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A Review of Optimal Chemotherapy Protocols: From MTD towards Metronomic Therapy

Published online by Cambridge University Press:  20 June 2014

U. Ledzewicz  and
H. Schättler
U. Ledzewicz*
Affiliation:
Dept. of Mathematics and Statistics, Southern Illinois University Edwardsville, Edwardsville, Illinois, 62026-1653, USA
H. Schättler
Affiliation:
Dept. of Electrical and Systems Engr., Washington University, St. Louis, Missouri, 63130-4899, USA
*
⋆Corresponding author. E-mail: [email protected]
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Abstract

We review mathematical results about the qualitative structure of chemotherapy protocols that were obtained with the methods of optimal control. As increasingly more complex features are incorporated into the mathematical model—progressing from models for homogeneous, chemotherapeutically sensitive tumor cell populations to models for heterogeneous agglomerations of subpopulations of various sensitivities to models that include tumor immune-system interactions—the structures of optimal controls change from bang-bang solutions (which correspond to maximum dose rate chemotherapy with restperiods) to solutions that favor singular controls (representing reduced dose rates). Medically, this corresponds to a transition from standard MTD (maximum tolerated dose) type protocols to chemo-switch strategies towards metronomic dosing.

Keywords

optimal controlcancer chemotherapyhomogeneous and heterogeneous tumor populationstumor immune system interactions
Type
Research Article
Information
Mathematical Modelling of Natural Phenomena , Volume 9 , Issue 4: Optimal control , 2014 , pp. 131 - 152
Copyright
© EDP Sciences, 2014

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