Abstract
A nonlinear model of a cross section of the cochlea is considered in the absence of cochlear fluids. The cochlear partition is modeled with two long thin plates connected with a row of springs. This system of linked resonators is described in terms of systems with multiple degrees of freedom. The relationship between normal and partial eigenfrequencies is established, and the resonance phenomena are considered.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
H. L. F. Helmholtz,On the Sensation of Tone, Dover, New York (1954) (republication of the 1885 edition).
S. M. Khanna and G. B. Leonard, “Basilar membrane tuning in the cat cochlea,”Science,215, 305–306 (1982).
P. M. Sellick, R. Patuzzi, and B. M. Johnstone, “Measurements of basilar membrane motion in the guinea pig using the Mössbauer technique,”J. Acoust. Soc. Am.,72, 131–141 (1982).
D. T. Kemp, “Stimulated acoustic emission from within the human auditory system,”J. Acoust. Soc. Am.,64, 1386–1391 (1978).
D. T. Kemp and A. M. Brown, “Wideband analysis of otoacoustic intermodulation,” in:Peripheral Auditory Mechanisms (J. B. Allen, J. L. Hall, A. Hubbard, S. T. Neely, and A. Tubis, eds.), Springer-Verlag, Berlin (1985), pp. 306–313.
W. E. Brownell, C. R. Bader, D. Bertrand, and Y. de Ribaupierre, “Evoked mechanical responses of isolated cochlear outer hair cells,”Science,227, 194–196 (1985).
D. H. Jen and C. R. Steele, “Electrokinetic model of cochlear hair cell motility,”J. Acoust. Soc. Am.,85 (2), 1667–1678 (1987).
W. E. Brownell, W. E. Shehata, and J. B. Imredy, “Slow electrically and chemically evoked volume changes in guinea pig outer hair cells,” in:Biomechanics of Active Movement and Deformation of Cells (N. Akkas, ed.), Springer-Verlag, New York (1989), pp. 493–498.
E. de Boer, “No sharpening? A challenge for cochlear mechanics,”J. Acoust. Soc. Am.,73, 567–573 (1983).
E. L. LePage, G. Reuter, S. Hong, and H. P. Zenner, “Summating baseline shifts and mechanical adaptation in a guinea pig cochlear explant shown with two optical displacement-sensing techniques,” in:Biophysics of Hair Cell Sensory Systems (H. Duifhuis, J. W. Horst, P. van Dijk, and S. M. Netten, eds.), World Scientific, Singapore (1993), pp. 240–248.
S. M. Novoselova, “Modes of the tectorial membrane, transversal eigenfunctions, and the origin of the outer hair cell oscillations,”Zap. Nauchn. Semin. POMI,218, 138–148 (1994).
V. M. Babich and S. M. Novoselova, “On vibrations of the basilar membrane in the mammalian cochlea,”Zap. Nauchn. Semin. LOMI,89, 54–62 (1979).
S. M. Novoselova, “A possibility of sharp tuning in a linear transversely inhomogeneous cochlear model,”Hear. Res.,41 (2), 125–136 (1989); Errata:Hear. Res.,46 (1/2), 179–180 (1990).
S. M. Novoselova, “Transversally inhomogeneous sharply tuned linear cochlear model,”Zap. Nauchn. Semin. POMI,210, 213–240 (1993).
A. Kronester-Frei, “Ultrastructure of the different zones of the tectorial membrane,”Cell Tiss. Res.,193, 11–23 (1978).
L. Brundin, A. Flock, and B. Canlon, “Tuned motile responses of isolated cochlear outer hair cells,”Acta Oto-Laryngol.,467, 229–234 (1989).
L. Brundin and I. Russel, “Sound induced movements and frequency tuning in outer hair cells isolated from the guinea pig cochlea,” in:Biophysics of Hair Cell Sensory Systems (H. Duifhuis, J. W. Horst, P. van Dijk, and S. M. van Netten, eds.), World Scientific, Singapore (1993), pp. 182–191.
M. C. Teich, C. Heneghan, S. M. Khanna, A. Flock, L. Brundin, and M. Ulfendahl, “Analysis of dynamical motion of sensory cells in the organ of Corti using the spectrogram,” in:Biophysics of Hair Cell Sensory Systems (H. Duifhuis, J. W. Horst, P. van Dijk, and S. M. van Netten, eds.), World Scientific, Singapore (1993), pp. 272–279.
Additional information
Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 239, 1997, pp. 197–210.
The author is grateful to Profs. V. M. Babich and E. de Boer for fruitful discussions and important comments. This work was supported by the Russian Foundation for Basic Research under grant 93-011-16148.
Rights and permissions
About this article
Cite this article
Novoselova, S.M. A system of linked resonators in the cochlea. J Math Sci 96, 3407–3414 (1999). https://doi.org/10.1007/BF02172818
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02172818