Numerical computation of diffusion on a surface

doi:10.1073/pnas.0504953102

Numerical computation of diffusion on a surface

^*Applied Numerical Algorithms Group, and ^¶Physical Biosciences Division, Lawrence Berkeley National Laboratory, Berkeley, CA 94720; ^‡Department of Mathematics, University of North Carolina, Chapel Hill, NC 27599; and Departments of ^§Bioengineering and ^∥Mechanical Engineering, University of California, Berkeley, CA 94720

Contributed by Phillip Colella, June 21, 2005

Abstract

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.

Footnotes

↵ † To whom correspondence may be addressed. E-mail: pcolella{at}lbl.gov or poschwartz{at}lbl.gov.
Author contributions: P.S., D.A., and P.C. designed research; P.S., D.A., P.C., A.P.A., and M.O. performed research; P.S., D.A., P.C., A.P.A., and M.O. analyzed data; and P.S., D.A., P.C., A.P.A., and M.O. wrote the paper.