On the MTD paradigm and optimal control for multi-drug cancer chemotherapy

Urszula Ledzewicz; Heinz Schättler; Mostafa Reisi Gahrooi; Siamak Mahmoudian Dehkordi

doi:10.3934/mbe.2013.10.803

Article Contents

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: September 30, 2012

Revised: November 30, 2012

Published: March 2013

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Abstract

In standard chemotherapy protocols, drugs are given at maximum tolerated doses (MTD) with rest periods in between. In this paper, we briefly discuss the rationale behind this therapy approach and, using as example multi-drug cancer chemotherapy with a cytotoxic and cytostatic agent, show that these types of protocols are optimal in the sense of minimizing a weighted average of the number of tumor cells (taken both at the end of therapy and at intermediate times) and the total dose given if it is assumed that the tumor consists 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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Mathematics Subject Classification: Primary: 49K15, 92C50; Secondary: 93C95.

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