Several deficiencies affecting previous "box" models of the cochlea are overcome in this paper. Both mechanical and hydrodynamical aspects are treated at a level adequate to the complexity of realistic cochlear structures. The dynamics of the cochlea as a passive physical system, in the linear approximation, is described by an integral equation. It is further shown that this equation describes the properties of the working cochlea, provided a force term that accounts for hair cell motility is included. Numerical solutions for different degrees of outer hair cells activity, obtained by matrix methods in the frequency domain, are presented. Amplitudes and phases of the computer-simulated traveling waves are in fair agreement with basilar membrane responses to tones measured in various experimental conditions.

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Nonlinearities affecting cochlear mechanics produce appreciable compression in the basilar membrane (BM) input/output (I/O) functions at the characteristic frequency for sound-pressure levels (SPLs) as low as 20 dB (re: 20 microPa). This is thought to depend upon saturation of the outer hair cell (OHC) mechanoelectrical transducer (MET). This hypothesis was tested by solving a nonlinear integrodifferential equation that describes the BM vibration in an active cochlea. The equation extends a previously developed linear approach [Mammano and Nobili, J. Acoust. Soc. Am. 93, 3320-3332 (1993)], here modified to include saturating MET, with a few corrections mainly concerning tectorial membrane resonance and OHC coupling to the BM. Stationary solutions were computed by iteration in the frequency domain for a wide range of input SPLs, generating BM I/O functions, frequency response envelopes, and two-tone distortion products. Traveling-wave amplitude envelopes were also computed for a fixed suppressor and several suppressed tones in order to evidence the phenomenon of two-tone suppression (frequency masking) at the mechanical level. All results accord nicely with experimental data.

Sounds originating from within the inner ear, known as otoacoustic emissions (OAEs), are widely exploited in clinical practice but the mechanisms underlying their generation are not entirely clear. Here we present simulation results and theoretical considerations based on a hydrodynamic model of the human inner ear. Simulations show that, if the cochlear amplifier (CA) gain is a smooth function of position within the active cochlea, filtering performed by a middle ear with an irregular, i.e., nonsmooth, forward transfer function suffices to produce irregular and long-lasting residual oscillations of cochlear basilar membrane (BM) at selected frequencies. Feeding back to the middle ear through hydrodynamic coupling afforded by the cochlear fluid, these oscillations are detected as transient evoked OAEs in the ear canal. If, in addition, the CA gain profile is affected by irregularities, residual BM oscillations are even more irregular and tend to evolve towards self-sustaining oscillations at the loci of gain irregularities. Correspondingly, the spectrum of transient evoked OAEs exhibits sharp peaks. If both the CA gain and the middle-ear forward transfer function are smooth, residual BM oscillations have regular waveforms and extinguish rapidly. In this case no emissions are produced. Finally, and paradoxically albeit consistent with observations, simulating localized damage to the CA results in self-sustaining BM oscillations at the characteristic frequencies (CFs) of the sites adjacent to the damage region, accompanied by generation of spontaneous OAEs. Under these conditions, stimulusfrequency OAEs, with typical modulation patterns, are also observed for inputs near hearing threshold. This approach can be exploited to provide novel diagnostic tools and a better understanding of key phenomena relevant for hearing science.

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