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.