Geodesic
Optimal solutions for a model of tumor anti-angiogenesis with a penalty on the cost of treatment
Urszula Ledzewicz1 ; Vignon Oussa1 ; Heinz Schättler2
1 Department of Mathematics and Statistics Southern Illinois University at Edwardsville Edwardsville, IL 62026-1653, U.S.A.
2 Department of Electrical and Systems Engineering Washington University St. Louis, MO 63130-4899, U.S.A.
Applicationes Mathematicae, Tome 36 (2009) no. 3, pp. 295-312

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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.
DOI : 10.4064/am36-3-4
Keywords: scheduling angiogenic inhibitors control vascularized tumor analyzed optimal control problem mathematical model developed biologically validated hahnfeldt cancer res formulations problem considered first primary tumor volume minimized given amount angiogenic inhibitors administered while balance between tumor reduction total amount angiogenic inhibitors given minimized second formulation optimal solutions problems presented compared

Urszula Ledzewicz 1 ; Vignon Oussa 1 ; Heinz Schättler 2

1 Department of Mathematics and Statistics Southern Illinois University at Edwardsville Edwardsville, IL 62026-1653, U.S.A.
2 Department of Electrical and Systems Engineering Washington University St. Louis, MO 63130-4899, U.S.A. 
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Urszula Ledzewicz; Vignon Oussa; Heinz Schättler. Optimal solutions for a model
 of tumor anti-angiogenesis with a penalty
 on the cost of treatment. Applicationes Mathematicae, Tome 36 (2009) no. 3, pp. 295-312. doi: 10.4064/am36-3-4

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