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Tytuł artykułu

Controllability of a model of combined anticancer therapy

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Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
Controllability of combination of antiangiogenic treatment and chemotherapy is considered. A model used in the paper is a finite-dimensional dynamical control system described by secondo order semilinear time invariant ordinary differential state equations. Using a generalized open mapping theorem, sufficient conditions for constrained local controllability in a given time interval are formulated and proved. These conditions require verification of constrained global controllability of the associated linear second-order dynamical control system.
Rocznik
Strony
123--138
Opis fizyczny
Bibliogr. 24 poz.
Twórcy
autor
  • Department of Automatic Control, Silesian University of Technology, Gliwice, Poland
  • Department of Automatic Control, Silesian University of Technology, Gliwice, Poland
Bibliografia
  • 1. Bartha K. and H. Rieger (2006) Vascular network remodeling via Lessel cooption, regression and growth in tumors. J. Theor. Biol. 241, 903-918.
  • 2. Camidge D.R. and D.I. Jordell (2005) Introduction to the cellular and molecular biology of cancer, chapter 24: Chemotherapy, Oxford University Press.
  • 3. d’Onofrio A. and A. Gandolfi (2004) Tumour eradication by antiangiogenic therapy analysis and extensions of the model by Hahnfeldt et al. (1999) Math. Biosci 191, 159-184.
  • 4. d’Onofrio A. and A. Gandolfi (2009) A family of models of angiogenesis and anti-angiogenesis anti-cancer therapy. Math. Med. Biol. 26 (1), 63-95.
  • 5. Ergun A., K. Camphausen, and L.M. Wein (2003) Optimal scheduling of radiotherapy and angio-genic inhibitors. Bull. Math. Biol. 65, 407-424.
  • 6. Folkman J. (1971) Tumor angiogenesis: therapeutic implications. N. Engl. J. Med. 295, 1182-1186.
  • 7. Forys U. and J. Poleszczuk (2011) A delay-differential equation model of HIV related cancer-immune system dynamics. Math. Biosci. Engineering, 8 (2), 627-641
  • 8. Hahnfeldt P., D. Panigraphy, J. Folkman and L. Hlatky (1999) Tumor development under angiogenic signaling: A dynamic theory of tumor growth, treatment response and postvascular dormacy. Cancer Res. 59, 4770-4778.
  • 9. Kaczorek T. (1993) Linear Control Systems, vol. I and vol. II. Research Studies Press and John Wiley, New York.
  • 10. Kaczorek T. (2002) Positive 1D and 2D Systems. Springer-Verlag, London.
  • 11. Kaczorek T. (2007) Polynomial and Rational Matrices. Applications in Dynamical Systems Theory. Springer-Verlag, London.
  • 12. Kerbel R.S. (1997) A cancer therapy resistant to resistance. Nature, 390, 335-340.
  • 13. Klamka J. (1991) Controllability of Dynamical Systems. Kluwer Academic Publishers, Dordrecht, The Netherlands.
  • 14. Klamka J. (1993) Controllability of dynamical systems-a survey. Archives of Control Sciences, 2(3/4), 281-307.
  • 15. Klamka J. (1996) Constrained controllability of nonlinear systems. Journal of Mathematical Analysis and Applications 201(2), 365-374.
  • 16. Klamka J. (2004) Constrained controllability of semilinear systems with multiple delays in control. Bulletin of the Polish Academy of Sciences. Technical Sciences. 52 (1), 25-30.
  • 17. Ledzewicz U. and H. Schättler (2007) Anti-angiogenic therapy in cancer treatment as an optimal control problem. SIAM J. Contr. Optim, 46, 1052-1079.
  • 18. Ledzewicz U. and H. Schättler (2008) Analysis of mathematical model for tumor anti-angiogenesis. Optim. Contr. Appl. Meth., 29, 41-57.
  • 19. Świerniak A. (2008) Direct and indirect control of cancer populations. Bulletin of the Polish Academy of Sciences Technical Sciences 56, 367-368.
  • 20. Swierniak A. (2009) Comparison of six models of antiangiogenic therapy. Applicationes Mathematicae, 36, 333-348.
  • 21. Swierniak A (2012) Combined anticancer therapy as a control problem. In: M. Bus lowicz and K. Malinowski, eds., Advances in Control Theory and Automation. Monograph of Committee of Automatics and Robotics PAS, Białystok, 251-263.
  • 22. Swierniak A. (2012a) Control problems related to three compartmental model of combined anticancer therapy. Proceedings. 20 IEEE Mediterrenean Conference on Automation and Control MED 12, Barcelona. IEEE Press, 1428-1433.
  • 23. Swierniak A. and K. Ploskonski (2010) Periodic control of antiangiogenic and combined anticancer therapies. IFAC Workshop of Periodic Control Systems PSYCO 2010, Antalya, CD ROM edition.
  • 24. Swierniak A. and J. Klamka (2011) Control properties of models of antiangiogenic therapy. In: K. Malinowski and R. Dindorf, eds., Advances in Automatics and Robotics (Post¸epy Automatyki i Robotyki). Monograph of Committee of Automatics and Robotics PAS, 16, Kielce, part 2, 300-312.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-984eb41b-152c-414c-91a0-8253a0e65c51
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