Optimal control for combination therapy in cancer

Proceedings of the IEEE Conference on Decision and Control

Volumn , Issue , 2008, Pages 1537-1542

  Ledzewicz, Urszula ^a   Schättler, Heinz ^b   D'Onofrio, Alberto ^c  

^a SOUTHERN ILLINOIS UNIVERSITY EDWARDSVILLE   (United States)

^b WASHINGTON UNIVERSITY IN ST LOUIS   (United States)

^c EUROPEAN INSTITUTE OF ONCOLOGY   (Italy)

Author keywords

[No Author keywords available]

Indexed keywords

OPTIMAL CONTROL SYSTEMS;

COMBINATION THERAPY; OPTIMAL CONTROL PROBLEM; OPTIMAL CONTROLS;

STRUCTURAL OPTIMIZATION;

EID: 62949247820     PISSN: 07431546     EISSN: 25762370     Source Type: Conference Proceeding    
DOI: 10.1109/CDC.2008.4738880     Document Type: Conference Paper

References (20)

1. A. Anderson and M. Chaplain, Continuous and discrete mathematical models of tumor-induced angiogenesis, Bull. Math. Biol., 60, 1998, pp. 857ff
2. 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), pp. 404ff
3. B. Bonnard and M. Chyba, Singular Trajectories and their role in Control Theory, Math'ematiques & Applications, vol. 40, Springer Verlag, Paris, 2003
4. A. Bressan and B. Piccoli, Introduction to the Mathematical Theory of Control, American Institute of Mathematical Sciences, 2007
5. F. Castiglione and B. Piccoli, Optimal control in a model of dendritic cell transfection cancer immunotherapy, Bulletin of Mathematical Biology, 68, (2006), pp. 255-274
6. L.G. de Pillis and A. Radunskaya, A mathematical tumor model with immune resistance and drug therapy: an optimal control approach, J. of Theoretical Medicine, 3, (2001), pp. 79-100
7. A. d'Onofrio, A general framework for modeling tumor-immune system competition and immunotherapy: mathematical analysis and biomedical inferences, Physica D, 208, 2005, pp. 220-235
8. A. d'Onofrio, Rapidly acting antitumoral anti-angiogenic therapies, Physical Review E, 76 (3), Art. No. 031920, 2007
9. 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, pp. 159-184
10. A. d'Onofrio and A. Gandolfi, The response to antiangiogenic anticancer drugs that inhibit endothelial cell proliferation, Appl. Math. and Comp., 181, 2006, pp. 1155-1162
11. A. Ergun, K. Camphausen and L.M. Wein, Optimal scheduling of radiotherapy and angiogenic inhibitors, Bull. of Math. Biology, 65, (2003), pp. 407-424
12. J. Folkman, Antiangiogenesis: new concept for therapy of solid tumors, Ann. Surg., 175, (1972), pp. 409-416
13. 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), pp. 4770-4775
14. R.S. Kerbel, A cancer therapy resistant to resistance, Nature, 390, (1997), pp. 335-336
15. D. Kirschner, S. Lenhart, and S. Serbin, Optimal control of chemotherapy of HIV, J. Math. Biol., 35, (1997), pp. 775-792
16. 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, pp. 945-950
17. U. Ledzewicz and H. Schättler, Anti-Angiogenic therapy in cancer treatment as an optimal control problem, SIAM J. Contr. Optim., 46, 2007, pp. 1052-1079
18. U. Ledzewicz and H. Schättler, Analysis of a mathematical model for tumor anti-angiogenesis, Opt. Contr. Appl. Meth., 29, (1), (2008), pp. 41-57
19. B. Piccoli and H.J. Sussmann, Regular synthesis and sufficiency conditions for optimality, SIAM J. Control Optimization, 39, (2000), pp. 359-410
20. A. Swierniak, A. d'Onofrio and A. Gandolfi, Control Problems related to tumor angiogenesis, Proceedings of IECON 2006, IEEE Press (2006), pp. 677-681