title: Optimal and suboptimal protocols for a class of mathematical models of tumor anti-angiogenesis.
abstract: Tumor anti-angiogenesis is a cancer treatment approach that aims at preventing the primary tumor from developing its own vascular network needed for further growth. In this paper the problem of how to schedule an a priori given amount of angiogenic inhibitors in order to minimize the tumor volume is considered for three related mathematical formulations of a biologically validated model developed by Hahnfeldt et al. [1999. Tumor development under angiogenic signalling: a dynamical theory of tumor growth, treatment response, and postvascular dormancy. Cancer Res. 59, 4770-4775]. Easily implementable piecewise constant protocols are compared with the mathematically optimal solutions. It is shown that a constant dosage protocol with rate given by the averaged optimal control is an excellent suboptimal protocol for the original model that achieves tumor values that lie within 1% of the theoretically optimal values. It is also observed that the averaged optimal dose is decreasing as a function of the initial tumor volume.
authors: Department of Mathematics and Statistics, Southern Illinois University at Edwardsville, Edwardsville, IL 62026-1653, USA. uledzew@siue.edu
authors: Urszula
authors: U
authors: Ledzewicz
authors: Heinz
authors: H
authors: Schättler
mesh_terms: D020533:Angiogenesis Inhibitors / Q000008:administration & dosage* / Q000627:therapeutic use; D000970:Antineoplastic Agents / Q000008:administration & dosage / Q000627:therapeutic use; D003131:Combined Modality Therapy; D004334:Drug Administration Schedule; D006801:Humans; D008954:Models, Biological; D015233:Models, Statistical; D009369:Neoplasms / Q000098:blood supply* / Q000188:drug therapy*; D009389:Neovascularization, Pathologic
chemical_list: D020533:Angiogenesis Inhibitors; D000970:Antineoplastic Agents