A Computer Simulation for 3D Vasculature-Based Oxygen Distribution and Tumour Growth

In this paper we present a three-dimensional (3D) tumourous cell growth model using a hybrid cellular automata (CA) and continuum-based method. The CA model is employed to simulate the competition between normal and cancer cells, whilst the continuum model is used for quantifying the oxygen diffusion in a 3D domain. A set of rules are implemented to govern cancerous/normal cell colony evolution. The vasculature, which is the constant source of oxygen and nutrients, is simulated using a constrained constructive optimization (CCO) algorithm. The diffusion equation of oxygen across the domain with an additional term to describe the oxygen uptake by cells was solved using a finite difference scheme. With this method we are able to simulate cancer cell growth under various hypoxia and oxygenated scenarios. It is clear from the simulations that different parameters in the diffusion equation and CA rules lead to drastically different growth patterns which may be physiologically relevant. In conclusion the proposed computational method provides a flexible framework that can be further extended to incorporate drug effects and intracellular signalling models.