Mathematical Models of Cancer Cell Plasticity

Figure 2

Discrete cell modelling, continuum modelling, and hybrid modelling, respectively, can be used to mathematically study tumour progression and metastasis. Discrete models can be classified into lattice-based models and lattice-free models. Lattice-based models can be further classified as Lattice Gas Cellular Automata (LGCA), Cellular Automata (CA), and Cellular Potts models (CPMs). Stochastic models and finite-difference approximation methods are used in lattice-free approaches. For continuum modelling, ordinary differential equations (ODEs) and partial differential equations (PDEs) are used. Logistic power and the Gompertz law are the basic ODEs used for continuum modelling. PDEs such as reaction-diffusion and partial integro-differential equations are also used for continuum modelling. Finally, hybrid models combine discrete and continuum approaches by modelling cell dynamics as discrete and certain tissue features such as oxygen, nutrient, drugs, etc. as continuum fields. To develop these mathematical models, various tumour microenvironmental factors such as matrix-degrading enzymes, extracellular matrix (ECM), oxygen, growth factors, inhibitors, etc. are considered.