title: Optimal strategy in chemotherapy for a Gompertzian model of cancer growth.
abstract: The problem of optimal cancer chemotherapy is reconsidered. For the assumed result of the therapy the cumulative negative toxic effect of the drug is minimized. The unknown function to be optimized is the time-dependent dose of the drug. The Gompertzian model of cell population growth is employed. The formulated problem of the calculus of variations is solved using the method of Miele (the method of extremization of linear integrals via Green's theorem). The optimal solution is unique and of "bang-bang" type with one switching point.
authors.affiliation: Warsaw University of Technology, Institute of Aeronautics and Applied Mechanics, ul. Nowowiejska 24,00-665 Warsaw, Poland.
authors.forename: Ryszard
authors.initials: R
authors.lastname: Maroński
mesh_terms: D000465:Algorithms; D001943:Breast Neoplasms / Q000188:drug therapy* / Q000473:pathology; D049109:Cell Proliferation / Q000187:drug effects*; D003198:Computer Simulation; D005260:Female; D006801:Humans; D008954:Models, Biological