Numerical computation of diffusion on a surface.
We present a numerical method for computing diffusive transport on a surface derived from image data. Our underlying discretization method uses a Cartesian grid embedded boundary method for computing the volume transport in a region consisting of all points a small distance from the surface. We obtain a representation of this region from image data by using a front propagation computation based on level set methods for solving the Hamilton-Jacobi and eikonal equations. We demonstrate that the method is second-order accurate in space and time and is capable of computing solutions on complex surface geometries obtained from image data of cells.
Schwartz
Peter
P
Applied Numerical Algorithms Group, Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA. poschwartz@lbl.gov
Adalsteinsson
David
D
Colella
Phillip
P
Arkin
Adam Paul
AP
Onsum
Matthew
M
D001692:Biological Transport / Q000502:physiology; D004058:Diffusion; D008433:Mathematics; D008954:Models, Biological; D013499:Surface Properties; D049490:Systems Biology