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Mathematical Biosciences and Engineering

2013, Volume 10, Issue 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
  • Received: 01 October 2012 Accepted: 29 June 2018 Published: 01 April 2013

  • MSC : Primary: 49K15, 92C50; Secondary: 93C95.

  • 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.

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

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  • 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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