Application of mathematical models to metronomic chemotherapy: What can be inferred from minimal parameterized models?
Metronomic chemotherapy refers to the frequent administration of chemotherapy at relatively low, minimally toxic doses without prolonged treatment interruptions. Different from conventional or maximum-tolerated-dose chemotherapy which aims at an eradication of all malignant cells, in a metronomic dosing the goal often lies in the long-term management of the disease when eradication proves elusive. Mathematical modeling and subsequent analysis (theoretical as well as numerical) have become an increasingly more valuable tool (in silico) both for determining conditions under which specific treatment strategies should be preferred and for numerically optimizing treatment regimens. While elaborate, computationally-driven patient specific schemes that would optimize the timing and drug dose levels are still a part of the future, such procedures may become instrumental in making chemotherapy effective in situations where it currently fails. Ideally, mathematical modeling and analysis will develop into an additional decision making tool in the complicated process that is the determination of efficient chemotherapy regimens. In this article, we review some of the results that have been obtained about metronomic chemotherapy from mathematical models and what they infer about the structure of optimal treatment regimens.
Dept. of Mathematics and Statistics, Southern Illinois University Edwardsville, Edwardsville, IL, 62026-1653, USA; Institute of Mathematics, Lodz University of Technology, 90-924, Lodz, Poland. Electronic address: uledzew@siue.edu.
Urszula
U
Ledzewicz
Dept. of Electrical and Systems Engineering Washington University, St. Louis, MO, 63130, USA. Electronic address: hms@wustl.edu.
Heinz
H
Schättler
D059250:Administration, Metronomic; D000970:Antineoplastic Agents / Q000008:administration & dosage* / Q000009:adverse effects; D003198:Computer Simulation; D003661:Decision Support Techniques; D004305:Dose-Response Relationship, Drug; D019008:Drug Resistance, Neoplasm; D006801:Humans; D015233:Models, Statistical; D008962:Models, Theoretical; D009369:Neoplasms / Q000188:drug therapy* / Q000473:pathology; D009716:Numerical Analysis, Computer-Assisted; D018579:Patient Selection; D013997:Time Factors; D016896:Treatment Outcome; D059016:Tumor Microenvironment
D000970:Antineoplastic Agents
Cancer therapy; Mathematical models; Metronomic chemotherapy; Optimal control; Tumor microenvironment