An analytic physically motivated model of the mammalian cochlea

Abstract: We develop an analytic model of the mammalian cochlea. We use a mixed physical-phenomenological approach by utilizing existing work on the physics of classical box-representations of the cochlea, and behavior of recent data-derived wavenumber estimates. Spatial variation is incorporated through a single independent variable that combines space and frequency. We arrive at closed-form expressions for the organ of Corti velocity, its impedance, the pressure difference across the organ of Corti, and its wavenumber. We perform model tests using real and imaginary parts of chinchilla data from multiple locations and for multiple variables. The model also predicts impedances that are qualitatively consistent with current literature. For implementation, the model can leverage existing efforts for both filter bank and filter cascade models that target improved algorithmic or analog circuit efficiencies. The simplicity of the cochlear model, its small number of model constants, its ability to capture the variation of tuning, its closed-form expressions for physically-interrelated variables, and the form of these expressions that allows for easily determining one variable from another make the model appropriate for analytic and digital auditory filter implementations as discussed here, as well as for extracting macromechanical insights regarding how the cochlea works.