The scheduling of angiogenic inhibitors minimizing tumor volume

• Autorzy: Ledzewiecz U. , Marriott J. , Maurer H. , Schättler H.
• Języki publikacji: EN

Abstrakty

EN

The efficiency of piecewise constant protocols with a small number of switchings is investigated for a mathematical model of tumor anti-angiogenesis formulated originally by Hahnfeldt et al. in [8]. By comparing with the theoretically optimal solution derived earlier [12] it will be seen that for the problem of minimizing the primary cancer volume with a given amount of angiogenic inhibitors to be administered constant protocols already provide very good suboptimal strategies.

Słowa kluczowe

EN

biomathematical modelling; optimal control; tumor anti-angiogenesis; realizable protocols

PL

modelowanie biomatematyczne; kontrola optymalna; sterowanie optymalne; guz antyangiogenny; uzyskiwanie protokołów

• Wydawca: University of Silesia, Institute of Informatics, Computer Systems Department
• Czasopismo: Journal of Medical Informatics & Technologies
• Rocznik: 2008
• Tom: Vol. 12
• Strony: 23--28
• Opis fizyczny: Bibliogr. 15 poz., rys., tab.

Twórcy

autor

Ledzewiecz U.

• Southern Illinois University at Edwardsville, Edwardsville, Il, USA

autor

Marriott J.

autor

Maurer H.

autor

Schättler H.

Bibliografia

• [1] ANDERSON A. and CHAPLAIN M., Continuous and discrete mathematical models of tumorinduced angiogenesis, Bull. Math. Biol., 60, (1998), pp. 857ff
• [2] ARAKELYAN L., VAINSTAIN V., and AGUR Z., A computer algorithm describing the process of vessel formation and maturation, and its use for predicting the effects of anti-angiogenic and anti-maturation therapy on vascular tumour growth, Angiogenesis, 5, (2003), 203ff
• [3] BOEHM T., Folkman J., BROWDER T., and O’REILLY M.S., Antiangiogenic therapy of experimental cancer does not induce acquired drug resistance, Nature, 390, (1997), pp. 404ff
• [4] d’ONOFRIO A. and GANDOLFI A., Tumour eradication by antiangiogenic therapy: analysis and extensions of the model by Hahnfeldt et al. (1999), Math. Biosci., 191, (2004), pp. 159-184
• [5] ERGUN A., CAMPHAUSEN K., and WEIN L.M., Optimal scheduling of radiotherapy and angiogenic inhibitors, Bull. of Math. Biology, 65, (2003), pp. 407-424
• [6] FOLKMAN J., Antiangiogenesis: new concept for therapy of solid tumors, Ann. Surg., 175, (1972), pp. 409-416
• [7] FOLKMAN J., Angiogenesis inhibitors generated by tumors, Mol. Med., 1, (1995), pp. 120-122
• [8] HAHNFELDT P., PANIGRAHY D., FOLKMAN J. and HLATKY L., Tumor development under angiogenic signaling: a dynamical theory of tumor growth, treatment response, and postvascular dormancy, Cancer Research, 59, (1999), pp. 4770-4775
• [9] KERBEL R.S., A cancer therapy resistant to resistance, Nature, 390, (1997), pp. 335-336
• [10] KLAGSBURN M. and SOKER S., VEGF/VPF: the angiogenesis factor found?, Curr. Biol., 3, (1993), pp. 699-702
• [11] LEDZEWICZ U. and SCH¨ ATTLER H., A synthesis of optimal controls for a model of tumor growth under angiogenic inhibitors, Proceedings of the 44th IEEE Conference on Decision and Control (CDC), Sevilla, Spain, December 2005, pp. 934-939
• [12] LEDZEWICZ U. and SCH¨ ATTLER H., Anti-Angiogenic Therapy in Cancer treatment as an Optimal Control Problem, SIAM J. on Control and Optimization, 46 (3), (2007), pp. 1052-1079
• [13] LEDZEWICZ U. and SCH¨ ATTLER H., Optimal and Suboptimal Protocols for a Class of Mathematical Models of Tumor Anti-Angiogenesis, J. of Theoretical Biology, 252, (2008), pg. 295-312
• [14] MAURER, H., B¨ USKENS, C., KIM, J.-H.R. and KAYA, C.Y., Optimization methods for the verification of second order sufficient conditions for bang–bang controls, Optimal Control Applications and Methods, 26, (2005), pp. 129–156
• [15] SWIERNIAK A., GALA G., GANDOLFI A. and d’ONOFRIO A., Optimization of angiogenic therapy as optimal control problem, Proceedings of the 4th IASTED Conference on Biomechanics, Acta Press, (Ed. M. Doblare), (2006), pp. 56-60