Computational and Mathematical Methods in Medicine
Volume 7 (2006), Issue 2-3, Pages 159-176
doi:10.1080/10273660600968978

Spatial Tumor-Immune Modeling

L. G. de Pillis,1 D. G. Mallet,2 and A. E. Radunskaya3

1Department of Mathematics, Harvey Mudd College, Claremont, CA 91711, USA
2School of Mathematical Sciences, Queensland University of Technology, Brisbane, Australia
3Department of Mathematics, Pomona College, Claremont, CA 91711, USA

Received 28 June 2006; Accepted 14 July 2006

Copyright © 2006 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

In this paper, we carry out an examination of four mechanisms that can potentially lead to changing morphologies in a growing tumor: variations in nutrient consumption rates, cellular adhesion, excessive consumption of nutrients by tumor cells and immune cell interactions with the tumor. We present numerical simulations using a hybrid PDE-cellular automata (CA) model demonstrating the effects of each mechanism before discussing hypotheses about the contribution of each mechanism to morphology change.