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The Influence of PK/PD on the Structure of Optimal Controls in Cancer Chemotherapy Models

1. Department of Mathematics and Statistics, Southern Illinois University at Edwardsville, Edwardsville, IL 62026-1653
2. Dept. of Electrical and Systems Engineering, Washington University, St. Louis, Missouri, 63130-4899

Mathematical models for cancer chemotherapy as optimal control problems are considered. Results on scheduling optimal therapies when the controls represent the effectiveness of chemotherapeutic agents, or, equivalently, when the simplifying assumption is made that drugs act instantaneously, are compared with more realistic models that include pharmacokinetic (PK) equations modelling the drug's plasma concentration and various pharmacodynamic (PD) models for the effect the concentrations have on cells.
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Keywords pharmaco- dynamics; cancer chemotherapy; singular controls.; optimal control; pharmacokinetics

Citation: Urszula Ledzewicz, Heinz Schättler. The Influence of PK/PD on the Structure of Optimal Controls in Cancer Chemotherapy Models. Mathematical Biosciences and Engineering, 2005, 2(3): 561-578. doi: 10.3934/mbe.2005.2.561

 

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Copyright Info: 2005, Urszula Ledzewicz, et al., licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution Licese (http://creativecommons.org/licenses/by/4.0)

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