Last update:
22-Apr-2024

Mathematical models describing biological phenomena comprise powerful tools for their understanding and provide further insight regarding their behavior. Modeling complex processes, such as a cancer tumor, can provide detailed description of the mechanisms governing the function of unique cancer cells, as well as their integrative function in a tumor as a heterogeneous cellular system. Furthermore, mathematical modeling of the results of in vitro experiments can highlight new hypotheses that can be tested experimentally, enriching thus, the value of the results of an in vitro study. In the current review, some of the most frequent and important techniques of mathematical modeling used in biology and medicine, as well as in the study of cancer, are described: differential equations, that can be either ordinary or partial, game theory and its most specialized form for biological phenomena – evolutionary game theory, agent-based modeling and finally cellular automata and dynamic cellular automata. The main points of each technique are discussed along with their advantages and limitations. Subsequently, specific examples of published research studies focusing on the investigation of cancer systems that make use of modeling methods are provided. The aim of this review is to provide an understanding of the value of mathematical modeling in cancer research and the way that it can integrate and predict experimental evidence that derive from in vitro studies.

Key words: Biological models, Cancer, Cellular automata, Game theory, Modeling.