Biomorphic Hopf-Amplifier

236 Pages·2008·16.43 MB·English

ETH Library
A nonlinear biomorphic Hopf-
amplifier model of the cochlea
Doctoral Thesis
Author(s):
Kern, Albert
Publication date:
2003
Permanent link:
https://doi.org/10.3929/ethz-a-004572861
Rights / license:
In Copyright - Non-Commercial Use Permitted
This page was generated automatically upon download from the ETH Zurich Research Collection.
For more information, please consult the Terms of use.
Diss. ETH No. 14915
A Nonlinear Biomorphic Hopf-Amplifier
Model of the Cochlea
A dissertation submitted to the
SWISS FEDERAL INSTITUTE OF TECHNOLOGY ZURICH
for the degree of
Doctor of Natural Sciences
presented by
Albert Kern
Dipl. Phys. ETH
born 07.09. 1971
citizen of Buchberg, Schaffhausen
accepted on the recommendation of
PD Dr. Ruedi Stoop, examiner
Prof. Dr. Rodney Douglas, co-examiner
Prof. Dr. Daniel Robert, co-examiner
Dr. Stefan Launer, co-examiner
2003
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Acknowledgements
I am profoundly indebted to Ruedi Stoop, my thesis advisor. He provided every
support I needed in order to accomplish this work. He awoke my interest in the field of
auditory research and, in particular, in cochlear modeling. Without his suggestions and
the innumerable discussions we had in our group, this thesis would not have been possible.
I am particularly grateful for his open mind towards new ideas, and his frank and honest
critiques. Whenever I had any problem, he was always willing to help me. I am also
grateful to the members of our research group, in particular to Jan-Jan van der Vyver
and Markus Christen. It was a great pleasure, and fun, to work with them, to organize
meetings and to - occasionally - have some drinks.
Stefan Launer and Daniel Robert deserve thanks for their advice and for many fruitful
discussions, which helped me to get acquainted with the field of cochlear mechanics. In
particular, from Stefan Launer I received many useful hints to literature.
I would also like to thank the directors of the Institute of Neuroinformatics, Rodney
Douglas and Kevan Martin, as they provided the environment in which I was able to do
research and complete my thesis.
My girlfriend, Marlies Gautschi, deserves special thanks for her support, especially in
the time while I was writing the thesis.
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Contents
Summary xiii
Zusammenfassung xv
1 Introduction 1
1.1 Fundamental Aspects of Hearing 1
1.2 Towards the Understanding of the Active Amplification Procès 3
1.3 Evolution and the Scene-Segmentation Problem 6
2 The Biophysics of the Perception of Sound 9
2.1 The Mammalian Cochlea 9
2.1.1 Strategies of Extending the Frequency Range 9
2.1.2 Structure of the Mammalian Cochlea 10
2.1.3 Orientation along the Cochlear Canal 13
2.2 Transmission of Acoustic Power to the Cochlear Fluid:
Matching of Impedances 14
2.2.1 Acoustic Impedances 15
2.2.2 Reflection and Transmission of Acoustic Waves 16
2.2.3 Impedance Matching by the Middle Ear 18
2.3 Traveling Waves in the Cochlea 20
2.3.1 Von Békésy's Observations 20
2.3.2 Driving of the Cochlear Partition 22
2.3.3 Properties of the Basilar Membrane 24
2.3.4 Emergence of Traveling Waves 25
2.4 The Organ of Corti 25
2.4.1 Basic Structure of the Organ of Corti 25
2.4.2 Inner and Outer Hair Cells 27
2.4.3 Tectorial Membrane 31
2.5 Active Amplification by Outer Hair Cells 31
2.5.1 Basilar Membrane Response of the Living Cochlea 31
2.5.2 Outer Hair Cell Motility 35
2.5.3 Micromechanical Motions of the Organ of Corti 36
2.5.4 Limit-Cycle Oscillations in Hair Cells 38
2.6 Nonlinear Phenomena 40
2.6.1 Compressive Nonlinearity of the Basilar Membrane Response 40
. ...
2.6.2 Suppression and Upward Spread of Masking 41
2.6.3 Combination-Tone Generation 42
2.7 Otoacoustic Emissions 43
2.7.1 Spontaneous Otoacoustic Emissions (SOAE) 43
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2.7.2 Transiently Evoked Otoacoustic Emissions (TEOAE) 43
2.7.3 Distortion Product Otoacoustic Emissions (DPOAE) 44
2.7.4 Electrically Evoked Otoacoustic Emissions (EEOAE) 44
3 A Short History of Cochlear Modeling 45
3.1 Classical Macromechanical Models 46
3.1.1 Electrical Transmission Line Analogy 48
3.1.2 One-Dimensional Model 51
3.1.3 Inadequacies of the One-Dimensional Model 54
3.1.4 Two-Dimensional Model 54
3.1.5 Three-Dimensional Model 56
3.1.6 Dissipation in the Cochlea 56
3.1.7 Active Macroscopic Models 58
3.2 Micromechanical Models 58
3.2.1 A Second Degree of Freedom 58
3.2.2 Active Micromechanical Models 58
3.3 Multimode Models 59
3.3.1 Traveling-Wave Amplifier Model 59
3.3.2 Feedforward-Coupling between Outer Hair Cells 60
3.4 New Directions in Cochlear Modeling 61
4 A Biomorphic Active Nonlinear Model of the Cochlea 63
4.1 Reasons for a New Cochlear Model 63
4.2 The Hopf Hypothesis 64
4.2.1 Hopf System as a Nonlinear Amplifier 64
4.2.2 Otoacoustic Emissions and Noise 67
4.2.3 Pitch Perception 68
4.3 Towards a Novel Cochlea Model 68
4.3.1 First Attempt: Arrays of Coupled Oscillators 68
4.3.2 The Coupling Problem 69
4.3.3 Energy-Based Approach 70
4.4 Coupling to the Hydrodynamic Wave - Elements ofCochlear Hydrodynamics 70
4.4.1 Two-Dimensional Surface Wave Analogy 70
4.4.2 Hydrodynamic Theory of Surface Waves 73
4.4.3 Dispersion Relation: Emergence of the Tonotopic Map 80
4.4.4 Energy Density in the Cochlea 85
4.5 Hydrodynamic Attenuation in the Cochlea 87
4.5.1 Attenuation Effects 87
4.5.2 Implications of Attenuation beneath a Vibrating Surface 89
4.5.3 Consequences for Cochlear Modeling 92
4.6 Passive Model 95
4.6.1 Amplitudes 95
4.6.2 Passive Response 96
4.6.3 Comparison with Experiments 99
4.6.4 Impedance of the Cochlea 101
4.6.5 Initial Conditions 106
4.7 Coupling to Active Amplifiers: Basic Hopf-Type Cochlea Model 108
4.7.1 A Strategy Towards Active Amplification 109
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4.7.2 Mathematical Formulation of the Active Mechanism Ill
4.7.3 Tuning of the Active Amplifier 115
4.7.4 Active Place Response 120
4.7.5 Active Frequency Response 122
4.7.6 Limitations of the Basic Hopf-Type Model 125
4.8 Longitudinal Coupling along the Basilar Membran 127
4.9 Passive Longitudinal Coupling: Surface Tension 127
4.9.1 Tension on a Free Surface 128
4.9.2 Dispersion Relation 129
4.9.3 Surface Tension on the Basilar Membrane 130
4.9.4 Potential Energy 135
4.9.5 Passive Response 136
4.9.6 Active Response 138
4.9.7 Limitations and Potential of Passive Longitudinal Coupling 141
4.10 Coupling between the Active Elements 142
4.10.1 Feedforward Coupling 142
4.10.2 Second Mode of Energy Propagation 144
4.10.3 Effects of the Second Mode 148
4.10.4 Optimal Model Responses with Feedforward Coupling 151
4.11 Active Amplification at Different Frequencies 155
4.11.1 Second Tonotopic Map 156
4.11.2 Tonotopic Tuning of Active Amplification 160
4.11.3 Approximations to the Tonotopic Variation of Model Parameters 165
. .
5 Modeling Meets Biophysics of Hair Cells 171
5.1 Physiological Justification of the Hopf Model 171
5.1.1 Active Amplification in Hair Cells 171
5.1.2 "True" Active Amplification or Negative Damping? 173
5.1.3 Compressive Nonlinearity 175
5.2 Phase-Locking and Entrainment: Stochastic Resonance and
Benefits of Noise 176
5.2.1 Entrainment and Phase-Locking of Hair Bundles 178
5.2.2 Stochastic Resonance 179
5.3 Conclusions 181
5.3.1 Hopf-Type Amplification in Mammalian Cochleae 181
5.3.2 New Frontiers in Cochlear Modeling 182
A Properties of the Wave Vector k(x,u) and the Group Velocity vg(x,u>) 185
A.l Points of Hydrodynamic Equivalence 185
A.2 Derivatives of vg{x,üo) 190
A.3 The Short-Wave Approximation 197
B Hardware Implementation of Cochlear Models 201
B.l Digital Signal Processing (DSP) Implementations 201
B.2 The Analog Silicon Cochlea 202
List of Publications 217
Curriculum Vitae 219
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List of Figures
2.1 Anatomical structure of the middle and inner ear 10
2.2 Section through the guinea pig cochlea 11
2.3 Section of the cochlear canal 12
2.4 Coordinate systems in the cochlea 14
2.5 Reflection and transmission of sound waves 17
2.6 Middle-ear transduction apparatus 19
2.7 Middle-ear transfer function 20
2.8 Von Békésy's measurements of traveling waves (1) 21
2.9 Von Békésy's measurements of traveling waves (2) 22
2.10 Generation of traveling waves 23
2.11 Internal structure of the organ of Corti (radial direction) 26
2.12 Longitudinal structure of the organ of Corti 27
2.13 Excitation of outer hair cells 28
2.14 Hair cell stereocilia 29
2.15 Tectorial membrane 30
2.16 Basilar membrane response near the base of the chinchilla cochlea 32
2.17 Basal frequency tuning curves 32
2.18 Basilar membrane input-output function 33
2.19 Response of the chinchilla cochlear partition near the apex 34
2.20 Apical frequency tuning curves 34
2.21 Length change of an isolated OHC 35
2.22 Potential deformation of the organ of Corti upon OHC contraction 37
2.23 Models for tip-link tension adaptation 39
2.24 Two-tone suppression on the basilar membrane 41
3.1 Simplifications for the classical model of the cochlea 47
3.2 Electrical analogs for hydrodynamic calculations 48
3.3 Electrical transmission line models (ID and 2D) 50
4.1 Stationary solution of the driven Hopf system 65
4.2 Surface wave analogy 71
4.3 Coordinate system employed for the surface wave treatment 74
4.4 Wave number and group velocity 83
4.5 Internal dissipation and dissipation caused by frictiononthevibratingbasi¬
lar membrane 94
4.6 Attenuation of the passive basilar membrane amplitude 97
4.7 Response shapes for different dissipation schemes 98
4.8 Passive response of the basilar membrane 99
4.9 Modulus of the basilar membrane impedance near the base 103
4.10 Input impedance of the cochlea, Zc(u) 105
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