Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations
Journal of Computational Physics
A computational model for organism growth based on surface mesh generation
Journal of Computational Physics
A surfactant-conserving volume-of-fluid method for interfacial flows with insoluble surfactant
Journal of Computational Physics
A simple embedding method for solving partial differential equations on surfaces
Journal of Computational Physics
On the Variational Approximation of Combined Second and Fourth Order Geometric Evolution Equations
SIAM Journal on Scientific Computing
The Flexible, Extensible and Efficient Toolbox of Level Set Methods
Journal of Scientific Computing
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A computational framework is presented for the simulation of eukaryotic cell migration and chemotaxis. An empirical pattern formation model, based on a system of nonlinear reaction-diffusion equations, is approximated on an evolving cell boundary using an arbitrary Lagrangian Eulerian surface finite element method (ALE-SFEM). The solution state is used to drive a mechanical model of the protrusive and retractive forces exerted on the cell boundary. Movement of the cell is achieved using a level set method. Results are presented for cell migration with and without chemotaxis. The simulated behavior is compared with experimental results of migrating Dictyostelium discoideum cells.