Numerical computation of diffusion on a surface

Proc Natl Acad Sci U S A. 2005 Aug 9;102(32):11151-6. doi: 10.1073/pnas.0504953102. Epub 2005 Aug 2.

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.

Publication types

  • Research Support, Non-U.S. Gov't
  • Research Support, U.S. Gov't, Non-P.H.S.

MeSH terms

  • Biological Transport / physiology
  • Diffusion
  • Mathematics
  • Models, Biological*
  • Surface Properties
  • Systems Biology*