title: Robustness of optimal controls for a class of mathematical models for tumor anti-angiogenesis.
abstract: We describe optimal protocols for a class of mathematical models for tumor anti-angiogenesis for the problem of minimizing the tumor volume with an a priori given amount of vessel disruptive agents. The family of models is based on a biologically validated model by Hahnfeldt et al. and includes a modification by Ergun et al, but also provides two new variations that interpolate the dynamics for the vascular support between these existing models. The biological reasoning for the modifications of the models will be presented and we will show that despite quite different modeling assumptions, the qualitative structure of optimal controls is robust. For all the systems in the class of models considered here, an optimal singular arc is the defining element and all the syntheses of optimal controlled trajectories are qualitatively equivalent with quantitative differences easily computed.
authors.affiliation: Department of Electrical and Systems Engineering, Washington University, St. Louis, Missouri 63130, United States. hms@wustl.edu
authors.forename: Heinz
authors.initials: H
authors.lastname: Schättler
authors.forename: Urszula
authors.initials: U
authors.lastname: Ledzewicz
authors.forename: Benjamin
authors.initials: B
authors.lastname: Cardwell
mesh_terms: D020533:Angiogenesis Inhibitors / Q000008:administration & dosage*; D000818:Animals; D000970:Antineoplastic Agents / Q000008:administration & dosage; D049109:Cell Proliferation / Q000187:drug effects; D003198:Computer Simulation; D004305:Dose-Response Relationship, Drug; D004360:Drug Therapy, Computer-Assisted / Q000379:methods*; D006801:Humans; D008954:Models, Biological; D009369:Neoplasms / Q000150:complications / Q000188:drug therapy* / Q000503:physiopathology*; D009389:Neovascularization, Pathologic / Q000150:complications / Q000188:drug therapy* / Q000503:physiopathology*; D016896:Treatment Outcome
chemical_list: D020533:Angiogenesis Inhibitors; D000970:Antineoplastic Agents