New approach to modeling of antiangiogenic treatment on the basis of Hahnfeldt et al. model

Mathematical Biosciences and Engineering

Volumn 8, Issue 2, 2011, Pages 591-603

  Poleszczuk, Jan ^a   Bodnar, Marek ^a   Foryś, Urszula ^a  

^a UNIVERSITY OF WARSAW   (Poland)

Author keywords

Angiogenesis; Antiangiogenic treatment; Ordinary differential equations; Tumor

Indexed keywords

ANGIOGENESIS INHIBITOR; ANTINEOPLASTIC AGENT;

ANIMAL; BIOLOGICAL MODEL; CELL PROLIFERATION; COMPUTER ASSISTED DRUG THERAPY; COMPUTER SIMULATION; CONFERENCE PAPER; DOSE RESPONSE; DRUG EFFECT; HUMAN; METHODOLOGY; NEOPLASM; NEOVASCULARIZATION (PATHOLOGY); PATHOPHYSIOLOGY; TREATMENT OUTCOME;

ANGIOGENESIS INHIBITORS; ANIMALS; ANTINEOPLASTIC AGENTS; ANTINEOPLASTIC COMBINED CHEMOTHERAPY PROTOCOLS; CELL PROLIFERATION; COMPUTER SIMULATION; DOSE-RESPONSE RELATIONSHIP, DRUG; DRUG THERAPY, COMPUTER-ASSISTED; HUMANS; MODELS, BIOLOGICAL; NEOPLASMS; NEOVASCULARIZATION, PATHOLOGIC; TREATMENT OUTCOME;

EID: 79955003443     PISSN: 15471063     EISSN: 15510018     Source Type: Journal    
DOI: 10.3934/mbe.2011.8.591     Document Type: Conference Paper

References (41)

1. B. Alberts, A. Johnson, J. Lewis, M. Raff, K. Roberts and P. Walter, "Molecular Biology of Cell", Garland Publishing, New York, 2007.
2. Z. Agur, L. Arakelyan, P. Daugulis and Y. Ginosar, Hopf point analysis for angiogenesis models, Discrete & Cont. Dyn. Sys. B, 4(2004), 29-38. (Pubitemid 38202953)
3. L. Arakelyan, V. Vainstein and Z. Agur, 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, Angiogenesis, 5(2002), 203-214. (Pubitemid 36687523)
4. I. D. Bassukas, Comparative Gompertzian analysis of alterations of tumor growth patterns, Cancer Research, 54(1994), 4385-4392. (Pubitemid 24273151)
5. M. Bodnar and U. Foryś, Three types of simple DDEs describing tumour growth, J. Biol. Sys., 15(2007), 453-471. (Pubitemid 350261761)
6. M. Bodnar and U. Foryś, Angiogenesis model with carrying capacity depending on vessel density, J. Biol. Sys., 17(2009), 1-25.
7. M. Bodnar and U. Foryś, Influence of time delays on the Hahnfeldt et al. angiogenesis model dynamics, Appl. Math. (Warsaw), 36(2009), 251-262.
8. th edition, Springer-Verlag, Berlin, 2007.
9. L. Preziosi, "Cancer Modeling and Simulation", Chapman & Hall, 2003.
10. A. d'Onofrio and A. Gandolfi, Tumor eradication by antiangiogenic therapy: Analysis and extensions of the model by Hahnfeldt et al. (1999), Math. Biosci., 191(2004), 159-184. (Pubitemid 39195231)
11. A. d'Onofrio and A. Gandolfi, The response to antiangiogenic anticancer drugs that inhibit endothelial cell proliferation, Appl. Math. Comput., 181(2006), 1155-1162. (Pubitemid 44646591)
12. A. d'Onofrio and A. Gandolfi, A family of models of angiogenesis and antiangiogensis anticancer therapy, Math. Med. Biol., 26(2009), 63-95.
13. A. d'Onofrio, A. Gandolfi and A. Rocca, The dynamics of tumour-vasculature interaction suggests low-dose, time-dense anti-angiogenic schedulings, Cell Prolif., 42(2009), 317-329.
14. A. Ergun, K. Camphausen and L. M. Wein, Optimal scheduling of radiotherapy and angiogenic inhibitors, Bull. Math. Biol, 65(2003), 407-424. (Pubitemid 36521826)
15. J. Folkman, Tumor angiogenesis: Therapeutic implications, N. Engl. J. Med., 285(1971), 1182-1186.
16. J. Folkman, Agiogenesis in cancer, vascular, rheumatoid and other disease, Nat. Med., 1(1995), 27-31.
17. J. Folkman, Angiogenesis, Ann. Rev. Med., 57(2006), 1-18. (Pubitemid 43261975)
18. U. Foryś and A. Marciniak-Czochra, Logistic equation in tumour growth modelling, Int. J. Appl. Math. Comp. Sci., 13(2003), 317-325.
19. S. A. Frank, "Dynamics of Cancer - Incidence, Inheritance, and Evolution", Princeton University Press, Princeton, 2007.
20. B. Gompertz, On the nature of the function expressive of the law of human mortality, and a new mode of determining the value of life contingencies, Phil. Trans. Roy. Soc., 115(1825), 513-585.
21. 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 Res., 59(1999), 4770-4775. (Pubitemid 29472873)
22. R. K. Jain, Taming vessels to treat cancer, Scientific American, 298(2008), 56-63. (Pubitemid 351182556)
23. R. K. Jain, Normalization of tumour vasculature: An emerging concept in antiangiogenic therapy, Science, 307(2005), 58-62. (Pubitemid 40093472)
24. A. K. Laird, Dynamics of tumour growth, Br. J. Cancer, 18(1964), 490-502.
25. A. K. Laird, Dynamics of tumour growth: Comparison of growth rates and extrapolation of growth curve to one cell, Br. J. Cancer, 19(1965), 278-291.
26. M. O. Leach, K. M. Brindle, J. L. Evelhoch, J. R. Griffiths, M. R. Horsman, A. Jackson, G. C. Jayson, I. R. Judson, M. V. Knopp, R. J. Maxwell, D. McIntyre, A. R. Padhani, P. Price, R. Rathbone, G. J. Rustin, P. S. Tofts, G. M. Tozer, W. Vennart, J. C. Waterton, S. R. Williams and P. Workman, The assessment of antiangiogenic and antivascular therapies in early-stage clinical trials using magnetic resonance imaging: Issues and recommendations, Br. J. Cancer, 92(2005), 1599-1610. (Pubitemid 40756468)
27. U. Ledzewicz and H. Schättler, Optimal control for a system modeling tumor antiangiogenesis, in "Proceedings of the ICGST International Conference on Automatic Control and System Engineering", (2005), 147-152.
28. U. Ledzewicz and H. Schättler, Antiangiogenic therapy in cancer treatment as an optimal control problem, SIAM J. Control Optim., 46(2007), 1052-1079.
29. U. Ledzewicz and H. Schättler, Analysis of a mathematical model for tumor anti-angiogenesis, Optimal Control Appl. Methods, 29(2008), 41-57. (Pubitemid 351354223)
30. U. Ledzewicz and H. Schättler, Optimal and suboptimal protocols for a class of mathematical models for tumor anti-angiogenesis, J. Theor. Biol., 252(2008), 295-312.
31. N. V. Mantzaris, S. Webb and H. G. Othmer, Mathematical modeling of tumor-induced angiogenesis, J. Math. Biol., 49(2004), 111-187. (Pubitemid 40882678)
32. J. D. Murray, "Mathematical Biology. An Introduction", Springer Verlag, New York, 2002.
33. M. S. O'Reilly, L. Holmgren, Y. Shing, C. Chen, R. A. Rosenthal, M. Moses, W. S. Lane, Y. Cao, E. H. Sage and J. Folkman, Agiostatin: A novel angiogenesis inhibitor that mediates the suppression of metastases by a Lewis lung carcinoma, Cell, 79(1994), 315-328. (Pubitemid 24324921)
34. M. S. O'Reilly, T. Boehm, Y. Shing, N. Fukai, G. Vasios, W. S. Lane, E. Flynn, J. R. Birkhead, B. R. Olsen and J. Folkman, Endostatin: An endogenous inhibitor of angiogenesis and tumor growth, Cell, 88(1997), 277-285. (Pubitemid 28015876)
35. J. Poleszczuk, Tumor development model under angiogenic signaling with dependence on vessel impairment, in "Proceedings of the Fourteenth National Conference on Application of Mathematics in Biology and Medicine", eds. M. Bodnar and U. Foryś, University of Warsaw, (2008), 104-109.
36. A. Świerniak, Comparison of six models of antiangiogenic therapy, Appl. Math. (Warsaw), 36(2009), 333-348.
37. A. Świerniak, G. Gala, A. Gandolfi and A. d'Onofrio, Optimization of anti-angiogenic therapy as optimal control problem, in "Proc. 4th IASTED Conf. on Biomechanics", ed. M. Doblaré, ACTA Press, (2006), 56-60.
38. A. Świerniak, A. d'Onofrio and A. Gandolfi, Control problems related to tumor angiogenesis, in "Proc. IEEE Industrial Electronics-IECON2006", (2006), 677-681.
39. P. E. Thorpe, Vascular targeting agents as cancer therapeutics, Clin Cancer Res., 10(2004), 415-427. (Pubitemid 38173977)
40. T. E. Wheldon, "Mathematical Models in Cancer Research", Hilger Publishing, Boston-Philadelphia, 1998.
41. J. C. Yang, L. Haworth, R. M. Sherry, P. Hwu, D. J. Schwartzentruber, S. L. Topalian, S. M. Steinberg, H. X. Chen and Steven A. Rosenberg, A randomized trial of bevacizumab, an anti-vascular endothelial growth factor antibody, for metastatic renal cancer, N. Engl. J. Med., 349(2003), 427-438.