Direct and indirect control of cancer populations

• Autorzy: Świerniak A.
• Języki publikacji: EN

Abstrakty

EN

This paper presents a brief survey of our research in which we have used control theoretic methods in modelling and control of cancer populations. We focus our attention on two classes of problems: optimization of anticancer chemotherapy taking into account both phase specificity and drug resistance, and modelling, and optimization of antiangiogenic therapy. In the case of chemotherapy the control action is directly aimed against the cancer cells while in the case of antiangiogenic therapy it is directed against normal cells building blood vessels and only indirectly it controls cancer growth. We discuss models (both finite and infinite dimensional) which are used to find conditions for tumour eradication and to optimize chemotherapy protocols treating cell cycle as an object of control. In the case of antiangiogenic therapy we follow the line of reasoning presented by Hahnfeldt et al. who proposed to use classical models of self-limiting tumour growth with variable carrying capacity defined by the dynamics of the vascular network induced by the tumour in the process of angiogenesis. In this case antiangiogenic protocols are understood as control strategies and their optimization leads to new recommendations for anticancer therapy.

Słowa kluczowe

EN

biomedical models; optimal control; nonlinear control systems; anticancer therapy

• Wydawca: Polska Akademia Nauk, Wydział IV Nauk Technicznych
• Czasopismo: Bulletin of the Polish Academy of Sciences. Technical Sciences
• Rocznik: 2008
• Tom: Vol. 56, nr 4
• Strony: 367--378
• Opis fizyczny: Bibliogr. 47 poz., rys.

Twórcy

autor

Świerniak A.

• Department of Automatic Control, Silesian University of Technology, 16 Akademicka St., 44-101 Gliwice, Poland

Bibliografia

• [1] A. Swierniak and Z. Duda, “Singularity of optimal control problems arising in cancer chemotherapy”, Math. Comp. Modeling 19, 255–262 (1994).
• [2] A. Swierniak and A. Polanski, “Irregularity of optimal control problem in scheduling cancer chemotherapy”, Appl. Math. Comp. Sci. 4, 263–271 (1994).
• [3] A. Swierniak, U. Ledzewicz, and H. Schattler, “Optimal control for a class of compartmental models in cancer chemotherapy”, Int. J. Appl. Math. Comput. Sci. 13, 357–368 (2003).
• [4] A. Swierniak, A. Polanski, Z. Duda, and M. Kimmel, “Phasespecific chemotherapy of cancer: optimisation of scheduling and rationale for periodic protocols”, Biocybernetics and Biomedical Engineering 16, 13–43 (1997).
• [5] A.J. Coldman and J.H. Goldie, “A stochastic model for the origin and treatment of tumors containing drug-resistant cells”, Bull. Math. Biol. 48, 279–292 (1986).
• [6] L.E. Harnevo and Z. Agur, “Use of mathematical models for understanding the dynamics of gene amplification”, Mutat. Res. 92, 17–24 (1993).
• [7] A. Swierniak, M. Kimmel, and A. Polanski, “Infinite dimensional model of evolution of drug resistance of cancer cells”, J. Math. Syst, Estim. Contr. 8, 1–17 (1998).
• [8] A. Swierniak, A. Polanski, M. Kimmel, A. Bobrowski, and J. Smieja, “Qualitative analysis of controlled drug resistance model – inverse Laplace and semigroup approach”, Contr. Cybern. 28, 61–74 (1999).
• [9] A. Swierniak, A. Polanski, J. Smieja, M. Kimmel, and J. Rzeszowska-Wolny, “Control theoretic approach to random branching walk models arising in molecular biology”, Proc of ACC Conference, 3449–3453 (2002).
• [10] M. Kimmel and A. Swierniak. “Control theory approach to cancer chemotherapy: benefiting from phase dependence and overcoming drug resistance”, Tutorials in Mathematical Biosciences III: Cell Cycle, Proliferation, and Cancer, Lecture Notes in Mathematics 1872, 185–222 (2006).
• [11] J. Smieja and A. Swierniak: “Comparison of phase specific chemotherapy models with and without taking into account drug resistance”, Proc. IASTED BioMED 417, CD-ROM (2004).
• [12] A. Swierniak and J. Smieja. “Analysis and optimization of drug resistant and phase-specific cancer chemotherapy models”, Math. Biosci. Eng. 2, 657–670 (2005).
• [13] H. Górecki, S. Fuksa, A. Korytowski, and W. Mitkowski, Optimal Control of Linear Systems with Quadratic Performance Index, PWN, Warsaw, 1983, (in Polish).
• [14] U. Ledzewicz, H. Schattler, and A. Swierniak, “Finite dimensional models of drug resistance and phase specificity”, J. Medical Inf. Techn. 8, IP5-IP13 (2004).
• [15] R.S. Kerbel, “A cancer therapy resistant to resistance”, Nature 390, 335–340 (1997).
• [16] P. Hahnfeldt, D. Panigraphy, J. Folkman, and L. Hlatky, “Tumor development under angiogenic signaling: a dynamic theory of tumor growth, treatment response and postvascular dormacy”, Cancer Res. 59, 4770–4778 (1999).
• [17] D.E. Axelrod, K.A. Baggerly, and M. Kimmel, “Gene amplification by unequal chromatid exchange: probabilistic modelling and analysis of drug resistance data”, J. Theor. Biol. 168, 151–159 (1994).
• [18] M. Kimmel and D.E. Axelrod, “Mathematical models of gene amplification with applications to cellular drug resistance and tumorigenicity”, Genetics 125, 633–644 (1994).
• [19] A. Swierniak, “Cell cycle as an object of control”, J. Biol. Syst. 3, 41–54 (1995).
• [20] B.W. Brown and J.R. Thompson, “A rationale for synchrony strategies in chemotherapy”, Epidemiology SIAM, 31–48 (1975).
• [21] J. Smieja, A. Swierniak, and Z. Duda Z. “Gradient method for finding optimal scheduling in infinite dimensional models of chemotherapy”, J. Theor. Medicine 3, 25–36 (2001).
• [22] H. Górecki, Analysis and Synthesis of Control Systems with Time Delay, WNT, Warsaw, 1993, (in Polish).
• [23] H. Górecki, S. Fuksa, P. Grabowski, and A. Korytowski, Analysis and Synthesis of Time Delay Systems, J. Wiley, Chichester, 1989.
• [24] L.S. Pontryagin, V.G. Boltyanski, R.V. Gamkrelidze, and J.F. Mishchenko, The Mathematical Theory of Optimal Processes, Mac Millan, New York, 1964.
• [25] H. Górecki. Optimization of Dynamic Systems, WNT, Warsaw, 1993, (in Polish).
• [26] R.B. Bate, “The optimal control of systems with transport lag”, Advances in Control Systems. 7, 165–224 (1969).
• [27] M.A. Connor, “Optimal control of systems represented by differential-integral equations”, IEEE Trans. on Autom. Contr. AC 17, 164–166 (1972).
• [28] J. Folkman, “Tumor angiogenesis: therapeutic implications”, N. Engl. J. Med. 295, 1182–1186 (1971).
• [29] J. Folkman, “Angiogenesis inhibitors generated by tumors”, Mol. Med. 1, 120–122 (1995).
• [30] N.V. Mantzaris, S. Webb, and H.G. Othmer, “Mathematical modeling of tumor-induced angiogenesis”, J. Math. Biol. 49, 111–127 (2004).
• [31] J. Denekamp “Angiogenesis, neovascular proliferation and vascular pathophysiology as targets for cancer therapy”, Brit. J. Radiol. 66, 181–196 (1993).
• [32] S. Davis and G.D. Yancopoulos, “The angiopoietins: Yin and Yang in angiogenesis”, Curr. Top. Microbiol. Immunol. 237, 173–185 (1999).
• [33] J. Bischoff, “Approaches to studying cell adhesion and angiogenesis”, Trends Cell Biol. 5, 69–73 (1995).
• [34] K. Bartha and H. Rieger, “Vascular network remodeling via vessel cooption, regression and growth in tumors”, J. Theor. Biol. 241, 903–918 (2006).
• [35] N. Weidner, “Intramural microvessel density as a prognostic factor in cancer”, Am. J. Path. 147, 9–19 (1995).
• [36] R.J. D’Amato, M.S. Loughnan, E. Flynn, and J. Folkman, “Thalidomide is an inhibitor of angiogenesis”, Proc. Natl. Acad. Sci USA 91, 4082–4085 (1994).
• [37] A. D’Onofrio and A. Gandolfi, “Tumour eradication by antiangiogenic therapy analysis and extensions of the model by Hahnfeldt et al (1999)”, Math. Biosci. 191, 159–184 (2004).
• [38] A. Swierniak, A. d’Onofrio, and A. Gandolfi, “Control problems related to tumor angiogenesis”, Proc. IEEE IECON 2006, 32 Annual Conf. IEEE IES, 677–681 (2006).
• [39] A. Ergun, K. Camphausen, and L.M. Wein, “Optimal scheduling of radiotherapy and angiogenic inhibitors”, Bull. Math. Biol. 65, 407–424 (2003).
• [40] U. Ledzewicz and H. Schattler, “A synthesis of optimal control for a model of tumour growth”, Proc. 44th IEEE CDC and ECC 2005, 934–939 (2005).
• [41] J. La Salle and S. Lefschetz, Stability by Lyapunov’s Direct Method, Academic Press, New York, 1961.
• [42] U. Ledzewicz and H. Schattler, “Analysis of mathematical model for tumor anti-angiogenesis”, Optim. Contr. Appl. Meth. 29, 41–57 (2008).
• [43] U. Ledzewicz and H. Schattler, “Anti-angiogenic teherapy in cancer treatment as an optimal control problem”, SIAM J. Contr. Optim. 46, 1052–1079 (2007).
• [44] A. Swierniak, “Control problem for antiangiogenic therapycomparison of six models”, Prepr. of 17th IFAC World Congress 15 (4), CD-ROM (2008).
• [45] A. Swierniak, “Control problems arising in combined antiangiogenic therapy and radiotherapy”, Proc. 5 IASTED Conf. on Biomedical Engineering, 113–117 (2007).
• [46] K. Simek, K. Fujarewicz, A. Swierniak, M. Kimmel, B. Jarzab, M. Wiench, and J. Rzeszowska, “Using SVD and SVM methods for selection, classification, clustering and modeling of DNA microarray data”, Eng. Appl. Artif. Intell. 17, 417–427 (2004).
• [47] B. Jarzab, M. Wiench, K. Fujarewicz, K. Simek, M. Oczko-Wojciechowska, J. Wloch, A. Czarniecka, E. Chmielik, D. Lange, A. Pawlaczek, S. Szpak, E. Gubala, and A. Swierniak, “Gene expression profile of papilllary thyroid carcinomas: sources of variability and diagnostic implications”, Cancer Res. 65, 1587–1597 (2005).