MODELING THE OTOLITH MEMBRANE USING BOUNDARY-FITTED COORDINATES

This paper describes a method for modelling biological processes that involve an irregular object. The process is assumed to be described by a system of partial differential equations in a planar region. The te chniques described are specifically designed for irregular regions. Th e example of displacements of the otolith membrane under the force of gravity is used to illustrate the techniques. In this problem, the dis placements are described by a nontrivial system of partial differentia l equations, and the membrane has the shape of an irregular ellipse. I t is assumed that the membrane is fixed along its boundary. The soluti on technique has three main steps: first, a set of points is placed on the membrane; then the partial differential equations are discretized using those points; and finally the discrete equations are solved The points are automatically generated using a numerical grid-generation technique, the equations are discretized using a transformation techni que, and the discrete equations are solved using an iterative method. The solution technique is capable of accurately modelling processes in irregular regions and is easier to program than competing techniques, especially when the geometry of the model is changed during the study . If the geometry changes, a new grid needs to he generated, but nothi ng else need he changed in the code to study the new situation.