title: New approach to modeling of antiangiogenic treatment on the basis of Hahnfeldt et al. model.
abstract: In the paper we propose a new methodology in modeling of antiangiogenic treatment on the basis of well recognized model formulated by Hahnfeldt et al. in 1999. On the basis of the Hahnfeldt et al. model, with the usage of the optimal control theory, some protocols of antiangiogenic treatment were proposed. However, in our opinion the formulation of that model is valid only for the antivascular treatment, that is treatment that is focused on destroying endothelial cells. Therefore, we propose a modification of the original model which is valid in the case of the antiangiogenic treatment, that is treatment which is focused on blocking angiogenic signaling. We analyze basic mathematical properties of the proposed model and present some numerical simulations.
authors.affiliation: University of Warsaw, Faculty of Mathematics, Informatics and Mechanics, Institute of Applied Mathematics and Mechanics, Warsaw, Poland. j.poleszczuk@mimuw.edu.pl
authors.forename: Jan
authors.initials: J
authors.lastname: Poleszczuk
authors.forename: Marek
authors.initials: M
authors.lastname: Bodnar
authors.forename: Urszula
authors.initials: U
authors.lastname: Foryś
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