Hybrid models of tumor growth

Abstract

Cancer is a complex, multiscale process, in which genetic mutations occurring at a subcellular level manifest themselves as functional changes at the cellular and tissue scale. The multiscale nature of cancer requires mathematical modeling approaches that can handle multiple intra-and extracellular factors acting on different time and space scales. Hybrid models provide a way to integrate both discrete and continuous variables that are used to represent individual cells and concentration or density fields, respectively. Each discrete cell can also be equipped with submodels that drive cell behavior in response to microenvironmental cues. Moreover, the individual cells can interact with one another to form and act as an integrated tissue. Hybrid models form part of a larger class of individual-based-models that can naturally connect with tumor cell biology and allow for the integration of multiple interacting variables both intrinsically and extrinsically and are therefore perfectly suited to a systems biology approach to tumor growth. Keywordshybrid models; individual cell based models; multiscale models; tumor growth; systems biology Mathematical and computational modeling of tumor growth is not new -in fact it goes back over 50 years. However, to some extent it has largely been ignored by the biological and medical communities. There are multiple reasons for this but two of the most significant revolve around the reductionist focus of biology and the lack of directly testable hypotheses from the models. By necessity much of the models of cancer were general, phenomenological and not specific to a type of cancer and therefore were plagued by a lack of experimental data to both parameterize and validate. That is not to say they were not useful. At their heart most mathematical models are mechanistic -focusing on the core processes that drive tumor growth and integrating them leading to predictions that are holistic by definition. This further contributed to the lack of biological interest in combining laboratory experiments with computational simulations. Most of the experimental biologists working in this field were more focused on the reductionist route revolving around specific genetic mutations or signaling pathways that were found to be important in cancer development. This led to the data explosion that motivated the advent of early systems biology and the development of bioinformatics. Mathematical biology and the mechanistic cancer models it produced were somewhat left behind, but little by little they have matured moving from simple non-spatial growth laws (gompertz) all the way to hybrid multiscale models discussed in this review. See also a list of previously published reviews in the Future Reading section. In the last few years mathematical and computational models of cancer have become more accepted by the biological community both as means to motivate experimentation but also as a route to integrate multiple experimental measurements to generate testable predictions. This shift has been par...

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