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2003 | 13 | 3 | 357-368
Tytuł artykułu

Optimal control for a class of compartmental models in cancer chemotherapy

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
We consider a general class of mathematical models P for cancer chemotherapy described as optimal control problems over a fixed horizon with dynamics given by a bilinear system and an objective which is linear in the control. Several two- and three-compartment models considered earlier fall into this class. While a killing agent which is active during cell division constitutes the only control considered in the two-compartment model, Model A, also two three-compartment models, Models B and C, are analyzed, which consider a blocking agent and a recruiting agent, respectively. In Model B a blocking agent which slows down cell growth during the synthesis allowing in consequence the synchronization of the neoplastic population is added. In Model C the recruitment of dormant cells from the quiescent phase to enable their efficient treatment by a cytotoxic drug is included. In all models the cumulative effect of the killing agent is used to model the negative effect of the treatment on healthy cells. For each model it is shown that singular controls are not optimal. Then sharp necessary and sufficient optimality conditions for bang-bang controls are given for the general class of models P and illustrated with numerical examples.
Rocznik
Tom
13
Numer
3
Strony
357-368
Opis fizyczny
Daty
wydano
2003
otrzymano
2003-03-01
poprawiono
2003-06-01
Twórcy
  • Institute of Automatic Control, Silesian University of Technology, ul. Akademicka 16, 44-100 Gliwice, Poland
  • Department of Mathematics and Statistics, Southern Illinois University, Edwardsville, Il, 62026-1653, USA
  • Department of Systems Science and Mathematics, Washington University, St. Louis, Mo, 63130-4899, USA
Bibliografia
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Typ dokumentu
Bibliografia
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Identyfikator YADDA
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