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Mathematical Modeling of Brain Tumor and Related Therapeutic Strategies
by
Gibin Powathil
University of Waterloo, Waterloo, Ontario,Canada
Coauthors: M Kohandel, S Sivaloganathan
Gliomas are the most common and aggressive primary brain tumors. The most common treatment protocols for these brain tumors are combinations of surgery, chemotherapy and radiotherapy. However, even with the most aggressive combination of surgery and radiotherapy and/or chemotherapy schedules, gliomas almost always recur resulting in a median survival time for patients of not more than 12 months. This highly diffusive and invasive nature of brain tumors makes it very important to study the effects of these combined therapeutic strategies in an effort to improve the survival time of patients. It is also important to study the tumor micro- environment, since the complex nature of the cerebral vasculature, including the blood brain barrier and several other tumors induced conditions such as hypoxia, high interstitial pressure, and cerebral edema affect drug delivery as well as the effectiveness of radiotherapy. Recently, a novel strategy using antiangiogenic therapy has been studied for the treatment of brain tumors. Antiangiogenic therapy interferes with the development of tumor vasculature and indirectly helps in the control of tumor growth. Recent clinical trials suggest that anti-angiogenic therapy is usually more effective when given in combination with other therapeutic strategies. In an effort to study the effects of the above mentioned therapeutic strategies, we consider a simple spatio-temporal model that incorporates the tumor cell growth and the effects of radiotherapy and chemotherapy. We study the effects of different schedules of radiation therapy, using a generalized linear quadratic model, and compare the results with published clinical data. The model is then extended to include the interactions of tumor vasculature and oxygen concentration, in an effort to explain tumor hypoxia, cerebral edema and high interstitial pressure (as well as their changes during antiangiogenic therapy). We also discuss the optimum way of sequencing these therapeutic strategies so as to maximize patient survival time.
Date received: May 2, 2008
Copyright © 2008 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cawd-49.