Abstract
We have developed a numerical solution method for one-dimensional cochlea models in the time domain. The method has particularly been designed for models with a cochlear partition having nonlinear and active mechanical properties. Our starting point is the partial differential equation describing the response of the basilar membrane to stapes movements. Using Galerkin’s principle, we reduce this equation to a system of ordinary differential equations in the time variable. The remaining initial value problem is solved by means of an explicit fourth order Runge-Kutta scheme with a variable-step routine.
The calculations show that the response of an active, nonlinear cochlea model is very much contingent on the solution method. Approaches that exclude or suppress reflection phenomena must be considered inappropriate.
The results obtained so far suggest that nonlinear and active modelling of cochlear mechanics should comply with the following conditions in order to be consistent with experimental data:
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( i)
The active and nonlinear properties must be tightly linked,
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( ii)
Omission of these properties must yield the classical description of cochlear macromechanics,
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(iii)
The active behaviour of the partition must be localized in a small longitudinal region of the cochlea.
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References
Boer, E. de (1983a). No sharpening? A challenge for cochlear mechanics, J. Acoust. Soc. Am. 73, 567–573.
Boer, E. de (1983b). On active and passive cochlear models — Towards a generalized analysis. J. Acoust. Soc. Am. 73, 574–576.
Borsboom, M.J.A. (1979). Linear and nonlinear one-dimensional cochlear models, Eng. D. thesis, Dept. of Mathematics and Informatics, Delft University of Technology.
Hall, J.L. (1974). Two-tone distortion products in a nonlinear model of the basilar membrane, J. Acoust. Soc. Am. 56, 1818–1828.
Kemp, D.T. (1978). Stimulated acoustic emissions from within the human auditory system, J. Acoust. Soc. Am. 64, 1386–1391.
Khanna, S.M. and Leonard, D.G.B. (1982). Basilar membrane tuning in the cat cochlea, Science 215, 305–306.
Kim, D.O., Neely, S.T., Molnar, C.E., and Matthews, J.W. (1980). An active cochlear model with negative damping in the partition: Comparison with Rhode’s ante-and postmortem observations. In: Psychophysical, physiological and behavioural studies in hearing. G. van den Brink and F.A. Bilsen (eds.), Delft Univ. Press, 7–15.
Neely, S.T. (1981). Fourth order partition mechanics for a two-dimensional cochlear model. Doctoral dissertation, Washington Univ., St. Louis.
Neely, S.T. and Kim, D.O. (1983). An active cochlear model showing sharp tuning and high sensitivity. Hearing Res. 9, 123–130.
Netten, S.M. van (1982). Een actief, niet-lineair cochlea model (in Dutch), M. Sc. thesis, Dept. of Biophysics, Univ. of Groningen.
Netten, S.M. van and Duifhuis, H. (1983). Modelling an active nonlinear cochlea. In: Proc. Mechanics of Hearing, E. de Boer and M.A. Viergever (eds.), Delft University Press/Martinus Nijhoff Publishers, pp. 143–151.
Rhode, W.S. (1971). Observations of the vibration of the basilar membrane in squirrel monkeys using the Mössbauer technique, J. Acoust. Soc. Am. 49, 1218–1231.
Rhode, W.S. (1978). Some observations on cochlear mechanics, J. Acoust. Soc. Am. 64, 158–176.
Sellick, P.M., Patuzzi, R., and Johnstone, B.M. (1982). Measurement of basilar membrane motion in guinea pig using the Mössbauer technique, J. Acoust. Soc. Am. 72, 131–141.
Viergever, M.A. (1980). Mechanics of the inner ear — a mathematical approach. Delft University Press.
Viergever, M.A. and Diependaal, R.J. (1983). Simulataneous amplitude and phase match of cochlear model calculations and basilar membrane vibration data. In: Proc. Mechanics of Hearing, E. de Boer and M.A. Viergever (eds.), Delft University Press/Martinus Nijhoff Publishers, pp. 53–61.
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© 1983 Delft University Press, The Netherlands
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Diependaal, R.J., Viergever, M.A. (1983). Nonlinear and Active Modelling of Cochlear Mechanics: A Precarious Affair. In: de Boer, E., Viergever, M.A. (eds) Mechanics of Hearing. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-6911-7_18
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DOI: https://doi.org/10.1007/978-94-009-6911-7_18
Publisher Name: Springer, Dordrecht
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