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Paradoxical waves and active mechanism in the cochlea. (English) Zbl 1333.76097

Summary: This paper is dedicated to Peter Lax. We recall happily Lax’s interest in the cochlea (and in all things biomedical), culminating in his magical solution of one version of the cochlea problem, as detailed herein. The cochlea is a remarkable organ (more remarkable the more we learn about it) that separates sounds into their frequency components. Two features of the cochlea are the focus of this work. One is the extreme insensitivity of the wave motion that occurs in the cochlea to the manner in which the cochlea is stimulated, so much so that even the direction of wave propagation is independent of the location of the source of the incident sound. The other is that the cochlea is an active system, a distributed amplifier that pumps energy into the cochlear wave as it propagates. Remarkably, this amplification not only boosts the signal but also improves the frequency resolution of the cochlea. The active mechanism is modeled here by a negative damping term in the equations of motion, and the whole system is stable as a result of fluid viscosity despite the negative damping.

MSC:

76Z05 Physiological flows
92C35 Physiological flow
92C10 Biomechanics
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References:

[1] R. P. Beyer, A computational model of the cochlea using the immersed boundary method,, J. Computational Physics, 98, 145 (1992) · Zbl 0744.76128
[2] P. J. Dallos, The active cochlea,, J. Neuroscience, 12, 4575 (1992)
[3] E. Givelberg, A comprehensive three-dimensional model of the cochlea,, J. Computational Physics, 191, 377 (2003) · Zbl 1024.92005
[4] A. J. Hudspeth, Integrating the active process of hair cells with cochlear function,, Nature Reviews Neuroscience, 15, 600 (2014)
[5] E. Isaacson, <em>A Numerical Method for a Finite-Depth, Two-Dimensional Model of the Inner Ear</em>,, Ph.D thesis (1979)
[6] R. J. LeVeque, Asymptotic analysis of a viscous cochlear model,, J. Acoustical Society of America, 77, 2107 (1985)
[7] R. J. LeVeque, Solution of a two-dimensional cochlea model using transform techniques,, SIAM J. Appl. Math., 45, 450 (1985) · Zbl 0576.76130
[8] R. J. LeVeque, Solution of a two-dimensional cochlea model with fluid viscosity,, SIAM J. Appl. Math., 48, 191 (1988) · Zbl 0647.92011
[9] C. S. Peskin, Flow patterns around heart valves: A numerical method,, J. Computational Physics, 10, 252 (1972) · Zbl 0244.92002
[10] C. S. Peskin, Lectures on Mathematical Aspects of Physiology (II) The Inner Ear,, in Mathematical Aspects of Physiology (eds. F.C. Hoppensteadt), 38 (1981) · Zbl 0461.92004
[11] C. S. Peskin, The immersed boundary method,, Acta Numerica, 11, 479 (2002) · Zbl 1123.74309
[12] J. J. Stoker, <em>Water Waves</em>,, Interscience Publishers Inc (1957) · Zbl 0078.40805
[13] G. von Bekesy, <em>Experiments in Hearing</em>,, Robert E. Krieger Publishing Company (1960)
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