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

Urszula Ledzewicz; Heinz Schättler; Urszula Ledzewicz; Heinz Schättler

doi:10.3934/mbe.2005.2.561

Mathematical Biosciences and Engineering

2005, Volume 2, Issue 3: 561-578. doi: 10.3934/mbe.2005.2.561

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

Urszula Ledzewicz ¹,
Heinz Schättler ²

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

Received: 01 January 2005 Accepted: 29 June 2018 Published: 01 August 2005
MSC : 49J15,92C50.

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.

Keywords:

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

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Abstract

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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