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Optimizing Chemotherapeutic Anti-cancer Treatment and the Tumor Microenvironment: An Analysis of Mathematical Models

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Systems Biology of Tumor Microenvironment

Part of the book series: Advances in Experimental Medicine and Biology ((AEMB,volume 936))

Abstract

We review results about the structure of administration of chemotherapeutic anti-cancer treatment that we have obtained from an analysis of minimally parameterized mathematical models using methods of optimal control. This is a branch of continuous-time optimization that studies the minimization of a performance criterion imposed on an underlying dynamical system subject to constraints. The scheduling of anti-cancer treatments has all the features of such a problem: treatments are administered in time and the interactions of the drugs with the tumor and its microenvironment determine the efficacy of therapy. At the same time, constraints on the toxicity of the treatments need to be taken into account. The models we consider are low-dimensional and do not include more refined details, but they capture the essence of the underlying biology and our results give robust and rather conclusive qualitative information about the administration of optimal treatment protocols that strongly correlate with approaches taken in medical practice. We describe the changes that arise in optimal administration schedules as the mathematical models are increasingly refined to progress from models that only consider the cancerous cells to models that include the major components of the tumor microenvironment, namely the tumor vasculature and tumor-immune system interactions.

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Acknowledgment

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, Edwardsville, IL, USA, 62026

    Urszula Ledzewicz

  2. Institute of Mathematics, Lodz University of Technology, Lodz, Poland

    Urszula Ledzewicz

  3. Department of Electrical and Systems Engineering, Washington University, St. Louis, MO, USA, 63130

    Heinz Schaettler

Authors
  1. Urszula Ledzewicz
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  2. Heinz Schaettler
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Correspondence to Urszula Ledzewicz .

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Editors and Affiliations

  1. H. Lee Moffitt Cancer Center & Research Institute, Tampa, Florida, USA

    Katarzyna A. Rejniak

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Ledzewicz, U., Schaettler, H. (2016). Optimizing Chemotherapeutic Anti-cancer Treatment and the Tumor Microenvironment: An Analysis of Mathematical Models. In: Rejniak, K. (eds) Systems Biology of Tumor Microenvironment. Advances in Experimental Medicine and Biology, vol 936. Springer, Cham. https://doi.org/10.1007/978-3-319-42023-3_11

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