A short overview of cellular automata in mathematical oncology

Abstract

Mathematical oncology has developed into an increasingly active interdisciplinary field, providing quantitative tools for the study of tumor growth, invasion, metastasis, treatment response, and therapy optimization. Within this field, cellular automata form an important class of models. This overview focuses on cellular automata and their extensions in the context of mathematical oncology. We first introduce the necessary mathematical preliminaries and then present the basic formalism of cellular automata, beginning with deterministic models and elementary cellular automata. We continue with a presentation of biologically motivated extensions, including probabilistic cellular automata, lattice-gas cellular automata, Cellular Potts models, and hybrid cellular automata. Particular attention is given to focusing this survey on the reader with some background in mathematics or computer science, who is interested in first discovering the biological applications of the model. Finally, we review selected works from the recent literature.