Mathematical medicine: modeling cancer and its treatments

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The application of physics and mathematics to medicine is one of the most rapidly growing areas of interdisciplinary research. Mathematical modeling can provide a quantitative framework to discuss, in detail, the interaction between all components of complex biological systems, as well as to test various therapeutic interventions. The combination of novel computational techniques and mathematical models, grounded in experimental and clinical data, thus provides a powerful new tool in biomedical research. One important application is to modeling tumor growth and its treatment.Cancer is an uncontrolled growth of cells that can occur in any tissue of the body. Tumors cannot grow beyond a certain size through simple diffusion of oxygen and other essential nutrients into the tumor. Angiogenesis, the formation of blood vessels from pre-existing vessels, is a crucial and observed step, through which a tumor obtains its own blood supply. Inhibition of tumor angiogenesis (anti-angiogenic therapy), to complement conventional radiotherapy and chemotherapy treatments, could be an effective strategy for the control of cancer, where such combinations would destroy both cancer and endothelial cells. However, with the destruction of the tumor blood vessels, chemotherapies and oxygen cannot effectively reach the tumor cells. Additionally, unlike the vasculature of normal tissues, tumor vessels are structurally and functionally abnormal. A complete understanding of the tumor microenvironment, and the response of a tumor (and its abnormal vasculature) to various treatments, is essential in determining optimal dosage, and in the scheduling and sequencing of combined treatment strategies. Mathematical modeling based on existing and novel biophysical models, as well as pre-clinical and clinical data, would certainly be very useful to study tumor growth and angiogenesis, and the effects of different treatments. The proposal includes the study of tumor growth and various types of cancer treatments, mainly radiotherapy, chemotherapy, and anti-angiogenic therapy. The modeling ranges from the molecular and cellular levels to macroscopic scales.