Pełnotekstowe zasoby PLDML oraz innych baz dziedzinowych są już dostępne w nowej Bibliotece Nauki.
Zapraszamy na https://bibliotekanauki.pl

PL EN


Preferencje help
Widoczny [Schowaj] Abstrakt
Liczba wyników
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

  • Agur Z., Arnon R. and Schechter B. (1988): Reduction of cytotoxicityto normal tissues by new regimens of phase-specific drugs. - Math. Biosci., Vol. 92, No. 1, pp. 1-15.
  • Alison M.R. and Sarraf C.E. (1997): Understanding Cancer-FromBasic Science to Clinical Practice. - Cambridge: Cambridge Univ. Press.
  • Andreef M., Tafuri A., Bettelheim P., Valent P., Estey E., Lemoli R., Goodacre A., Clarkson B., Mandelli F. and Deisseroth A. (1992): Cytokineticresistance in acute leukemia: Recombinant human granulocyte colony-stimulatingfactor, granulocyte macrophage colony stimulating factor, interleukin 3 andstem cell factor effects in vitro and clinical trials with granulocytemacrophage colony stimulating factor. - Haematolology and Blood Transfusion, Vol. 4, Acute Leukemias-Pharmakokinetics, pp. 108-117.
  • Bonadonna G., Zambetti M. and Valagussa P. (1995): Sequential ofalternating Doxorubicin and CMF regimens in breast cancer with more then 3 positive nodes. Ten years results. - JAMA, Vol. 273, No. 5, pp. 542-547.
  • Brown B.W. and Thompson J.R. (1975): A rationale for synchronystrategies in chemotherapy, In: Epidemiology (D. Ludwig and K.L. Cooke, Eds.). -Philadelphia: SIAM Publ., pp. 31-48.
  • Calabresi P. and Schein P.S. (1993): Medical Oncology, Basic Principles and Clinical Management of Cancer. - New York: Mc Graw-Hill.
  • Chabner B.A. and Longo D.L. (1996): Cancer Chemotherapy and Biotherapy. - Philadelphia: Lippencott-Raven.
  • Clare S.E., Nahlis F. and Panetta J.C. (2000): Molecular biology of breast cancer metastasis. The use of mathematical models to determine relapse and to predict response to chemotherapy in breast cancer. - Breast Cancer Res., Vol. 2, No. 6, pp. 396-399.
  • Coly L.P., van Bekkum D.W. and Hagenbeek A. (1984): Enhanced tumorload reduction after chemotherapy induced recruitment and synchronization in aslowly growing rat leukemia model (BNML) for human acute myelonic leukemia. - Leukemia Res., Vol. 8, No. 6, pp. 953-963.
  • Dibrov B.F., Zhabotynsky A.M., Krinskaya A.M., Neyfakh A.V., Yu A. and Churikova L.I. (1985): Mathematical model of cancer chemotherapy. Periodic schedules of phase-specific cytotoxic agent administration increasing the selectivity of therapy. - Math. Biosci., Vol. 73, No. 1, pp. 1-31.
  • Dibrov B.F., Zhabotinsky A.M., Yu A. and Orlova M.P. (1986): Mathematical model of hydroxy urea effects on cell populations in vivo. - Chem-Pharm J., Vol. 20, No. 2, pp. 147-153, (in Russian).
  • Duda Z. (1994): Evaluation of some optimal chemotherapy protocols byusing a gradient method. - Appl. Math. Comp. Sci., Vol. 4, No. 2, pp. 257-262.
  • Duda Z. (1997): Numerical solutions to bilinear models arising incancer chemotherapy. - Nonlinear World, Vol. 4, No. 1, pp. 53-72.
  • Eisen M. (1979): Mathematical Models in Cell Biology and Cancer Chemotherapy. - Berlin: Springer.
  • Fister K.R. and Panetta J.C. (2000): Optimal control applied to cell-cycle-specific cancer chemotherapy. - SIAM J. Appl. Math., Vol. 60, No. 3, pp. 1059-1072.
  • Goldie J.H. and Coldman A. (1998): Drug Resistance in Cancer. - Cambridge: Cambridge Univ. Press.
  • Holmgren L., O'Reilly M.S. and Folkman J. (1995): Dormancy of micrometastases: balanced proliferation and apoptosis in the presence of angiogenesis suppression. - Nature Medicine, Vol. 1, No. 2, pp. 149-153.
  • Kaczorek T. (1998): Weakly positive continuous-time linear systems. - Bull. Polish Acad. Sci., Vol. 46, No. 2, pp. 233-245.
  • Kimmel M. and Świerniak A. (1983): An optimal control problem related to leukemia chemotherapy. - Sci. Bull. Silesian Univ. Technol., Vol. 65, s. Automatyka, pp. 120-130.
  • Kimmel M., Świerniak A. and Polański A. (1998): Infinite-dimensional model of evolution of drug resistance of cancer cells. - J. Math. Syst. Estim. Contr., Vol. 8, No. 1, pp. 1-16.
  • Kimmel M. and Traganos F. (1986): Estimation and prediction of cell cycle specific effects of anticancer drugs. - Math. Biosci., Vol. 80, No. 2, pp. 187-208.
  • Konopleva M., Tsao T., Ruvolo P., Stiouf I., Estrov Z., Leysath C.E., Zhao S., Harris D., Chang S., Jackson C.E., Munsell M., Suh N., Gribble G., Honda T., May W.S., Sporn M.B. and Andreef M. (2002): Novel triterpenoid CDDO-Me is a potent inducer of apoptosis and differentiation in acute myelogenous leukemia. - Blood, Vol. 99, No. 1, pp. 326-335.
  • Kozusko F., Chen P., Grant S.G., Day B.W. and Panetta J.C. (2001): A mathematical model of in vitro cancer cell growth and treatment with the antimitotic agent curacin A. - Math. Biosci., Vol. 170, No. 1, pp. 1-16.
  • Krener A. (1977): The high-order maximal principle and its application to singular controls. - SIAM J. Contr. Optim., Vol. 15, No. 2, pp. 256-293.
  • Ledzewicz U. and Schättler H. (2002a): Optimal bang-bang controls for a 2-compartment model of cancer chemotherapy. - J. Optim. Th.Appl., Vol. 114, No. 3, pp. 609-637.
  • Ledzewicz U. and Schättler H. (2002b): Analysis of a cell-cycle specific model for cancer chemotherapy. - J. Biol. Syst., Vol. 10, No. 3, pp. 183-206.
  • Luzzi K.J., MacDonald I.C., Schmidt E.E., Kerkvliet N., Morris V.L., Chambers A.F. and Groom A.C. (1998): Multistep nature of metastatic inefficiency: dormancy of solitary cells after successful extra vasation and limited survival of early micrometastases. - Amer. J. Pathology, Vol. 153, No. 3, pp. 865-873.
  • Lyss A.P. (1992): Enzymes and random synthetics, In: Chemotherapy Source Book, (M.C. Perry, Ed.). - Baltimore: Williams and Wilkins, pp. 403-408.
  • Martin R.B. (1992): Optimal control drug scheduling of cancer chemotherapy. - Automatica, Vol. 28, No. 6, pp. 1113-1123.
  • Noble J. and Schättler H. (2002): Sufficient conditions for relative minima of broken extremals in optimal control theory. - J. Math. Anal. Appl., Vol. 269, No. 1, pp. 98-128.
  • Panetta J.C., Yanishevski Y., Pui C.H., Sandlund J.T., Rubnitz J., Rivera G.K., Ribeiro R., Evans W.E. and Relling M.V. (2002a): A mathematical model of in vivo methotrexate accumulation in acute lymphoblastic leukemia. - Cancer Chemother. Pharmacol., Vol. 50, No. 5, pp. 419-428.
  • Panetta J.C., Wall A., Pui C.H., Relling M.V. and Evans M.V. (2002b): Methotrexate intracellular disposition in acute lymphoblastic leukemia: Amathematical model of gammaglumatyl hydrolase activity. - Clinical Cancer Res., Vol. 8, No. 7, pp. 2423-2439.
  • Pontryagin L.S., Boltyanskii V.G., Gamkrelidze R.V. and Mishchenko E.F. (1964): The Mathematical Theory of Optimal Processes. - New York: MacMillan.
  • Swan G.W. (1990): Role of optimal control in cancer chemotherapy. - Math. Biosci., Vol. 101, No. 2, pp. 237-284.
  • Świerniak A. (1994): Some control problems for simplest differential models of proliferation cycle. - Appl. Math. Comp. Sci., Vol. 4, No. 2, pp. 223-232.
  • Świerniak A. (1995): Cell cycle as an object of control. - J.Biol. Syst., Vol. 3, No. 1, pp. 41-54.
  • Świerniak A. and Duda Z. (1995): Bilinear models of cancer chemotherapy-singularity of optimal solutions, In: Math. Population Dynam. (O. Arino, D. Axelrod, M. Kimmel, Eds.). -Vol. 2, pp. 347-358.
  • Świerniak A. and Kimmel M. (1984): Optimal control application to leukemia chemotherapy protocols design. - Sci. Bull. Silesian Univ. of Technol., Vol. 74, s. Automatyka, pp. 261-277, (in Polish).
  • Świerniak A., Polański A. and Kimmel M. (1996): Optimal control problems arising in cell-cycle-specific cancer chemotherapy. - Cell Prolif., Vol. 29, No. 1, pp. 117-139.
  • Świerniak A., Polański A. and Duda Z. (1992): 'Strange' phenomena in simulation of optimal control problems arising in cancer chemotherapy. - Proc. 8th Prague Symp. Computer Simulation in Biology, Ecology and Medicine, pp. 58-62.
  • Tafuri A. and Andreeff M. (1990): Kinetic rationale for cytokine-induced recruitment of myeloblastic leukemia followed bycycle-specific chemotherapy in vitro. - Leukemia, Vol. 12, No. 4, pp. 826-834.

Typ dokumentu

Bibliografia

Identyfikatory

Identyfikator YADDA

bwmeta1.element.bwnjournal-article-amcv13i3p357bwm
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.