Constraints imposed by zero-crossing invariance on cochlear models with two mechanical degrees of freedom

The zero crossings of basilar-membrane (BM) responses to clicks are nearly independent of stimulus intensity. This work explores the constraints that this invariance imposes on one-dimensional nonlinear cochlear models with two degrees of freedom (2DoF). The locations of the poles and zeros of the BM admittance, calculated for a set of linear models in which the strength of the active force is progressively decreased, provides a playground for evaluating the behavior of a corresponding nonlinear model at increasing stimulus levels. Mathematical constraints on the model parameters are derived by requiring that the poles of the admittance move horizontally in the s-plane as the active force is varied. These constraints ensure approximate zero-crossing invariance over a wide stimulus level range in a nonlinear model in which the active force varies as a function of the local instantaneous BM displacement and velocity. Two different 2DoF models are explored, each capable of reproducing the main qualitative characteristics of the BM response to tones (i.e., the tall and broad activity pattern at low stimulus levels, the large gain dynamics, and the partial decoupling between gain and phase). In each model, the motions of the two masses are compared with response data from animal experiments.