In order to standardize the description of chromaticity, the Inter- national Congress on Illumination agreed on three artificial standards. These were chosen so that a monochromatic light at any wavelength in the visible spectrum is matched by an average observer by the amounts •*/b y~\-> i>\ shown in Figure 1. The curve y K has the same shape as the average photopic luminosity curve; it gives the luminosity of a given light. The curves were normalized so that a white light (of equal 122 Neural Aspects of Vision \1 : I spectral density at all wavelengths) is matched by equal amounts of the three standards. Symbolically, this last may be stated as 4 |*780 m.n /*780 my /»780 mji *x d* = y*d\ = z k dX J380 van J380 mu J380 mp. Any colored light can be analyzed spectrophotometrically to give its spectral density E K . This is defined so that the total energy E is given by E = E x dX I or in other words E x = -p- J Many spectral densities E A will give the same sensation. To specify the sensation, three numbers, X, Y, Z, are needed ; in terms of the artificial standards above X = J x k E K dX Y = j y k E k dX and Z = \ z A E A dX where all three integrals are evaluated from 380 nux to 780 mju. These color-matching experiments are based on human response. Because they require subjective information, similar experiments are difficult to perform on laboratory or wild animals. Nonetheless, con- siderable evidence indicates that many vertebrates, and even insects, have color vision. However, the cat, whose eye is anatomically more like the human's than is the eye of any other animals except the primates, is believed to lack color vision. (The primate eyes are all so similar that the anatomist, Polyak, in discussing the retina lumps together humans and other primates in all his diagrams.) Since so much of the available data on color vision comes from humans, most attempts to explain color vision on cellular levels emphasize human vision. In the past, one of the major factors considered in testing any theory of color vision was its ability to account for various types of color defects. People whose color vision is normal are called trichromats since they need three colored lights to match the hues. Those needing only two colored lights are called dichromats and those with no color distinctions, mono- chromats. Four different types of dichromasy are known. Persons with two of these distinguish only blue and yellow. In this category, the group protanopes identifies red and blue-green colors as gray and has low luminosity sensitivity in the red. In contrast, the deuteranopes have a normal luminosity sensitivity in the red but identify greens and purple reds as gray. The other two types of dichromats distinguish red and 4 These integrals are usually written as extending over the wavelength range from zero to infinity. However, x x , y x , and z* are zero at all wavelengths outside of the range 380 m/x to 780m^t. 7: 1/ Neural Aspects of Vision 123 green but not blue. In this category, the tritanopes see purplish blue and greenish yellow as gray, whereas the tetartanopes see all blue and yellow as gray. Several types of monochromasy exist. In one type, called cone blindness, only rods are present in the retina. This type of monochro- mats show a loss of acuity; they retain the scotopic luminosity curve only. This strongly supports the connection between the rods and the scotopic vision. To further complicate matters, there are various inbetween defi- ciencies, such as protanomalous trichromasy, in which the red and blue- green sensitivities are markedly less than normal, but all three colors are necessary for matching hues. Almost any combination the reader can imagine is known to occur in humans. Two general types of theories of color vision have been maintained in the past. One of these, the tricolor theory, was supported historically by Young, Helmholtz, and Maxwell. The other type of theory, the oppo- nents or antagonist theory, has appealed -to many psychologists; its many variations are each associated with a person's name such as Hering, Ladd-Franklin, or Adams. The scheme presented in this text is essen- tially that developed by the biophysicist, Talbot, who emphasized that both theories have some elements of truth. His detailed picture makes more use of the specific structures of the retina than do most of the other theories. Briefly, the tricolor theories assumed that there were in the retina three pigments, B, G, and R, having maximum absorptions in the blue, green, and red regions respectively. These pigments were postulated to exist in separate receptors which sent impulses to the brain producing responses B', G', and R'. According to this theory, the brain "com- puted" yellow and white from G' and R' at high luminosities and white from B' at low luminosities. The original forms of the tricolor theory had difficulties with several types of color blindness and with white- black vision. Even the best refinements failed to use the detailed neuron structure of the retina. This last oversimplification seems most mis- leading. (See Figure 10, Chapter 2, page 42.) In contrast to the tricolor theories, which attempted to assign a minimum of types of retinal actions, the antagonist (or opponents) theories regarded the retina as the basis of considerably more complex actions. The opponents theories postulated that there were six retinal responses which occurred in antagonistic pairs. Excitation leading to any single response was supposed to suppress the action of the other member of the pair. These six retinal responses were identified as blue-yellow, red-green, and black-white. Various forms of the oppo- nents theories had less trouble explaining black-white vision and several 124 Neural Aspects of Vision /7 : 2 forms of color blindness than did the tricolor theories. Most of the opponents theories attempted to assign retinal distinctions to three different photosensitive pigments or did not specify in any detail how the retina actually produced these responses. The theory discussed in the next section presents a model which includes both a tricolor mechan- ism in the rods and cones and also an antagonist mechanism, which it assigns to the neurons of the retina. As in all antagonist theories, it assumes that the brain carries out or duplicates the antagonistic action when it receives different impulses from the two eyes or contradictory signals from one eye. 2. Cellular Mechanisms The tricolor and antagonist theories were originally based almost exclusively on psychophysical evidence. There is considerable other information available in terms of which any theory of vision must ultimately stand or fall. The evidence from histology, electrophysi- ology, biochemistry, and communication must all be included before a theory of vision can be considered complete. The scheme described in the following pages was developed by Talbot in an attempt to syn- thesize these diverse lines of evidence into a model which would be con- venient both to use and to form a basis for designing additional ex- periments. It is used in this text as a convenient scheme in terms of which many different types of phenomena may be described. Talbot started with the idea that any proposed scheme of color vision must contain at least three different color receptors, although only two types, the rods and the cones, are known. Talbot assumed that the receptors included two types of cones indicated by 8 and i in Figure 2, as well as rods indicated by p. These are connected to cell bodies labeled a for rods and b for the cones. (The letters on these and the other cell bodies discussed are those assigned by Polyak in his book, The Retina.) The three types of receptors, 8, t, and p, are assumed to have different absorption spectra. The receptor p is postulated to contain the pigment rhodopsin (visual purple) whose spectral absorption peak is in the blue- green at 497 nux; this type of receptor is used for blue vision in this theory. The cone i is assumed to have iodopsin whose spectrum has an absorption peak near the green at 562 m/x. (Actually, Talbot desires i to represent red, so he has had to add a contribution from p and 8 labeled dz in the figure.) The third receptor 8 is a green-absorbing cone of exact nature unspecified. Talbot suggests this might be a modified form of rhodopsin, "daylight rhodopsin." The necessity of this 8 cone for which there is 7 : 2/ Neural Aspects of Vision 125 neither histological nor biochemical evidence is the greatest weakness of this model. Nonetheless, a minimum of three photosensitive pig- ments is needed for any type of theory of color vision. Axons from the cell bodies a and b synapse with processes from neuron cell bodies in the next layer of the retina. The latter neurons are called bipolar cells. Several different types can be distinguished called d, e, f, h, i, k, and /. The d cells are large ; they are connected to several rods -c Daylight Cones 6 lodopsin Cones 2 Rods and Cones 3 Membrane A Cell Bodies 5 Synapses 6 Bipolar Cells 7 Synapses 8 Ganglion Cells Photopic White Centers G,R Centers ^B,Y Centers Scotopic White Centers 9 Optic !> Nerve Fibers Figure 2. Simplified form of Talbot's scheme for assigning function to the known histological elements of the retina. Letters refer to known cell types. Numbers on right refer to retinal layers described in Chapter 2. Arrows with numbers show locations of deficiencies hypothesized to explain four types of color blindness. After S. A. Talbot, "Retinal Color Mechanism," J. Optical Soc. Am. 41 : 936 (1951). and at least one cone. The e and /cells are smaller, each connected to several cones. The h cells are midget bipolars which synapse with only one neuron on the side toward the brain. The i cells are called centrifugal amacrine bipolars for they synapse only with the ganglion cells 126 Neural Aspects of Vision \1 : 2 of the eighth retinal layer. The k and / types are lateral amacrine cells synapsing with the other bipolars of the same layer. The cell bodies of the innermost layer of neurons in the retina are called ganglion cells. Three identified types are used in Talbot's model. The largest are the m cells which synapse with fibers from d, e, and f bipolars. The middle-sized p cells also synapse, albeit in a different fashion, with fibers from d, e, and/. Finally, the smallest cell bodies, labeled s, synapse only with one h bipolar. Any attempt to assign a function to each of these elements is guess- work. In this proposed model, it is assumed that the neurons have a natural firing period even when they are not stimulated by the rods and cones. The cell bodies of the latter also produce the spike action- potentials even when the rods and cones are not exposed to light. As discussed in Chapters 4 and 5, a network of neurons, such as exist in the retina, can add, subtract, multiply, and divide in a fashion somewhat similar to an electronic digital computer. The action potentials which go to the brain may be a complex function of the incident light. Talbot states that since the h-s pathway is the only one which does not become more diffuse as it proceeds toward the central nervous system, it can carry the detail necessary for acuity perception. There- fore, he assigns it the role of black and white vision under photopic conditions. Because the d-m pathway represents the largest, easiest to excite cells, and because it is connected to the rods p, it must carry the scotopic white information. To produce antagonistic effects, the responses of the three receptors could be combined at successive neurons as illustrated in Figure 2. The responses of p and 8 are added at d to give a blue response B. The spikes of i (as reproduced by f) and of d are added at p to give a red response. Because the B and G fibers synapse very close to the side of the m and p cells respectively, their spikes are assumed to be inhibitory, that is, they slow down the natural firing rate. Yellow, made up from G and R, would then accelerate m, whereas R would accelerate p. Thus, Talbot has an antagonist theory whereby white and black are antago- nistic at the ganglion cell s, blue and yellow at the ganglion cell m, and green and red at the ganglion cell p. In order to decrease a firing rate, m and p must have a normal firing rate regulated by feedback loops set up through the k and / bipolars. Similarly, in order to suppress the effects of glare and scattering within the eye and to decrease firing during prolonged stimulation, fibers such as those of the i type cell must be present. Neural sharpening can also be produced by i, k, and / cells. Anatomically, Talbot's model is quite successful in assigning a role to almost all of the histologically distinct neuron types in the retina. 7:2/ Neural Aspects of Vision 127 He does not assign a role to the n, o, and r ganglion cells of Polyak and has to assume two types of cones, although there is no direct evidence for the latter. The model is successful in using three basic photosensi- tive pigments which are acted on in a positive manner as demanded by the tricolor stimulus theories of Young and Helmholtz. It also has all the advantages of the opponents theories in having B-Y, R-G, W-S antagonists in the response of the retinal nerves. One must assume, as do other opponents theories, similar antagonistic actions in the central nervous system in analyzing conflicting information. In addition to the histological and psychophysical evidence strongly supporting this model, several other types of detailed subjective informa- tion can be correlated using the theory of color vision outlined above, In particular, the evidence for the role of the rods in blue color vision, experiments with test patches of color on light-adapted eyes, kinetic experiments, and abnormal vision will be discussed. The role of the rods in scotopic vision is agreed upon quite generally. The absorption curve of the pigment rhodopsin in the rods is similar to the scotopic luminosity curve, and many indirect lines of evidence support the role of the rods in scotopic vision. The connection between the rods and blue vision is supported by subjective observation. For example, green and blue appear brighter peripherally where there are more rods, whereas yellow and red are brighter at the fovea. Similar support comes from studies of the narrow range of intensities between the scotopic threshold and the threshold at which color is identified. Sub- jects usually experience a sensation of gray in this achromatic range. The size of achromatic range is greater for red than for blue. Because the rods alone are stimulated in the achromatic range, this suggests that the rods p are intimately connected with blue vision. Other types of data concerning the thresholds for color vision come from studies using light-adapted eyes and narrow test patches illumin- ating 1° or 2° of the visual field. Many variations have been tried using eyes adapted to various colored lights and using the same or other colored lights as test patches. Other experiments have presented test patches in different parts of the visual field. All of the experiments indicate at least six characteristic absorption curves. Attempts to assign these curves to different receptors implies six pigments. No evidence from either histology or biochemistry can be interpreted to make six pigments a reasonable number. By contrast, the scheme diagrammed in Figure 2 is in accord with at least six spectra if the experiments are really fatiguing the neural elements as well as the receptors. If one admits different fatigue curves for cell types p, 8, t, d, e, f, h, m, and p, one can predict that there may be a very large number of absorption curves for light-adapted eyes under varying conditions. 128 Neural Aspects of Vision \1 : 2 Similar experiments, using much smaller test fields, show that in the photopic eye the central 20' of the fovea lacks blue, and the central 15' lacks both blue and yellow. This is to be expected from the model under discussion for the fovea contains no rods. In the absence of rods, there would also be no d or m type cells. At 570 m^u, a wavelength in the yellow, the central 15' of the fovea give a gray sensation. This supports the antagonistic roles of green and red used in the model at the p type cells. (Note that yellow would normally be sensed by the m type cells, supposedly missing from the fovea.) Time" measurements have fascinated many biophysicists. In the eye, one can measure kinetic curves of recovery rate to bright illuminations of various durations. At least four different time constants can be found by these experiments. For short flashes of 0.02-0.10 sec, there is a very rapid recovery. For longer exposures, there is an after image for 0.5 to 5 sec, a recovery of the cone threshold from 20 to 200 sec, and a recovery of the rod threshold (dark adaptation) between 4 and 40 minutes. Talbot's model with three receptors, k, /, and i cells, all contributing to the time constants, predicts the existence of several kinetic curves, more so than the above experiments reveal. Additional kinetic constants can be found from stimulating the eye by means other than light. A wide variety of stimuli, such as magnetic fields of 60 cps, electrical stimuli, and excess pressure, all produce visual sensations. In the dark-adapted eye, the sensation is reported to be blue, corresponding to the fact that the large fibers of the d-m system are easiest to stimulate. In a series of experiments, eyes were light- adapted and then the electrical threshold stimulus needed to elicit a light sensation was determined. Under these conditions, a series of kinetic recovery curves is obtained which are more rapid than the times for recovery of rod and cone vision. Hence, the neurons themselves must be stimulated. A final conclusion from these experiments is that fatiguing or blocking does occur at the neural level within the retina, so that the 1° and 2° test patch experiments are not exclusively measure- ments of dye spectra. Concerning abnormal vision, Figure 2 has arrows or numbers marked for the structures suggested missing in (1) protanopia (the i cones), (2) deuteranopia (the p cell fiber to the optic nerve), (3) tritanopia (the rods), and (4) tetartanopia (the yellow connections from e and /to d). The detailed account will not be reviewed here. Suffice it to point out that, with a complex system of this nature, plus duplicate mechanisms within the central nervous system, there is almost no end of types of color blindness possible. The theory of vision outlined in Figure 2 can account for any known or conceivable type of color blindness. In the present section, the results of subjective experiments on color 7:3/ Neural Aspects of Vision 129 discrimination have been developed around a single cellular model based on histological findings and the actions of neurons. This model has helped to organize and combine the experimental data obtained from a variety of approaches using many techniques. It is useful in that it orders past knowledge about the visual mechanisms in a form that is easy to remember; it will be used in succeeding sections to describe evidence from electrical measurements of spike potentials, as well as to interpret neural sharpening and analyses. 3. Direct Neural Measurements Measurements of neural spike potentials were made by Hartline and his co-workers who recorded impulses from the optic nerves of limulus and vertebrate eyes. The eye of the king crab, limulus, is particularly simple because it consists of many individual rodlike receptors called ommatidia. Each of these receptors is connected to an individual nerve fiber. When the nerve is dissected until just one fiber remains intact, a slow natural Dark On Off Time Light Figure 3. Diagrammatic representation of response of a single limulus ommatidium. The vertical lines represent spike potentials. Solid horizontal line represents light on. Note dark rate, on-burst, steady rate in light, off-burst, and return to dark rate. After H. K. Hartline, H. G. Wagner, and F. Ratliff, "Inhibition in the Eye of Limulus,'" J. Gen. Physiol. 39: 651 (1956); H. K. Hartline and F. Ratliff, "Inhibitory Inter- action of Receptor Units in the Eye of Limulus,'''' J. Gen. Physiol. 40:357 (1957). firing rate is observed in the dark. This is illustrated in Figure 3. If a threshold stimulus is applied to this single ommatidium, an extra spike is observed. If light stimuli considerably above threshold are used, the response is somewhat more complicated as is also shown in Figure 3. Initially, there is a very rapid (transient) burst of spikes as the light is turned on. This is followed by a slower steady-state "firing" rate far faster than the dark rate. The steady-state rate is a function of the intensity of the light stimulus. When the stimulus is removed (that is, the light is turned off), there is another transient burst of spikes, followed by a gradual return to the dark rate. There is no reason to doubt that 130 Neural Aspects of Vision \1 : 3 individual retinal rods and cones of vertebrates would follow this same pattern. Another type of experiment carried out by Hartline and his co-workers involved the vertebrate eye. These experiments were more difficult to perform and also much more difficult to interpret in a quantitative fashion. Nonetheless, the results molded the thinking of everyone who has worked in the field of vision since then. In these experiments, the vertebrate eye was removed with the optic nerve intact. The nerve was dissected until just one fiber remained. Through many experi- ments, a variety of types of fibers were found. All showed a spontan- eous, rhythmic background firing. Some increased this rate on stimu- lation; more of them were almost completely "silent" during intense stimulation showing a strong "on" and a strong "off" burst of spike potentials. In other words, these experiments produced just the results expected from the model in Figure 2. (Or maybe one should reverse this, since the experiments came first.) Another method of obtaining electrophysiological data is to remove the cornea, lens, and vitreous humor of an intact eye. Electrodes are passed over the surface of the retina until the response is that of a single nerve fiber. Granit, in Sweden, has used this method in detail. In snakes, rats, frogs, and guinea pigs, he found that most fibers gave the normal photopic threshold curve. He calls these dominators. Other fibers giving different, characteristic spectra Granit calls modulators. In most animals, Granit found three, sometimes four modulators, whose spectra differed from the photopic threshold curve. Granit's data show very clearly the need for an inhibition mechanism during continuous illumination. The animal data are hard to interpret in terms of human vision owing to controversies over whether the animals really see colors as separate sensations. Moreover, Granit's criterion for observing antagonistic effects was very weak. These experiments with exposed retinas do provide evidence for a mechanism such as that provided by the i cells in Talbot's model. In summary, then, the direct neural measurements indicate that vertebrate nerve fibers of the optic nerve show more response when a light intensity changes than during continuous illumination; in many cases, the rate of spike formation is depressed or abolished during strong illumination. This is in direct contrast to the response of individual re- ceptors whose rate is apparently increased on direct stimulation. Complex neural interaction (that is, computation) is an important part of retinal function. In this respect, the retina acts like a part of the brain. The retina is a subdivision of the brain in terms of its embryological formation. It further resembles the brain in giving rise to electrical potentials, which are similar in some ways to the electroencephalographic potentials. 7 : 4/ Neural Aspects of Vision 131 4. Neural Sharpening and Analyses Inhibition in the retina can be demonstrated in other ways. One of the more striking is the process called neural sharpening. Similar effects in hearing were discussed in the last chapter. Sharpening within the retina was demonstrated directly in the experiments of Hartline and co-workers with limulus eyes. The nerve fibers from the ommatidia go through a complex plexus, not clearly understood anatomically, in which the various fibers apparently synapse with one another. If two receptors are stimulated instead of one, as described in Section 3, their Inhibition Steady Inhibited Partially Dark On Rate by B Relieved I I I IIHI 11 1 Fiber Light Inhibited by Dark On Inhibited by A A + C Light Dark On B Fiber C Fiber Time Light Figure 4. Diagrammatic representation of three ommatidia. A and C are so far separated that there is no mutual interaction. However, both A and C interact with B. After H. K. Hart- line, H. G. Wagner, and F. RatlifT, " Inhibition in the Eye of Limulm" J. Gen. Physiol. 39: 651 (1956) ; H. K. Hartline and F. RatlifT, "Inhibitory Interaction of Receptor Units in the Eye of Limulus" J. Gen. Physiol. 40: 357 (1957). responses can be shown to be interrelated. These relationships exist at the ommatidia themselves but are abolished if the nerve fibers are dis- sected free (that is, removed from the plexus) from the ommatidia to the points of observation (and cut thereafter) . Thus, the interrelationships depend on the neural plexus. As a result, the stimulation of one ommatidium raises the threshold and decreases the steady-state firing rate of the second ommatidium used. These effects are reciprocal and are important only for very close neighbors. The response of an individual receptor, then, depends on the state of stimulation of its neighbors (or more correctly, on the firing rate of its neighbors). For example, one may choose three receptors, A, B, and C, such that A and B inhibit each other and B and C inhibit each other but A and C are too far apart to have an appreciable mutual effect. The results of this experiment are illustrated in Figure 4. If one 132 Neural Aspects of Vision \1 : 4 stimulates A and observes a firing rate, it can be reduced by simul- taneously stimulating B. If now C is also stimulated, the firing rate of B will be reduced, thereby permitting the rate of A to rise toward its original value. Thus, the response of any receptor, although affected directly only by its neighbors, depends in a complicated manner on the responses of all the other receptors. Similar mutual inhibitions have been observed in vertebrate eyes between the receptors exciting one ganglion cell. It is tempting to hypothesize that in the limulus these mutual interactions are the result of direct interfiber synapses, but in the human retina they are mediated by h and k type cells. This mutual inhibition of neighboring receptors serves to increase acuity by decreasing the effects of glare and of scatter- ing within the eye. It also makes the threshold much higher near a bright object. Thus, gradations at the edge of a bright light appear much sharper to the eye than to a series of independent photocells. Sharpening effects of this type are well known in psychophysical studies. They support the idea that neighboring receptors do inhibit each other. Psychophysical evidence, however, cannot clarify whether these effects in human vision occur at the receptors themselves or at the first set of neurons with which the rod and cone fibers synapse. It is even possible that a major portion of the sharpening in human vision occurs within the central nervous system. A different type of neural analysis has been demonstrated by Land and his associates. They found that, although the description given previously in this chapter for color discrimination was valid for large patches of color or for one or two colors in the visual field, it was very misleading for color vision as it normally occurs. To show this, they used two photographic slides, one exposed in the short wavelength region of visible light and the other in the long wavelength region. When these were used simultaneously but illuminated with two different broad bands of light, the natural color sensations were reproduced. Similar experiments with narrow bands of light (that is, monochromatic lights) produced about two-thirds of the possible colors. The effective colors depended only on the per cent of the maximum (or average) of each light transmitted and not on their absolute intensities. It further depended on a random (or gaussian) distribution of small patches of colors such as occur in the normal visual field. These results can be brought into accord with the model in Figure 2 by very slightly modifying the assumptions made. One notes in that model that although three receptors are excited, essentially two ratios are used for color vision under photoptic conditions. These are the ratios of the responses of the m and p type cells to that of the s type cells. It is clear that only the two ratios can be important and not the absolute 7:5/ Neural Aspects of Vision 133 rates of firing of m and p, or else color sensation would (on this model) vary rapidly with light intensity. For specific color sensations, these ratios must be compared with standards. For large patches of light of the same color, these standards must exist within the nervous system. To reconcile the model with Land's experiments, it is necessary to assume that with small randomly distributed patches of colors, the nervous system computes an average value for each ratio and then compares the ratios to this average rather than to absolute standards. Teleologically, this would be desirable because it permits one to dis- tinguish colors independently of the exact spectrum of the lighting used — clouds in the sky, and so on. The model of Figure 2, with this added assumption, predicts correctly that two broad bands of light, illuminating two slides, should be able to produce all possible color sensations. Two narrower bands cannot excite as many different values for the ratios of the responses of the m and p cells to the response of the s cells, and hence cannot simulate all colors. This interpretation emphasizes that the model of Figure 2 uses three types of receptors and is thereby a tricolor model. However, the data from these three are analyzed as one absolute value, used for acuity and brightness sensations, and as two ratios used for color sensations. One might well ask if the added assumption is valid. Although more experi- ments are necessary to answer this question, it may be noted that at any rate the assumption of average standards instead of absolute ones is, a priori, no more unreasonable than the possibility of neural sharpening. (As recently as 1950 the latter was considered unlikely.) Another question one might raise is whether the nervous system uses the same standards for the mjs and p/s ratios throughout the visual field. Land's experiments show that people identify colors correctly with three different pairs of broad bands of light in three different parts of the visual field. Teleologically, this also is desirable because it allows one to recognize colors as the same, some of which are in direct sunlight and others in shade. Whether the model of Figure 2 continues to prove useful, or needs to be drastically revised, the experiments described in this section indicate that the nervous system carries out many complex, computer-like actions. As with most actions of this nature, the exact neural mechanisms are not well understood even though the evidence for their occurrence is very strong. 5. Cortical Representation The complex series of synapses of the visual pathway through the 134 Neural Aspects of Vision \1 : 5 central nervous system is shown in Figure 5. It should be noted that responses from either eye for a given area in the visual field eventually Central Circle Represents Macular Zone Widest Spacings Represent Monocular Fields Each Quadrant a Different Slant of Line Projection on Right Retina A. Amacrine Cells B. Bipolar Cells C Cones G. Gang/ion Cells H. Horizontal Cells P. Pigment Cells R. Rods Projection on Right Lateral Geniculate Body Lateral Geniculate Body 'Hah:'::- ■.•: , ':'&!&Zi Projection on ^~***iz iv*j.i:^ Left Occipital Lobe Projection on Right Occipital Lobe Figure 5. Neural pathways of vision in the central nervous system. Copyright The CIBA Collection of Medical Illustrations, by Frank H. Netter, M.D., Vol. 1, "The Nervous System," 1953. 7:6/ Neural Aspects of Vision 1 35 appear (or are "projected onto") the occipital lobe of the cerebral cortex opposite to the half of the visual field containing the object. Further, the area of maximum acuity around the fovea occupies a major portion of the surface of the cortex. The stimuli are not simply transmitted through the synapses. At various points in the midbrain, auxiliary fibers lead off to autonomic systems, such as the feedback loops controlling the iris, and to tear, blinking, and sudden withdrawal centers. Moreover, a great deal of data processing may occur at these synapses. For example, potentials at the retina follow a light blinking 1 ,000 times per second, those in the midbrain barely follow 100 times per second, whereas the cortical potentials can at most follow 10 per second. The potentials on the surface of the occipital lobe occur first locally and then spread over the entire cortex. Under the action of anesthesia, the local potentials do not spread as far. No one yet knows the exact role of these potentials or their relation- ship to conscious sensations. The complexity of the synapses and responses of the visual pathway cannot but fill us with awe and wonder. Unraveling the clues to the role of the various parts is a challenging problem. 6. Summary of Vision Vision can be studied from many different points of view. In Chapter 2, the physical properties of light waves and optical systems necessary for vision were discussed. Likewise, the gross anatomy and histology of the vertebrate eye were described. These topics all are within the realm of definitive, quantitative knowledge unlikely to change in the near future. In Chapter 3, novel uses of vision in homing and navigation of birds and bees were discussed. These uses depend critically on the actions of the central nervous system. In this chapter, the neural aspects of vision were organized around a model, illustrated by Figure 2. Many phenomena of vision can be described in terms of this model, such as color vision, photopic and scotopic vision, all experiments supporting a tricolor theory, all experi- ments supporting an antagonist theory, kinetic data, coding in the optic nerve and retinal potentials. The model uses most of the known histological structures (as well as one unknown one, the "daylight rod" 8) . The model can be modified to bring it into accord with the experi- ments by Land and his associates. This model also can explain all varieties of visual defects. Nonetheless, one must expect that as more data are gathered and new types of experiments are designed, the model must eventually yield to a more sophisticated one. 136 Neural Aspects of Vision REFERENCES 1. Judd, D. B., "Basic Correlates of the Visual Stimulus," Handbook of Experi- mental Psychology, S. S. Stevens, ed. (New York: John Wiley & Sons, Inc., 1951), pp. 811-867. 2. Polyak, Stephen, Retina : The Anatomy and the Histology of the Retina in Man, Ape, and Monkey, Including the Consideration of Visual Function, the History of Physiological Optics, and the Histological Laboratory Technique (Chicago, Illinois: University of Chicago Press, 1941). 3. Talbot, S. A., "Recent Concepts of Retinal Color Mechanisms," J. Opt. Soc.Am.il: 895-941 (1951). 4. Hartline, H. K., and F. Ratliff, "Inhibitory Interaction of Receptor Units in the Eye of Limulus," J. Gen. Physiol. 40: 357-376 (1957). 5. Land, E. H., "Experiments in Color Vision," Scientific Am. 200: 84-99 (May 1959). 8 Muscles I. introduction A very general property of all living matter is the ability it has to alter its size or shape by contracting or expanding a given region of its body. In most of the higher animals, certain cells or groups of cells are special- ized to contract or relax, thereby changing the position and shape of the animal. Other similar groups of cells contract and relax to pump fluids (blood) through the animal, force food through the digestive tract, and so forth. Aggregates of these specialized contractile cells are called muscle tissues, or simply muscles. All other forms of protoplasm exhibit a contractility similar to that of muscles, but the latter are specialized to emphasize this property of contractility. Thus, contractility is trivially obvious in human muscles but can also be demonstrated in all living cells. Muscles have been of interest to biophysicists for many years; their study will probably remain one of the fields of biophysical research for years to come. Most of the earlier studies on muscles were part of a larger field called biomechanics. This field was explored primarily by workers who, because of their backgrounds and training, labeled themselves physiol- ogists and anatomists. Today, biomechanics per se has passed out of 137 138 Muscles /8 :2 the fields of active research except for experiments on specialized topics such as body resonances and tissue elasticity. These topics are part of biophysics (although they are not described in this text) . Starting some time in the 1920's, muscles were studied as biochemical complexes. At the same time, biophysicists related the heat changes which occurred in muscles to a mixture of chemical and mechanical effects. These studies markedly influenced the direction of biochemical research as a whole and still form part of the basis for current models of oxidative mechanisms in protoplasm. A slight refinement in the above-mentioned biochemical and thermal studies involves the use of extraction techniques. The muscles are ground up; certain compounds, for example, myosin, are extracted and purified; and then their properties are studied. It is believed that the nature of the contractile process should be related to the properties of the chemical constituents of muscles. Recent advances in research on the contractile process in muscles have come about through the use of highly specialized physical instrumenta- tion and by the introduction of the ideas and concepts of molecular structure and form. Thus, muscle studies are increasingly falling within the scope of biophysics and biophysical chemistry. For example, the enzyme reactions and the optical density changes in living muscle have been followed by using specially constructed spectrophotometers. Like- wise, microelectrode techniques have made it possible to observe the magnitude and form of the electrical surface potentials, as well as the action potential spikes which precede contraction. Perhaps most important of all, a special physical tool, the electron microscope, has been used to extend the range of observation to smaller size pieces of muscle than can be seen with the light microscope. The interpretation of electron micrographs of muscles has dramatically altered the accept- able models of muscular contraction, at the same time emphasizing the need for further studies of protein structure before muscular contraction can be understood on a molecular level. 2. Anatomy Muscles are found in all of the more advanced animals, both invertebrate and vertebrate. All are transducers converting chemical energy into electrical energy, heat energy, and useful mechanical energy. Muscles appear in a variety of sizes and shapes ; they differ in the forces they can exert and in their speed of action. In this chapter, only vertebrate muscles will be discussed. Anatomically, muscles can be classified in many ways, in terms of 8 : 2/ Muscles 139 function, of innervation, of body location, of embryological develop- ment, and of histology. The histologic classification is the most widely used and probably the least ambiguous. Histologically, one can dis- tinguish, in the vertebrates, two types of muscles : striated and smooth. Striated muscle, when viewed under the microscope, appears to have alternate dark and light bands distributed in a regular pattern across long fibers. Smooth muscle consists of shorter fibers with no striations. Striated muscles form a large portion of our meat diet. If one examines a piece of steak, one notes there are large bundles or sub- divisions of the muscle. The entire muscle is surrounded by a sheath of connective tissue. Between the large bundles comprising the muscle run connective tissues, blood vessels, and nerves. Each large bundle is then divided into smaller bundles, and each of these is finally subdivided H I Mitochondrion I * m ■ I I VY Sarco/emma m I0|JL. Nucleus Figure I. Diagram of striated muscle fiber. Each fiber con- tains many nuclei and mitochondria. In general, the fiber is not as straight as shown in the diagram. The different bands are characterized as follows. The A Band stains dark and is anisotropic (birefringent) ; it is also called the Q disc. The / Band stains less and is isotropic; it is also called the J disc. The Z disc, in middle of/ band, stains darkly. The H zone is the less stained region in middle of A band. into "muscle fibers." The major portion of the striated muscle is made up of these fibers, 10-100 /x in diameter, and of lengths that reach 100 cm or more in the larger vertebrates. A piece of the fiber under high magnification would look something like Figure 1. Each fiber is crossed by a number of bands, each with its own name. The ends of the fibers of many striated muscles are attached to tendons. Throughout the length of the muscle fiber run still smaller fibers called myofibrils. These possess the same characteristic striations of the original muscle fibers. For reasons not at all understood, the corresponding bands of adjacent myofibrils are lined up with one another, thereby causing the striation of the entire muscle fiber. Besides the fibrils, a striated muscle fiber contains several other organelles and 140 Muscles /8 : 2 is surrounded by a special membrane called the sarcolemma. (The prefixes myo- and sarco- both are used widely to identify muscle and muscle-like structures.) The organelles include small bodies associated with oxidative mechanisms known as mitochondria, as well as many nuclei. Thus, one may regard the striated muscle fiber as a single, polynuclear cell, but the entire concept of cell becomes rather meaning- less in this connection. Three types of striated muscles are known : ( 1 ) the skeletal muscles which form long, unbranched fibers with the nuclei distributed just inside the outer edge of the fiber, (2) special muscles of the face and head region, which are made up of branched fibers with cell nuclei located just inside the outer edge of the fiber, and (3) cardiac muscle in which the nuclei are at the center of the fiber cross section and in which all of the fibers branch to such an extent that very few ends can be found. In addition, cardiac muscle has intercalated discs which occur between the cell nuclei and divide the fibers into units resembling cells. This chapter emphasizes vertebrate skeletal muscles. Chapter 9 describes various aspects of the action of cardiac muscle. As can be seen in Figure 1 , there are a number of bands present along the striated muscle fiber. They are common to all striated muscles. The bands which stain dark are also birefringent ; that is, they split unpolarized light into two beams. Any such substance also transmits light at a velocity which depends on the angle between the plane of polarization and the fiber axis. This birefringence is believed to be due to the lining up of large protein macromolecules, but the exact molecular basis is not well understood in the muscle striations. The birefringent bands are labeled A, for anisotropic, that is, index of refraction depends on direction of the incident light. By contrast, the less heavily stained bands have no polarizing pro- perties. They are labeled /, for isotropic. In many ways, the / bands are harder to understand than the A bands, for it is believed that the protein molecules are oriented in both. In the center of the / band is a darker staining disc called the Z disc. In the center of the A band is a lighter staining region called the H zone. Because the cell concept is not too helpful in discussing muscle fibers, the repeating unit is called a sarcomere. It is chosen to run from one Z disc to the next. A sarcomere may include no nuclei, or one, or even more than one ; it is in no sense of the word a cell. Vertebrate muscles which are not striated are called smooth because they are not made up of bundles of small groups of fibers. Smooth muscles, by contrast to striated ones, consist of short spindle-shaped cells of isotropic material. The cells usually are 15-20 /z long, though some reach a length of 500 \i. A diagram of a typical smooth muscle 8 : 3/ Muscles 141 cell is shown in Figure 2. The maximum cell thickness at the center of the spindle is usually about 6 fx. Intact striated muscles rarely contract more than a small fraction of their original length. Smooth muscles, in contrast, change their length manyfold. This large change is believed to be due to a slipping of one smooth muscle cell over another. In all cases of muscular contraction, little if any change of volume occurs. Muscles are sometimes classified by criteria other than histological ones. In terms of function and innervation, muscles are separated into voluntary and involuntary. For an objective definition, those muscles under direct control of the frontal gyrus of the cerebral hemisphere i 1 might be called voluntary. By and large, ^ striated muscles are voluntary and smooth Figure 2. A smooth muscle cell, muscles are involuntary, but this is not a hard and fa'st rule. Certain smooth muscles are under conscious voluntary control in some individuals and not in others. Likewise, very few individuals can voluntarily control all of their striated muscles. Muscles may be classified by their kinetic properties. In terms of speed of response, smooth muscles such as bladder and uterine muscles often take several seconds to contract. Striated muscle, in contrast, usually contracts rapidly, often reaching its maximum response in a few milliseconds. Within the same animal, faster muscles are usually paler and slower ones are usually darker. (The chicken is a particularly good example of this. The wing muscles work rapidly and are pale, whereas the slower leg muscles are dark.) This color is more closely associated with an oxygen-storing protein called myoglobin than it is with the histological structure. In the next section, the kinetics of the contraction of striated skeletal muscles are described. 3. Physical Changes during Muscular Contraction A. Changes of Tension and Length When a muscle is stimulated it twitches. If the muscle is held at con- stant length, it develops a force, whereas if it is weighted down it contracts and does work. The two simplest situations to study are constant length (isometric) and constant force (isotonic). To eliminate the nervous control, it is possible to remove the muscle from the animal body or to cut the nerve fibers. 142 Muscles /8 : 3 If one stimulates an excised muscle by means of an electrical shock (or a mechanical impulse, or heat, cold, and so on), a twitch occurs. If the stimuli are spaced a long time apart, the muscle relaxes to its original € r " J/ -A Is, § 5 5% Length of Twitch Varies with Particular Muscle, Temperature, and pti I _L_L_LJ_i_+ 1 25 |xsec f/\ r\ /v^ ! Time (a) Time (b) AL/L Tetany Fatigue sec ' * ■ Time (c) Figure 3. Curves of contraction, (a) Occasional stimulation shows twitches. Arrows indicate stimuli, (b) Frequent stimulation leads to summation, (c) Prolonged tetany leads to fatigue. Note the difference in the time scale as compared to (a) and (b). After S. Cooper and J. C. Eccles, J. Physiol. 69:377 (1930). length between twitches, and a contraction curve is obtained of the shape shown in Figure 3a, for isotonic contractions. If the stimulus is repeated before relaxation occurs, summation is observed as shown in Figure 3b. With still more rapidly repeated stimulation, a smooth contraction curve results such as shown in Figure 3c. The steady con- traction is called tetany. All muscles will eventually fatigue and fail to contract, even though stimulated. This type of fatigue probably never occurs in the healthy intact animal, as the nervous system undergoes fatigue before the muscles do. Curves illustrating the strength of isometric and isotonic contractions are shown in Figures 4a and 4b, in terms of effect of length on tension developed in isometric contraction and of load on shortening produced during isotonic contraction. Only in isotonic contraction is work done. It is easy to show that the maximum work is done at half the maximum load for muscles for which the straight line relationship of Figure 4a is valid. The straight line can be described by 8 : 3/ Muscles 143 AL = AL max (1 - - ) -*max where AL is the contraction and F is the load. The work W done on the load is W = FAZ max (1 - £ ) "max This work W is a maximum when dW dF that is, when F = IF, 2 *■ max Striated muscles, in general, can develop large forces against a given load but even in tetany can contract only a small amount. In the Figure 4. (a) Isotonic contraction. Change in length is plotted as a function of load for a muscle supporting a fixed load (isotonic). The straight line is an approximation only. (b) Isometric tension. Maximum tension developed is plotted as a function of length for a muscle held at various fixed lengths (isometric). vertebrate body, the skeletal muscles all develop far larger forces than the loads they move. However, the load moves more than the muscle contracts. This is accomplished by the lever action of the muscles and bones with the joints serving as pivots. As shown in Figure 5, the mechanical advantage is considerably less than one, that is, force of the muscle is much greater than load, and the muscle motion is much less than load motion. To study muscular contraction, it would appear desirable to work with single muscle fibers. However, these are difficult to obtain and few people have succeeded in preparing them. Most experiments have been done on whole muscle. 144 Muscles /8 : 3 B. Interaction with the Nervous System In the intact animal, the muscle contracts following stimulation by the nervous system. The incoming impulses in the nerve fibers are called electrical spike potentials; similar spike potentials travel along the Humerus Triceps Group Figure 5. The muscles and the bones of the arm. The lower arm acts as a lever pivoted at the elbow. The biceps, which applies force to the lever, is attached to the radius near the elbow. The load is applied to this lever at the wrist. There- fore, the theoretical mechanical advantage (TMA) is about 0.1. Muscles moving most limbs have TMA's of 0.05 to 0.4. Adapted from THE WORLD BOOK ENCYCLOPEDIA with permission © 1961 by Field Enterprises Educational Corporation. All rights reserved. muscle fibers. The interactions of the nerve and muscle fibers and the magnitude and form of the electrical potentials across the sarcolemma are important physical characteristics of muscle. Each muscle fiber is separately innervated. Each has at its end a special structure called the muscle end plate, near which one or more nerve fibers also end. The nerve and muscle endings, together with the space between them, is called the myoneural junction. When a spike potential reaches the nerve endings, the latter secrete a special chemical substance, 8 : 3/ Muscles 145 probably acetylcholine, which is probably also important in the trans- mission of impulses across synapses between nerves. (Acetylcholine and its action are described more completely in Chapter 4.) The released acetyl- choline diffuses across the myoneural junction (which is of the order of a few tenths of a micron) and stimulates the formation of a spike potential in the muscle fiber. The acetylcholine is rapidly destroyed by a protein catalyst, cholinesterase, present in the muscle end plate. Under certain conditions, the myoneural junction acts as a "computer," putting out a number of muscle spike potentials different from the number of incoming nerve spike potentials. The muscle fiber membrane is polarized, just as is the axon membrane discussed in Chapter 4. An action spike potential, similar to that in -90mv Figure 6. Spike potential of striated muscle. V is the poten- tial difference inside minus that outside the sarcolemma. The arrow indicates application of stimulus. In cardiac muscle, the peak of the crest of the action potential lasts much longer. nerves, is the first result of stimulation of a muscle fiber, whether the stimulus be the physiological one from the nervous system or an arti- ficial one, that is, electrical, mechanical, or heat. A typical muscle spike potential is shown in Figure 6. The action potential differs from that in nerves only in the duration of the peak, which lasts much longer in muscle than in nerve. Originally, the muscle potentials were recorded by means of so-called "bipolar" or "differentiating" electrodes which measured the potential difference between two neighboring spots on the muscle. These gave no possibility of measuring a resting or d-c potential, nor any certainty of the size of the cellular potentials. These electrodes have been replaced by microelectrodes made by drawing out a capillary glass tube to a diameter of less than 1 /x. The tiny capillaries may be inserted through the wall of a single muscle fiber without damaging the fiber. With such probes, it is possible to measure both the resting potential and the action 146 Muscles /8 : 3 potential of skeletal muscle fibers. An additional difficulty is that the muscle fiber moves during contraction. Provision must be made to permit the microelectrode to move with the fiber. When this is done, consistent records can be obtained of the potentials across the sarco- lemma of single muscle fibers. The spike potential always precedes contraction. After the crest of the spike has passed, the membrane potential starts to return to normal. At this time, the rate . of heat production increases. A fraction of a millisecond later, there is a slight relaxation, and then the mechanical contraction of the twitch starts. How the spike potential "signals" the muscle fiber to begin the chemical changes necessary for a twitch is completely unknown. Nonetheless, the spike always precedes a twitch and somehow all the myofibrils do contract simultaneously. Within all skeletal muscles are sensing organs known as proprioceptors or pacinian corpuscles. These continuously send back "reports" to the central nervous system on the state of contraction of the muscle. Thus, in any muscular motion, a complex process occurs involving multiloop feedback systems. The nervous system signals the muscle to contract. As it does so, the muscle sends many reports indicating its contraction to the central nervous system. These and similar proprioceptor reports from other muscles reach the central nervous system where they are all "analyzed." As a result of this analysis, the original muscle is "in- structed" or controlled to contract faster or slower so as to achieve the desired location. This process has appealed to servomechanism experts who have carried out quite detailed analyses of muscular contraction. Although such analyses can never supply new facts, they have made it possible to understand qualitatively the organizing principles of the muscle-nervous system relationship. The problem of muscular fatigue also appears to involve the nervous system. A denervated muscle can be held in tetany by repeated stimulation until it tires. However, if the motor nerve causing a muscle to contract is stimulated, it can be shown that the myoneural junction fatigues before the muscle does. Similarly, if the entire normal animal is stimulated (for example, by poking it with a hot soldering iron), it can be shown that fatigue sets in at the synapses in the central nervous system before the myoneural junction has fatigued. C. Heat Production Besides studying forces, work, and electrical changes, several bio- physicists have followed a quite different approach, namely the measure- ment of the heat produced by resting and contracting muscles. Muscles produce extra heat when they are working; the extra heat accompanies 8 : 4/ Muscles 147 the conversion of chemical energy to mechanical work. These heat measurements are based essentially on temperature measurements. They are difficult because the maximum temperature rise associated with a muscle twitch is only 0.003 °C, and the heat is developed very rapidly. A. V. Hill refined his techniques to the point that he could resolve a few million ths of a degree change in a few milliseconds. Hill's experiments showed there were three different types of heat production occurring during muscular contraction. The first, called resting heat, is associated with metabolism in the resting muscle. The second type of heat production, initial heat, accompanies actual con- traction and relaxation. The third general type is called recovery heat; it is liberated for 20-30 min following activity. The resting heat is an indication of continuous metabolism in the muscle. It can be altered by stretching the muscle as well as by changes in ionic strength in the surrounding fluids. It is not a constant or simple quantity. When a muscle contracts and then relaxes, the second type of heat pro- duction overrides the resting heat production. This initial heat con- sists of several components. While the muscle contracts, it develops a "maintenance heat" which starts just after the spike potential passes and continues until relaxation. Some of this maintenance heat is actually produced before contraction occurs. There is, in addition, a "heat of shortening." Under isotonic conditions when the muscle lengthens, a heat of relaxation is measured equal to the work done by the load. These heat changes attracted the interest of many investigators. However, they are difficult to interpret. There is no simple relationship between the work done and the extra heat produced. The reasons for the rise in heat production before contraction and the dependence of resting heat on muscle length are still not understood. This basic lack of understanding emphasizes the incompleteness of current molecular models of muscular activity. 4. Muscle Chemistry In the previous section, the various physical changes accompanying muscular contraction were presented. These all involve molecular changes and the conversion of chemical free energy to other forms of energy. Accordingly, it is appropriate to examine the chemical con- stituents of muscle. These include the types of molecules active during contraction and relaxation. The chemical transformations necessary for energy production are also indicated. There are more water molecules within the muscle, and indeed within 148 Muscles /8 : 4 the myofibril, than any other type of molecule. Present theories do not assign any specific role to these water molecules, aside from forming a medium through which the contractile molecules act and also through which the energy-carrying molecules diffuse. The various organelles within the muscle, for example, nuclei and mitochondria, have the same composition as those of other cells. The ionic concentration within the muscle fibers is similar to that within nerve fibers described in Chapter 4. The one unique component, outside of the myofibrils, is the protein myoglobin. This is a red pigment similar to the hemoglobin of red blood cells except that myoglobin has about one-fourth the mole- cular weight and only one iron atom per molecule (hemoglobin has four iron atoms per molecule). Myoglobin is generally believed to act as a storage for oxygen within the muscle fiber. The myofibrils contain unique molecules not found in other tissues. Three proteins, myosin, actin, and tropomyosin, are all found in high concentrations. All three are members of a general class of proteins called globulins, when classified in terms of their solubilities. (Proteins are condensation polymers formed from small monomers known as amino acids. The structure of proteins, including those in muscle, is discussed more fully in Chapter 15.) The actin is similar to many other globulins in that it can exist in either a globular (sphere-like) form or a fibrillar form. Small changes in the ionic strength, pH, or temperature can convert some globulins reversibly from the fibrillar to the globular form. (In the fibrillar form, they are believed to be arranged in a helical structure described in Chapter 15.) The striking physical changes which take place as myosin and actin shift from one form to the other suggest that they might be the molecules actually responsible for contraction. Present evidence, discussed more fully in Section 6, supports the conclusion that these three proteins form the contractile elements. However, the premise that they change from globular to fibrillar form appears to be completely fallacious. Rather, it appears that myosin, actin, and tropomyosin are always in the fibrillar form in intact muscles. They are formed into thin filaments, visible only with the electron microscope. These filaments are believed to develop the actual contractile forces. The proteins, myosin, actin, and tropomyosin are large molecules organized into filaments that are long on an atomic scale. When the myofibril contracts and relaxes, it uses chemical energy which is derived from a much smaller molecule called adenosine triphosphate, or A TP. This small molecule is the source of immediately available chemical energy for chemical syntheses, for muscular contraction, and for the active transport of ions and metabolites across cell membranes. A wide variety of systems within all vertebrate cells can use ATP as a source of 8 : 4/ Muscles 149 energy. When this happens, the molecule ATP is split into adenosine diphosphate, ADP, and inorganic phosphate (£). Symbolically, one may write this as ATP - ADP + ® + energy (Readers without previous knowledge of biochemistry should not allow them- selves to be dismayed by this jargon of letters like ATP and ADP. Many people who use them don't know the structural formula represented by these symbols; all one needs to know is the stoichiometric formula written above. The physical forms of ATP and ADP must be very important for their actions, but no one yet has succeeded in relating these concepts. The molecule ATP is made up of one molecule of the purine, adenine; one molecule of the pentose sugar, ribose; and three phosphate groups joined by pyrophosphate bonds. Its structural formula is shown below, but the reader unfamiliar with biochemistry is advised to stick to the symbol ATP rather than trying to remember the structure. H— N— H H /^ O t -o — P — o H Adenine plus ribose forms the molecule adenosine. Adenosine plus one phosphate condenses to adenylic acid or adenosine monophosphate, AMP. The latter plus another phosphate condenses to ADP. Energy is released when ATP is split to ADP and when ADP is split to AMP and (?). ) There seems to be no doubt, from a large variety of experiments, that ATP is the source of energy used in muscular contraction. Just how this occurs is not clear. For instance, ATP might be split before the muscle contracts or just as it contracts. An alternative possibility is that the muscle proteins store energy which is used during the twitch and then is slowly built up again from ATP during recovery. ATP might form a complex with the muscle proteins. Recent experiments indicate that several intermediates must exist between ATP and the contractile proteins. Some of the evidence for the direct interaction of ATP comes from experiments with purified myosin and with actin and myosin. If solutions of these proteins in the globular form are mixed with ATP, they form fibers. In the fibrillar form, ATP causes actin-myosin fibers to contract. Moreover, ATP is split in this process because the protein myosin acts as an enzyme catalyzing the splitting of ATP into ADP plus 150 Muscles /8 : 4 phosphate. Furthermore, if frogs' muscles are soaked in 50 per cent glycerol for months to remove the smaller molecules and then ATP is added, the muscles contract. These brief summaries of many detailed experiments can be interpreted to indicate the role of ATP in muscular contraction, or they may all be artifacts or physiologically unimportant DPNH to Cytochrome System 6H 2 H to DPN in Cytochrome System About 34ATP I2H 2 Figure 7. Major steps in the oxidation of glucose. The input consists of glucose and oxygen. Water and GO a are formed and energy is stored as ATP, the form used in muscular con- traction. Krebs cycle and cytochrome system enzymes are in the mitochondria; glycolytic enzymes are not in the mito- chondria. facts. Direct, spectrophotometric measurements support the latter view, that ATP does not react with the contractile elements. All that is certain is that protein changes occur when the muscle contracts and that ATP is used up to supply the energy for this process. The steps in the synthesis of ATP from ADP and (P) at the expense of 8 : 5/ Muscles 151 other forms of chemical energy are more clearly understood. This process is a result of the oxidation of many substrates, most of the free energy liberated being used to form ATP. Figure 7 shows several of the major groups of steps in the use of glucose to form ATP. In the absence of oxygen, or in the presence of limited amounts of oxygen, the process stops at lactic acid, as is the case in an active muscle. After activity, the muscle slowly oxidizes the lactic acid the rest of the way to C0 2 and water. These processes are not unique to muscle but occur in all vertebrate cells. Another important compound in muscles is creatine. Just as ADP can be phosphorylated to store energy, creatine can be made to store energy in the form of a phosphate compound, creatine phosphate. In the muscle, there is a dynamic balance between the creatine-creatine phosphate system and the ATP-ADP system. Thus, creatine-phosphate acts as a storage depot whose energy can be utilized about as readily as that of ATP. Chemical studies have revealed many of the basic energy trans- formations that accompany the changes from relaxed-muscle + glucose + oxygen to contracted-muscle + C0 2 + water. Inherently, how- ever, these methods cannot describe the molecular details of the actual mechanical changes which occur in the active muscle. 5. Electron-Microscope Studies of Muscles In Section 2, the structure of striated muscles was discussed. In the present section, this discussion will be further amplified to include observations made by electron microscopy and by X-ray diffraction. As was noted earlier, each striated muscle can be broken down into large bundles of small groups of single muscle fibers. Each muscle fiber is some 10-100 /x in diameter and is very long, perhaps as long as the entire muscle. The muscle fiber contains nuclei, mitochondria, and other formed elements as well as myofibrils. The myofibrils are about 1 /x in diameter and may have lengths comparable to that of the entire muscle fiber. Each myofibril is striated with the same bands as the entire muscle fiber. The myofibrils consist of units similar to that shown in Figure 8 which start with the Z disc or membrane and contain one-half of an / band, an A band with a H zone in the middle, one-half of the next / band, and then another Z disc. Electron-microscope techniques have shown that the myofibrils, in turn, are made up of smaller filaments of two types, thick and thin. The thick ones are about 100 A (that is, 0.01 fx) in diameter and about 2 ft 152 Muscles /8 :5 (that is, 20,000 A) long, whereas the thin ones are about 50 A in diameter and 1.5 /x long. These filaments also possess a periodicity or striation, but it is only about 400 A long, a distance that is short compared to the striations on the myofibril. (Indeed, the entire filament is com- parable in length to one "unit" along the myofibril.) The dimensions and periodicities of the filaments have been measured independently by X-ray diffraction and by electron-microscope techniques. The two types of data agree well when changes due to dehydration (necessary for electron microscopy but not X-ray diffraction) are included in the calculated results. At one time, X-ray studies of the form of the filaments were inter- preted to show that the general arrangement of amino acids within the proteins changed from a so-called "a form" to a "jS form" during contraction (see Chapter 15). Subsequent studies have shown that this Figure 8. Sliding model of myofibrillar structure. The dis- tance from one Z disc (or membrane) to the next is one myo- fibrillar unit. During contraction the thick and thin filaments keep the same length but intermesh more completely. The thick filaments are myosin. The thin one contains actin and presumably also tropomyosin. After H. E. Huxley and J. Hanson, "Structure of cross-striated myofibrils," Biochim. Biophys. Acta 23: 229 (1957). interpretation was wrong ; the form of the filaments remains unchanged during contraction. The filaments are made up of helical protein chains but with a nonintegral number of amino acid residues per turn. The entire structure repeats about every 400 A. Theories which assign muscular shortening to a change in the length or form of the protein molecules all have difficulties explaining these data from electron microscopy and X-ray diffraction, which show that the protein mole- cules do not change in shape or form during contraction. Modern electron-microscope techniques permit the determination of still more details of the structure of the myofibrils. It is possible to make electron micrographs of the "ultra structure" of the muscle without dispersing or homogenizing it in any way. For these studies, the muscle is first fixed to harden the protein elements. Then it is "stained" with a heavy metal to increase contrast in the electron microscope. Next, it is filled with, and imbedded in, a plastic such as butyl methacrylate. 8 : 5/ Muscles 153 Finally, it is cut into sections a few hundred angstroms thick. When these sections are examined in the electron microscope, most are cut at such angles to the myofibrils that they are useless for analysis, but a few will be either at right angles to the myofibrils or along the myofibril. (A great deal of judgment is necessary to discard most of the sections as useless.) These studies have been interpreted to show that the / bands consist of thin filaments joined by a membrane at their centers (the Z disc). The H zone consists only of thick fibers and the A band is a region of overlap between the thick and thin filaments. These are arranged in a regular array with a definite number of thin filaments surrounding a thick one, varying from two in the flight muscles of insects to six in some vertebrate muscles. Between the thick and thin filaments, there appears to be a series of bridges spaced about 50 or 60 A apart. The length of the A band, with the H zone in its center, is then the length of the thick filament as shown in Figure 8. When a muscle (or a myofibril) contracts, the length of the A band remains constant. This implies that the thick filaments do not change in length. Extraction studies have shown that the thick filaments consist entirely of myosin and that they probably contain all the myosin. Chemical studies com- bined with electron microscopy have shown that the thin filaments contain actin and another protein, presumably tropomyosin. When the muscle fiber contracts, both the / band and the H zone are shortened. The decrease in length of both these regions is comparable. Therefore, as is shown in Figure 8, the length of the thin filaments also must remain unchanged on contraction. The interpretation of the electron micrographs, then, is that the thin filaments somehow slide in between the thick ones as the muscle contracts. Just how the thick filaments slide along the thin filaments is a matter of speculation. One might imagine that it takes an ATP molecule to open each bridge between thick and thin filaments and that these then moved in some sort of ratchet fashion in finite steps. The rate of splitting of ATP by myosin and the number of ATP molecules used per twitch both make this finite jump-type motion possible. Again, one might suppose that small kinks appear along the thin filaments and that these move along one bridge at a time. No doubt the reader can construct a few other speculative models himself. Even if one accepts completely the interpretation of the electron micrographs presented above, there still remain several questions at the molecular level, concerning the mechanism of muscular contraction. It is not known how the muscle action potential triggers the contraction process, although it is known that the action potential always precedes contraction. It is not clear how the numerous filaments all move in a 154 Muscles /8 : 6 coordinated manner. The details of the coupling, from the free energy released by splitting ATP to the mechanical energy expended by the muscle, are all unknown. 6. Summary Muscles are the contractile elements of animals. They act as trans- ducers converting chemical energy into mechanical energy. Muscles in vertebrates can be classified according to function and to morphology. Of the various types, the striated muscles, usually associated with voluntary motion, have been studied in greatest detail. Their efficiency, the tensions developed at constant length, and the shortening produced with various loads have all been measured and are well known for many different muscles. Each striated muscle consists of bundles of small groups of individual muscle fibers. These fibers make up the muscle. The single, striated muscle fiber, about 10 /x, in diameter, is surrounded by a single mem- brane electrically polarized in a fashion similar to that of a nerve fiber. The initial step in the contraction process is an action or spike potential, very similar to that of nerve fibers. This spike potential is normally initiated at the muscle end plate but can also be produced by the same types of stimuli which affect nerve fibers. Within the striated muscle fiber are many nuclei, mitochondria, microsomes, and so forth, as well as long myofibrils having the same striations as the muscle fiber. The myofibrils contain two types of filaments which in turn are composed of helical fibers of the proteins myosin, actin, and tropomyosin. The two types of filaments appear to overlap in electron micrographs of extended muscles; they intermesh more completely in similar electron micrographs of contracted muscles. The changes during contraction are brought about at the expense of chemical energy stored as ATP. The energy of ATP is released when the latter is split into its com- ponents, ADP and phosphate. This splitting is catalyzed by enzymes called ATP-ases. The protein, myosin, is an ATP-ase, but it may not be active in this fashion in intact myofibrils. The molecular details of how the energy is transferred from ATP to mechanical contractions are not known. The details are not clear on the behavior of the protein filaments within the myofibril as contraction is occurring. The con- centration of ATP is "buffered" by the creatine-creatine phosphate system. The net loss of organic phosphate (that is, ATP and creatine phosphate) is restored by the oxidation of glucose. Oxidations in muscles follow the same pathways as in other tissues. 8 :'6/ Muscles 155 Thus, the basic physical parameters of the gross phenomena associated with muscular contraction are well known, and many of the chemical mechanisms are similar to those in other tissues. In contrast, the molecular description of muscular contraction is an active research area. The ideas involved demand a knowledge of active transport (see Chapter 19) to understand the membrane action, enzyme kinetics (see Chapters 17 and 18) to describe the synthesis and use of ATP, and protein structure (see Chapter 15) to describe the filaments and their behavior during contraction. REFERENCES There are many books which deal only with the contraction of striated muscles. Most physiology, biochemistry, and anatomy texts have at least a chapter on this subject. The following list is neither complete nor exhaustive but contains a limited number of references which the author feels to be especially useful to readers wishing to pursue this subject more thoroughly. 1. Best, C. H., and N. B. Taylor, The Physiological Basis of Medical Practice 7th ed. (Baltimore, Maryland: The Williams & Wilkins Company, 1961). 2. Heilbrunn, L. V., An Outline of General Physiology (Philadelphia: W. B. Saunders Company, 1952). 3. Szent-Gyorgi, Albert, Chemistry of Muscular Contraction 2nd ed. (New York: Academic Press, Inc., 1951). 4. Butler, J. A. V,, and J. T. Randall, eds., Progress in Biophysics and Biophysical Chemistry (London, England: Pergamon Press, Ltd., 1954) Vol. 4. a. Wilkie, D. R., "Facts and Theories About Muscle," pp. 288-324. b. Weber, H. H., and Hildegard Portzehl, "The Transference of the Muscle Energy in the Contraction Cycle," pp. 60-111. 5. Ramsey, R. W., "Muscle: Physics," Medical Physics, Otto Glasser, ed. (Chicago, Illinois: Year Book Publishers, Inc., 1944) Vol. 1, pp. 784-798. 6. Morales, M. F., Jean Botts, J. J. Blum, and T. L. Hill, "Elementary Processes in Muscle Action: An Examination of Current Concepts," Physiol. Rev. 35: 475-505 (July 1955). 7. Gaebler, O. H., ed., Enzymes: Units of Biological Structure and Function (New York: Academic Press, 1956). a. Mommaerts, W. F. H. M., "The Actomyosin System and Its Participation in Organized Enzyme Reactions," pp. 317-324. b. Morales, M. F., "Is Energy Transferred From ATP to Myosin at the Moment That ATP Is Split?" pp. 325-336. 8. Huxley, H. E., "The Contraction of Muscle," Scientific Am. 199: 66-82 (Nov. 1958). 9. Huxley, A. F., "Muscle Structure and Theories of Contraction," Progress in Biophysics and Biophysical Chemistry, J. A. V. Butler and B. Katz, eds. (New York: Pergamon Press, 1957) Vol. 7, pp. 255-318. 156 Muscles 10. Whitelock, O. v. S., ed., "Second Conference on Physicochemical Mechanism of Nerve Activity and Second Conference on Muscular Contraction," (Monograph) Ann. New York Acad. Sc. 81: 215-510 (1959). 9 Mechanical and Electrical Character of the Heartbeat I. Role of the Vertebrate Circulatory System All vertebrates possess a closed circulatory system. The blood which circulates through this system is a suspension of various types of single cells in a viscous solution of proteins and inorganic salts. The blood is pumped; that is, it is forced to flow through the closed circulatory system. The organ which does the pumping is called the heart. The circulatory system in vertebrates carries oxygen from special exchange organs (lungs or gills) to the other tissues. It also transports carbon dioxide from the tissues back to the lungs or gills. In some amphibia, the skin also serves as an auxiliary gas exchanger. In any case, the blood flows through a special exchange organ in which very thin, moist walls separate the blood from the external environment. Besides dissolved gases, foods and metabolic waste products are also carried by the blood. The endocrine secretions likewise are trans- ported from gland to target organ by the blood stream. Finally, the 157 158 Mechanical and Electrical Character of the Heartbeat /9 : 2 blood contains antitoxins and phagocytic cells which help protect the organism from external invaders. The vertebrate circulatory system, then, is a major internal trans- portation line for chemical substances. The vessels into which the heart pumps blood are named arteries. These branch into smaller and smaller arteries; the smallest are called arterioles. The arterioles empty into the capillaries. Here, most of the exchanges occur between the blood and the surrounding tissues. The capillaries join to form venules, which in turn join to form larger and larger veins leading back to the heart. The circulatory system is not completely closed, however. Some fluid leaves the capillaries, passing into the tissue spaces; it is then called lymph. The lymph filters back slowly through several nodes, finally entering the venous portion of the circulatory system. 2. Blood Pressures and Velocities Before the action of the heart is examined, the flow of the blood through the arteries and veins will be discussed briefly. The flow of the blood can be described in terms of its linear velocity v and its pressure p. The velocity v is, in general, a function both of time and of the point in space at which it is measured. The pressure p is the force per unit area of the fluid. It is a scalar quantity; that is, p is independent of the orientation of the areas used to define it. The zero point for pressure is somewhat arbitrary. So-called "gauge pressure" is the difference between the absolute pressure and the atmospheric pressure. Absolute pressure is measured relative to a zero of no net external forces on the system. Pressure is a stress and has the dimensions of force per unit area. In the mks system it is measured in newtons/m 2 . Instead of absolute units, pressure is often measured in terms of the height of a column of liquid which it will support. Thus, it may be measured in terms of meters of mercury or meters of water. Some convenient reference numbers to remember are: 1 atmosphere = 1.0 x 10 5 newtons/m 2 1 meter of H 2 = 9.8 x 10 3 newtons/m 2 1 meter of Hg = 1.33 x 10 5 newtons/m 2 Any convenient height units may be used. The most frequent ones in describing the circulatory system are mm of Hg. Besides pressure and velocity, another fundamental property of a fluid is its density p. For all purposes in this chapter, the blood may be considered as incompressible. Its density is approximately that of water. 9 : 2/ Mechanical and Electrical Character of the Heartbeat 159 A fluid like the blood may possess both kinetic and potential energy. The kinetic energy per unit volume T is T = l P v* The potential energy per unit volume V results from both the pressure on the fluid, 1 and its height h above the earth. In physics texts, it is shown that, for an incompressible fluid V= pgh+p The total energy per unit volume H then is H = p + P gh+ \ P v* (1) Bernoulli's equation states that H is a constant. It is true only for nonviscous liquids. In general, the variation of H gives the change in energy per unit volume. The blood loses energy for each cycle in the capillaries. The heart, in pumping, increases the energy per unit volume of blood as the latter passes through the heart. Thus, the heart might be called a chemicomechanical transducer. When an incompressible fluid flows through a closed system, either the volume flow rate Q (volume per unit time) must be constant at all points or the volume of the system must change. To a first approxima- tion, the average volume of the circulatory system remains constant. Accordingly, the average volume flow rate will usually be the same at all points in the circulatory system. (There are a number of conditions under which more, or fewer, blood vessels are open. For instance, during activity, the blood flow to the muscles increases as more capillaries are open. Similarly, the swelling of erectile tissue is due to expansion of blood sinuses resulting from decreased arteriolar resistance.) The variation of blood velocity » in a mammal is diagrammed in Figure 1. Although the arteries and veins are much larger than the capillaries, there are so many capillaries that the total cross-sectional area of the tubes open to the blood is much greater than in the larger vessels. Accordingly, the linear velocity of the blood in the capillaries is smaller than in the arteries and veins. The pulsations in the arteries are possible because the walls are elastic and stretch from the force of each heartbeat. In a similar manner, one may diagrammatically represent the pressure variations. These are shown in Figure 2. The maximum arterial pressure is called the systolic pressure, and the minimum arterial pressure is called the diastolic pressure. The pressure falls by the time the blood 1 Purists will no doubt object to calling p a form of potential energy per unit volume, but this is satisfactory for discussions of the circulatory system. 160 Mechanical and Electrical Character of the Heartbeat /9 : 2 reaches the capillaries, and the pressure fluctuations are smoothed out. As the blood enters the venous system, the pressure is still lower. Just before the blood enters the heart, the gauge pressure is negative; because -S? o to .82 -rS Arteries 1 Veins .8 fl A !\ l\ ft n n £ VvWWta 1/l/i tt> .C ^1 \i\i\j\i\i\i\i\j\j \ Q = AV A = na a = cross section of vessel A = total cross section v = linear velocity Q — volume flow rate Figure I . Linear velocity of the blood. Since the volume flow rate, Q, remains approximately constant throughout the cir- culatory system, a low linear velocity, v, means a large cross section A. In the capillaries, the vessel cross sections, a, are small, but the number in parallel, n, is so large that A is greater in the capillaries than in the arterioles or veins. After G. H. Best and N. B. Taylor, The Physiological Basis of Medical Practice, 7th ed. (Baltimore, Md. : Williams and Wilkins Com- pany, 1961). -7^ 120 ft I A n « X I mMiw. e UUUfi. - 90 0) c 3 8 60 c_ n. §> 30 o CD 00 -S? Arteries .O •2? c I Veins Figure 2. Variation of blood pressure at fixed time, shown are gauge pressure in a normal, adult human. Values 9 : 3/ Mechanical and Electrical Character of the Heartbeat 161 this pressure is very small, it is conveniently measured in mm of water. In a normal adult human, the venous gauge pressure at the heart is about —40 mm of H 2 0. The arteries and veins have similar flow rates but verv different pressures. Accordingly, both have about the same diameter (0.5-12.5 mm i.d.), but the arterial walls are thick and elastic, whereas the venous walls are very thin. The larger pressures in the arteries make reverse flow unlikely; valves limit reverse flow in the veins. The capillaries are the location of most exchanges of gases, meta- bolites, and metabolic products. They are thin walled and small in diameter. A red blood cell, 8 /* in diameter, distorts the shape of the capillary as it passes through. At the capillary walls, the excess gauge pressure, osmotic forces, and active transport all combine to promote exchanges between the blood stream and the surrounding tissues. 3. The Vertebrate Heart In warm-blooded vertebrates, the heart keeps pumping for the entire life of the organism. If the heart stops even for a short time, the animal dies. This continuous activity is regulated by both the nervous and the endocrine systems. However, even without these regulatory influences, the heart maintains its rhythmic beat. In cold-blooded animals, the temperature also influences the heart rate. At close to freezing tempera- tures, their heart rate slows almost to zero. The heart of the cold-blooded vertebrates is simpler than the mam- malian heart. Most fishes and amphibians have a heart made up of a series of chambers as shown in Figure 3. The first, which receives the blood from the veins, is called the sinus venosus. It is the pacemaker and originates the heartbeat. The reptilian heart, also shown in Figure 3, is more specialized. Instead of one auricle, there are two. One receives blood from the lungs only and the other from the remainder of the body. This system is more efficient in aerating the blood than is that of the amphibians and fishes. The sinus venosus does not exist as a separate chamber, but its homolog persists as a sino-auricular (s-a) node on the wall of the auricle serving the body proper. The mammalian heart is illustrated in diagrammatic form in Figure 4. It consists of four chambers : two auricles and two ventricles. The blood from all the body except the lungs enters the right auricle. It is forced from there into the right ventricle, then into the lungs and back to the left auricle. From there it is forced into the left ventricle and finally through the aorta to all arteries of the body except those going to the 162 Mechanical and Electrical Character of the Heartbeat /9 : 3 Sinus j Venosus f Superior Aorta Vena Cava Pulmonary Artery Right Auricle Inferior Vena Cava Pulmonary Vein Left Auricle Incomplete Septum (a) (b) Figure 3. Diagrams offish and reptile hearts, (a) Fish heart. The muscular walls develop successively higher pressures in the sinus venosus, auricle, and finally ventricle, (b) Reptile heart. Note the incomplete septum allowing mixing of blood from both auricles within the ventricle. Superior Vena Cava Aorta from Head to Bod y and Neck Pulmonary Artery to Lungs Semilunar Valve S-A Node A- V Node Tricuspid Valve Pulmonary Valve Inferior Vena Cava from Trunk and Limbs Pulmonary Vein from Lungs Mitral Valve A-V Bundle Complete Septum Figure 4. Diagram of the human heart. Arrows show direc- tion of blood flow. 9 : 4/ Mechanical and Electrical Character of the Heartbeat 163 lungs. Thus, the blood in a complete circuit goes through the heart twice, once through the left side and once through the right side. This system is highly efficient in supplying oxygen and removing carbon dioxide, for all the blood passes through the lungs on each trip around the circulatory system. The walls of the heart consist primarily of muscle tissue. As in all other striated muscles, the fiber membranes are normally polarized, the inside being 90 mv negative relative to the outside. Just before con- traction occurs, an action current passes over the membrane, reversing its polarity for a short period of time. The form and nature of these action currents are similar to those of nerve fibers discussed in Chapter 4. The large mass of fibers contracting simultaneously in the heart effect- ively acts as a large number of electric cells, all in parallel, and each with a high internal impedance. Although the net current from each fiber is small, the current from the entire muscle is appreciable, giving rise to measurable potential changes on the body surface. 4. The Heart Sequence A. Over-all Sequence The mammalian heart pumps blood with uniform sequence which repeats each beat. First the auricles contract, forcing blood through the auriculoventricular (a-v) valves into the ventricles. Then the ventricles contract. This shuts the a-v valves and opens the semilunar and pul- monary valves. As the ventricles continue to contract, blood is forced into the aorta and pulmonary arteries. Finally, as the ventricles relax, the semilunar and pulmonary valves close. The entire sequence is presented in more detail in Figure 5, which shows, with a common time base, the auricular pressure, the ventricular pressure, the aortic pressure, and the ventricular volume for a human heart. Also, on the same base are shown the electrocardiograph (ekg) record and the sonograph record of a microphone placed against the chest. Heart pressures have been measured directly in both man and animals. The ventricular volumes have been found by X-ray techniques. From the diagram, it is clear that the blood flows from the ventricle into the aorta only during a small part of the cycle. While this is happening, the ventricular volume falls to a minimum value, but the pressure remains close to its maximum. Likewise, an examination of the figure shows that the valves open and shut as the direction of the pressure difference across them changes. The sonograph obtained by putting a broad-band microphone on the chest is strikingly different from what a 164 Mechanical and Electrical Character of the Heartbeat /9 : 4 person hears through a stethoscope. The two can be made quite similar by differentiating the sonograph output twice. Aortic Pressure Ventricular Pressure ^i- Auricular Pressure Ventricular Volume Electro- cardiogram Heart Sounds Systole Diastole Figure 5. Pressure sequences in the left side of the heart. The significance of the vertical lines is as follows : 1 . the mitral valve closes; 2. the semilunar valve opens; 3. the systolic pressure reaches a maximum; 4. the semilunar valve closes; 5. the mitral valve opens; 6. end of heart sound; and 7. the auricle starts to contract. After C. H. Best and N. B. Taylor, The Physiological Basis of Medical Practice, 7th ed. (Baltimore, Md. : Williams and Wilkins Company, 1961). B. Electrical Events The heart pulses rhythmically and with a definite sequence. The beat is initiated at the sino-auricular (s-a) node, shown in Figure 4. The node acts in a fashion similar to a relaxation oscillator putting out an electrical pulse (about every -^ of a minute in man). This pulse spreads 9 : 4/ Mechanical and Electrical Character of the Heartbeat 165 in all directions as an electrochemical impulse over the surface of the auricle, causing the muscle fibers to contract. When two pulses reach the opposite side of the auricle from two directions, they annihilate each other because the contracted muscle will not conduct another impulse. Besides causing the auricle to contract, the electrochemical pulse, originating at the s-a node, also stimulates the auriculo-ventricular (a-v) node (see Figure 4). This node, after a short time delay of about 0.1 sec or slightly less, puts out a new electrical pulse which is conducted down a special group of fibers called the a-v bundle, diagrammatically illustrated in Figure 4. These fibers terminate in the central muscular wall between the two ventricles. From these terminals, the pulse spreads over the walls of the ventricles causing them to contract. The s-a node resembles a free-running electronic multivibrator con- trolling a second multivibrator, the a-v node, which in turn controls a third multivibrator, the ventricle itself. Many factors suggest this analogy. The fundamental rate of the s-a node can be varied by two different sets of nerves which act to speed or slow the rate of firing of the s-a node. This is analogous to tuning either the resistance or the capacity of a free-running multivibrator. In some cases, the s-a node fails. Then the a-v node takes over control of the heart. The auricular contraction is no longer properly syn- chronized with the ventricular action, but this is by no means fatal. The a-v node behaves as an electrical multivibrator synchronized by pulses from the s-a node. When free-running, it has a slower firing rate (about 50 beats per min in man). If the a-v node also fails, the heart neither stops, nor does the animal die. Rather, the auricular and ventricular walls take over control directly. Their free-running rate is still slower (about 30 beats per min in man) . The ventricles and auricles are then completely independent in their times of contractions. On the average, the auricular beat then interferes with, rather than promotes, circulation. The cardiac muscle fibers, like skeletal-muscle and nerve fibers, have a resting potential around 90 mv, the outside being positive relative to the inside. As in skeletal-muscle and nerve fibers, the action potentials are about 120 mv; that is, the outside is 30 mv negative relative to the inside at the peak of the spike. All three types of fibers are also similar in that the concentration of potassium ions is much higher within the cell than in the surrounding medium, whereas the sodium ion concentrations are just the reverse. The cardiac muscle fibers differ markedly from skeletal muscle and nerve fibers in the kinetics of the recovery to the resting potential. In the largest mammalian nerve axons, this takes a fraction of a millisecond. In smaller nerve axons and skeletal muscle fibers, the recovery period is 166 Mechanical and Electrical Character of the Heartbeat /9 : 4 2-5 msec. By contrast, some cardiac muscle fibers take as long as 200 msec to recover their resting potential. This period of time is com- parable to the period of contraction of the ventricle. A closely related property is the recovery of the normal low net permeability to potassium ions. When the resting potential of a voltage- clamped squid axon is suddently decreased, the net permeability to potassium ions rises rapidly and then falls. The cardiac muscle cells, in contrast, do not recover their original impermeability to potassium until after the membrane potential returns to its original value. Like nerve and skeletal muscle, cardiac muscle exhibits a so-called "positive after potential," during which time the resting potential is greater in magnitude, around 100 mv instead of 90 mv, the outside being positive relative to the inside. The after potential may last close to 500 msec before it is completely abolished. (The U-wave of the electro- cardiogram appears about at the height of the positive after potential. The U-wave is very small; it barely shows on the diagram in Figure 5.) The exact roles played by potassium and sodium ions in the resting and action potentials of cardiac muscle are not known. Nonetheless, all experiments indicate that, except for time constants, and perhaps some absolute values, the electrical behavior of cardiac muscle is very similar to that of squid axons discussed in Chapters 4 and 24. C. Energy Each time the heart beats, it converts chemical energy into hydro- dynamic energy. The rate of work, that is, power, expended by the heart varies with the activity of the organism. At rest, both the heart output per beat and the number of beats per minute are comparatively low. During strenuous exertion, both increase. The work done at each beat is of two types, kinetic and potential (compare Equation 1 , p. 159). Because the aorta is on the same level as the heart, the potential energy is purely hydrostatic. Thus, from Equation 1, the work per milliliter is H = \ P v* + p (2) If q is the volume per stroke, then the work w per stroke is w = qH = ± P qv 2 + pq (3) where the bar indicates average values. Of even greater interest is the power II developed by the heart. To find this, one must replace the stroke volume q by the volume rate of flow Q (also called the heart output). Including the contribution of both halves of the heart leads to the expression n = p R Q + p L Q + Ip%Q + h P 4Q W 9 : 4/ Mechanical and Electrical Character of the Heartbeat 167 The subscripts refer to the right and left halves. Because the system is closed, Q is the same for both. Equation 4 is exact and involves no approximations. It is the hydro- dynamic power delivered by the heart. For humans, one may simplify Equation 4 by several approximations. The velocities in the aorta and pulmonary artery are about the same, whereas the aortic pressure is sixfold greater. Hence, one may write n=$pLQ + p%Q (5) Because blood leaves the ventricles during only a small part of each cycle (see Figure 5), the mean square velocity v 2 will be very different from the square of the average velocity (v) 2 . For humans, it has been found that y2 = 3.5(y) 2 The average volume velocity Q must .be equal to the cross section A of the aorta times the average linear velocity v, that is - Q Substituting these into Equation 5 leads to the following formula for the power developed by the human heart n*t&« + 55f£ (6) It is instructive to substitute a few numbers in this formula. Some typical human values are At rest Active Both p = 100 mm of Hg p = 100 mm of Hg A = 0.81 cm 2 Q = 3.5 1/min Q = 35 1/min /> = 1 gm/ml Converting to mks units and substituting in Equation 6 gives At rest Active p L Q 1.0 w 10 w "hydrostatic" power 1 A 6 3.5pQ 3 0.13 w 130 w — "kinetic" power A 2 n 1.1 w 140 w — total heart power It should be noted that for the human at rest the kinetic energy delivered 168 Mechanical and Electrical Character of the Heartbeat /9 : 5 to the blood is negligible, whereas during vigorous exercise it is the major type of hydrodynamic energy. 5. Electrocardiograph/ Every time the heart beats, electrical potential changes occur within it. These potentials spread to the surface of the body. Electrodes at almost any pair of points on the surface of the body will show potential differ- ences related in time to the heartbeat. A record of these potential differences is called an electrocardiogram; the recording equipment is an electrocardiograph. The recording equipment and the records are often indicated by the abbreviations ekg or ecg. Electrical changes at the surface of the heart were first demonstrated in 1856. Electrocardiography, the science of measuring the associated potentials, did not really develop until physical instrumentation made possible the detection of these small potentials. The first big step was the application of the string galvanometer to electrocardiography in 1903. This was the work of Einthoven, whose ideas dominated the field for many years. Today, all electrocardiographs depend on the action of electronic amplifiers. In this field, as is the case in so many others, the rapid advances have resulted from the widespread application of electronic techniques. The electrocardiogram is used in many clinical diagnoses of heart ailments. It is widely used because of its convenience and also because of the large amount of information which can be obtained without any surgical procedures or any discomfort to the patient. The electrocardiogram is a record of electrical potential differences at the surface of the body. The heart, however, is not the only source of potentials at the body surface ; it is necessary to distinguish between those potentials due to the heart and those originating from other organs. Every muscle within the body undergoes potential changes as its fibers contract. The magnitude of the action potentials for all nerves and all muscle fibers is about 120 mv. The motion of any skeletal muscle can give rise to body-surface potential differences comparable to the ekg potentials. To limit this source of distortion, the ekg is often recorded with the patient lying down. In addition to potentials of muscular origin, there are also d-c body surface potentials. These exist between the two hands, the hands and the feet, and so forth, and may be as large as 0. 1 mv. These potentials can be eliminated by suitable electronic design of the recording appara- tus. (It is interesting to note parenthetically that the origin of these 9: 5/ Mechanical and Electrical Character of the Heartbeat 169 d-c potentials is not well understood. The d-c potential between the two arms of many women shows a sharp maximum on one day during the middle of the menstrual cycle. At one time, it was believed that these were associated with ovulation, but the correlation is very poor.) The ekg potentials can be observed between almost any pair of points on the surface of the human body. If the two points are reasonably separated, the maximum potential difference observed is of the order of 1.0 mv. The ekg has the same period as the heart. Traditionally, three wires were attached to the subject, one to each arm, and the third to the left leg. The ekg was then recorded between the members of each of the three resulting pairs of leads. Whether the electrocardiogram is recorded between two points on the surface of the body or between one point and a neutral electrode, it Figure 6. A typical ekg. P wave precedes auricular contrac- tion and QRS complex is associated with ventricular contrac- tion. Exact height of wave depends on lead used. always has the shape shown in Figure 6. The neutral electrode can be formed by immersing the subject in a tub of water and placing the electrode far from the body. Provided low resistance electrodes are used, the curve will always have the general shape shown. The various bumps on the ekg are called waves. The P-wave occurs just before auricular contraction. The QRS-complex is associated with the start of ventricular contraction, and the T-wave occurs at the end of ventricular contraction. The amplitude of the ekg waves is shown in the table on page 170. In addition, a smaller U-wave follows the T-wave after ventricular relaxation. Most frequently, electrodes are placed on both arms and on the left foot, and quite commonly are also placed on the back and on the chest. The ekg's are usually described in terms of leads, which means the poten- tial difference between two points. This is confusing terminology because two wires, each ordinarily called a lead, are necessary for one ekg lead. 170 Mechanical and Electrical Character of the Heartbeat /9 : 5 TABLE I Normal Human Electrocardiogram Patterns Amplitude Duration EKG in in Relationship to heart cycle interval millivolts seconds (Figure 5) P 0.1 0.008 Precedes auricular contraction about 0.02 sec by P-Q 0.0 0.15-0.20 A-V delay time Q. 0.1 0.04-0.08 R 1.0 0.04-0.08 Precedes ventricular contraction S 0.1 S-T 0.0 0.1 -0.25 Ventricular ejection T 0.1 0.1 Follows ventricular relaxation T-P 0.0 0.3 Diastole In ekg terminology, the potential differences in the three leads are numbered as Lead I : V 1 = V L - V R (7) Lead I : Vj - = v L - V R Lead II : V u - - v F - v R Lead III : v m = = v F - v L where L, R, and F refer to the left arm, right arm, and foot, respectively, and the potentials with the three subscripts refer to the values between these points and a neutral electrode. Elementary algebra reduces these three equations to V n = V m + V 1 (8) that is, if any two of the three "standard" leads are measured the third is thereby determined. This seems trivial, and probably did also to Einthoven, who first pointed it out, but physiologists have dignified Equation 8 by the name "Einthoven's law." In the following sections of this chapter, the heart is approximated by an equivalent dipole. This equivalent dipole is constant for the QRS- complex and is similar for the P- and T-waves. On the cellular level, the heart cannot be regarded as a mere dipole. It was noted in the last section that at the start of every heartbeat, an electrical spike potential originates at the s-a node and spreads out in all directions over the auricle. Thereafter, the a-v node emits a pulse which travels as a spike potential down the Purkinje fibers of the auriculoventricular bundle of His to initiate a contraction of the muscle fibers of the septum between the two ventricles. The spike potential travels down around the septum and then up the outer sides of the ventricles. In every region, the appearance of the spike potential is followed by a contraction. The 9 : 6/ Mechanical and Electrical Character of the Heartbeat 171 spread of the spike potential over the ventricle takes about 60 msec. As it starts down the interventricular septum, the Q-wave appears on the electrocardiogram recorded at the surface of the body. The R-wave coincides roughly with the spike reaching the bottom (apex) of the heart and starting up the outer ventricular walls. The S-wave appears as the spike potential reaches the top of the ventricle. 6. Physics of Dipoles Einthoven stated that if the three lead voltages given in Equation 7 were represented as vectors directed along the sides of an equilateral triangle, all three could be represented as the projections of a single vector on this triangle. As is seen in Figure 7, this follows for any set of voltages. Although this procedure can be carried out for any three points, it has significance only if the resulting vector V indicates or is related to the axis of the heart. The use of an equi- lateral triangle is based on the assumption that the three points chosen are electrically equidistant from the heart. If this is the case, one should find that Figure 7. Einthoven's tri- angle. From the figure it can be shown that V x = V cos0;F„= V cos (60° - d) = ^Vcosd + i\/2Vsin0; V m = F~cos (120° - d) = -£Fcos 6 + JvTFsin 9; .-. V u = V m + V v V c = Wl + V B + V,) = (9) Albeit this is hard to test because "neutral" electrodes are never truly neutral, the pre- ceding condition is approximately satisfied. However, it is far from exact. To obtain three-dimensional information, a fourth electrode is placed on the back or chest. Its voltage, relative to a neutral electrode, is designated by V B . The ekg "lead" voltage V 1V is given by v IV = v B - v c where V c is an approximately neutral lead formed as above. V 1V tends to show up heart abnormalities in front or back of the midline of the heart, whereas the first three ekg leads tend to de-emphasize this type of abnormality. To develop a more precise picture of the basis of the electrocardio- gram, it is helpful to be familiar with electrical theory of a more advanced nature. This theory of current sources in a conducting medium is presented in this section. Those whose mathematical background does 172 Mechanical and Electrical Character of the Heartbeat /9 : 6 not include differential equations are advised to omit the remainder of this section and to accept certain statements in the next section as a matter of faith. The heart behaves as a group of current sources in a finite conducting medium. A current source is an emf whose internal resistance is much Terminal Source R Equivalent to External Load R Equivalent to External Load Source R«r R«r (a) R Equivalent to External Load Source R»r (b) Figure 8. (a) Current source. Two equivalent forms are shown. In either case, if r > R, the current source approxi- mations can be made, namely, I = I = E /r V=RI Thus V and / are determined by I and the load, (b) Voltage source. If r <^ R, the voltage source approximations can be made, namely, I=E /R V=E Thus V and I are determined by E and the load. greater than the external load. Thus, the external current will remain constant no matter how the external load is varied. A current source is illustrated in Figure 8. (A voltage source is one in which the internal resistance is so low that the terminal voltage will remain constant as the external load resistance is varied.) The tissues surrounding the heart are electrically similar and comparatively low in impedance. Because the heart muscle may be regarded as a group of current sources, the 9 : 6/ Mechanical and Electrical Character of the Heartbeat 173 potential between any two external points will be the sum of the poten- tials due to each of the current sources acting independently. (This superposition theorem is not true for voltage sources.) The potential due to a group of current sources in an infinite con- ducting medium can be used to find an approximation to the currents Right Arm t*--~. (a) (b) Figure 9. (a) Vector relationship for finding potential V t due to current source I t at A. (b) Geometrical relationship between heart dipole along 6 = and arms and foot. This diagram is used in deriving the equations on page 175. produced in the body by the heart. For convenience, the two terminals in Figure 8 will be treated as two sources, one positive and the other negative. Let the location of the i th current source be denoted by the vector distance r t from the origin of the coordinate system as shown in Figure 9. Then the current due to this source, considered by itself, will spread throughout the medium giving rise to a potential V t (r) at the point r from the origin. Because there are no net charges in the medium, the potential V t must obey the Laplacian equation V 2 Vi = (This is shown in any electricity and magnetism text.) Because the tissues have a finite conductivity y there will be a current density J i throughout the medium originating from the i th current source 174 Mechanical and Electrical Character of the Heartbeat /9 : 6 This is a special case of Ohm's law. The unique solution choosing V = at infinity is m = I -rS .= i y\r- r t \ This may be expanded in a series in 1/r. Expanding, one obtains V(r) = y r 2h + ±(lti)^+ 2^g2/i[3(vr) a - R 2 ] + ••• Because no net charge enters or leaves the heart, the first sum is zero. The second sum is called the dipole moment, p; that is ?«24 ih A first approximation to the potential due to current sources in an infinite conducting medium is to replace them by an equivalent dipole p. The potential at r (referred to V = at infinity) is V(r)J4 ' yr 3 The preceding expression was obtained for an infinite medium. If one restricts the heart to a sphere of radius R, a somewhat more com- plex expression is necessary. Consider the equivalent dipole p located at the center of a sphere and oriented along the 6 = axis of the sphere. In this case — ^ — * p ■ r = pr cos 6 At small values of r, the potential must approach that of a dipole in an infinite medium, namely T/ p cos 6 yr 2 as r-> whereas at the surface, the radial current must be zero, so that — = at r = R or The unique solution to this approximation is r 2 + R 3J v _p cos 6(1 y which, at the surface of the sphere, reduces to V {R) = W (10) 9 : 7/ Mechanical and Electrical Character of the Heartbeat 175 This is clearly only an approximation but is useful in describing the electrocardiogram. Equation 10 may be applied directly to the standard ekg leads. If the line to the foot makes an angle a with the heart vector, then the right arm is located at 6 = a + 120° and the left at 6 = a — 120° as shown in Figure 9. Therefore, the three voltages, V L , V R , and V F , should be 3P cos(a - 120°) L ~ y R 2 3P cos (a + 120°) R ~ y R 2 3P cos a Vf = ~~w The three lead voltages may be found by the appropriate differences, and the validity of Equations 8 and 9 can be noted. Thus, the Einthoven triangle is as valid as the spherical approximation with a dipole current source. Clearly, the representation as a dipole is misleading and at best an approximation. The standard ekg leads are not necessarily the best ones. Various attempts to improve these are discussed in Section 8. Nonetheless, the four or five leads (including both chest and back) have been used for most clinical and diagnostic purposes. 7. Vector Electrocardiography In attempts to increase the information obtained from the electro- cardiogram, various schemes have been developed. The most success- ful, called vectorcardiography, records the magnitude, location, and spatial orientation of the equivalent heart dipole as a function of time. As has been pointed out, the physical relationship between the equivalent dipole and the cellular events in the heart is not in any way obvious. The abnormalities producing a given change in the heart potentials cannot be logically related to the change in many instances. In spite of the inability to logically interpret the vector electrocardiogram, it can still form a powerful diagnostic tool for clinical work. The equiva- lent dipole is referred to as the heart vector. The rationale behind these systems is presented in this section. Calculations, confirmed by model experiments, show that the use of the four standard ekg leads could give rise to very erroneous interpreta- tions of the location and orientation of the heart vector for hearts as 176 Mechanical and Electrical Character of the Heartbeat /9 : 7 eccentric 2 as those occurring in normal humans. When one adds to this the effects of the nonspherical shape of the human body, it seems very reasonable that the use of the four standard leads loses a great deal of the available information. An integral part of vector electrocardiography is the equivalent dipole or heart vector. The discussion in the last section illustrated that a net dipole is the first approximation to any distribution of current sources whose net sum is zero. There are an infinite number of distributions which have the same vector dipole as a first approximation. It is in no way obvious that the heart should be well represented by the dipole approximation. Two different types of experiments, which have shown that this approximation is almost as good as the experimental data, are discussed in the following paragraphs. Let the heart vector be denoted by p. It is conventional to represent this as a sum of three vectors directed along the cartesian axes. One may write P = Pxi + Pyj + pS where the subscripts refer to the scalar components of/), and i,j, and k are unit vectors directed along the x, y, and z axes. Then at any point on the periphery, the voltage V (relative to ground) may be written as a linear sum of the three components of the heart vector; that is to say V = ap x + pp x + v p 2 In general, the three constants a, jS, rj will depend on the location of the dipole, the location of the observation point, and the shape of the torso. The three quantities a, £, r\ will be constant for the entire QRS-complex if the heart can be represented as a dipole. If V is measured at four points, one may write four equations V l = a lPx + PlPy + r\\Pz V 2 = 0. 2 p x + P 2 py + 7] 2 p 2 V 3 = O-zPx + fizPy + V3pz V± = a 4 /> z + Pip y + r\±p z These may be regarded as four nonhomogeneous, linear equations in the three unknowns p x , p y , and p z . For most sets of the (a, j8, v\)\ and the V's, there are no consistent solutions for p x , p y , and p z . If, however, the heart vector is a good approximation, the fourth equation should be a linear combination of the first three. This, then, is a simple, un- ambiguous test of the dipole approximation. Measurements on humans in which four pairs of wires are used, that is, four independent leads, have shown that the QRS-complex can be 2 Eccentric here means displaced from the vertical and horizontal center of the torso. 9 : 8/ Mechanical and Electrical Character of the Heartbeat 177 fitted very well by an equivalent dipole for a variety of different sets of points. The P- and T-waves of the ekg definitely cannot be described by the same dipole. Moreover, although the error in fitting F 4 with a linear combination of V x , V 2 , and V 3 is small, it is definitely larger than experimental error. Another test of the dipole approximation is that of mirror images. For the central dipole in a sphere, discussed in Section 7, the equator of the sphere is a zero potential line. Any two points equidistant from the equator will have potentials which are equal in magnitude but opposite in sign. They are called mirror points. For the human torso (or indeed even for a cylinder with an eccentric dipole), the zero potential line is not an anatomically or geometrically obvious feature. Nonethe- less, it could be located by finding mirror images if (and only if) the dipole approximation is a good one. Experiments have revealed the existence of a mirror point for the QR§-complex at any arbitrary point on the torso. This also confirms the validity of the dipole approxima- tion. The data are good enough to show the best mirror points are not perfect mirror points. However, the errors are too small to compute a meaningful quadrupole moment. In practice, the heart vector can be found by two different methods. If one wishes to determine the position of the heart vector in an indivi- dual, a lengthy series of determinations of mirror points is sufficient. The other alternative is to use a combination of a series of leads that allows one to compute magnitude and direction of the heart vector without knowing its location. Only the latter seems practical for any clinical purpose. Several persons have set up systems of linear combinations of five to 16 points of contact with the torso. The aim is to arrive at a set of points which is independent of the exact body shape or the location of the heart but which reveals the direction and magnitude of the heart vector. These "orthogonal" systems have been increasingly successful in recent years. The success of an equivalent dipole representation of the QRS- complex seems both fortuitous and unfortunate. It implies that the ekg information obtainable from separate parts of the heart is very slight. The validity of the dipole approximation implies that one can measure an average which reflects solely the properties of the heart, but one cannot distinguish individual regions within the heart. 8. Summary The heart is a large mass of muscle which pumps blood through the 178 Mechanical and Electrical Character of the Heartbeat /9 : 8 vertebrate circulatory- system. Its physical activity- may be described in terms of the velocities and pressures acquired by the blood at various points of the circulatory system and also in terms of the power expended. The heart not only does work but also contains tissues which produce periodic beats in a fashion similar to that of a series of electronic multi- vibrators. The firing rate of the normal control element, the s-a node, can be increased or decreased both by the nervous system and by certain hormones. Like the fibers of all striated muscle, the heart fibers are traversed by a spike potential before contraction. These spike potentials appear as current sources immersed in the surrounding fluid. The resulting body surface potentials are called electrocardiographic potentials. These are of such a form that the heart may be well approximated by a single dipole. Systems to find the orientation and magnitude of best equivalent dipole are called vectorcardiography. Although clinically useful and challenging to the imagination of the physicist, the equivalent heart dipole seems to lack any basic relationship to the heart itself. REFERENCES 1. The following monograph is very complete and well worth reading by any- one wishing to pursue the subject in detail. A large part of the material in this chapter is based on it. Whitelock, O. v. S., ed., "The Electrophysiology of the Heart," Ann. New York Acad. Sc. 65: 653-1145 (Aug. 1957). 2. Best, C. H., and N. B. Taylor, The Physiological Basis of Medical Practice (Baltimore, Maryland: Williams & Wilkins Company), 7th ed., 1961. Read the chapters on the heart and circulatory system. 3. Glasser, Otto, ed., Medical Physics (Chicago, Illinois: Year Book Publishers, Inc., 1950) Vol. 2. a. Hamilton, W. F., "Circulatory System: Arterial Pulse," pp. 186-188. b. King, A. L., "Circulatorv System: Arterial Pulse; Wave Velocity," pp. 188-191. c. Hamilton, W. F., "Circulatory System: Heart Output," pp. 191-194. d. Landowne. M., and L. N. Katz, "Circulatory System: Heart; Work and Failure," pp. 194-206. e. Green, H. D., "Circulatory System: Methods," pp. 208-222. f. Nickerson, J. L., "Circulatory System: Methods; Ballistocardio- graph," pp. 222-225. g. Jochim, K. E. } "Circulatory System: Methods; Electromagnetic Flowmeter," pp. 225-228. h. Green, H. D., "Circulatory System: Physical Principles," pp. 228- 251. Mechanical and Electrical Character of the Heartbeat 179 4. Johnston, F. D., "Electrocardiography," Medical Physics, Otto Glasser, ed. (Chicago, Illinois: Year Book Publishers, Inc., 1944) Vol. 1, pp. 352-361. 5. Schmitt, O. H., and Ernst Simonson, "The Present Status of Vector- cardiography," Arch. Int. Med. 96: 574-590 (Nov. 1955). 130 Discussion Questions — Part B DISCUSSION QUESTIONS— PART B 1. The cell wall of the alga Nitella conducts spike potentials similar to those found in nerve and muscle fibers. Describe the equipment necessary to test the dependence of spike height on K + concentration. What are the results of such experiments? 2. Some of the evidence for the activity of acetylcholine in nerves is based on studies of the electrical eels. Describe the electrical organ of Torpedo, in the terminology of anatomy, histology, electricity, and biochemistry. 3. The terms "spatial summation" and "temporal summation" are used to describe some of the phenomena called "synaptic computation" in Chapter 4. What is the experimental evidence which shows that these occur ? 4. Describe how one can show that at the giant synapse in the crayfish, transsynaptic conduction is a purely electrical phenomena, whereas in the human spinal cord it is mediated by special transmitter substances. 5. The compound GABA, gamma aminobutyric acid, has been found to occur in large amounts in the central nervous system and to inhibit trans- synaptic conduction. What is the evidence for its action? What is the relationship of GABA to the computation-like functions of the nervous system? 6. The feedback loops controlling the iris have been studied anatomically and from the point of view of a servomechanism. Describe both in more detail than given in the text. Most servomechanisms can be stimulated at their characteristic frequency and caused to oscillate. How was it demon- strated that iris control can be caused to oscillate in a similar fashion ? 7. What is an autocorrelator ? What is the relationship between the auto- correlation function and the Fourier transform? Use this to demonstrate why the autocorrelator is useful for electroencephalographic studies. 8. What special precautions must be taken in constructing electroencephalo- graphic amplifiers? Describe a practical electronic circuit for such an amplifier and analyze its action. 9. Various mathematical theories have been proposed to describe the motion of the cochlea. Describe the essential features of the theory developed by Fletcher. Be sure to note all approximations which have been made. 10. What is known about the lateral line organs of fish ? 11. Many moths have only a limited number of nerve fibers associated with their hearing organs. What is the evidence that only these fibers are active? How might one try to reconcile this with the moth's ability to avoid bats? 12. Describe a recent experiment using arm analogs of the cochlea to study hearing. Discussion Questions — Part B 181 13. One method of studying visual systems is to "drive" the eye with a flashing light. Describe the ability to follow as a function of frequency of: the retinal potentials; the potentials in the optic nerve; the nerve potentials in the midbrain; and the cortical potentials. 14. Sketch the anatomical features of the visual system of limulus. Describe in more detail the type of experiment summarized in Figure 4 of Chapter 7. Include descriptions of the light source, light-intensity measurements, preparation of nerve fibers, measuring equipment, and conclusions reached. 15. The electrical potentials of the eyeball are sometimes referred to as electroretinograms. Describe the magnitude of the potentials obtained and their time dependence. Illustrate their use with a detailed description of one experiment depending on electroretinograms. 16. The experiments of Land on color vision in a heterochromatic field are reviewed briefly in Chapter 7. Expand this discussion, emphasizing its significance for theories of color vision. * 17. Ramsey has used single muscle fibers for studies of their mechanical properties. How does he prepare these fibers? Compare his results with those for whole, excised muscles. 18. The various types of heat produced during muscular contraction are described briefly in Chapter 8. Expand on this description; include equip- ment necessary to make the measurements, the type of raw data obtained, and their interpretation. 19. Contrast the resting and action potentials of various forms of skeletal muscle, cardiac muscle, of nerves, and of the alga Nitella. Include magnitude of the potentials, time course of the spike, and dependence on ionic con- centrations. 20. Illustrate the changes in the thick and thin filaments during muscular contraction in terms of the model of A. F. Huxley. Show what type of electron-microscope pictures would be expected for longitudinal sections, for transverse sections at various points along the myofibrillar unit, and for several oblique sections. 21. Ballistocardiography consists of measuring the reaction of the body to the thrust of the heart on the blood. How are ballistocardiographs con- structed? What does a typical record look like? How is it related to the electrocardiogram ? 22. The heart rate is controlled by two sets of nerves. These in turn are activated by centers in the central nervous system in response to impulses from certain pressure-sensitive and 2 /C0 2 -sensitive organs. Fill in the anatomical details to the extent they are known. Represent the over-all system, in block diagram form, as interlocking negative feedback loops. 23. Abnormalities in the electrocardiogram are used to diagnose many 182 Discussion Questions — Part B heart disorders. What are several types of pathological conditions which alter the electrocardiogram ? How is the electrocardiogram changed ? 24. Pressure pulses are transmitted along the arterial walls for each heart- beat. These travel at a much greater rate than the blood. Outline the theory describing this transmission in tubes with viscoelastic walls and filled with an ideal fluid. 25. Newtonian fluids have coefficients of viscosity which are independent of fluid velocity in streamline flow. Describe the experiments which show that blood is non-newtonian. Characterize its viscosity. c Physical Microbiology Introduction to Part C This section of the text deals with the physical properties of cells and groups of cells as revealed by various bio- physical studies. The first chapter of Part C, Chapter 10, describes cellular events produced by ionizing radiations. This topic is continued in Part D, Chapter 16, "Molecular Action of Ionizing Radiations." Some scientists consider the material in these two chapters as synonymous with biophysics, whereas others feel that the effects of ionizing radiations should not even be considered as part of bio- physics. The emphasis, in Chapter 10, has been placed on the use of ionizing radiations to study the fundamental properties of biological systems. Not all radiations are damaging. In Chapter 11, the physical properties of cells and of groups of cells revealed by nondestructive electromagnetic and ultrasonic irradia- tion are discussed. This is followed by two chapters deal- ing with the effects of high intensity ultrasound; the second of these two, Chapter 13, illustrates one of the areas in which advanced mathematical training is helpful. The last chapter of Part C is a description of the physico- chemical properties of virus particles. Such particles lie between biological cells and molecules in their complexity and in their physical and chemical properties. The dis- cussion of virus particles is intermediate between the other topics of Part C and the contents of Part D. 183 IO Cellular Events Produced by Ionizing Radiations I. Ionizing Radiation as a Biological Tool Possible radioactive fallout from tests of atomic bombs is an international concern; all nations realize that radiation from fallout has deleterious effects on human beings. Such radiation damage is unique neither to fallout nor to humans. A number of different types of radiations give rise to similar changes in all living systems. These effects result from ionizations occurring within the living cells. Radiations producing ionization include alpha, beta, and gamma rays; neutrons; protons; deuterons; and X rays. Similar cellular changes can also be produced by ultraviolet irradiation. A number of complicated responses follow the exposure of the human body, or for that matter, of any vertebrate or higher plant, to ionizing radiations. These responses may be divided into two types: somatic or body effects which occur in the individual, and genetic effects which are transmitted to future generations. The somatic responses in humans include such phenomena as loss of hair; skin disorders; dysfunction of the 185 186 Cellular Events Produced by Ionizing Radiations / 1 : I systems manufacturing blood cells; complete destruction of certain tissues: and induction of malignant growths. The entire subject of somatic responses to ionizing radiations is very complex; empirical knowledge extends beyond that which can be explained in terms of the basic cellular events. No attempt is made in this text to describe the details of the responses of complex organisms to ionizing radiation. Rather., in this chapter, the cellular events are emphasized. These in turn can be described in terms of molecular phenomena, the presentation of which comprises Chapter 16. Genetic effects, in contrast to the somatic ones, occur originally in only one cell, even in higher plants and animals. These genetic effects are also discussed in this chapter. Ionizing radiations are destructive to living cells. In most cases, this ■- c Q Distance from Source Figure I. The attenuation of a proton beam passing through tissue. destruction is undesirable to humans. However, in controlled labora- tory experiments, the effect of ionizing radiations can be used to study the organization of the biological cell. In particular, the effects of ionizing radiation are useful for studies of cellular division and of genetics. The use of ionizing radiation as a tool to study biological systems is emphasized in this text. The various types of ionizing rrdiations and related subatomic particles are summarized in Appendix D, for the benefit of those un- familiar with atomic physics. It is sufficient here to note that all these types produce ionization along their path. The heavier ones follow a straight path of definite length; the uniformity' of this path length is illustrated by the graph in Figure 1. The lighter ionizing radiations cannot be described in terms of a definite path length, because the path 10:1 Z-. or zing '-'-'- '--'. \- : 187 lengths of the individual particles are widely varied. It is possible to determine a maximum distance of penetration such that the remaining energv is less than 1 per cent of the incident ener^r r one may deter- mine the distance at which the radiation has decreased to less than background . It is often of greater biological importance to express the ionization than to detail the path length. The ionization is expressed in terms of dosage, but there is no generally accepted set of units. Instead, various dosage units are used. These are described in the following section. 2. Dosage The effects of several different types of radiation can be described in terms of the ionization they produce-- Historically, the oldest unit used to measure dosage was denned in terms of the ionization produced in air. This unit is called the roentgen and is abbreviated r. It is denned for X ravs and y ravs as: ""The roentgen I r is the quantity of X or gamma radiation . . . producing 1 esu of ions of either sign per Q.01293 gm of air." This mass of air. 0.01293 gm. occupies one ml at 0~C and 760 mm of Hg pressure. An alternate form is that lr is the quantity of X or gamma radiation which loses 83.4 ergs gm of a: To extend this definition to other types of radiation the following units have sometimes been used: 1 rep = roentgen equivalent physical — quantity of radiation. of any tvpe. producing energy losses of 83.- - gm in water or tissue . 1 rem = roentgen equivalent man' — quantity of radiation, of anv tvpe. producing effects in man equivalent to lr of X or gamma radiation. This unit depends on the s "ecific effect in man used as the criterion. 1 reb = roentgen equivalent biologic a. — sam - anim als or plants may be used instead of man. Accordingly this is also an equivoc:.- definition. 1 rod = quantity of radiation of any type producir- losses of 100 ergs gm of absorbing material. For X and y rays, lr is between 1 rad and I 1 The figure of 83 ergs gm can be found - - - : - 5 :: - i electron-volts per ion pair in br: a ^ bond. - appeals constant for all substances, although - most bonds. The extra energy app; - electronic excitation within the ions iorr. 188 Cellular Events Produced by Ionizing Radiations /I0 : 2 1 nvt = thermal neutron flux per cm 2 times time in seconds. 1 Mdwjct = 3 x 10 17 nvt. 1 pile unit = 10 17 nvt plus associated gammas and fast neutrons. These units are all used in the literature. The r was originally defined for X rays and is too firmly imbedded in medical terminology to be completely discarded. It would appear far more desirable to express dosage either in terms of energy loss per gram without extra symbols or in terms of the number of particles and their energy. The list of different dosage units is included here because they are all used to describe experiments in biophysics. The ratio of the rem to the r is sometimes called the relative bio- logical effectiveness, abbreviated RBE. The accompanying table gives some RBE factors. It should be repeated that these values will vary widely depending on the criterion used. TABLE I Some RBE Factors Radiation RBE X 1 gamma 1 1.0 Mev beta particle 1 0.1 Mev beta particle 1.08 Thermal neutron 2-5 1.0 Mev proton 8.5 0.1 Mev proton 10 Fast neutron 10 5 Mev alpha 15 1 Mev alpha 20 Various committees have set up maximum permissible doses for persons working near radiation. The maximum permissible dose is defined as the highest level at which the probability of producing harm- ful somatic effects is so low that it cannot be measured. Over the course of years, various maximum permissible doses have been chosen. As more knowledge has been obtained, these have decreased steadily. Thus, from 1935 to 1947, an accumulated dose of 0.1 rem per day was considered permissible. This was then lowered to a maximum of 0.3 rem per week. In 1957, the maximum permissible dose was further lowered to 5 rem per year for each year over eighteen years of age. Even these levels might produce appreciable genetic damage and might give rise to malignant tumors. It seems likely that the maximum permissible doses will be further lowered in the future. These values are for whole-body irradiation of radiation workers. Levels for the entire 10:3/ Cellular Events Produced by Ionizing Radiations 189 population are set at one tenth those of radiation workers, on the assumption that genetic changes as well as somatic ones would be undetectable. By 1960, radiation doses to the entire population included about 4 rem in thirty years from background, about 5 rem in thirty years from medical and dental sources, and about 0.3 rem from 1946-1959 from fall-out. The last-mentioned number will continue to increase. A further discussion of fall-out is included in Section 6. 3. Mitosis and Meiosis Many of the abnormal cellular events resulting from ionization become apparent as a result of cellular division. To appreciate the significance of these alterations, it is necessary to be acquainted with the normal mechanisms of cell division. In most cells, this occurs in a series of characteristic steps called mitosis. This is modified in the formation of the cells of sexual reproduction (the sperm and egg cells) into a homol- ogous series of steps referred to as meiosis. The major exceptions to the more or less universal nature of mitosis and meiosis are the bacteria which do not possess a clearly defined nucleus and divide in a less organized fashion. Figure 2 illustrates the process of mitosis. The chromosomes within the cell nucleus are believed to carry most of the genetic information of the cell, controlling its form, metabolism, and function. However, as shown in Figure 2a, the chromosomes do not exist as such in the nucleus during most of the cell life. Rather, during the period between divisions they appear broken up into heavily staining birefringent granules called chromatin material. This portion of the cell life between divisions is called interphase. As the cell prepares to divide, the chromatin material is organized into long filaments which pull together to form chromosomes. These are double filaments at this point in mitosis, which is called prophase. Simultaneously, a spindle starts to form, the nuclear membrane starts to dissolve, and the nucleoli disappear. This stage is shown in Figure 2b. In the next stage, metaphase, the chromosomes attach at a specific point, the centromere (also called kinetochore), to the spindle, and line up at the center of the cell. As shown in Figure 2c, the nuclear mem- brane is completely gone. The chromosomes then each pull apart into two separate fibers and follow the spindles to the cell centers. In the absence of a spindle (which 190 Cellular Events Produced by Ionizing Radiations / 10 : 3 results from certain types of irradiation), the chromosomes do not divide. The forces causing the chromosomes to adhere to the spindle at the centromere, to separate, and to migrate are not at all understood. The observed phenomena known as anaphase are shown in Figure 2d. Note that each half of the cell now has the same number and types of chromo- somes as the original one in Figure 2b. Centriole \ Nucleolus Cytoplasm^ Nucleus with Chromatin (e) Telophase. New nuclear membranes appear. Chromosomes elongate. Cells divide. (a) Interphase. Vegetative growth phase. Chromosomes do not exist as distinct entities. (b) Late prophase. Nucleolus has faded. Nuclear membrane has disappeared. Centriole has divided and spindle is forming. Double stranded chromosomes have formed; dots represent centromeres. (c ) Metaphase. Chromosomes line up on equatorial plate midway between centrioles. Chromosomes attach to spindle at centromeres. (d) Late anaphase. In anaphase centromeres divide. Daughter centromeres move as if pulled to opposite centrioles. Cell starts to divide. Figure 2. Diagrammatic outline of mitotic cycle. Each cell starts with two homologous chromosomes, distinguished in the diagram by showing their centromeres as dots and squares. Modified from Life : An Introduction to Biology by G. G. Simpson, C. S. P. Hendrigh, and L. H. Tiffany, © 1957, by Harcourt, Brace & World, Inc. Finally, as illustrated in Figure 2e, new nuclear membranes form and the cell pinches in two during the final stage called telophase. If no spindle forms, each cell ends up with about half the original number of chromosomes and eventually dies. In normal mitosis, by contrast, one ends up with two duplicates of the original cell. These duplicates are sometimes referred to as daughter cells. In the normal cells, the chromosomes occur as pairs. The two members of the pair have similar shapes and are believed to control the same characteristics. If the two members of the pair are not identical, one will be dominant for each character and the other recessive; the cell and the individual usually reflect only the dominant character. How- ever, one chromosome will not be dominant for all the characteristics it 10 : 3/ Cellular Events Produced by Ionizing Radiations 191 controls. During mitosis, each chromosome is split and, therefore, the daughter cells have the same character as the original cell. During meiosis, however, the two homologous chromosomes line up together, entwine about one another, and then separate along the spindle to opposite poles. Thus, the egg and sperm cells end up with half the number of chromosomes as the normal body cells. This division is not completely random because each egg or sperm cell con- tains one member of each pair of chromosomes. When the sperm fertilizes the egg cell, the normal number is re-formed. Figure 3 illus- trates diagrammatically the chromosome changes in meiosis. (a) Interphase. As in Fig. 2(a). (d) Late anaphase. As in Fig. 2(d), except each daughter cell has half the original number of chromosomes. Crossing over can occur in early anaphase. (e) Telophase. Two haploid cells are formed. Note each chromosome is double stranded. (b) Late prophase. As in Fig. 2(b). Cell is called diploid. Metaphase. Homologous chromosomes pair up at centromeres and line up along equatorial plane. Pairs twist around each other, forming 4 -stranded groups. Crossing over can occur. (f) Haploid cells grow and undergo mitosis, resulting in four haploid cells. Chromosomes are shown within these for diagrammatic purposes. Some of the last 4 grow, forming double-stranded chromosomes and becoming the active cells of sexual reproduction. Figure 3. Note that if there are pairs of homologous chromo- somes, the cell is called diploid, whereas if there are only half this number of chromosomes, the cell is called haploid. For discussion of crossovers, see Figure 4. Modified from Life : An Introduction to Biology by G. G. Simpsom, C. S. P. Hendrigh, and L. H. Tiffany, © 1957, by Harcourt, Brace & World, Inc. 192 Cellular Events Produced by Ionizing Radiations / 10 : 4 By and large, the different characteristics are segregated during meiosis according to the member of the homologous pair on which they are located. However, occasionally pieces of the chromosomes break off during meiosis. The broken pieces then rejoin the same homol- ogous pair, but often a part of chromosome A will join the remainder of A' and vice versa. This breaking and re-forming is known as crossing over. This is hard to observe in animals which reproduce slowly, such as the large mammals, because crossing over is a rare event. However, in fruit flies, wasps, microorganisms, and viruses, the rate of reproduction is so large that the frequencies of crossing over between two loci can be accurately measured. Figure 4 shows a possible crossing over during meiosis. b c d e f g h i j a b c d e f g' h' i' j' -•- a b c d e f g h i j a' b' c' d' e' f g h i j Before After Figure 4. One type of crossover. Letters show locations along chromosomes. This is schematic only; most chromosomes are not straight lines and are always twisted when crossovers occur. Dot indicates centromere. For instance, a might represent blue eyes, a' brown; and g might represent tall, g' short. Then the offspring with no crossover would always have blue eyes and be tall. With the crossovers shown, blue eyes can occur with short. After H. J. Mueller, Chapter 7 in Radiation Biology, Vol. 1, Part 1, A. Hollaender, ed., (New York: McGraw-Hill Book Company, Inc., 1954). One action of all ionizing radiation and ultraviolet light is to increase the frequency of crossing over of parts of homologous chromosomes. Far from being undesirable, this is a beneficial effect increasing the minor variations within the population. Ultraviolet irradiation strongly favors crossing over as opposed to other genetic changes to be discussed. Radiation-induced crossovers have increased man's knowledge of genetic mechanisms. 4. Visible Cellular Effects The cellular changes resulting from ionizing radiation are essentially independent of the type of irradiation, provided similar ionization occurs. 10 : 4/ Cellular Events Produced by Ionizing Radiations 193 The visible cellular effects of irradiation may be divided into two types : those concerned with mitosis (or lack thereof) and those producing degeneration, often leading to cellular death. The sensitivity to irradia- tion varies markedly from one cell to another. By and large, the cells of higher animals and plants are more sensitive than those of the lower ones. Also, faster growing cells are altered by lower doses of irradiation than more mature cells. The most sensitive part of most cells is the nucleus. Direct hits in a very narrow region can alter the mitotic figures or the progress of mitosis. This has been demonstrated most convincingly by Zirkle and Bloom and their co-workers, who have used pinpoint beams of protons and ultraviolet (uv) photons on single cells. They exposed single cells of different types to these microbeam radiations. The beam cross section was of the order of 8 /z in diameter. The apparatus was arranged so that the area exposed could be located simultaneously with an optical microscope, and also so that the cell could be followed after irradiation. The entire progress was recorded on a motion picture film, with intervals of several seconds between pictures. At low doses, no cytological changes were observed when the beam passed through the cytoplasm only. However, when the same types of cells were irradiated with the proton or uv beam passing through the nucleus, the process of mitosis was often altered. If irradiation occurred during the resting phase, when distinct chromosomes cannot be observed, a variety of abnormal effects were produced during the next mitosis, including broken chromosomes, pairs of chromosomes stuck together, and uneven division of chromosomes. During mitosis, when one particu- lar region of the chromosome, the centromere, was hit by as few as a dozen protons, the chromosome no longer lined up with the others. Eventually, it was forced into one of the two daughter cells forming either an auxiliary nucleus or a lobe of the existing one. Higher doses were needed on any other part of the chromosomes to alter mitosis, although these doses were small compared to those necessary to produce damage when used on the cytoplasm only. Several abnormal mitoses are shown in Figures 5-7. During mitosis, a spindle of fine threads forms and appears to pull the chromosomes apart. Irradiation of the spindle or cytoplasm by protons had little or no effect on the spindle. However, irradiation of any part of the cytoplasm with doses of uv photons several times those used on chromosomes did alter the spindle. The arrangement of the chromo- somes was changed ; they split into two groups of chromosomes instead of each pair splitting in two. The nonmitotic visible cellular changes observed are much less pro- nounced. In extreme cases of high doses to single cells, the cell 194 Cellular Events Produced by Ionizing Radiations / 10 : 4 membrane is damaged. Most of the subcellular structures, such as mito- chondria, neurofibrils, and myofibrils remain unaltered at doses which lead eventually to cellular death. Chromatin thread from A does not separate (a) Prophase as in Fig. 2(b). Chromosome A is bombarded with protons in crosshatched area. (b) Normal metaphase as in Fig. 2 (c). (c) Anaphase. Chromosome A forms bridge. (d ) Telophase incomplete owing to extra bridge between nuclei. Figure 5. Diagrammatic representation of results when micro- beam of ionizing radiation strikes prophase chromosome. Similar results are obtained due to irradiation during meta- phase. The cells of muscle divide only occasionally and those of the adult vertebrate nervous system not at all. Cytological changes in these types of cells are very hard to demonstrate at reasonable doses of ionizing radiation. In contrast, cells of most epithelial tissues (covering layers such as skin) are continually dividing, as are those responsible for forming erythrocytes (red blood cells) and leucocytes (white blood cells) . These rapidly dividing cells are sensitive to all types of ionizing radiations. Malignant tumor cells also divide rapidly; treatment with heavy doses of radiation tends to stop this process. (It also probably induces changes in the nuclei of surrounding cells which may lead to new types of malignant growths.) 10 : 4/- Cellular Events Produced by Ionizing Radiations 195 Most of the effects on rapidly dividing cells are associated with alterations in the chromosomal material or spindle. The microbeam experiments of Zirkle and co-workers indicate that chromosomal changes are extremely local. This suggests they are direct effects associated with a sensitive volume. Dosage studies likewise show that only a single (a) Prophase as in Fig. 2 (b). Chromosome B' is bombarded with protons at the centromere. (b) Metaphase. Chromosome B' does not line up on equatorial plate. (c) Anaphase. Chromosome B' drifts to one side without separating. (d) Telophase. Chromosome B' forms extra lobe on upper nucleus. Lower cell lacks B . Figure 6. Diagrammatic representation of abnormality result- ing from bombarding centromere of one chromosome with ionizing radiation. Similar results are obtained if the centromere is irradiated during metaphase. The reader is reminded that the chromosome shapes and numbers are purely diagrammatic. ionization is necessary in this critical volume. In contrast, the changes induced by uv photons in the spindle were not direct effects ; they could be induced by irradiation of any part of the cytoplasm. Thus, both direct and indirect effects are important. There are several exceptions to the rule that rapidly dividing cells are more sensitive to ionizing radiations than are other cells. Some types of rapidly growing tumors are quite insensitive, whereas lymphocytes which divide only occasionally are among the most sensitive. The reasons for these differences are not known. In all cases tested, a decrease of oxygen tends to decrease the effect of the ionizing radiation. Furthermore, certain substances such as the 196 Cellular Events Produced by Ionizing Radiations /I0 : 5 amino acid cysteine, which tend to react with free radicals formed in the irradiation of water, limit the cellular damage of ionizing radiations. Both the oxygen effect and that of the protective agents can be inter- Prophase. Ultraviolet irradiation of the cytoplasm causes spindle to disappear. Much greater doses are needed than those necessary in direct irradiation of the chromosomes. Irradiated area (b) False metaphase. Chromosomes fail to line up at equatorial plate. (c) False anaphase. Cell constriction starts, but chromosomes fail to divide . (d) In telophase, two new nuclei form. The chromosome division is uneven and the cells eventually die . Figure 7. Diagrammatic representation of abnormal cellular division resulting from cytoplasmic irradiation with ultra- violet photons. All spots in the cytoplasm are equally sensitive. preted to support the role of free radicals such as 2 H and OH as the primary elements in the cellular action of ionizing radiation. However, they can be equally well interpreted as altering the products formed by the direct interaction of the ionizing radiation with the chemical con- stituents of the cells (see Chapter 16). 5. Genetic Effects At dosage levels producing little or no visible cellular damage, it is still possible to alter the genetic material of the cell so that the progeny will be different. This is true whether one uses simple one-celled plants and animals, or complex organisms such as the mammals and the higher plants. In every case, these genetic effects occur within a single cell and may be classed as cellular events. Just like the visible changes 10 : 5/ Cellular Events Produced by Ionizing Radiations 197 produced in cells, the genetic effects are not very different for X rays, gamma rays, beta rays, protons, and so on. Even neutrons and ultra- violet irradiation give rise to qualitatively similar genetic effects, although comparing their dosages in terms of ion pairs is not very meaningful. Genetic changes are explained in terms of alterations of one or more chromosomes. Specific places along the chromosomes are associated with final body characteristics such as height, eye color, and number of fingers. These spots are called genes. Along each chromosome there are a large number of such genes. However, along a homologous pair of chromosomes, the homologous genes control the same characteristics. Thus, in a human, with 24 pairs of chromosomes per body cell, each pair controls a given set of characteristics. In a highly inbred population, both chromo- somes of the pair will usually be the same, but in normal populations the two chromosomes usually will contain many different genes. The dominant gene will determine the body characteristic. The recessive gene, though not altering body form, may be transmitted genetically. It was discovered first with the mold neurospera that each gene apparently controlled one enzyme. (Enzymes are biological catalysts of a protein nature which control the rate of most chemical and physical processes in living cells. They are discussed more fully in Chapters 17 and 18.) This idea led to the hypothesis of a one gene-one enzyme relationship. Because the idea of the gene was a somewhat fuzzy one, genes are now often defined biochemically as the part of a chromosome associated with a given enzyme. Further studies of crossovers, particularly in neurospera and viruses, but also in the fruit fly, drosophila, have shown that even this definition of the gene — that is, the part of the chromosome associated with one enzyme — may be misleading. Each enzyme is a protein made up of amino acids ; changes in very small regions along a chromosome, perhaps in pieces 20 A long, can alter one amino acid in an enzyme. However, it is not customary to call this small piece a gene. When any of these tiny regions along the chromosome is altered, the genetic character transmitted will be changed. Such changes are referred to as mutations. Most mutations are recessive; that is, they are carried along and reproduced in the chromosomes without changing the body form until descendants occur in which both chromosomes have this mutation. Most mutations are also lethal; that is, the progeny, both of whose chromosomes have this mutation, either fail to form as embryos or else do not reach maturity. A few mutations, perhaps one in 10,000, are desirable in that they lead to a characteristic favoring the survival of the species. The frequency of mutation in bacteria, paramecia, fruit flies, 198 Cellular Events Produced by Ionizing Radiations / 1 : 5 neurospera, mice, and man is increased by exposure to ionizing radi- ations. This produces breaks in the chromosomes which come together hV VWWVWAAA*- Centromere / Normal Broken Double stranded (Prophase) Lost as Dicentric - Prevents No Completion of Centromere Telophase Cell Division (a) Break in one chromosome prior to division Normal WWWWWW, -#- Two Breaks Translocation Jmv- Alternate Translocation -ANv- Lost ■^ W*/WV -#- -—o -r -#. WWWW- Dicentric (b) Translocation due to one break in each of two chromosomes JVWWWWVWWW -V wwvwwv Normal Two Breaks J VWA — o Lost o Centric Ring Chromosome -VWVWWWW^ -w vww VWWWV — O {^J Centric Chromosome [_ os f Ring (c) Two breaks forming ring chromosome VWWWVW>- VWWVW*- V — wvwwww- Normal Two Breaks Inversion (d) Two breaks forming inversion Figure 8. Breaks in chromosomes. Shapes are diagrammatic only and have no physical significance. Broken ends are not similar to normal chromosome ends but act sticky. They tend to recombine with other broken ends. The site of the break is always altered no matter how recombination occurs. After H.J. Mueller, Chapter 7 in Radiation Biology, Vol. 1, Part 1, A. Hollaender, ed., (New York: McGraw-Hill Book Company, Inc., 1954). (recombine) in many fashions, some very bizarre. Some types of breaks observed with fruit flies are shown in Figure 8. Ionizing radiations may also damage or alter chromosomes without actually breaking them. 10 : 5/ Cellular Events Produced by Ionizing Radiations 199 Instead of trying to use the word "gene" in discussing radiation damage, many investigators now describe their results in new terms like cistron, recon, and muton. The cistron is based on experiments in the so-called "cis" and "trans" configurations. The trans configuration corresponds to having two mutations, one on each member of a pair of chromosomes. If no normal offspring are formed, the two mutations are said to be noncomplementary. The cis configuration consists of both mutations on the same chromo- some and a normal (that is, a so-called "wild-type") chromosome for the other member of the homologous pair. The cis configuration forms a control. In order to be able to use this analysis, the cis con- figuration must correspond to normal individuals. This shows that both mutations are recessive when compared to the normal. If, in addition, the trans configuration showed the two mutations to be noncomplementary, then they must block the same function. Under these circumstances, the two mutations are said to be in the same cistron. Each cistron in turn is made up of smaller chromosomal regions defined in terms of crossover frequency. By studying relative crossover frequencies for different mutations, and from a knowledge of the chromosome length, one can estimate the minimum separation for crossing over. The unit of length for this minimum separation is called the recon. Likewise, the critical length of the chromosome which must be altered for a mutation to occur is called the muton. Experiments with viruses support the idea that the muton and recon are both about 20 A long, although the recon is probably shorter than the muton. These results are in accord with the view that genetic mutations induced by ionizing radiation occur due to ionizations in a small critical volume. Studies of the variation of mutation rate with dosage for higher animals have been interpreted in terms of the critical volume target theory. These data led to a volume whose diameter lay between 70 and 80 A. At one time, when the gene was believed to be a structural unit, these figures were discarded as being a factor of 100 to 1,000 times too small. All theory suggested that if the critical volume differed from the gene, it should be larger because of the influence of ionizations in the water (nucleoplasm) surrounding the chromosome. This point of view is presented in Reference 2 at the end of this chapter. It represented the views commonly held in 1952. It is now apparent that the best estimates of the critical volume, a sphere about 60 A in diameter, are larger than the recon or the muton. Thus, apparently, chromosomes are sensitive both to direct hits and to ones very close by but are not altered by ionizations more than about 3 uifji (30 A) away. 200 Cellular Events Produced by Ionizing Radiations /I0 : 6 6. Evolution, Mutation, and Fall-Out The rate of mutation of all living systems is increased by ionizing radiation. One may wonder, then, if it is not possible to speed up the process of evolution by artificially producing mutations by ionizing radiation. This has been done successfully with fruit flies within the laboratory. It is important not to generalize too quickly however, for most of the mutations occurred in highly inbred lines and brought them closer to the wild-type fruit fly outside the laboratory. Further, they were adapting to an environment (the laboratory) different from that which had controlled their evolution. This beneficial effect depended on a number of factors : an unusual environment, an inbred line, and perhaps most important of all, the production of such a large number of offspring that most could be discarded while still maintaining the population. This indicates that exposure of humans to ionizing radiation will have far more harmful effects than beneficial ones. The frustrated lives caused by most unsuccessful mutations; our social mores which provide an existence for the idiot and the physically incapable; our protection of the rights of diabetics to have children ; and our slow rate of repro- duction — all would work against us if more mutations were produced. Moreover, the extra survival value of mental, physical, or moral abilities is minimized in our culture. Barring a dramatic departure from present civilization, an increased mutation rate would work strongly against humans, not for them. Moreover, such effects are insidious ones, often not appearing for many generations. With this in mind, one may compare the observed natural mutation rate with the background radioactivity in which the organism lives. In the case of the fruit fly, the dose from background radioactivity is only sufficient to account for about 10-15 per cent of the natural mutation rate. Higher animals are more sensitive to ionizing radiation. In the mouse, the background radiation can account for about 30 per cent of the natural mutation rate. There is evidence to suggest that in humans the total body dose of approximately 10 rep over 30 years may account for more than 30 per cent of the observed mutations. Because the background radiation has an effect on humans, and because it is desirable to decrease rather than increase the mutation rate in them, it is important to limit the radiation dose on people at least until they are past the reproductive age. One principal source of overdosage in the past has been the indiscriminant use of X rays for medical and dental tests. These often exceed the total body dose due to background radiation. It is desirable to avoid X-ray exposures of 10 : 7/ Cellular Events Produced by Ionizing Radiations 201 pregnant women under almost all circumstances; even dental use of X rays contributes a significant dose to the developing embryo. Background radioactivity is due in part to cosmic rays, which are still beyond human control, and, in part, to radioactive elements in the air, soil, water, food, and our bodies. Since 1950, the total background radiation has risen detectably as a result of testing nuclear weapons. These tests release radioactive fission products into the upper atmos- phere. Then radioactive atoms fall out over the surface of the earth, both near the original test site and farther away. The fall-out in 1961 had not reached such proportions that it greatly increased the back- ground radiation, but any increase, no matter how small, can be expected to increase the mutation rate. It is not proposed to debate here whether the supposed benefits of testing atomic and nuclear weapons outweigh the best estimates of the genetic cost. It is important to emphasize that genetic damage to survivors would be a major long- term result of any war involving nuclear weapons. The greatest immediate biological danger from fall-out appears to be the production of radioactive isotopes which are incorporated into the organism, particularly C 14 and Sr 90 . These had reached limits in 1961 in some parts of the world where the rate of carcinogenesis (production of new cancers) might be detectably increased by these isotopes. This type of damage would also be multiplied manyfold for the survivors of a nuclear war. 7. Summary Many types of ionizing radiation produce similar effects in all living cells. The different types of radiation, their measurement in terms of dosage and target theory, and their action are discussed in this chapter. The cellular effects may be divided into two types: visible and genetic. The former consist primarily of changes in the pattern of cell division called mitosis, although other effects, particularly the death of lympho- cytes, are also observed. Direct microbeam experiments show that some mitotic effects involve the direct action of the ionizing radiation on or near the chromosomes, whereas other effects result from irradiation anywhere within the cell. These studies have confirmed the role of the chromosomes in carrying genetic information and have emphasized the physical action of the centromere during mitosis. Genetic effects produced by ionizing radiations and ultraviolet light include increasing the frequency of crossover and the production of mutations. The former is the predominant effect with ultraviolet irradiation, and the latter occurs with all the types of irradiation dis- cussed in this chapter. The mutations consist primarily of lethal 202 Cellular Events Produced by Ionizing Radiations /I0 : 7 recessives ; increased mutation rates are highly undesirable for mankind. In contrast, the controlled use of ionizing radiations has greatly enhanced genetic knowledge as well as made possible the production of better plant species. Indiscriminate use of clinical X rays and increased fall-out from atomic testing both can produce increased mutation rates. The present fall-out levels are just at the limit where the generation of new cancers and induction of the genetic effects might be detectable. Both of these deleterious results would be manyfold worse among any population surviving a nuclear war. REFERENCES 1. Miner, R. W., ed., "Ionizing Radiation and the Cell," (Monograph) Ann. New York Acad. Sc. 59: 467-664 (1955). a. Bloom, William, R. E. Zirkle, and R. B. Uretz, "Irradiation of Parts of Individual Cells. III. Effects of Chromosal and Extrachromosal Irradiation on Chromosome Movements," pp. 503-5 r3. b. Patt, H. M., "Factors in the Radiosensitivity of Mammalian Cells," pp. 649-664. 2. Hollaender, Alexander, ed., Radiation Biology: Volume I. High Energy Radiation (New York: McGraw-Hill Book Company, Inc., 1954). a. Muller, H. J., "The Nature of the Genetic Effects Produced by Radiation," pp. 351-473. b. Muller, H. J., "The Manner of Production of Mutations by Radia- tion," pp. 475-626. c. Bloom, William, and Margaret A. Bloom, "Histological Changes After Irradiation," pp. 1091-1143. 3. Bovey, F. A., Effects of Ionizing Radiation on Natural and Synthetic High Polymers (New York: Interscience Publishers, 1958). 4. Bacqu, Z. M., and Peter Alexander, Fundamentals of Radio bio logy (London, England: Butterworth & Co., Ltd., 1955). 5. Tatum, E. L., "The Status of Gene-Enzyme Relationship," part II, O. H. Gaebler, ed., Enzymes: Units of Biological Structure and Function (New York: Academic Press, Inc., 1956) pp. 107-176. 6. Zirkle, R. E., "Partial-Cell Irradiation," Advances in Biological and Medical Physics, J. H. Lawrence, and C. A. Tobias, eds. (New York: Academic Press, Inc., 1957) Vol. 5, pp. 103-146. 7. Benzer, Seymour, "The Elementary Units of Heredity," A Symposium on the Chemical Basis of Heredity, W. D. McElroy, and Bentley Glass, eds. (Baltimore : Johns Hopkins University Press, 1957) pp. 70-93. 8. U.S. National Committee on Radiation Protection, "Maximum Per- missible Amounts of Radioisotopes in the Human Body and Maximum Permissible Concentrations in Air and Water," National Bureau of Standards Handbook 52 (Washington, D.C.: Government Printing Office, 1953). Cellular Events Produced by Ionizing Radiations 203 9. U.S. National Committee on Radiation Protection and Measurements, "Permissible Dose From External Sources of Ionizing Radiations," National Bureau of Standards Handbook 59 (Washington, D.C.: Government Printing Office, 1954). a. Addendum to Handbook 59 (1958). Several articles on fall-out and its effect on man can be found in Science. II The Absorption of Electro- magnetic and Ultrasonic Energy I. Role of Nonionizing Radiation Both electromagnetic and ultrasonic energy may be absorbed by tissues and cells without any specific damage at the cellular or molecular level. The energy absorbed is converted to heat. If the power absorbed becomes sufficiently large, the cells and their protein constituents heat up to such a high temperature that they are irreversibly altered. The result is identical to the changes produced by the direct application of heat. Many types of irradiation do produce specific types of cellular damage. In the previous chapter, the action of ionizing radiation was considered. These ionizing radiations include electromagnetic radiation, provided the photon energy is sufficiently high. Photons of X-ray and y-ray wavelengths produce ionizations or break bonds within biological cells. Photons of ultraviolet wavelengths excite reactive states in proteins and nucleic acids. In the present chapter, only electromagnetic energy of much longer wavelengths will be considered ; this includes a broad band from the microwave region to d-c electrical currents. 204 11:2/ The Absorption of Electromagnetic and Ultrasonic Energy 205 Other types of radiation can damage cells without producing ioniza- tion. For example, under certain conditions single cells suspended in a liquid are fractured when irradiated with acoustic energy. This is always accompanied by a process called cavitation, in which small bubbles or holes form in the liquid. These and other destructive actions of ultrasonics are discussed in Chapter 11. If the acoustic power is not too high, or if cavitation is suppressed, exposed biological cells absorb some of the ultrasonic energy. This nondestructive absorption of ultrasound is also discussed in the present chapter. When any type of energy is absorbed, it is eventually converted to heat. The phenomena considered in this chapter are grouped together because the conversion of incident energy to heat is the direct, immediate effect. The different tissues of the human body, and different single cells, all have differing absorptions, both for electromagnetic energy and for ultrasonic energy. Thus, it is possible to selectively heat certain tissues and certain portions of the human body. This heating action is known as diathermy. Local heating of tissues promotes recovery from many disorders. Diathermy is the direct medical application of the phenomena discussed in this chapter. The absorption of electromagnetic and ultrasonic energy has, however, a more fundamental significance. It is an important tool for building a complete picture of the physical nature of biological cells and tissues. As such, it supplements knowledge gained by looking through a micro- scope and also supplements studies of molecular biology. 2. Electrical Impedances The absorption of electromagnetic energy in tissues can be described only in the language of electricity and magnetism. Several important definitions are summarized in Table I of Appendix C. Any reader not well versed in electrical terminology and definitions is asked to study that appendix before proceeding with the current chapter. Magnetic terms were completely omitted from Table I, but magnetic fields exist whenever a current flows. Thus, if one passes an alternating current through tissues (or other conductors), a magnetic field H will be generated. Likewise, if a tissue (or other conductor) is subjected to a changing magnetic induction B, an emf will be induced in it. The proportionality constant between B and H is called the magnetic permeability, /x. These added terms, along with a few others, are summarized in the following table. 206 The Absorption of Electromagnetic and Ultrasonic Energy /I I : 2 Supplement to TABLE I, Appendix C Quantity Symbol Defining Equation Units Magnetic induction B dF = 10 x B) webers/m 2 Magnetic field H V x H = \ttJ ampere/m Electric displacement D V • D = 4rrp coulomb/m 2 Dielectric constant e D = eE — Magnetic permeability H> B = fjiH — Conductivity a J = A-C Generator (a) i WWWVW 1 Cell %, ~#* JO- S'" -0" A-C Generator (b) Figure I. (a) Diagrammatic representation of single cell in an electric field. The resistance of the suspending medium is lower in regions a and c than b because the cross section occupied by the suspending medium is greater at a and c than at b. (b) Equivalent lumped electrical parameters for the preceding diagram. The cell wall is represented as a capacitor. A better approximation would include a leakage resistance in parallel with the capacitor. Resistors a, b, and c represent the suspending medium in regions a, b, and c respectively. membrane, but this hope has been unrealized as yet. Perhaps the most impressive aspect of these data is their similarity from one cell type to another. Plant cells, animal cells, nerve axons, and egg cells all overlap in their electrical constants. The following are the orders of magnitude obtained for most cells. The internal or protoplasmic resistivity varies from 10 to 30,000 ohm • cm, with 300 being common for most mammalian cells. For cat nerve, a value of 720 ohm • cm was measured. However, for other nerves, values as low as 10 ohm -cm have been found. The areal capacitance varies 210 The Absorption of Electromagnetic and Ultrasonic Energy /I I : 3 from 0.1 to 3 /ufd/cm 2 . Few values lie outside of the range 0.8 to 1.1. One low measurement of 0.01 /xfd/cm 2 has been obtained for a frog nerve, but other nerve measurements are in the 0.6 to 1.2 /xfd/cm 2 range. Values for the leakage areal resistance of the cell membrane vary from 25 to 10,000 ohm -cm 2 or higher. Nerve and muscle measurements have yielded both extremes. Similar considerations apply to the electrical characteristics of whole tissues. Their impedance is hard to separate in terms of cellular Figure 2. The frequency dependence of the dielectric constant of muscle. Note the three regions labeled with Greek letters indicating three types of relaxation. After H. P. Schwan and G. F. Kay, "Conductivity of Living Tissues," Annals of the New York Academy of Sciences 65: 1007 (1957). parameters but may be represented as a lumped resistivity and capacity. The ratio of the capacity to that of a vacuum is the dielectric constant. A plot of effective dielectric constants against frequency has the shape shown in Figure 2. It should be borne in mind that a variety of effects contribute to this general shape. The region labeled f3 is the one related to the change from conductance around the cells to conductance through the cells. The complex shape of the curve indicates a variety of cell sizes and shapes. The region labeled y is due to molecular relaxations discussed below. The low frequency changes labeled a indicate some other type of phenomena which is not clearly understood. Similar low frequency changes in resistivity can be seen in Figure 3. Although neither can be explained clearly, it appears likely that both are due to some common mechanism. Moreover, the low frequencies at which these occur indicate that comparatively large pieces of material are involved. All molecules tend to become polarized in an electric field. In an 11:3/ The Absorption of Electromagnetic and Ultrasonic Energy 211 alternating field, the molecule must reverse its polarization each half cycle. 2 Above the relaxation frequency the electric field changes so fast that the molecular polarization no longer follows it. The larger the molecule, the lower the relaxation frequency. The dielectric constant and resistivity of the molecules drop fairly abruptly from higher values below the relaxation frequency to lower values above the relaxation frequency. Proteins have relaxation frequencies in the range of mega- cycles apparently without effect on the lumped parameters of tissues. 1,000- 5 400 E O 200 .5 .to 100 40 20 10 1 1 l I I i l 1 1 a - ^\^_ - - \ - - i i I i I 1 l \ 3 8 10 4 5 6/ log f (cps) Figure 3. Resistivity of muscle as a function of frequency. Note the similarity of the relaxation regions for Figures 2 and 3. After H. P. Schwan and C. F. Kay, "Conductivity of Living Tissues," Annals of the New York Academy of Sciences 65: 1007 (1957). Small molecules such as those of water exhibit similar relaxations in the region of 10 10 cps, giving rise to region y in Figures 3 and 4. The low frequency relaxation, in region a, must represent the behavior of some part of the cell that is large compared to a protein molecule. The frequency dependence of the resistivity and dielectric constants of many different types of tissues are all similar. These are also similar to that of blood. The resistivity of blood, particularly at low frequencies, is lower than that of most other tissues, owing to its high water content. The values for muscle, liver, spleen, pancreas, lung, and kidney are all very similar, except that below 10 5 cps they are higher than that for blood. Exceptions to the preceding general pattern are brain tissue, fat tissue, and bone. The last, with its high content of calcium phos- phate crystals, is very different from soft tissues. Its impedance is 2 For small molecules with a permanent dipole moment, this implies an actual physical rotation. For small molecules without a permanent dipole moment, and for all large molecules, this change involves a rearrangement of the electron orbitals and of the atomic spacings within the molecule. 212 The Absorption of Electromagnetic and Ultrasonic Energy /I I : 3 much higher than that of the softer tissues, particularly at low frequencies. Fatty tissue is very different because fat is an excellent electrical insulator. Tissues of this nature show a much higher resistivity and a much lower dielectric constant than do those with more water. The general shape of the resistivity and dielectric curves is similar to that for 1 F 1 1 ii db/A -Curves 1-4 1 | 0.2 db/cm - Curve 5 V - 0.1 / - 0.07 - ^^^^"^ - 0.05 - L>^^ ^~ ^l———^* - 0.04 0.03 r — ^~^~~~/~^' ~~~ - 0.02 / ^^^ 0.01 - ~/^"^ - 0.007 — il 1 ill i .4 0.7 1.0 2.0 4.0 7.0 10 Frequency (mc) 20 Figure 4. Ultrasonic absorption by blood. Curve 1 shows absorption per wavelength for packed red blood cells. Curve 2 illustrates similar absorption per wavelength for whole blood. Curve 3 is a plot of the absorption per wavelength for whole blood computed from the absorption of plasma proteins and hemoglobin. Curves 4 and 5 diagram the ultrasonic absorp- tion of plasma in db per wavelength and db per cm, respectively. After E. L. Carstensen and H. P. Schwan, J. Acous. Soc. America 31 : 185 (1959). muscle. Brain tissue has more fat-like material (lipids) than does muscle. At lower frequencies, its resistivity is close to that of fatty tissues. How- ever, this resistivity falls rapidly as the frequency is raised from one to 10 megacycles (10 6 to 10 7 cps). Its value above this frequency range is close to that of the nonfatty tissues. Its dielectric constant is within the range of the watery tissues at all frequencies. In concluding this section, it should be noted that the electrical impedance of biological cells supports the picture of a cell consisting of 11:4/ The Absorption of Electromagnetic and Ultrasonic Energy 213 an electrically conducting cytoplasm surrounded by a poorly conducting, lipid membrane with a high dielectric constant. These electrical data are interesting as physical properties of the cells but have not yet been related in detail to the differences between cells. 4. Ultrasonics Mechanical vibratory energy has the same end effect on cells and tissues as does the electromagnetic energy discussed in the previous section of this chapter, namely it heats them. The rate of heating is comparatively small for low frequency mechanical vibrations. The frequency range used for most heating studies is above the audible; it is referred to as ultrasonic. The absorption of ultrasonic energy is not inherently different from that of energy at audible frequencies. Some authors refer to nonauditory uses of acoustics as "sonics," but in this text the more common name "ultrasonic" is used. Ultrasonic vibrations, then, are the sound waves whose frequency is above the audible range. The properties and mathematical descrip- tions of audible sound waves in air are discussed in Appendix A. There, it is emphasized that in air, sound waves are compressional waves characterized by a sound pressure (also called acoustic pressure) p and a local particle velocity v. The acoustic pressure p and particle velocity v are propagated throughout the medium with a characteristic wave velocity c. During the propagation, the wave may also be attenuated. The properties of the medium can be summarized in a quantity analogous to the electrical impedance, called the characteristic impedance Z. It is defined for plane waves as the ratio z = ? V The real part of this impedance R represents the propagation of un- attenuated sound waves. The value of R is given by the product pc, where p is the density medium and c the velocity of sound. The imaginary part of Z represents attenuation, that is, the absorption per unit length. For many purposes, it is convenient to describe a medium in terms of the real part of the impedance pc and the attenuation factor. This pair of numbers is completely equivalent to Z. The attenuation factor is the ratio by which the pressure amplitude is decreased in traveling one unit distance. Often, the log of this ratio is given, expressed, for example, as decibels/cm. (For a definition of decibels, see Chapter 1 .) Absorption of ultrasonic energy by biological cells and tissues is more complicated than similar absorption in a gas. In a solid or liquid, 214 The Absorption of Electromagnetic and Ultrasonic Energy /I I : 5 some of the longitudinal (that is, compressional) wave is converted into a transverse (or shear) wave. This wave is attenuated very rapidly in viscous media such as protoplasm. In addition, ultrasonic waves are scattered and absorbed at all cell interfaces. This is greatly accentuated when there is a large change in pc, such as at a bone-soft tissue interface, but is an important factor- even if the change in pc is small. The wavelength of ultrasonic energy is much smaller than that of electromagnetic energy of the same frequency. This means the passage of ultrasonic energy through tissues can be confined to a much smaller volume than can electromagnetic energy. For example, the ultrasonic wavelength is about 1 .5 mm at 1 mc, whereas the electromagnetic wave- length is about 300 meters. An ultrasonic beam 0.25 mm in diameter is feasible at 1 mc ; an electromagnetic beam would be at least 50 meters in diameter at the same frequency. A result of this short ultrasonic wavelength is that ultrasonic absorption or reflection can be used, just as X rays, to determine the structures within living organisms. Various systems have been devised for this. All of them are superior to X rays, in that ultrasonograms (as they are called) have no known harmful effects. In contrast, more information is usually obtained from an X-ray photograph than from most of the ultrasonograms developed to date. If the intensity and duration of the ultrasonic energy is raised suffi- ciently, destructive effects can be produced. These are discussed in greater detail in Chapter 12. In the present chapter, only non- destructive absorption will be discussed further. 5. Nondestructive Effects of Ultrasound The absorption of ultrasonic energy at frequencies above about 250 kc has been studied for many different types of tissues obtained from various mammals. The real part of the acoustic impedance (that is, pc) is essentially the same for all tissues. The exception is bone, which has a much higher pc than any other tissue. In contrast, the absorption of ultrasonic energy varies markedly from one soft tissue to another. Perhaps the easiest data to interpret are those obtained for blood. It is possible to measure separately the contributions to the absorption due to the proteins dissolved in the plasma, the hemoglobin within the red blood cells, and the cellular structure itself. These measurements show that the absorption per wavelength increases monotonically as the frequency is raised from 0.5 to 20 mc. This gradual increase, however, is slower than would be expected for a simple viscoelastic medium. The studies of blood showed that the ultrasonic absorption due to 11:5/ The Absorption of Electromagnetic and Ultrasonic Energy 215 hemoglobin is similar to that due to the plasma proteins. Absorption by proteins represents the major part of the ultrasonic absorption in blood. A much smaller effect can be observed in dilute suspensions of blood cells, which may be attributed to the motion of the liquid relative to the cells. The absorption coefficient for whole blood is about 0.2 db/cm at 1 mc, or in other units about 0.03 db per wavelength. The second figure is correct within a factor of two throughout the frequency range 0.7 to 10 mc; that is to say, the absorption per wavelength increases only very slowly with increasing frequency. The graphs in Figure 4 show this variation. Figure 5 shows the variation of the absorption per wavelength over a greater frequency range. This slow increase is extremely difficult to understand. All simple theories indicate that the absorption per wavelength should be pro- portional to the frequency. The failure of the simple theories is ^ 10 7 5 x Q- 3 2- i.O 0.7 = 0.5 b °- 0.3 c 5 0.2 §■ I 0.1 -S? J3 S 7 vt Red Cells (90 vol.%) °» Plasma vo Carstensen, Li, Schwan, 1953 » • Gramberg, 1956 I I L_i ''''I 5 7 5 7 10" l J J I0 Q c J J ' 10° L J J ' 10' Frequency (cps) Figure 5. Ultrasonic absorption of red blood cells and plasma from 30 kc to 10 mc. Note that the absorption per wave- length changes only fivefold when the frequency changes three hundredfold. (To convert nepers to db, multiply by 8.7.) After E. L. Carstensen, with permission. "explained" by saying that relaxations occur and that, as a result, the protein molecules no longer move as a whole at higher frequencies, or else somehow parts of the molecules become free to slip back and forth past other parts. Even on this model, the absorption per wavelength should be approximately independent of frequency only in a very- narrow frequency region. Instead, the absorption depends only slightly on the frequency over the entire range from 0.3 to 20 mc (that is, almost a 100: 1 ratio or about six octaves). It is still possible to explain away 216 The Absorption of Electromagnetic and Ultrasonic Energy /I I : 5 this discrepancy by stating that there are a large number of different relaxations which occur with a fairly uniform distribution of relaxation frequencies. At best, this explanation is highly artificial because the origin of these relaxations is unknown. It is possible that a more com- plete model of protein structure might increase the understanding of this process. Conversely, these apparent relaxations are one type of data that can be used to test any theory of protein structure. (The structure E o 5 1.00 -v. J. 7 are constants, j the square root of - 1 , and S n (d, «A) = 2 ^n (COS 6) *" m = In this, the a's are constants and P™ is the mth associated Legendre polynomial of order n. It may be readily shown that 1 a / . a dS n \ 1 d* _ n(n + 1) It is possible to satisfy the boundary conditions only if the frequency has certain discrete values given by ,2 T n{n - \){n + 2) «:--,^ . - . . (11) " /V* 3 1 + [n + 1/ p. For the lowest possible mode, n = 2, this becomes for Pi = Po = 1, a>i = 4.87a- 3 (12) This formula has been used to estimate some of the interfacial tensions referred to earlier. When a higher harmonic is used, the values obtained for Tare lower than those computed from Equation 12. 240 Mechanical Resonances of Biological Cells / 1 3 : 3 3. Gelatinous-Shell Model The static experiments used to measure interfacial tensions of nonmobile or slowly moving cells could be interpreted in other ways. Some involving ultracentrifugation may measure the tensile strength of the cell membrane. Others, depending on the gravitational distortion of cell shape, may actually be measuring the rigidity of an elastic outer layer (or cortex) of the individual cell. In a like fashion, the optimum frequencies, or resonances, observed in the ultrasonic destruction of single cells in acavitating suspension can also be interpreted as due to resonant vibrations of a rigid spherical cell immersed in, and filled with, an in- compressible fluid. This rigid-shell model is very different from the interfacial-tension model, in terms of both its mechanical structure and its biochemical make-up. However, its predictions for distortions and resonances of biological cells are very similar to those of the interfacial-tension model. Indeed, there is no simple way to distinguish one from the other. The rigidity of the cell cortex is negligible compared to steel, glass, or even wood. Rigidities are described by elastic moduli called coefficients of rigidity or shear moduli, which are about 10 8 -10 10 dynes/cm 2 for solid objects. All protein gels have much smaller, but nonetheless measurable, shear moduli in the range of 10 3 -10 5 dynes/cm 2 . Assuming gelatinous properties for the outer layers of the single cell leads to pre- dicted resonant frequencies in the ranges observed for protozoans and erythrocytes. The rigid-shell model is considerably more complex than the inter- facial-tension model. The analysis of the resonances of the rigid-shell model is similar to that of closed rigid shells in air. The restriction of a closed shell is important because most analyses of the vibrations of shells and plates assume no extension of the midsurface of the shell, a condition which cannot be met for closed shells. For vibrations of rigid shells with extension of the midsurface in air, both the kinetic and potential energies are proportional to the shell thickness h. Most of the modes occur at frequencies independent of h. For the cell cortex, the liquid on both sides may move, as well as the cell cortex. Accordingly, some of the resonant frequencies depend on the effective thickness of the cortex h or, at any rate, on its ratio to the effective cell radius a. This is shown by a detailed derivation. Rather than attempting to present the entire derivation, only the results will be described. Two general types of motion of the shell are considered, those which include radial motion as well as tangential motion, and those involving tangential motion only. The latter are simpler and will be described first. 13:3/ Mechanical Resonances of Biological Cells 241 The tangential-type modes are not affected by the intra- and extra- cellular liquids, to the extent that these liquids may be considered as having negligible viscosity. This tangential-motion-only mode may be described by a displacement in the ifj direction only, which will be denoted by *F. Because the liquids slip freely over the surface, these modes and frequencies are independent of h. They are described by T = ^^oW^(cos^)],-^ (13) ag --£-.(»- l)(» + 2) Ps a where A n is a constant, \x is the shear modulus and p s is the shell density. Values of \x in the range of 10 3 dynes/cm 2 lead to the resonant frequencies in the ranges observed for the optima for cellular destruction in cavitating acoustic fields. In modes with both radial and tangential motion, there are both a radial displacement R(r, 6) and a tangential displacement 0(r, 6). (This argument could be made more general by including a displace- ment *F, and allowing R, 0, and *¥ to depend on iff as well as r and 9. However, very little is gained at the expense of making the notati