title: Optimizing Chemotherapeutic Anti-cancer Treatment and the Tumor Microenvironment: An Analysis of Mathematical Models.
abstract: We review results about the structure of administration of chemotherapeutic anti-cancer treatment that we have obtained from an analysis of minimally parameterized mathematical models using methods of optimal control. This is a branch of continuous-time optimization that studies the minimization of a performance criterion imposed on an underlying dynamical system subject to constraints. The scheduling of anti-cancer treatments has all the features of such a problem: treatments are administered in time and the interactions of the drugs with the tumor and its microenvironment determine the efficacy of therapy. At the same time, constraints on the toxicity of the treatments need to be taken into account. The models we consider are low-dimensional and do not include more refined details, but they capture the essence of the underlying biology and our results give robust and rather conclusive qualitative information about the administration of optimal treatment protocols that strongly correlate with approaches taken in medical practice. We describe the changes that arise in optimal administration schedules as the mathematical models are increasingly refined to progress from models that only consider the cancerous cells to models that include the major components of the tumor microenvironment, namely the tumor vasculature and tumor-immune system interactions.
authors.affiliation: Department of Mathematics and Statistics, Southern Illinois University Edwardsville, Edwardsville, IL, USA, 62026. uledzew@siue.edu.|Institute of Mathematics, Lodz University of Technology, Lodz, Poland. uledzew@siue.edu.
authors.forename: Urszula
authors.initials: U
authors.lastname: Ledzewicz
authors.affiliation: Department of Electrical and Systems Engineering, Washington University, St. Louis, MO, USA, 63130.
authors.forename: Heinz
authors.initials: H
authors.lastname: Schaettler
mesh_terms: D020533:Angiogenesis Inhibitors / Q000493:pharmacokinetics / Q000627:therapeutic use*; D003198:Computer Simulation; D003603:Cytotoxins / Q000493:pharmacokinetics / Q000627:therapeutic use*; D004334:Drug Administration Schedule; D004338:Drug Combinations; D054796:Drug Dosage Calculations; D042783:Endothelial Cells / Q000187:drug effects / Q000276:immunology / Q000473:pathology; D006801:Humans; D015233:Models, Statistical; D009369:Neoplasms / Q000098:blood supply / Q000188:drug therapy* / Q000276:immunology / Q000378:metabolism; D009389:Neovascularization, Pathologic / Q000188:drug therapy* / Q000276:immunology / Q000378:metabolism / Q000473:pathology; D059016:Tumor Microenvironment / Q000187:drug effects / Q000276:immunology
chemical_list: D020533:Angiogenesis Inhibitors; D003603:Cytotoxins; D004338:Drug Combinations
keywords: Anti-angiogenic therapy; Mathematical modeling; Metronomic chemotherapy; Optimal control; Optimization of cancer treatments; Tumor immune system interactions; Tumor microenvironment