Mathematical modeling as a tool for planning anticancer therapy.
We review a large volume of literature concerning mathematical models of cancer therapy, oriented towards optimization of treatment protocols. The review, although partly idiosyncratic, covers such major areas of therapy optimization as phase-specific chemotherapy, antiangiogenic therapy and therapy under drug resistance. We start from early cell cycle progression models, very simple but admitting explicit mathematical solutions, based on methods of control theory. We continue with more complex models involving evolution of drug resistance and pharmacokinetic and pharmacodynamic effects. Then, we consider two more recent areas: angiogenesis of tumors and molecular signaling within and among cells. We discuss biological background and mathematical techniques of this field, which has a large although only partly realized potential for contributing to cancer treatment.
Swierniak
Andrzej
A
Institute of Automatic Control, Silesian University of Technology, Akademicka 16, 44-100 Gliwice, Poland.
Kimmel
Marek
M
Smieja
Jaroslaw
J
D000818:Animals; D000970:Antineoplastic Agents / Q000493:pharmacokinetics / Q000494:pharmacology*; D002453:Cell Cycle / Q000187:drug effects; D019008:Drug Resistance, Neoplasm; D006801:Humans; D008954:Models, Biological; D009369:Neoplasms / Q000188:drug therapy* / Q000503:physiopathology; D009389:Neovascularization, Pathologic / Q000188:drug therapy; D015398:Signal Transduction / Q000187:drug effects
D000970:Antineoplastic Agents