Time Domain Computation of a Nonlinear Nonlocal Cochlear Model with Applications to Multitone Interactions in Hearing

A nonlinear, nonlocal cochlear model of the transmission line type is studied in
order to capture the multitone interactions and resulting tonal suppression effects. The model can
serve as a module for voice signal processing, and is a one-dimensional (in space) damped dispersive
nonlinear PDE based on the mechanics and phenomenology of hearing. It describes the motion of
the basilar membrane (BM) in the cochlea driven by input pressure waves. Both elastic damping
and selective longitudinal fluid damping are present. The former is nonlinear and nonlocal in BM
displacement, and plays a key role in capturing tonal interactions. The latter is active only near
the exit boundary (helicotrema), and is built in to damp out the remaining long waves. The initial
boundary value problem is numerically solved with a semi-implicit second order finite difference
method. Solutions reach a multi-frequency quasi-steady state. Numerical results are shown on two
tone suppression from both high-frequency and low-frequency sides, consistent with known behavior
of two tone suppression. Suppression effects among three tones are demonstrated by showing how
the response magnitudes of the fixed two tones are reduced as we vary the third tone in frequency
and amplitude. We observe qualitative agreement of our model solutions with existing cat auditory
neural data. The model is thus a simple and efficient processing tool for voice signals.