title: Numerical computation of diffusion on a surface.
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.
authors.affiliation: Applied Numerical Algorithms Group, Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA. poschwartz@lbl.gov
authors.forename: Peter
authors.initials: P
authors.lastname: Schwartz
authors.forename: David
authors.initials: D
authors.lastname: Adalsteinsson
authors.forename: Phillip
authors.initials: P
authors.lastname: Colella
authors.forename: Adam Paul
authors.initials: AP
authors.lastname: Arkin
authors.forename: Matthew
authors.initials: M
authors.lastname: Onsum
mesh_terms: D001692:Biological Transport / Q000502:physiology; D004058:Diffusion; D008433:Mathematics; D008954:Models, Biological; D013499:Surface Properties; D049490:Systems Biology