Mathematical models of heterogeneity in cancer cell growth: a review

Cancer is characterized by unregulated growth of certain cells in the body, often leading to a rapid growth of tumors in vital organs. Various treatments have been proposed and given to cancer patients, including combinations of radiation, chemotherapy, and immunotherapy, with varying rates of success. Characterization of the disease (and the search for a cure) is made more challenging by the observed heterogeneous behavior and variability of growth rates of cells, particularly cells forming tumors in various stages of development. Heterogeneity refers to apparently dissimilar traits and behavior of individual cells or cell subpopulations, despite originating from a common tumor or parental line. In the last several decades, developments in mathematical biology, together with increasing availability of sophisticated laboratory equipment (aided by powerful computers) has provided a framework for the quantification and study of cell traits, including variability. We review some recent work on heterogeneity and growth variability in the context of mathematical models proposed. In the models presented, variance in cell proliferation rate distribution signals heterogeneity, so that mechanisms tuning variance are considerations for treatment strategies. We look into previous work and studies on sources of variability and stochasticity, and some numerical approaches are discussed, in order to deal with huge gene networks implicated in the complex process of cell division, proliferation and heterogeneity.