THE SCHEDULING OF ANGIOGENIC INHIBITORS MINIMIZING TUMOR

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.

[1]  Alberto Gandolfi,et al.  Optimization of antiangiogenic therapy as optimal control problem , 2006 .

[2]  J. Folkman,et al.  Angiogenesis Inhibitors Generated by Tumors , 1995, Molecular medicine.

[3]  M. Chaplain,et al.  Continuous and discrete mathematical models of tumor-induced angiogenesis , 1998, Bulletin of mathematical biology.

[4]  H. Schättler,et al.  A Synthesis of Optimal Controls for a Model of Tumor Growth under Angiogenic Inhibitors , 2005, Proceedings of the 44th IEEE Conference on Decision and Control.

[5]  Shay Soker,et al.  VEGF/VPF: The angiogenesis factor found? , 1993, Current Biology.

[6]  Urszula Ledzewicz,et al.  Optimal and suboptimal protocols for a class of mathematical models of tumor anti-angiogenesis. , 2008, Journal of theoretical biology.

[7]  U. Ledzewicz,et al.  ANTI-ANGIOGENIC THERAPY IN CANCER TREATMENT AS AN OPTIMAL CONTROL PROBLEM , 2007 .

[8]  Thomas Boehm,et al.  Antiangiogenic therapy of experimental cancer does not induce acquired drug resistance , 1997, Nature.

[9]  Z. Agur,et al.  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 tumor growth , 2004, Angiogenesis.

[10]  Alberto Gandolfi,et al.  Tumour eradication by antiangiogenic therapy: analysis and extensions of the model by Hahnfeldt et al. (1999). , 2004, Mathematical biosciences.

[11]  R. Kerbel.  A cancer therapy resistant to resistance , 1997, Nature.

[12]  P. Hahnfeldt,et al.  Tumor development under angiogenic signaling: a dynamical theory of tumor growth, treatment response, and postvascular dormancy. , 1999, Cancer research.

[13]  H. Maurer,et al.  Optimization methods for the verification of second order sufficient conditions for bang–bang controls , 2005 .

[14]  L. Wein,et al.  Optimal scheduling of radiotherapy and angiogenic inhibitors , 2003, Bulletin of mathematical biology.

[15]  J. Folkman,et al.  Anti‐Angiogenesis: New Concept for Therapy of Solid Tumors , 1972, Annals of surgery.