Nonlinear Modeling and Simulation of Tumor Growth

The effects of the interaction between cellularand tumor-scale processes on cancer progression and treatment response remain poorly understood (for instance, the crucial role of the microenvironment in cancer growth and invasion [95, 65, 184, 183, 160, 110, 66, 166]). Three-dimensional tissue morphology, cell phenotype, and molecular phenomena are intricately coupled; they influence cancer invasion potential by controlling tumor-cell proliferation and migration [78, 187, 198]. Hypoxia [88, 210, 186, 70, 91], acidosis [91, 199, 96], and associated diffusion gradients, caused by heterogeneous delivery of oxygen and nutrients and removal of metabolites [104, 103] due to highly disorganized microvasculature [92, 106] and often exacerbated by therapy (e.g., anti-angiogenic [160, 177]), can induce heterogeneous spatial distribution and invasiveness of tumor cells through a variety of molecular [175, 209, 208, 44, 165, 173, 145, 118, 28, 29, 190, 156, 185, 120, 122, 24, 160, 177, 174, 61] and tissue-scale [59, 127, 72] mechanisms corresponding to different tissue-scale invasive patterns [78, 164, 194, 167, 111, 187, 198, 204, 117, 206, 64, 179, 75, 77, 53, 172]. Such complex systems, dominated by large numbers of processes and highly nonlinear dynamics, are difficult to approach by experimental methods alone and can typically be better understood only by using appropriate mathematical models and sophisticated computer simulations, complementary to laboratory and clinical observations. Mathematical modeling has the potential