Numerical grid generation: foundations and applications
Numerical grid generation: foundations and applications
Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations
Journal of Computational Physics
Interpolation on a triangulated 3D surface
Journal of Computational Physics
Crystal growth and dendritic solidification
Journal of Computational Physics
A simple level set method for solving Stefan problems
Journal of Computational Physics
A Cartesian grid embedded boundary method for Poisson's equation on irregular domains
Journal of Computational Physics
The fast construction of extension velocities in level set methods
Journal of Computational Physics
A non-oscillatory Eulerian approach to interfaces in multimaterial flows (the ghost fluid method)
Journal of Computational Physics
The integrated space-time finite volume method and its application to moving boundary problems
Journal of Computational Physics
A Cartesian grid embedded boundary method for the heat equation on irregular domains
Journal of Computational Physics
Adaptive Mesh Methods for One- and Two-Dimensional Hyperbolic Conservation Laws
SIAM Journal on Numerical Analysis
Transport and diffusion of material quantities on propagating interfaces via level set methods
Journal of Computational Physics
Journal of Computational Physics
Diffusion on a curved surface coupled to diffusion in the volume: Application to cell biology
Journal of Computational Physics
A New Ghost Cell/Level Set Method for Moving Boundary Problems: Application to Tumor Growth
Journal of Scientific Computing
Hi-index | 31.45 |
Eukaryotic cell crawling is a highly complex biophysical and biochemical process, where deformation and motion of a cell are driven by internal, biochemical regulation of a poroelastic cytoskeleton. One challenge to built quantitative models that describe crawling cells is solving the reaction-diffusion-advection dynamics for the biochemical and cytoskeletal components of the cell inside its moving and deforming geometry. Here we develop an algorithm that uses the level set method to move the cell boundary and uses information stored in the distance map to construct a finite volume representation of the cell. Our method preserves Cartesian connectivity of nodes in the finite volume representation while resolving the distorted cell geometry. Derivatives approximated using a Taylor series expansion at finite volume interfaces lead to second order accuracy even on highly distorted quadrilateral elements. A modified, Laplacian-based interpolation scheme is developed that conserves mass while interpolating values onto nodes that join the cell interior as the boundary moves. An implicit time stepping algorithm is used to maintain stability. We use the algorithm to simulate two simple models for cellular crawling. The first model uses depolymerization of the cytoskeleton to drive cell motility and suggests that the shape of a steady crawling cell is strongly dependent on the adhesion between the cell and the substrate. In the second model, we use a model for chemical signalling during chemotaxis to determine the shape of a crawling cell in a constant gradient and to show cellular response upon gradient reversal.