The Mechanics and Biophysics of Hearing pp 387-394 | Cite as
Mathematical Analysis of a Nonlinear Model for Hybrid Filtering in the Cochlea
Abstract
It has been established over the past decade that intact outer hair cells (ORC) are responsible for the sensitive tips of cochlear tuning curves (reviews by Davis, 1983; Kim, 1986; Kiang et a!., 1986; Dallos, 1988; Hudspeth, 1989). The most common view is that the ORCs do not add a distinct filter system, but modify the passive hydromechanical response of the cochlea to provide a single enhanced system (Neely and Kim, 1983; Geisler, 1986; Zwicker, 1986). The hypothesis of two distinct filter systems, however, provides straightforward accounts (Goldstein, 1990) for strong suppression of CF responses by lower frequency stimuli (Abbas and Sachs, 1976; Duifhuis, 1980; Costalupes et al., 1987), and for simple-tone interference phenomena (Kiang and Moxon, 1972; Gifford and Guinan, 1983; Liberman and Kiang, 1984). Recent observations by Brundin et a!. (1989) of mechanical tuning by isolated OHCs support the view that the ORCs operate as distinct electromechanical filters. We arc developing a hybrid filter model that quantitatively represents the nonlinear mechanical response of the basilar membrane at each place in terms of two nonlinearly interacting bandpass nonlinearity (BPNL) filters (Goldstein, 1989, 1990). This work revives and provides a new perspective on the significance of earlier work in modeling cochlear nonlinear responses as BPNL signal processing (Goldstein, 1967; Engebretson and Eldredge, 1968; Schroeder, 1969; Pfeiffer, 1970; Sachs, 1975; Duifhuis, 1976, 1980; Johnstone, 1980; Geisler, 1985). Earlier questions on the physical basis of BPNL response characteristics are now answered by extensive experimental evidence that nonlinear mechanical response of the basilar membrane is responsible for cochlear frequency tuning and is the major source of extracochlear nonlinear phenomena (Rhode, 1971; Sellick et al., 1982; Patuzzi et al., 1984; Robles et al., 1986, 1989). Both analytic and computational methods are useful for developing the multiple-BPNL (MBPNL) model of basilar-membrane hybrid response. The computational method provides the detailed model responses required to establish the model’s ability to account for complex experimental data (Goldstein, 1990). The analytic method provides insight on the global properties of the model and guides the detailed studies (Duifhuis, 1976; Goldstein, 1989). In this paper we present a basic perturbation analysis of the MBPNL model, and highlight several issues.
Keywords
Outer Hair Cell Basilar Membrane Tuning Curve Small Signal Gain Combination TonePreview
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References
- Abbas, P.J. and Sachs, M.B. (1976) Two–tone suppression in auditory–nerve fibers: Extension of a stimulus response relationship. I. Acoust. Soc. Am. 59, 112–122.Google Scholar
- Bmndin, L., Flock, A. and Canlon, B. (1989) Sound induced motility of isolated outer hair cells is frequency specific. Nature 342, 814–816.Google Scholar
- Costalupes, J.A., Rich, N.C. and Ruggero, M.A. (1987) Effects of excitatory and nonexcitatory suppressor tones on two–tone rate suppression in auditory nerve fibers. Hear. Res. 26, 155–164.Google Scholar
- Dallos, P. (1988) Cochlear neurobiology: Some key experiments and concepts of the past two decades. In: Auditory Function (Eds: Edelman, G.M., Gall, W.E. and Cowan, W.M.) Wiley, NY, pp. 153–188.Google Scholar
- Davis, H. (1983) An active process in cochlear mechanics. Hear. Res. 9, 79–80.Google Scholar
- Duifhuis, H. (1976) Cochlear nonlinearity and second filter: Possible mechanism and implications. J. Acoust. Soc. Am. 59,408–423. Duifhuis, H. (1980) Level effects in psychophysical two–tone suppression. 1. Acoust. Soc. Am. 67, 914–927.Google Scholar
- Duifhuis, H. (1989) Power law nonlinearities: A review of some less familiar properties. In: Cochlear Mechanisms (Eds: Wilson, J.P. and Kemp, D.T.) Plenum Press, NY, pp. 395–401.Google Scholar
- Engebretson, A.M. and Eldredge, D.H. (1968) Model for the nonlinear characteristics of cochlear potentials. 1. Acoust. Soc. Am. 44, 548–554.Google Scholar
- Fahey, P.F. and Allen, J.B. (1985) Nonlinear phenomena as observed at the ear canal and at the auditory nerve. J. Acoust. Soc. Am. 77, 599–612.Google Scholar
- Geisler, C.D. (1985) Effects of a compressive nonlinearity in a cochlear model. J. Acoust. Soc. Am. 78, 257–260.Google Scholar
- Geisler, C.D. (1986) A model for the effect of outer hair cell motility on cochlear vibrations. Hear. Res. 24, 125–13.Google Scholar
- Gifford, M.L. and Guinan, U. (1983) Effects of crossed–olivocochlear–bundle stimulation on cat auditory nerve fiber responses to tones. 1. Acoust. Soc. Am. 74, 115–123.Google Scholar
- Goldstein, J.L. (1967) Auditory nonlinearity. 1. Acoust. Soc. Am. 41, 676–689.Google Scholar
- Goldstein, J.L. (1989) Updating cochlear driven modeJs of auditory perception: A new model for nonlinear auditory frequency analyzing filters. In: Working Models of Human Perception (Eds: EIscndoom, B. and Bouma, H.) Academic Press, London, pp. 19–57.Google Scholar
- Goldstein, J.L. (1990) Modeling rapid waveform compression on the basilar membrane as multiplebandpass. nonlinearity filtering. Hear. Res., in press. Goldstein, J.L. and Kiang, N.Y.S. (1968) Neural correlates of the aural combination tone 2f1–f2. Proc. IEEE 56, 981–992.Google Scholar
- Hudspeth, AJ. (1989) How the ear’s works work. Nature 341,397–404.Google Scholar
- Johnstone, J.R. (1980) The generation of combination tones. Hear. Res. 3, 253–256.Google Scholar
- Kiang, N.Y.S. (1984) Peripheral neural processing of auditory information. In: Handbook of Physiology.The Nervous System III (Ed: Darian-Smith. I.) The American Physiological Society. Bethesda, MD. pp. 639–674.Google Scholar
- Kiang, N.Y.S ., Moxon, E.C. and Levine. R.A. (1970) Auditory–nerve activity in cats with normal and abnormal cochlea. In: Sensorineural Hearing Loss (Eds: Wolstenholme. G.E.W. and Knight. J.) Churchill. London, pp. 714–730.Google Scholar
- Kiang, N.Y.S. and Moxon, E.C. (1972) Physiological considerations in artificial stimulation of the inner ear. Ann. Otol. Rhinol. Laryngol. 81. 714–730.Google Scholar
- Kiang, N.Y.S ., Liberman, M.C ., Sewell. W.F. and Guinan. 1.1. (1986) Single unit clues to cochlear mechanisms. Hear. Res. 22.171–182.Google Scholar
- Kim, D.,. (1986) A review of nonlinear and active cochlear models. In: Peripheral Auditory Mechanisms (Eds: Allen, J.B ., Hubbard. A ., Neely, S.T. and Tubis. A.) Springer. NY. pp. 239– 249.Google Scholar
- Liberman, M.C. and Kiang, N.Y.S. (1984) Single neuron labeling and chronic cochlear pathology. IV. Stereocilia damage md alterations in rate- and phase–level functions. Hear. Res. 16. 75–90.Google Scholar
- Neely, S.T. and Kim, D.,. (1983) An active cochlear model showing sharp tuning and high sensitivity. Hear. Res. 9.123–130.Google Scholar
- Patuzzi, R ., Sellick, P.M. and Johnstone, B.M. (1984) The modulation of the sensitivity of the mammalian cochlea by low frequency tones III. Basilar membrane motion. Hear. Res. 13. 19– 27.Google Scholar
- Pfeiffer, R.R. (1970) A model for two–tone inhibition of single cochlear–nerve fibers. J. Acoust. Soc. Am. 48, 1373–1378.Google Scholar
- Rhode, W.S. (1971) Observations of the vibrations of the basilar membrane in squirrel monkeys using the Mossbauer technique. J. Acoust. Soc. Am. 49. 1218–1231.Google Scholar
- Robles, L., Ruggero, M.A. and Rich, N.C. (1986) Basilar membrane mechanics at the base of the chinchilla cochlea. I. Input. output functions, tuning curves and response phases. J. Acoust. Soc. Am. 80. 1364–1374.Google Scholar
- Robles, L.. Ruggero, M.A. and Rich, N.C. (1989) Nonlinear interactions in the mechanical response of the cochlea to two-tone stimuli. In: Cochlear Mechanisms (Eds: Wilson. J.P. and Kemp. D.T.) Plenum, NY. pp. 369–375. Ryan. A. and Dallos, P. (1975) Effect of absence of outer hair cells on behavioral auditory threshold. Nature 253, 44–46.Google Scholar
- Sachs, R.M. (1975) Perception of 2f1-f2o An Auditory Distortion Product. Ph.D. Dissertation. Dept. of Audiology. Northwestern University, Evanston. lL.Google Scholar
- Sachs, M.B. and Kiang, N.Y.S. (1968) Two–tone inhibition in auditory-nerve fibers. J. Acoust. Soc. Am. 43, 1120–1128.Google Scholar
- Schmiedt, R.A. (1982) Boundaries of two-tone rate suppression of cochlear–nerve activity. Hear. Res. 7, 335–351.Google Scholar
- Schroeder, M.R. (1969) Relation between critical bands in hearing and the phase characteristics of cubic difference tones. 1. Acoust. Soc. Am. 46, 1488–1492.Google Scholar
- Sellick, P.M. and Russell, I. (1979) Two-tone suppression in cochlear hair cells. Hear. Res. 1, 227–236.Google Scholar
- Sellick, P.M., Patuzzi, R. and Johnstone, B.M. (1982) Measurement of basilar membrane motion in the Guinea pig using the Mossbauer technique. J. Acoust. Soc. Am. 72, 131–141.Google Scholar
- Smoorenburg, G.F. (1972) Combination tones and their origin. J. Acoust. Soc. Am. 52, 615–632.Google Scholar
- Zwicker, E. (1986) A hardware cochlear nonlinear preprocessing model with active feedback. J. Acoust. Soc. Am. 80, 146–153.Google Scholar