Modeling Cell Boundary Dynamics: Mark Zajac

My talk will culminate in a model for chemical gradient detection by migrating cells that change shape. I will first present a method for solving reaction-advection-diffusion equations inside a deforming region, with a moving boundary. The method employs a "distance map" that is constructed by storing the shortest distance to the boundary at each node on a grid. The gradient of the distance map provides a vector that points from each node to the boundary, which is a known distance away. These vectors and corresponding distances give exactly the displacements that will move nodes onto the boundary, from points nearby. This yields a structured, boundary-fitted grid that provides the basis for a finite-volume method