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We develop a mathematical model to simulate the effects of a cell-cycle-specific chemotherapy like paclitaxel on a breast cancer tumor cell population. Initially, we examine the model of cell-cycle specific chemotherapy developed by J. C. Panetta in 1997. We then attempt to include the effects of tumor necrosis in a modified model in order to simulate the effects of paclitaxel on a metastasized breast cancer tumor. After running treatment simulations on this model using Matlab, we see that the inclusion of necrosis affects the necessary strength and length of cancer treatment. We then move on to experiment with optimal control methods. We apply optimal control theory to the original Panetta model and the new necrosis model with the goal of minimizing cancer cell population and total chemotherapy drug administered over a given time interval. We prove existence of such an optimal control for both the Panetta and necrosis models, and in examining the form, we find that the optimal treatment schedule is greatly affected by this control.
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Johnson, Adriana, "Optimal Control of Cell-Cycle-Specific Chemotherapy: An Examination of the Effects of Necrosis" (2012). Senior Projects Spring 2012. 335.