Abstract
Angiogenesis is the growth of new capillaries from preexisting ones. The ability to trigger angiogenesis is one of the hallmarks of cancer, and is a necessary step for a tumor to become malignant. This paper discusses computational modeling of tumor-induced angiogenesis with particular reference to mathematical modeling, numerical simulation, and comparison with experiments. We describe the basic biological phenomena associated with angiogenesis, and discuss how they can be incorporated into mathematical models. We emphasize the crucial role of numerical methods for model development. In particular, computational methods for tumor angiogenesis need to be geometrically flexible and capable of dealing with higher-order derivatives, which suggests isogeometric analysis as an ideal candidate. Finally, we propose an algorithm based on graph theory as a potential method for quantitative validation of tumor angiogenesis models.
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