Vol: 57(71) No: 2 / June 2012 |
Comparison of Path Tracking Flat Control and Working Point Linearization Based Set Point Control of Tumor Growth with Angiogenic Inhibition
Dániel András Drexler
Department of Control Engineering and Information Technology, Budapest University of Technology and Economics, Magyar tudósok krt. 2., 1117, Budapest, phone: (361) 463-4027, e-mail: firstname.lastname@example.org
Department of Control Engineering and Information Technology, Budapest University of Technology and Economics, Magyar tudósok krt. 2., 1117, Budapest, e-mail: email@example.com
Department of Control Engineering and Information Technology, Budapest University of Technology and Economics , Magyar tudósok krt. 2., 1117, Budapest, e-mail: firstname.lastname@example.org
Department of Control Engineering and Information Technology, Budapest University of Technology and Economics , Magyar tudósok krt. 2., 1117, Budapest, e-mail: email@example.com
Budapest University of Technology and Economics, and John von Neumann Faculty of Information Technology, Óbuda University , Magyar tudósok krt. 2., 1117, Budapest, and Bécsi út 96/b, H-1034 Budapest, e-mail: firstname.lastname@example.org
Keywords: flat control, exact linearization, path tracking control, tumor growth control, angiogenic inhibition
Targeted molecular therapies (TMT) represent new perspectives in cancer treatment, fighting against the specific characteristic of the investigated tumor. Antiangiogenic therapy represents a specific TMT and its role is to stop the angiogenesis of the tumor, the process of forming new blood vessels; hence, to stop tumor growth. Proper control algorithms for tumor growth control with angiogenic inhibition are analyzed in the current article in order to find optimal therapeutic protocols. Two slightly different approaches are compared: nonlinear control by exact linearization with path tracking control, and linear control by working point linearization with set point control. The control strategies are compared in terms of the characteristics of the input signal (the inhibitor, drug intake) that is crucial if the therapy will be put into practice.
 M. Malvezzi, A. Arfé, P. Bertuccio, F. Levi, C. La Vecchia, and E. Negri, “European cancer mortality predictions for the year 2011”, Annals of Oncology, doi:10.1093/annonc/mdq774, 2011.
 D. A. Drexler, L. Kovács, J. Sápi, I. Harmati, Z. Benyó, “Model-based analysis and synthesis of tumor growth under angiogenic inhibition: a case study”, In Proc. of the IFAC WC 2011 – 18th World Congress of the International Federation of Automatic Control, Milano, Italy, pp. 3753-3758, August 2011.
 J. M. Pluda, “Tumor-associated angiogenesis: mechanism, clinical implications, and therapeutic strategies”, Seminars in Oncology, vol. 24(2), pp. 203-218, 1997.
 G. J. Kellof, C. W. Boone, V. E. Steele, J. R. Fay, R. A. Lubey, J. A. Criwel and C. C. Sigman, “Mechanistic considerations in chemopreventive drug development”, Journal of Cellular Biochemistry – Supplement, vol. 20, pp. 1-24, 1994.
 American Cancer Society, “Antiangiogenesis Treatment”, http://www.cancer.org/acs/groups/cid/documents/webcontent/002988-pdf.pdf , 2012.
 R. S. Kerbel, “A cancer therapy resistant to resistance”, Nature, vol. 390, pp. 335-336, 1997.
 Y. Y. Qian, H. Zhang, Y. Hou, L. Yuan, G. Q. Li, S. Y. Guo, H. Tadashi and Y. Q. Liu, “Celastrus Orbiculatus extract inhibits tumor angiogenesis by targeting vascular endothelial growth factor signaling pathway and shows potent antitumor activity in hepatocarcinomas in Vitro and in Vivo”, Chinese Journal of Integrative Medicine, pp. 1-9, 2011.
 R. Kerbel and J. Folkman, “Clinical translation of angiogenesis inhibitors”, Nature Reviews, Cancer, vol. 2, pp. 727-739, 2002.
 P. Hahnfeldt, D. Panigrahy, J. Folkman and L. Hlatky, “Tumor Development Under Angiogenic Signaling: A Dynamical Theory of Tumor Growth, Treatment response, and Postvascular Dormancy”, Cancer research, vol. 59, pp. 4770-4775, 1999.
 U. Ledzewicz and H. Schätler, “A synthesis of Optimal Controls for Model of Tumor Growth under Angiogenic Inhibitors”, In Proc. of the 44th IEEE conference on Decision and Control, and the European Control Conference 2005, pp. 934-939, December 2005.
 A. Ergun, K. Camphausen and L. M. Wein, “Optimal Scheduling of Radiotherapy and Angiogenic Inhibitors”, Bulletin of Mathematical Biology, vol. 65, pp. 407-424, 2003.
 J. Sápi, D. A. Drexler, I. Harmati, Z. Sápi and L. Kovács, “Linear state-feedback control synthesis of tumor growth in antiangiogenic therapy”. In Proceedings of SAMI 2012 – 10th International Symposium on Applied Machine Intelligence and Informatics, Herlany, Slovakia, pp. 143-148, January 2012.
 A. Szeles, J. Sápi, D. A. Drexler, I. Harmati, Z. Sápi and L. Kovács, “Model-based Angiogenic Inhibition of Tumor Growth using Modern Robust Control Method”, In Proc. of IFAC 2012 – 8th IFAC Symposium on Biological and Medical Systems, Budapest, Hungary, pp. 1-6, August 2012.
 D. A. Drexler, I. Harmati and L. Kovács, “Optimal control of tumor growth using antiangiogenic chemotherapy”, In Proc. of MACRo 2011 – 3rd International Conference on Recent Acievements in Mechatronics, Automation, Computer Sciences and Robotics, Targu Mures, Romania, pp. 273-284, April 2011.
 L. Kovács, P. Szalay, T. Ferenci, D. A. Drexler, J. Sápi, I. Harmati, Z. Benyó, “Modeling and Optimal Control strategies with High Public Health Impact”, In Proc. of INES 2011 – 15th International Conference on Intelligent Engineering System, Poprad, Slovakia, pp. 23-28, June 2011.
 D.A. Drexler, J. Sápi, A. Szeles, I. Harmati, A. Kovács, L. Kovács, “Flat control of tumor growth with angiogenic inhibition”, In Proc. of SACI 2012 – 7th International Symposium on Applied Computational Intelligence and Informatics, Timisoara, Romania, pp. 179-183, May 2012.
 K. J. Gotink and H. M. W. Verheul, “Anti-angiogenic tyrosine kinase inhibitors: what is their mechanism of action?”, Angiogenesis, vol. 13, pp. 1-14, 2010.
 A. Isidori, Nonlinear Control Systems, Springer-Verlag London, 1995.
 R.E. Precup and S. Preitl, “Optimisation criteria in development of fuzzy controllers with dynamics”, Engineering Applications of Artificial Intelligence, vol. 17(6), pp. 661-674, 2004.