Antiangiogenic therapy in cancer treatment as an optimal control problem

SIAM Journal on Control and Optimization

Volumn 46, Issue 3, 2007, Pages 1052-1079

  Ledzewicz, Urszula ^a   Schättler, Heinz ^b  

^a SOUTHERN ILLINOIS UNIVERSITY EDWARDSVILLE   (United States)

^b WASHINGTON UNIVERSITY IN ST LOUIS   (United States)

Author keywords

Antiangiogenic therapy; Cancer treatment; Geometric methods; Optimal control

Indexed keywords

ANTI-ANGIOGENIC THERAPIES; ANTIANGIOGENIC; APPLIED MATHEMATICS; BLOOD SUPPLY; CANCER THERAPIES; GEOMETRIC METHODS; OPTIMAL CONTROL PROBLEM (OCP); OPTIMAL CONTROL THEORY (OCT); VALIDATED MODEL;

ALUMINUM; COMPUTER NETWORKS; CONTROL THEORY; INTERSECTIONS; WEIGHT CONTROL;

MATHEMATICAL MODELS;

EID: 42749090784     PISSN: 03630129     EISSN: None     Source Type: Journal    
DOI: 10.1137/060665294     Document Type: Article

References (18)

1. Z. AGUR, L. ARAKELYAN, P. DAUGULIS, AND Y. GINOSAR, Hopf point analysis for angiogenesis models, Discrete Contin. Dyn. Sys. Series B, 4 (2004), pp. 29-38.
2. B. BONNARD AND J. DE MORANT, Toward a geometric theory in the time-minimal control of chemical batch reactors, SIAM J. Control Optim., 33 (1995), pp. 1279-1311.
3. A.E. BRYSON AND Y.C. HO, Applied Optimal Control, Hemisphere, Washington, DC, 1975.
4. L. CESARI, Optimization - Theory and Applications, Springer-Verlag, New York, 1983.
5. 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 (2004), pp. 159-184.
6. A. ERGUN, K. CAMPHAUSEN, AND L.M. WEIN, Optimal scheduling of radiotherapy and angiogenic inhibitors, Bull. Math. Bio., 65 (2003), pp. 407-424.
7. U. FORYS, Y. KEIFETZ, AND Y. KOGAN, Critical-point analysis for three-variable cancer angiogenesis models, Math. Biosci. Eng., 2 (2005), pp. 511-525.
8. J.H. GOLDIE, Drug resistance in cancer: A perspective, Cancer Metastasis Rev., 20 (2001), pp. 63-68.
9. P. HAHNFELDT, D. PANIGRAHY, J. FOLKMAN, AND L. HLATKY, Tumor development under angiogenic signaling: A dynamical theory of tumor growth, treatment response, and post-vascular dormancy, Cancer Res., 59 (1999), pp. 4770-4775.
10. R.S. KERBEL, A cancer therapy resistant to resistance, Nature, 390 (1997), pp. 335-336.
11. A.J. KRENER, The high order maximal principle and its application to singular extremals, SIAM J. Control Optim., 15 (1977), pp. 256-293.
12. U. LEDZEWICZ AND H. SCHÄTTLER, A synthesis of optimal controls for a model of tumor growth under angiogenic inhibitors, in Proceedings of the 44th IEEE Conference on Decision and Control, Sevilla, Spain, 2005, pp. 934-939.
13. U. LEDZEWICZ AND H. SCHÄTTLER, Optimal control for a system modelling tumor antiangiogenesis, ICGST-ACSE J., 6 (2006), pp. 33-39.
14. U. LEDZEWICZ AND H. SCHÄTTLER, Application of optimal control to a system describing tumor anti-angiogenesis, in Proceedings of the 17th International Symposium on Mathematical Theory of Networks and Systems (MTNS), Kyoto, Japan, 2006, pp. 478-484.
15. U. LEDZEWICZ AND H. SCHÄTTLER, Analysis of optimal controls for a mathematical model of tumor anti-angiogenesis, Optimal Control Appl. Methods, to appear.
16. L.A. LOEB, A mutator phenotype in cancer, Cancer Res., 61 (2001), pp. 3230-3239.
17. H. SCHÄTTLER AND M. JANKOVIC, A synthesis of time-optimal controls in the presence of saturated singular arcs, Forum Math., 5 (1993), pp. 203-241.
18. L.S. PONTRYAGIN, V.G. BOLTYANSKII, R.V. GAMKRELIDZE, AND E.F. MISHCHENKO, The Mathematical Theory of Optimal Processes, Macmillan, New York, 1964.