title: Optimal and suboptimal protocols for a mathematical model for tumor anti-angiogenesis in combination with chemotherapy.
abstract: We consider the problem of minimizing the tumor volume with a priori given amounts of anti-angiogenic and cytotoxic agents. For one underlying mathematical model, optimal and suboptimal solutions are given for four versions of this problem: the case when only anti-angiogenic agents are administered, combination treatment with a cytotoxic agent, and when a standard linear pharmacokinetic equation for the anti-angiogenic agent is added to each of these models. It is shown that the solutions to the more complex models naturally build upon the simplified versions. This gives credence to a modeling approach that starts with the analysis of simplified models and then adds increasingly more complex and medically relevant features. Furthermore, for each of the problem formulations considered here, there exist excellent simple piecewise constant controls with a small number of switchings that virtually replicate the optimal values for the objective.
authors.affiliation: Department of Mathematics and Statistics, Southern Illinois University Edwardsville, Edwardsville, Illinois 62026-1653, United States. uledzew@siue.edu
authors.forename: Urszula
authors.initials: U
authors.lastname: Ledzewicz
authors.forename: Helmut
authors.initials: H
authors.lastname: Maurer
authors.forename: Heinz
authors.initials: H
authors.lastname: Schättler
mesh_terms: D020533:Angiogenesis Inhibitors / Q000008:administration & dosage; D000818:Animals; D000970:Antineoplastic Agents / Q000008:administration & dosage; D000971:Antineoplastic Combined Chemotherapy Protocols / 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