Modelling the Tumour Growth Along a Complex Vasculature Using Cellular Automata

Abstract

In this paper we present a tumourous cell growth model based on cellular automata (CA), where a colony composed of competing normal and cancer cells was placed in an array intertwined with blood vessels. The CA models are able to incorporate both cell growth and complex vascular geometry at the microcirculation level, whereby CA rules are implemented to govern cell development, evolution and death. The vasculature, which is the constant source of oxygen, was generated using a diffusion-limited aggregation-based CA model, whilst the diffusion of oxygen molecules across the domain was implemented, first, using a “random walk” approach and then employing classic diffusion law. With appropriate rules of CA implemented the cancer cells were able to grow at a faster rate and spread a greater distance compared to the normal cells. Once the cancer cells were allowed to proliferate over the vasculature, they would dominate the model lattice and, in one case, overwhelm the normal cells. However, normal cells also own the ability to defend themselves from the invasion of cancerous cells. It was clear from this model that with metastasis tumours exhibit far more dangerous characteristics as they suffocate, control and direct the growth of normal cells. The proposed growth model can be further extended to incorporate more growth patterns and control mechanisms.