A+ CATEGORY SCIENTIFIC UNIT

Optimal solutions for a model of tumor anti-angiogenesis with a penalty on the cost of treatment

Volume 36 / 2009

Urszula Ledzewicz, Vignon Oussa, Heinz Schättler Applicationes Mathematicae 36 (2009), 295-312 MSC: 49J15, 93C50. DOI: 10.4064/am36-3-4

Abstract

The scheduling of angiogenic inhibitors to control a vascularized tumor is analyzed as an optimal control problem for a mathematical model that was developed and biologically validated by Hahnfeldt et al. [Cancer Res. 59 (1999)]. Two formulations of the problem are considered. In the first one the primary tumor volume is minimized for a given amount of angiogenic inhibitors to be administered, while a balance between tumor reduction and the total amount of angiogenic inhibitors given is minimized in the second formulation. The optimal solutions to both problems are presented and compared.

Authors

  • Urszula LedzewiczDepartment of Mathematics and Statistics
    Southern Illinois University at Edwardsville
    Edwardsville, IL 62026-1653, U.S.A.
    e-mail
  • Vignon OussaDepartment of Mathematics and Statistics
    Southern Illinois University at Edwardsville
    Edwardsville, IL 62026-1653, U.S.A.
  • Heinz SchättlerDepartment of Electrical
    and Systems Engineering
    Washington University
    St. Louis, MO 63130-4899, U.S.A.
    e-mail

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