Mathematical Biosciences and Engineering, 2013, 10(3): 803-819. doi: 10.3934/mbe.2013.10.803.

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On the MTD paradigm and optimal control for multi-drug cancer chemotherapy

1. Dept. of Mathematics and Statistics, Southern Illinois University Edwardsville, Edwardsville, Illinois, 62026-1653
2. Dept. of Electrical and Systems Engineering, Washington University, St. Louis, Mo 63130

In standard chemotherapy protocols, drugs are given at maximum tolerated doses(MTD) with rest periods in between. In this paper, we briefly discuss therationale behind this therapy approach and, using as examplemulti-drug cancer chemotherapy with a cytotoxic and cytostatic agent, show thatthese types of protocols are optimal in the sense of minimizing a weightedaverage of the number of tumor cells (taken both at the end of therapy and atintermediate times) and the total dose given if it is assumed that the tumorconsists of a homogeneous population of chemotherapeutically sensitive cells.A $2$-compartment linear model is used to model the pharmacokinetic equations for the drugs.
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Keywords multi-drug treatments.; chemotherapy; Optimal control

Citation: Urszula Ledzewicz, Heinz Schättler, Mostafa Reisi Gahrooi, Siamak Mahmoudian Dehkordi. On the MTD paradigm and optimal control for multi-drug cancer chemotherapy. Mathematical Biosciences and Engineering, 2013, 10(3): 803-819. doi: 10.3934/mbe.2013.10.803

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