全部 标题 作者
关键词 摘要

OALib Journal期刊
ISSN: 2333-9721
费用:99美元

查看量下载量

相关文章

更多...

Quantitative Reappraisal of the Helmholtz-Guyton Resonance Theory of Frequency Tuning in the Cochlea

DOI: 10.1155/2011/435135

Full-Text   Cite this paper   Add to My Lib

Abstract:

To explore the fundamental biomechanics of sound frequency transduction in the cochlea, a two-dimensional analytical model of the basilar membrane was constructed from first principles. Quantitative analysis showed that axial forces along the membrane are negligible, condensing the problem to a set of ordered one-dimensional models in the radial dimension, for which all parameters can be specified from experimental data. Solutions of the radial models for asymmetrical boundary conditions produce realistic deformation patterns. The resulting second-order differential equations, based on the original concepts of Helmholtz and Guyton, and including viscoelastic restoring forces, predict a frequency map and amplitudes of deflections that are consistent with classical observations. They also predict the effects of an observation hole drilled in the surrounding bone, the effects of curvature of the cochlear spiral, as well as apparent traveling waves under a variety of experimental conditions. A quantitative rendition of the classical Helmholtz-Guyton model captures the essence of cochlear mechanics and unifies the competing resonance and traveling wave theories. 1. Introduction New data have created an opportunity to revisit central problem of audition: the function of the cochlea as a real-time frequency analyzer. This intellectual puzzle has attracted a large number of thinkers over the years, who have conducted extensive research in cochlear modeling [1–7]. Controversy continues, however, regarding which features of the various models are essential [8–11]. Most popular today are theories describing traveling waves that propagate longitudinally along the basilar membrane. However, criticisms of traveling wave models include suggestions that the traveling wave focusing is not sufficiently sharp and that computed peak displacements of the basilar membrane are on the order of one nanometer or less, perhaps too small to effectively stimulate hair cells [6, 12]. One path forward is to create increasingly detailed three-dimensional computational models [3, 4, 13]. The Cal Tech model of the cochlea, for example [3], uses the immersed boundary method to calculate the fluid-structure interactions at the San Diego Supercomputing Center. Six surfaces of immersed material in the cochlea are partitioned into 25 computational grids comprising 750,000 points. There is a fluid grid of 223 points [3]. In one report, the simulation of two milliseconds of time required approximately 18 hours of dedicated computation on a supercomputer [4]. The present paper takes a much

References

[1]  J. B. Allen, “Two dimensional cochlear fluid model: new results,” Journal of the Acoustical Society of America, vol. 61, no. 1, pp. 110–119, 1977.
[2]  S. J. Elliott, E. M. Ku, and B. Lineton, “A state space model for cochlear mechanics,” Journal of the Acoustical Society of America, vol. 122, no. 5, pp. 2759–2771, 2007.
[3]  “A Comprehensive Three-Dimensional Model of the Cochlea,” http://pcbunn.cacr.caltech.edu/Cochlea/jcp_paper.pdf.
[4]  “Detailed Simulation of the Cochlea: Recent Progress Using Large Shared Memory Parallel Computers,” http://pcbunn.cacr.caltech.edu/Cochlea.
[5]  F. Mammano and R. Nobili, “Biophysics of the cochlea: linear approximation,” Journal of the Acoustical Society of America, vol. 93, no. 6, pp. 3320–3332, 1993.
[6]  L. Robles and M. A. Ruggero, “Mechanics of the mammalian cochlea,” Physiological Reviews, vol. 81, no. 3, pp. 1305–1352, 2001.
[7]  J. Zwislocki, “Theory of the acoustical action of the cochlea,” Journal of the Acoustical Society of America, vol. 22, pp. 778–784, 1950.
[8]  G. V. Bekesy, “Current status of theories of hearing,” Science, vol. 123, no. 3201, pp. 779–783, 1956.
[9]  A. Dancer, “Experimental look at cochlear mechanics,” Audiology, vol. 31, no. 6, pp. 301–312, 1992.
[10]  M. A. Ruggero, “Cochlear delays and traveling waves: comments on “experimental look at cochlear mechanics”,” Audiology, vol. 33, no. 3, pp. 131–142, 1994.
[11]  A. Bell, “Hearing: travelling wave or resonance?” PLoS Biology, vol. 2, no. 10, e337, 2004.
[12]  W. S. Rhode, “Observations of the vibration of the basilar membrane in squirrel monkeys using the Mossbauer technique,” Journal of the Acoustical Society of America, vol. 49, no. 4, pp. 1218–1231, 1971.
[13]  P. J. Kolston and J. F. Ashmore, “Finite element micromechanical modeling of the cochlea in three dimensions,” Journal of the Acoustical Society of America, vol. 99, no. 1, pp. 455–467, 1996.
[14]  H. Helmholtz, On the Sensations of Tone as a Physiological Basis for the Theory of Music, Thomas, Green, and Company, London, UK, 3rd edition, 1895.
[15]  A. Guyton, Textbook of Medical Physiology, W. B. Saunders, London, UK, 1st edition, 1956.
[16]  A. Guyton, Function of the Human Body, W. B. Saunders, Philadelphia. Pa, USA, 1959.
[17]  L. M. Cabezudo, “The ultrastructure of the basilar membrane in the cat,” Acta Oto-Laryngologica, vol. 86, no. 3-4, pp. 160–175, 1978.
[18]  S. Liu and R. D. White, “Orthotropic material properties of the gerbil basilar membrane,” Journal of the Acoustical Society of America, vol. 123, no. 4, pp. 2160–2171, 2008.
[19]  A. Kassimali, Matrix Analysis of Structures, Brooks/Cole Publishing Company, Pacific Grove, Calif, USA, 1999.
[20]  A. Hubbard, “A traveling-wave amplifier model of the cochlea,” Science, vol. 259, no. 5091, pp. 68–71, 1993.
[21]  M. Homer, A. Champneys, G. Hunt, and N. Cooper, “Mathematical modeling of the radial profile of basilar membrane vibrations in the inner ear,” Journal of the Acoustical Society of America, vol. 116, no. 2, pp. 1025–1034, 2004.
[22]  G. V. Bekesy, Experiments in Hearing, McGraw Hill, New York, NY, USA, 1960.
[23]  J. Keen, “A note on the length of the basilar membrane in man and and in various animals,” Journal of Anatomy, vol. 74, pp. 524–527, 1940.
[24]  J. D. Miller, “Sex differences in the length of the organ of Corti in humans,” Journal of the Acoustical Society of America, vol. 121, no. 4, pp. EL151–EL155, 2007.
[25]  M. di Fiore, Atlas of Human Histology, Lea & Febiger, Philadelphia, Pa, USA, 5th edition, 1981.
[26]  R. C. Naidu and D. C. Mountain, “Basilar membrane tension calculations for the gerbil cochlea,” Journal of the Acoustical Society of America, vol. 121, no. 2, pp. 994–1002, 2007.
[27]  H. Wada, M. Sugawara, T. Kobayashi, K. Hozawa, and T. Takasaka, “Measurement of guinea pig basilar membrane using computer-aided three- dimensional reconstruction system,” Hearing Research, vol. 120, no. 1-2, pp. 1–6, 1998.
[28]  D. R. Lide, Ed., CRC Handbook of Chemistry and Physics, CRC Press, Boca Raton, Fla, USA, 76th edition, 1995.
[29]  S. Puria, W. T. Peake, and J. J. Rosowski, “Sound-pressure measurements in the cochlear vestibule of human-cadaver ears,” Journal of the Acoustical Society of America, vol. 101, no. 5, pp. 2754–2770, 1997.
[30]  V. Summers, E. De Boer, and A. L. Nuttal, “Basilar-membrane responses to multicomponent (Schroeder-phase) signals: understanding intensity effects,” Journal of the Acoustical Society of America, vol. 114, no. 1, pp. 294–306, 2003.
[31]  A. Recio and W. S. Rhode, “Basilar membrane responses to broadband stimuli,” Journal of the Acoustical Society of America, vol. 108, no. 5 I, pp. 2281–2298, 2000.
[32]  A. Recio, N. C. Rich, S. S. Narayan, and M. A. Ruggero, “Basilar-membrane responses to clicks at the base of the chinchilla cochlea,” Journal of the Acoustical Society of America, vol. 103, no. 4, pp. 1972–1989, 1998.
[33]  T. Lin and J. J. Guinan Jr., “Time-frequency analysis of auditory-nerve-fiber and basilar-membrane click responses reveal glide irregularities and non-characteristic-frequency skirts,” Journal of the Acoustical Society of America, vol. 116, no. 1, pp. 405–416, 2004.
[34]  D. D. Greenwood, “A cochlear frequency-position function for several species—29 years later,” Journal of the Acoustical Society of America, vol. 87, no. 6, pp. 2592–2605, 1990.
[35]  P. J. Kolston, “Comparing in vitro, in situ, and in vivo experimental data in a three-dimensional model of mammalian cochlear mechanics,” Proceedings of the National Academy of Sciences of the United States of America, vol. 96, no. 7, pp. 3676–3681, 1999.
[36]  L. A. Geddes and L. E. Baker, Principles of Applied Biomedial Instrumentation, Wiley-Interscience, New York, NY, USA, 3rd edition, 1989.
[37]  G. V. Bekesy, “The variation in phase along the basilar membrane with sinusoidal vibrations,” Journal of the Acoustical Society of America, vol. 19, pp. 452–460, 1947.
[38]  A. Guyton, Function of the Human Body, W. B. Saunders, Philadelphia, Pa, USA, 1964.
[39]  G. V. Bekesy, “Current status of theories of hearing,” Science, vol. 123, no. 3201, pp. 779–783, 1956.
[40]  G. V. Bekesy, “On the resonance curve and the decay period at various points on the cochlear partition,” Journal of the Acoustical Society of America, vol. 21, pp. 245–254, 1949.
[41]  D. O. Kim, C. E. Molnar, and R. R. Pfeiffer, “A system of nonlinear differential equations modeling basilar membrane motion,” Journal of the Acoustical Society of America, vol. 54, no. 6, pp. 1517–1529, 1973.
[42]  R. V. Hingorani, P. P. Provenzano, R. S. Lakes, A. Escarcega, and R. Vanderby Jr., “Nonlinear viscoelasticity in rabbit medial collateral ligament,” Annals of Biomedical Engineering, vol. 32, no. 2, pp. 306–312, 2004.
[43]  S. Timoshenko and S. Woinowsky-Krieger, Theory of Plates and Shells, McGraw-Hill, New York, NY, USA, 2nd edition, 1959.
[44]  D. Manoussaki, R. S. Chadwick, D. R. Ketten, J. Arruda, E. K. Dimitriadis, and J. T. O'Malley, “The influence of cochlear shape on low-frequency hearing,” Proceedings of the National Academy of Sciences of the United States of America, vol. 105, no. 16, pp. 6162–6166, 2008.
[45]  H. Cai, D. Manoussaki, and R. Chadwick, “Effects of coiling on the micromechanics of the mammalian cochlea,” Journal of the Royal Society Interface, vol. 2, no. 4, pp. 341–348, 2005.

Full-Text

Contact Us

service@oalib.com

QQ:3279437679

WhatsApp +8615387084133