Various aspects of cancer growth have been described using game-theoretic models. Many of these, however, use mean field approaches to study the dynamics of the interactions between individual agents involved. This, in many cases, has shown to exhibit dynamics very different from those observed using spatial game theory: The latter can e.g. explain long-term stable co-existence of mutualistic agents —as frequently observed in nature— in cases where the former predicts their extinction.
In my project I model the process of cancer cells invading the extracellular matrix (ECM) after breaking free from a primary avascular tumour.
Cancer cells diffuse through space, indirectly degrade the ECM via matrix degrading enzymes (MDEs), and respond to the MDEs’ movement and proliferation signals. This is, by its very nature, a space-dependent process, which I take into account by using a spatially explicit individual-based modelling approach:
The cancer cells’ movement rules and the distribution of matrix degrading enzymes are derived from a system of reaction-diffusion-taxis partial differential equations (PDEs). Discretisation of these grants a description of the evolution of the local number of individuals. Now local interactions between cancer cells and ECM can be represented using an individual-based game-theoretic approach, where payoff is awarded in terms of reproductive fitness according to a player’s strategy in a two-player game whenever two or more individuals are in the same position.
Currently, I am studying the numerical results of the hybrid model computationally. Subsequently, I will compare them to those obtained using a continuum model in order to ensure the model’s robustness.