Pole-zero descriptions of active cochlear micromechanics derived from in vivo measurements

Compared with an explicit lumped-parameter model of the micromechanics, a pole-zero description appears to be more abstract, but has the advantage of requiring fewer parameters. This makes it suitable for directly fitting to measured responses, using an overall model of the coupled cochlea. Such a fitting procedure is used with the in vivo measurements of basilar membrane motion, obtained with OCT by Lee at al. (2015). The accuracy of the model is quantified in terms of the average mean square difference between its complex frequency response and those of the measurements, and this error is calculated as a function of the excitation level used in the experiments, for different orders of micromechanical model and with either 1D or 3D fluid coupling. A single-degree-of-freedom micromechanical model, representing a passive cochlea with 2 poles and 1 zero, has a significantly higher error at low excitation levels than at high excitation levels, as expected. The error with a two degree-of-freedom micromechanical model, representing an active cochlea with 4 poles and 3 zeros, is low at both high and low levels of excitation and is further reduced if 3D fluid coupling is assumed. Although the pole-zero model does not lead to a unique lumped-parameter representation, it does indicate some of the properties that such a model must have.