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Tumor Microenvironment and Anticancer Therapies: An Optimal Control Approach

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Mathematical Oncology 2013

Abstract

In this paper, results about the structure of cancer treatment protocols that can be inferred from an analysis of mathematical models with the methods and tools of optimal control are reviewed. For homogeneous tumor populations of chemotherapeutically sensitive cells, optimal controls are bang-bang corresponding to the medical paradigm of maximum tolerated doses (MTD). But as more aspects of the tumor microenvironment are taken into account, such as heterogeneity of the tumor cell population, tumor angiogenesis and tumor-immune system interactions, singular controls which administer agents at specific time-varying reduced dose rates become optimal and give an indication of what might be the biologically optimal dose (BOD).

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Acknowledgements

This material is based upon work supported by the National Science Foundation under collaborative research Grants Nos. DMS 1311729/1311733. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.

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Authors and Affiliations

  1. Department of Mathematics and Statistics, Southern Illinois University, Edwardsville, Illinois, 62026, USA

    Urszula Ledzewicz

  2. Department of Electrical and Systems Engineering, Washington University, St. Louis, Missouri, 63130, USA

    Heinz Schättler

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  1. Urszula Ledzewicz
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  2. Heinz Schättler
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Correspondence to Urszula Ledzewicz .

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Editors and Affiliations

  1. International Prevention Research Institute, Lyon, France

    Alberto d'Onofrio

  2. Istituto di Analisi dei Sistemi ed Informatica "Antonio Ruberti"—CNR, Rome, Italy

    Alberto Gandolfi

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Ledzewicz, U., Schättler, H. (2014). Tumor Microenvironment and Anticancer Therapies: An Optimal Control Approach. In: d'Onofrio, A., Gandolfi, A. (eds) Mathematical Oncology 2013. Modeling and Simulation in Science, Engineering and Technology. Birkhäuser, New York, NY. https://doi.org/10.1007/978-1-4939-0458-7_10

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