A fully continuous individual-based model of tumor cell evolution

Authored by Glenn F Webb, Pablo Gomez-Mourelo, Eva Sanchez, Luis Casasus

Date Published: 2008

DOI: 10.1016/j.crvi.2008.08.010

Sponsors: No sponsors listed

Platforms: No platforms listed

Model Documentation: Other Narrative Mathematical description

Model Code URLs: Model code not found

Abstract

The aim of this work is to develop and study a fully continuous individual-based model (IBM) for cancer tumor invasion into a spatial environment of surrounding tissue. The IBM improves previous spatially discrete models, because it is continuous in all variables (including spatial variables), and thus not constrained to lattice frameworks. The IBM includes four types of individual elements: tumor cells, extracellular macromolecules (MM), a matrix degradative enzyme (MDE), and oxygen. The algorithm underlying the IBM is based on the dynamic interaction of these fourelements in the spatial environment, with special consideration of mutation phenotypes. A set of stochastic differential equations is formulated to describe the evolution of the IBM in an equivalent way. The IBM is scaled up to a system of partial differential equations (PIDE) representing the limiting behavior of the IBM as the number of cells and molecules approaches infinity. Both models (IBM and PDE) are numerically simulated with two kinds of initial conditions: homogeneous MM distribution and heterogeneous MM distribution. With both kinds of initial MM distributions spatial fingering patterns appear in the tumor growth. The output of both simulations is quite similar. To cite this article: P Gomez-Mourelo et al., C R. Biologies 331 (2008). (C) 2008 Academie des sciences. Published by Elsevier Masson SAS. All rights reserved.

Tags

systems Aggregation invasion Equations Limit dynamics Derivation