Optimal Control for a System Modelling Tumor Anti-Angiogenesis
U. Ledzewicz¹, H. Sch¨attler^2
1Dept. of Mathematics and Statistics, Southern Illinois University at Edwardsville, Edwardsville, Illinois, 62026-1653, USA
²Dept. of Electrical and Systems Engineering, Washington University, St. Louis, Missouri, 63130-4899, USA

Abstract:

The scheduling of angiogenic inhibitors to control vascularized tumor is analyzed as an optimal control problem. For the underlying dynamics the model by Ergun, Camphausen and Wein [3], which is an approximation and simplification of the more complex model developed by Hahnfeldt et al. [4], is taken. Two formulations of the problem are considered. In the first model optimal controls minimize the tumor volume for a given amount of angiogenic inhibitors to be administered while the second formulation tries to achieve a balance between tumor reduction and total amount of angiogenic inhibitors given. For both models a full synthesis of optimal solutions is presented and the differences in the two solutions are discussed.
                                                                 

Keywords: Optimal control, bang-bang and singular controls, cancer treatments, angiogenic inhibitors.

Biographies:

URSZULA LEDZEWICZ, July 1995 : Promotion to the rank of Full Professor , July 1990 : Promotion to the rank of Associate Professor, September 1987 : Assistant Professor at the Department of Mathematics and Statistics, Southern Illinois University at Edwardsville, August 1986 - May 1987 : Visiting Assistant Professor, Louisiana State University,  Baton Rouge, LA, 1984 - 1986 : Assistant Professor at the Department of Mathematics, University of Lodz, Lodz, Poland,        1984 : Ph.D in Applied Mathematics at the University of Lodz, Lodz, Poland,       1979 - 1984 : Teaching Assistant at the Department of Mathematics, University of Lodz, Lodz, Poland,        1979 : Masters degree in Mathematics at the University of Lodz, Lodz, Poland

 

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