Comparison of finite difference method and mesh analysis for state-space models of the cochlea

In this paper, we demonstrate that instabilities of the cochlear transmission-line model depend on numerical solutions. The transmission-line model approximates the fluid motion and the mechanical vibration in the cochlea. The mechanical vibration is enhanced by active cochlear feedback gain. For a realistic cochlea, spatial distribution of the feedback gain is varied randomly. However, most modeling studies set the gain to be constant as in an ideal cochlea because the spatial variation of the gain affects divergence of the calculation. To discretize the cochlear model for computation, the finite difference method and mesh analysis have been proposed. The finite difference method has been commonly used to solve the model represented in mechanical form; mesh analysis has been used to solve the model represented as an electro-acoustical circuit. This paper develops a state-space model of the cochlea for each of the two methods. The state-space formulation is well suited for testing instabilities of the model. As the result, both models show similar responses and stabilities under constant feedback gain (the ideal cochlea). On the other hand, with a randomly varied gain factor (the realistic cochlea), the model discretized by the finite difference method demonstrates greater instability than the model discretized by the mesh analysis.