A Two-Dimensional Nonlinear Nonlocal Feed-Forward Cochlear Model and Time Domain Computation of Multitone Interactions

Abstract

Abstract.A two-dimensional cochlear model is presented, which couples the classical second order partial differential equations of the basilar membrane (BM) with a discrete feed-forward (FF) outer hair cell (OHC) model for enhanced sensitivity. The enhancement (gain) factor in the model depends on BM displacement in a nonlinear nonlocal manner in order to capture multifrequency sound interactions and compression effects in a time-dependent simulation. The FF mechanism is based on the longitudinal tilt of the OHCs in feeding the mechanical energy onto the BM. A numerical method of second order accuracy in space and time is formulated by reducing the unknown variables to the BM with the representation of eigenfunction expansions. Though the nonlinear coupling with OHCs created an implicit algebraic problem at each time step, the structure of the FF mass matrix is found to permit a decomposition into a sum of a time-independent symmetric positive definite part and the remaining time-dependent part. A fast iterative method is devised and shown to converge with only the inversion of the time-independent part of the mass matrix. The time-dependent computation is studied by comparing with steady state solutions (frequency domain solutions) in the linear regime and by a convergence study in the nonlinear regime. Results are shown on OHC amplification of BM responses, compressive output for large intensity input, and nonlinear multitone interactions such as tonal suppression, noise suppression, and distortion products. Qualitative agreement with experimental data is observed.

Computational and conditioning issues of a discrete model for cochlear sensorineural hypoacusia

“…Firstly, we summarize the model introduced in [10]. In the latter model the forces applied by OHC on the BM are assumed proportional to the total force acting on the BM (OHC act like piezo-electric actuators that push BM).…”

“…In particular, a threedimensional model was described in [12] in order to obtain a realistic simulation of the complex processes taking place in the Organ of Corti. More recently, a remarkable and operational two-dimensional model was introduced in [10], by coupling the classical second order linear Partial Differential Equations (PDE) for the Basilar Membrane (BM) with a nonlinear active and discrete feed-forward Outer Hair Cells (OHC) model.…”

“…The discretization scheme and the corresponding algorithm utilized in [10] is certainly extremely interesting, but, unfortunately, has some disadvantages.…”

“…It is also important to point out that the paper [10] was mainly oriented to the modeling of patients with normal hearing or, more precisely, without a Sensorineural Hearing Loss (SHL). The convergence of the corresponding numerical method was in fact guaranteed by assuming that the gain factor α(x, u) of the active part of the model could be efficiently described by an integral function of the BM displacement u(x, t) and max u {α(x, u)} be everywhere less than one with a suitably small time step.…”

Hydro-Elastic Waves in a Cochlear Model: Numerical Simulations and an Analytically Reduced Model

“…Therefore it has been suggested that part of the basilar membrane response is due to an active internal mechanism that enhances the passive response. To account for this, a class of active models such as [19,7] layer nonlinearities on top of these passive transmission line models.…”