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Cancer Chemotherapy for Heterogeneous Tumor Cell Populations and Drug Resistance

  • Chapter
Optimal Control for Mathematical Models of Cancer Therapies

Part of the book series: Interdisciplinary Applied Mathematics ((IAM,volume 42))

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Abstract

The results of the previous chapter are consistent with the classical MTD paradigm in medicine: give as much of the drug as possible immediately. This makes perfect sense in many situations: cancer is a widely symptomless disease which, once finally detected, often is in an advanced stage where immediate action is required. Then the aim simply is to be as toxic as possible to the cancerous cells. However, this presumes that cells can be killed, i.e., that the tumor population consists of chemotherapeutically sensitive cells. Malignant cancer cell populations on the other hand are often highly genetically unstable and coupled with fast proliferation rates; this leads to a great variety in the structure of the cells within one tumor—the number of genetic errors present within one cancer cell can lie in the thousands [220]. Consequently, many tumors consist of heterogeneous agglomerations of subpopulations of cells that show widely varying sensitivities toward the actions of a particular chemotherapeutic agent [104, 107]. Coupled with the fact that growing tumors also exhibit considerable evolutionary ability to enhance cell survival in an environment that is becoming hostile, this leads to multi-drug resistance of some strains of the cells. Naturally, it makes sense to combine drugs with different activation mechanisms to reach a larger population of the tumor cells—and this is what is being done—but the sad fact remains that some cells develop multi-drug resistance to a wide variety of even structurally unrelated drugs. There may even exist subpopulations of cells that are not sensitive to the treatment from the beginning (ab initio, intrinsic resistance). For certain types of cancer cells, there are simply no effective agents known.

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Authors and Affiliations

  1. Electrical and Systems Engineering, Washington University, St. Louis, MO, USA

    Heinz Schättler

  2. Mathematics and Statistics, Southern Illinois University Edwardsville, Edwardsville, IL, USA

    Urszula Ledzewicz

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  1. Heinz Schättler
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  2. Urszula Ledzewicz
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Schättler, H., Ledzewicz, U. (2015). Cancer Chemotherapy for Heterogeneous Tumor Cell Populations and Drug Resistance. In: Optimal Control for Mathematical Models of Cancer Therapies. Interdisciplinary Applied Mathematics, vol 42. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-2972-6_3

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