The Complete Solution of the Basilar Membrane Condition in Two Dimensional Models of the Cochlea

In two-dimensional models of the cochlea, basilar membrane behaviour has to satisfy a mixed type boundary condition. In this paper this condition will be studied using the complex plane. Its solution is given in terms of the most general solution of Laplace’s equation for pressure. The result shows complex membrane pressure as a linear combination of two independent functions. Taking advantage of the well-known frequency to place mapping, the solution is written as a frequency invariant closed shape. This representation is useful in giving a physical interpretation of membrane motion in relation to fluid flow in cochlear models. Due to the frequency invariance, no time consuming numerical methods are necessary to find response curves for membrane pressure or velocity.