A cellular automaton model for tumour growth in inhomogeneous environment

Abstract

Most of the existing mathematical models for tumour growth and tumour-induced angiogenesis neglect blood flow. This is an important factor on which both nutrient and metabolite supply depend. In this paper we aim to address this shortcoming by developing a mathematical model which shows how blood flow and red blood cell heterogeneity influence the growth of systems of normal and cancerous cells. The model is developed in two stages. First we determine the distribution of oxygen in a native vascular network, incorporating into our model features of blood flow and vascular dynamics such as structural adaptation, complex rheology and red blood cell circulation. Once we have calculated the oxygen distribution, we then study the dynamics of a colony of normal and cancerous cells, placed in such a heterogeneous environment. During this second stage, we assume that the vascular network does not evolve and is independent of the dynamics of the surrounding tissue. The cells are considered as elements of a cellular automaton, whose evolution rules are inspired by the different behaviour of normal and cancer cells. Our aim is to show that blood flow and red blood cell heterogeneity play major roles in the development of such colonies, even when the red blood cells are flowing through the vasculature of normal, healthy tissue.

Vascular remodelling of an arterio-venous blood vessel network during solid tumour growth

“…Recently discrete agent-based models for tumour-induced angiogenesis were coupled to models of tumour growth (Zheng et al, 2005;Bartha and Rieger, 2006;Lee, Bartha and Rieger, 2006;Friboes et al, 2007;Welter, Bartha and Rieger, 2008;Wiese et al;Macklin et al, 2008). A growing tumour coopting the vessels of the normal tissue was considered with a pre-existing static capillary network without angiogenesis or regression in (Alarcon et al, 2003;Betteridge et al, 2006) and with a fully dynamic capillary network in Lee, Bartha and Rieger, 2006;Welter, Bartha and Rieger, 2008;Owen et al, 2008).…”

A Hybrid Model Describing Different Morphologies of Tumor Invasion Fronts

“…However, all these approaches overlook the behavior and the mutual interactions of single cells, which, as seen, are fundamental in determining the invasiveness of cancers and the subsequent metastatization. Discrete techniques, which include cellular automata and agent-based models [2,4,34,37,44,56,71], are instead able to preserve the identity of each simulated indi- vidual, to more naturally capture their biophysical properties, such as shape change, adhesion and intrinsic motility, and to handle local dynamics. On the contrary, purely discrete models translate complex microscopic processes into simple phenomenological rules, are difficult to study analytically and the associated computational cost rapidly increases with the number of cells modeled, which makes it difficult to simulate lesions longer than one millimeter.…”

Nonlinear simulation of the effect of microenvironment on tumor growth

“…Because a 1 mm tumor spheroid has over 500,000 cells, these methods can quickly become unwieldy when studying tumors of any significant size. For some examples of cellular automata modeling, see Anderson (2005), Alarcón et al (2003), and Mallett and de Pillis (2006), and see Mansury et al (2002) and Abbott et al (2006) for examples of agentbased modeling.…”