Implementation of the level set method for continuum mechanics based tumor growth models

A computational framework for simulating growth and transport in biological materials based on continuum models is proposed. The advantages of the finite difference methodology employed are generality and relative simplicity of implementation. The Cartesian mesh/level set method developed here provides a computational tool for the investigation of a host of transportbased tissue/tumor growth models, that are posed as free or moving boundary problems and may exhibit complicated boundary evolution including topological changes. The methodology is tested here on a widely studied ”incompressible flow” type tumor growth model with a numerical implementation in two dimensions; comparisons with results obtained from a linear analysis of the model and with other recently published numerical solutions provide a quantitative assessment of the numerical solution methodology. The implementation has been structured such that extension to three-dimensional simulations is straightforward from an algorithmic perspective.