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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-am36-3-4,
author = {Urszula Ledzewicz and Vignon Oussa and Heinz Sch\"attler},
title = {Optimal solutions for a model of tumor anti-angiogenesis with a penalty on the cost of treatment},
journal = {Applicationes Mathematicae},
volume = {36},
year = {2009},
pages = {295-312},
zbl = {1173.49004},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-am36-3-4}
}
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) pp. 295-312. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-am36-3-4/