The mechanical waveform of the basilar membrane. III. Intensity effects

Mechanical responses in the basal turn of the guinea-pig cochlea were measured with broad-band noise stimuli and expressed as input–output cross-correlation functions. The experiments were performed over the full range of stimulus intensities in order to try to understand the influence of cochlear nonlinearity on frequency selectivity, tuning, signal compression and the impulse response. The results are interpreted within the framework of a nonlinear, locally active, three-dimensional model of the cochlea. The data have been subjected to inverse analysis in order to recover the basilar-membrane (BM) impedance, a parameter function that, when inserted into the (linearized version of that) model, produces a model response that is similar to the measured response. This paper reports details about intensity effects for noise stimulation, in particular, the way the BM impedance varies with stimulus intensity. In terms of the underlying cochlear model, the decrease of the “activity component” in the BM impedance with increasing stimulus level is attributed to saturation of transduction in the outer hair cells. In the present paper this property is brought into a quantitative form. According to the theory [the EQ-NL theorem, de Boer, Audit. Neurosci. 3, 377–388 (1997)], the BM impedance is composed of two components, both intrinsically independent of stimulus level. One is the passive impedance $Z^{\mathrm{pass}}$ and the other one is the “extra” impedance $Z^{\mathrm{extra}}.$ The latter impedance is to be multiplied by a real factor $\gamma$ $\text{(0⩽γ⩽1)}$ that depends on stimulus level. This concept about the composition of the BM impedance is termed the “two-component theory of the BM impedance.” In this work both impedances are entirely derived from experimental data. The dependence of the factor $\gamma$ on stimulus level can be derived by using a unified form of the outer-hair-cell transducer function. From an individual experiment, the two functions $Z^{\mathrm{pass}}$ and $Z^{\mathrm{extra}}$ are determined, and an approximation ${\mathrm{(Z}}^{\mathrm{pass}}{\mathrm{+\gamma Z}}^{\mathrm{extra}})$ to the BM impedance constructed. Next, the model response (the “resynthesized” response) corresponding to this “artificial” impedance is computed. The same procedure is executed for several stimulus-level values. For all levels, the results show a close correspondence with the original experimental data; this includes correct prediction of the compression of response amplitudes, the reduction of frequency selectivity, the shift in peak frequency and, most importantly, the preservation of timing in the impulse response. All these findings illustrate the predictive power of the underlying model.