Open Access

ARTICLE

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

Cosmina S. Hogea¹, Bruce T. Murray¹, James A. Sethian^2,3

1 Department of Mechanical Engineering, Binghamton University, USA
2 Department of Mathematics and Lawrence Berkeley National Laboratory, University of California, Berkeley, USA
3 This author was supported in part by the Applied Mathematical Sciences subprogram of the Office of Energy Research, U.S. Department of Energy, under Contract Number DE-AC03-76SF00098, and the Division of Mathematical Sciences of the National Science Foundation

Fluid Dynamics & Materials Processing 2005, 1(2), 109-130. https://doi.org/10.3970/fdmp.2005.001.109

Abstract

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 transport-based 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.

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