Hybrid models of tumor growth.

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 intracellular 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.