Bang-bang and singular controls in a mathematical model for combined anti-angiogenic and chemotherapy treatments

Proceedings of the IEEE Conference on Decision and Control

Volumn , Issue , 2009, Pages 2280-2285

  Ledzewicz, Urszula ^a   Maurer, Helmut ^b   Schättler, Heinz ^c  

^a SOUTHERN ILLINOIS UNIVERSITY EDWARDSVILLE   (United States)

^b UNIVERSITY OF MÜNSTER   (Germany)

^c WASHINGTON UNIVERSITY IN ST LOUIS   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

CHEMOTHERAPY; OPTIMAL CONTROL SYSTEMS;

CHEMOTHERAPEUTIC AGENTS; CHEMOTHERAPY TREATMENT; CYTOTOXIC AGENTS; EXPLICIT EQUATIONS; MONO-THERAPY; NUMERICAL RESULTS; OPTIMAL CONTROL PROBLEM; SINGULAR CONTROL;

STRUCTURAL OPTIMIZATION;

EID: 77950851120     PISSN: 07431546     EISSN: 25762370     Source Type: Conference Proceeding    
DOI: 10.1109/CDC.2009.5400735     Document Type: Conference Paper

References (19)

1. T. Boehm, J. Folkman, T. Browder, and M.S. O'Reilly, Antiangiogenic therapy of experimental cancer does not induce acquired drug resistance, Nature, 390, (1997), 404-407
2. B. Bonnard and M. Chyba, Singular Trajectories and their role in Control Theory, Springer Verlag, Paris, 2003
3. A. Bressan and B. Piccoli, Introduction to the Mathematical Theory of Control, American Institute of Mathematical Sciences, 2007
4. A. d'Onofrio and A. Gandolfi, Tumour eradication by antiangiogenic therapy: analysis and extensions of the model by Hahnfeldt et al., Math. Biosci., 191, (2004), 159-184
5. A. d'Onofrio, Rapidly acting antitumoral anti-angiogenic therapies, Physical Review E, 76 (3), Art. No.031920, (2007)
6. A. d'Onofrio, U. Ledzewicz, H. Maurer and H. Schättler, On Optimal Delivery of Combination Therapy for Tumors, Math. Biosci., (2009), to appear, doi: 10.1016/j.mbs.2009.08.004
7. A. Ergun, K. Camphausen and L.M. Wein, Optimal scheduling of radiotherapy and angiogenic inhibitors, Bull. of Math. Biology, 65, (2003), 407-424
8. J. Folkman, Antiangiogenesis: new concept for therapy of solid tumors, Ann. Surg., 175, (1972), 409-416
9. 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, 59, (1999), 4770-4775
10. R.S. Kerbel, Tumor angiogenesis: past, present and near future. Carcinogensis, 21, (2000), 505-515
11. U. Ledzewicz, J. Munden, and H. Schättler, Scheduling of Angiogenic Inhibitors for Gompertzian and Logistic Tumor Growth Models, Disc. and Cont. Dyn. Syst., Series B, 12, (2009), 415-438
12. U. Ledzewicz and H. Schättler, A synthesis of optimal controls for a model of tumor growth under angiogenic inhibitors, Proc. 44th IEEE Conf. on Dec. and Contr., Sevilla, Spain, 2005, 945-950
13. U. Ledzewicz and H. Schättler, Anti-Angiogenic therapy in cancer treatment as an optimal control problem, SIAM J. Contr. Optim., 46, (2007), 1052-1079
14. U. Ledzewicz and H. Schättler, Analysis of a mathematical model for tumor anti-angiogenesis, Opt. Contr. Appl. Meth., 29 (2008), 41-57.
15. U. Ledzewicz, H. Schättler and A. d'Onofrio, Optimal control for combination therapy in cancer, Proc. 47th IEEE Conf. on Dec. and Contr., Cancun, Mexico, (2008), 1537-1542
16. H. Maurer, C. Büskens, J.-H. Kim and Y. Kaja, Optimization techniques for the verification of second-order sufficient conditions for bang-bang controls, Optimal Control, Applications and Methods, 26, (2005), 129-156
17. A. Swierniak, A. d'Onofrio and A. Gandolfi, Control Problems related to tumor angiogenesis, Proceedings of IECON 2006, IEEE Press (2006), 677-681
18. A. Swierniak, Modelling combined angiogenic and chemotherapy, Proc. of the Fourteenth National Conference on Appl. of Math. in Biology and Medicine, Leszno, Poland, (2008), 127-133
19. A. Swierniak, Direct and indirect control of cancer populations, Bull. Polish Acad. of Scie., Tech. Sci., 56 no.4, (2008), 367-378