Cancer is a result of the uncontrolled growth of abnormal cells. Solid tumors possess two distinct phases of growth - the avascular and the vascular phases. In the former, the tumor nodules do not contain a vas-cular network and thus receive nutrients and growth factors via diffusion through the host tissue. As a result, these nodules typically remain small and grow at most to several mm in diameter. The transition to metastasis and malignancy typically starts with angiogenesis. Angiogenesis is the development of a tumor-induced neovascular network that grows from the main circulatory system to the tumor in response to an imbalance of proangiogenic growth factors that are released by hypoxic tumor cells. This provides the tumor with a direct supply of nutrients and growth-promoting factors. The vascularized tumor typically invades the host microenvironment and has significant metastatic potential. By the time a tumor reaches a clinically detectable size, it is usually in the vascular growth phase. In these lecture notes, we provide a brief overview of the multiphase mathematical modeling of solid tumor growth that has been developed to describe all phases of tumor progression. We demonstrate that mathematical modeling and numerical simulation can provide im-portant insight into the root causes of solid tumor invasion and metas-tasis, and can provide and aid in assessing effective treatment strategies.
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