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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

    Related Papers:

  • 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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    [1] Cambridge University Press, 1997.
    [2] Springer Verlag, Series: Mathematics and Applications, 40, 2003.
    [3] (in German), 2nd ed., Deutscher Apotheker -Verlag, Stuttgart, Germany.
    [4] Lecture Notes in Biomathematics, 30, Springer Verlag, 1979.
    [5] J. of Theoretical Biology, 220 (2003), 545-554.
    [6] Scientific Bulletin of the Silesian Technical University, 65 (1983), 120-130.
    [7] J. of Mathematical Biology, 64 (2012), 557-577.
    [8] J. of Optimization Theory and Applications - JOTA, 114 (2002), 609-637.
    [9] J. of Biological Systems, 10 (2002), 183-206.
    [10] J. of Medical Information Technology, 8 (2004), 5-13.
    [11] Discrete and Continuous Dynamical Systems, Series B, 6 (2006), 129-150.
    [12] SIAM J. on Control and Optimization, 46 (2007), 1052-1079.
    [13] Control and Cybernetics, 38 (2009), 1501-1523.
    [14] in "Chemotherapy Source Book" (ed. M. C. Perry), Williams &Wilkins, Baltimore, (1992), 403-408.
    [15] Cancer Chemotherapy and Pharmacology, 50 (2002), 419-428.
    [16] MacMillan, New York, 1964.
    [17] Springer Verlag, 2012.
    [18] Proc. of the 51st IEEE Conference on Decision and Control, Maui, (2012), 7691-7696.
    [19] Cancer Research, 24 (1964), 1295-1302.
    [20] Int. J. of Applied Mathematics and Computer Science, 13 (2003), 297-305.
    [21] Mathematical Biosciences, 101 (1990), 237-284.
    [22] Proceedings of the 12th IMACS World Congress, Paris, 4 (1988), 170-172.
    [23] Applied mathematics and Computer Science, 4 (1994), 223-233.
    [24] J. of Biological Systems, 3 (1995), 41-54.
    [25] Bulletin of the Polish Academy of Sciences, Technical Sciences, 56 (2008), 367-378.
    [26] Int. J. Applied Mathematics and Computer Science, 13 (2003), 357-368.
    [27] Cell Proliferation, 29 (1996), 117-139.
    [28] Control and Cybernetics, 28 (1999), 61-75.
    [29] Nonlinear Analysis, 47 (2000), 375-386.
    [30] J. of Clinical Oncology, 11 (1993), 820-821.
    [31] Boston-Philadelphia: Hilger Publishing, 1988.
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  • © 2013 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)
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