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Vol. 1: P. Waltman, Deterministic Threshold Models in the Theory Vol. 30: M. Eisen, Mathematical Models in Cell Biology and Cancer
of Epidemics. V, 101 pages. 1974. Chemotherapy. IX, 431 pages. Jg79.
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Edited by P. van den Driessche. VI, 280 pages. 1974. 1979.
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1974. by G. Bruni et al. XI, 273 pages. 1979.
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Vol. 5: Mathematical Analysis of Decision Problems in Ecology. Vol. 34: R. Collins, T.J. van der Werff, Mathematical Models of the
Proceedings 1973. Edited by A. Charnes and W. R. Lynn. VIII, 421 Dynamics of the Human Eye. VII, 99 pages. 1980.
pages. 197 5.
Vol. 35: U. an der Heiden, Analysis of Neural Networks. X, 159 pages.
Vol. 6: H. T. Banks, Modeling and Control in the Biomedical Sciences. 1980.
V. 114 pages. 1975. Vol. 36: A. WCirz·Busekros, Algebras in Genetics. VI, 237 pages.
Vol. 7: M.C. Mackey, ion Transport through Biological Membranes, 1980.
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1976. P. Tautu. XI, 511 pages. 1980.
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pages. 1976. Proceedings, 1g79, Edited by C. Barigozzi. VI, 417 pages. 1980.
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by J. Berger, W. Buhler, R. Repges, and P. Tautu. XII, 281 pages. 1976. Edited by T. Vincent and J. Skowronski. XII, 236 pages. 1981.
Vol. 12: A. V. Holden, Models of the Stochastic Activity of Neurones. Vol. 41: Modeles Mathematiques en Biologie. Proceedings, 1978.
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D. L. Solomon and C. Walter. VI, 240 pages. 1g77. VIII, 282 pages. 1g81.
Vol. 14: L.M. Ricciardi, Diffusion Processes and Related Topics in Vol. 43: Mathematical Modeling on the Hearing Process. Proceed·
Biology. VI, 200 pages. 1977. ings, 1980. Edited by M. H. Holmes and L.A. Rubenfeld. V, 104 pages.
Vol. 15: Th. Nagylaki, Selection in One· and Two·Locus Systems. 1981.
VIII, 208 pages. 1977. Vol. 44: Recognition of Pattern and Form. Proceedings, 1979. Edited
Vol. 16: G. Sampath, S.K. Snnivasan, Stochastic Models for Spike by D. G. Albrecht. Ill, 226 pages. 1982.
Trains of Single Neurons. VIII, 188 pages. 1977. Vol. 45: Competition and Cooperat1on in Neutral Nets. Proceedings,
Vol. 17: T. Maruyama, Stochastic Problems in Population Genetics. 1g82. Edited by S. Amari and M.A. Arbib. XIV, 441 pages. 1982.
VIII, 245 pages. 1977. Vol. 46: E. Walter, Identifiability of State Space Models with applica·
lions to transformation systems. VIII, 202 pages. 1982.
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Edited by D. E. Matthews. VII, 385 pages. 1977. Vol. 47: E. Frehland, Stochastic Transport Processes in Discrete
Biological Systems. VIII, 169 pages. 1g82.
Vol. 19: Measuring Selection in Natural Populations. Edited by
F. B. Christiansen and T.M. Fenchel. XXXI, 564 pages. 1g77. Vol. 48: Tracer Kinetics and Physiologic Modeling. Proceedings,
1983. Edited by R. M. Lambrecht and A. Rescigno. VIII, 509 pages.
Vol. 20: J. M. Cushing, lntegrodifferential Equations and Delay
1983.
Models in Population Dynamics. VI, 196 pages. 1977.
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1977. Edited by R. Heim and G. Palm. VI, 244 pages. 1978. ceedings, 1981. Edited by M. Cosnard, J. Demongeot and A. Le
Breton. VII, 400 pages. 1983.
Vol. 22: F. M. Scudo and J. R. Z1egler, The Golden Age of Theoretical
Ecology: 1923-1940. XII, 490 pages. 1978. Vol. 50: D. H. Anderson, Compartmental Modeling and Tracer
Kinetics. VII, 302 pages. 1983.
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200th Anmversary. Proceedings 1977. Edited by R. E. Miles and Vol. 51: Oscillations in Mathematical Biology. Proceedings, 1982.
J. Serra. XII, 338 pages. 1978. Edited by J.P. E. Hodgson. VI, 196 pages. 1g83.
Vol. 24: F.L. Bookste<n, The Measurement of Biological Shape and Vol. 52: Population Biology. Proceedings, 1982. Edited by
Shape Change. VIII, 1g1 pages. 1978. H. I. Freedman and C. Strebeck. XVII, 440 pages. 1983.
Vol. 25: P. Yodz1s, Competition for Space and the Structure of Vol. 53: Evolutionary Dynamics of Genetic Diversity. Proceedings,
Ecological Communities. VI, 191 pages. 1g78. 1g83. Edited by G.S. Mani. VII, 312 pages. 1984.
Vol. 26: M. B Katz, Questions of Uniqueness and Resolution in Vol. 54: Mathematical Ecology. Proceedings, 1g82. Edited by
Reconstruction from Projections. IX, 175 pages. 1978. S.A. Levin and T. G. Hallam. XII, 513 pages. 1984.
Vol. 27: N. MacDonald, T1me Lags '" B1olog1cal Models. VII, 112 Vol. 55: Modelling of Patterns in Space and Time. Proceedings,
pages. 1g78. 1g93. Edited by W. Jliger and J.D. Murray. VIII, 405 pages. 1g84.
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Vol. 2g: Kinetic Logic - A Boolean Approach to the Analys1s of Vol. 57: Mathematics in Biology and Medicine. Proceedings, 1g93.
Complex Regulatory Systems. Proceedings, 1g77. Edited by R. Tho· Edited by V. Capasso, E. Grosso and S. L Paveri.f'ontana. XVIII,
mas. XIII, 507 pages. 1g7g, 524 pages. 1985.
ctd. on inside back cover
Lecture Notes in
Biomathematics
Managing Editor: S. Levin
87
P. Dallas C. D. Geisler J.W. Matthews
M.A. Ruggero C. R. Steele (Eds.)
The Mechanics and
Biophysics of Hearing
Proceedings of a Conference held at the
University of Wisconsin, Madison, WI, June 25-29, 1990
~i1
Springer-Verlag Berlin Heidelberg GmbH
Editorial Board
Ch. Delisi M. Feldman J. 8. Keller M. Kimura
S. Levin (Managing Editor) R. May J. D. Murray G. F. Oster
A.S. Perelson L.A. Segel
Editors
Peter Dallos
Auditory Physiology Laboratory and Department of Neurobiology
and Physiology, Northwestern University
Evanston, IL 60208, USA
C. Daniel Geisler
Department of Neurophysiology and Department of
Electrica! and Computer Engineering
University of Wisconsin-Madison,
Madison, Wl 53706, USA
John W. Matthews
Computer Systems Laboratory, Washington University
St. Louis, MO 63110, USA
Mario A. Ruggero
Department of Otolaryngology, University of Minnesota
Minneapolis, MN 55414, USA
Charles R. Steele
Division of Applied Mechanics, Stanford University,
Stanford, CA 94305, USA
Mathematics Subject Classification (1980): 92-06
ISBN 978-0-387-97473-6 ISBN 978-1-4757-4341-8 (eBook)
DOI 10.1007/978-1-4757-4341-8
This work is subject to copyright. Ali rights are reserved, whether the whole or part of the material
is concerned, specifically the rights of translation, reprinting, re-use of illustrations, recitation,
broadcasting, reproduction on microfilms or in other ways, and storage in data banks. Duplication
of this publication or paris thereof is only permitted under the provisions of the German Copyright
Law of September 9, 1965, in its current version, and a copyright fee must always be paid.
Violations fali under the prosecution act of the German Copyright Law.
© Springer-Verlag Berlin Heidelberg 1990
Printing and binding: Beltz Offsetdruck, Hemsbach/Bergstr.
2146/3140-543210-Printed on acid-free paper
Introduction
This compendium represents the proceedings of a five-day symposium held at the
University of Wisconsin, Madison between June 25 and 29, 1990. The remarkably rapid progress
of hearing science during the past twenty years has been punctuated by two series of international
symposia. One series began as meetings whose purpose it was to bring physiologists and
psychophysicists together. These triennial meetings continue to the present time at various
locations in Europe. A second series of meetings has been designed to enhance interchange among
neurobiologists, biophysicists and mathematical modelers dealing with cochlear function. The
present volume is the latest in this second series.
In the late seventies and early eighties hearing science entered a revolutionary state in which
many fundamental tenets of the cochlea's functioning required reassessment. Key discoveries,
among them outer hair cell influence upon cochlear output, otoacoustic emissions, outer hair cell
motility and multiplicity of schemes of producing cochlear tuning in different species, provided the
rungs of the ladder upon which we climb. The frame of the ladder was made of new and refined
techniques applied to cochlear measurements that pem1itted new views of the system. The
assimilation and invention of techniques for measuring low-level motion and force, intracellular
measurements in vivo and a bewildering array of in vitro methods, including those examining
single channel properties and cell motility, yielded a comucopia of data. The emerging view of the
mammalian cochlea, based on these methods and experiments, is that of a highly nonlinear
distributed feedback system, in which outer hair cells provide local mechanical feedback to the
basilar membrane-tectorial membrane complex under stimulus and efferent control to produce the
remarkable frequency selectivity and sensitivity of the audit01y periphe1y.
Being an extraordinarily complex mechano-hydraulic and bio-electric system, the cochlea
has fascinated physicists and engineers since Helmholtz' time. The past decade's developments in
the laboratory were paralleled by advances in computing and modeling. An additional element that
made recent modeling efforts particularly valuable is a new and highly developed communication
process among experimenters and modelers. To this end, symposia have been organized with the
avowed purpose of bringing these two species together and fostering their intermarriage. The
Madison meeting continues a series of such international symposia focused on cochlear function.
It follows in the spirit of the first of these meetings at Delft in 1983 (Mechanics of Hearing, Edts.
E. de Boer and M.A. Viergever, Delft University Press, Delft, 1983) as well as the previous
meeting at Keele in 1988 (Cochlear Mechanisms, Edts. J.P. Wilson and D.T. Kemp, Plenum
Press, New York, 1989). The tradition of these symposia will continue, providing the periodic
overviews and summaries that are so necessary in a rapidly advancing discipline.
As the table of contents indicates, we achieved an excellent balance between theoreticians
and experimentalists, reflecting the healthy state of the field. It is also apparent that many
ingredients necessary for understanding cochlear function are present in this volume. We begin
with experiments and models pertaining to the physiology and motility of individual hair cells and
address one of the key issues: what is the relevance of motility to cochlear mechanics? The book
continues with several papers on general cochlear physiology and with a major section on
otoacoustic emissions. The study of these emitted sounds, whose origin is in the cochlea, has
been one of the most profitable avenues of recent inquiry. Another productive line of research,
measuring macromechanical movements with ever increasing precision, dates back to Bekesy's
work and is producing some of the most definitive inforn1ation about cochlear function. Our
compendium closes with two sections on general and nonlinear cochlear models.
Ill
The symposium on The Mechanics and Biophysics of Hearing was supported by the
National Institute of Deafness and other Communication Disorders (DC00009-01) and by the
National Science Foundation (BNS-8919879). We thank the Department of Neurophysiology,
University of Wisconsin for its hospitality and the departmental staff for their untiring efforts on
the conference's behalf. Particular thanks are extended toP. J-leinritz, R. Klipstein and R.
Sorensen . The conference logo was designed by C. Dizack. The editors dedicate this volume to
the memory of the late modeler-experimenter, Juergcn Tonndorf who passed away last year.
August, 1990 Peter Dallos
C. Daniel Geisler
John W. Matthews
Mario A. Ruggero
Charles R. Steele
IV
Introduction III
v
CONTENTS
1. Hair Cell and Cilia l
Calcium ions and the adaptation of the transducer current in turtle 2
cochlear hair cells
M.G. Evans, R. Fettiplace and A.C. Crawford
Structural abnormalities in inner hair cells following kanamycin-induced 10
outer hair cell loss
CM. Hackney, D.N. Furness and P.S. Steyger
Modelling input-output characteristics of the inner hair cell 18
J.W. Horst and P.C. de long
Calcium ions promote rapid mechanically evoked movements of hair bundles 26
F: Jaramillo, J. Howard and AJ. Hudspeth
Modulation of voltage responses to 100Hz tones by high frequency 34
tones in cochlear hair cells
M. Kossl and I.J. Russell
Movements and mechanical properties of ampullary hair bundles and of 42
their kinocilium
A. Rasch and U. Thurm
2 Hair Cell Motility 51
The effect of cytoplasmic turgor pressure on the static and dynamic 52
mechanical properties of outer hair cells
W.E. Brownell and W.E. Shehata
The nonlinearity of outer hair cell motility: implications for cochlear 61
physiology and pathology
BN. Evans, R. Hal/worth and P. Dallos
Fast outer hair cell motility: how fast is fast? 69
J. Santos-Sacchi
Elastic behavior of the outer hair cell wall 76
C.R. Steele
3. Relevance of Motility to Macromechanics 85
A model for cochlear vibrations based on feedback from motile 86
outer hair cells
C.D. Geisler and X. Shan
Does the cochlear amplifier produce reactive or resistive forces? 96
P J. Kolston and G.F. Smoorenburg
The basilar membrane nonlinear input-output function 106
G.K. Yates
Active cochlear feedback: Required structure and response phase 114
J.J. Zwislocki
v
4. Electrophysiology
Spontaneous activity of auditory afferent neurones in the spiral
ganglion of the pigeon
A.W. Gummer
Two-tone rate suppression in auditory nerve fibers: Time course of
suppression and excitation in peri-stimulus time histograms
K.G. Hill and A.R. Palmer
Further evidence for tuning mechanisms of high dynamic order in
lower vertebrates
E.R. Lewis, M.G. Sneary and X. Yu
Observations on structure and function of the olivocochlear projections
in cat
M.C. Liberman
The sting is in the tail
V.F. Prijs, J. Keijzer, R. Schoonhoven and H. Versnel
5. Emissions
Can basilar membrane tuning be inferred from distortion measurement?
A.M. Brown and S.A. Gaskill
Changes in stimulus frequency otoacoustic emissions produced by
two-tone suppression and efferent stimulation in cats
J.J. Guinan, Jr.
Growth functions of tone burst evoked and distortion-product
otoacoustic emissions in humans
F .P. Harris and R. Probst
Sound induced changes in electrically evoked cochlear emissions
A.E. Hubbard, H.H. Nakajima, E.S. Olson and D.C. Mountain
Chaotic dynamics of otoacoustic emissions
D.H. Keefe, E.M. Burns, R. Ling and B. Laden
Observations on simultaneous SFOAE and DPOAE generation
and suppression
D.T. Kemp, D.N. Brass and M. Souter
Components of the 2f1-f2 distortion product in the earcanal of the
bobtailed lizard
G.A. Manley, C. Koppl and B.M. Johnstone
Active and passive ADP components in mammalian and avian ears
S.J. Norton and E.W. Rubel
A generalized Vander Pol-oscillator cochlea model
M.P.M.G. Van den Raadt and H. Duifhuis
Quantitative evaluation of limit-cycle oscillator models cf spontaneous
otoacoustic emissions
C.L. Talmadge, G.R. Long, W.J. Murphy and A. Tubis
Actively and passively generated acoustic distortion at 2f1-f2 in rabbits
M.L. Whitehead, B.L. Lonsbury-Martin and G.K. Martin
Effects of tympanic membrane modification on distortion product
otoacoustic emissions in the cat ear canal
M.L. Wiederhold
Spontaneous otoacoustic emission generators behave like coupled oscillators
H.P. Wit
VI
6. Macromechanical Measurements 269
Measurement of middle ear transfer function in cat, chinchilla and 270
guinea pig
L. Decory, R.B. Franke and A.L. Dancer
Helmholtz revisited: direct mechanical data suggest a physical model 278
for dynamic control of mapping frequency to place along the
cochlear partition
E.L. LePage
Measurements of basilar membrane tuning and distortion with laser 288
Doppler velocimetry
AL. Nuttall, D.F. Dolan and G. Avinash
In vivo measurement of basilar membrane stiffness 296
E.S. Olson and D.C. Mountain
Two-tone distortion products in the basilar membrane of the chinchilla 304
L. Robles, M.A. Ruggero and N.C. Rich
Systemic injection of furosemide alters the mechanical response to sound 314
of the basilar membrane
M.A. Ruggero and N.C. Rich
7. General Cochlear Models 323
Modeling the noise damaged cochlea 324
J.B. Allen
Wave propagation modes and boundary conditions for the 333
Ulfendahl-Flock-Khanna (UFK) preparation
E. de Boer
On dipoles and the radiating membrane 340
J.S.C. van Dijk
Approximate evaluation of cochlear model tuning from the wave 348
development graph
S.M. Novoselova
The fractal doubly stochastic Poisson point process as a model for the 354
cochlear neural spike train
M.C. Teich, R.G. Turcott and S.B. Lowen
The impedance of the organ of Corti 362
G. Zweig
8. Nonlinear Models 371
Implementation of a nonlinear wave-digital filter cochlear model 372
D H. Friedman
Nonlinear transmission line model can predict the statistical properties of 380
spontaneous otoacoustic emissions
M. Furst
Mathematical analysis of a nonlinear model for hybrid filtering in the cochlea 387
J.L. Goldstein
Automatic gain control in cochlear mechanics 395
R.F. Lyon
Non-linearity in a computational model of the response of the 403
basilar membrane
R. Meddis, MJ. Hewitt and T.M. Shackleton
Level dependence of the latency of cochlear transients 411
S.T. Neely
VII
Section 1
Hair Cell and Cilia
