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Determination of the pharmaceutical treatment-dosage for cancer patients using non-linear optimization techniques

Mavromatakis Iason

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Summary

Cancer, a disease first documented thousands of years ago, remains one of the most important issues of medicine, troubling numerous scientists and researchers, as well as individual patients. In this study, a non-linear mathematical model of tumor growth with immune response, under the effects of chemotherapeutic treatment, is presented. After analyzing the dynamics of the cells and the possible equilibria of the drug-free system, their interactions with the drug are examined. Later on, two cost-efficient optimal control approaches are reviewed, based on Direct Collocation and State-Dependent Riccati Equation methods, and then they are extended further so that they can be practically applied to patients. Ultimately, the results from each method are presented, providing an overall better regimen, when compared to previous studies, by successfully eradicating the tumor and keeping the side-effects of chemotherapy to a minimum.

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