A numerical method was presented for computing diffusive transport on a surface derived from image data. The underlying discretization method used a Cartesian grid embedded boundary method for computing the volume transport in a region consisting of all points a small distance from the surface. A representation of this region was obtained from image data by using a front propagation computation based upon level-set methods for solving the Hamilton-Jacobi and eikonal equations. It was demonstrated that the method was second-order accurate in space and time, and was capable of computing solutions on complex surface geometries obtained from image data of cells.

Numerical Computation of Diffusion on a Surface. P.Schwartz, D.Adalsteinsson, P.Colella, A.P.Arkin, M.Onsum: Proceedings of the National Academy of Sciences, 2005, 102[32], 11151-6