A deterministic model of growth factor-induced angiogenesis

Bulletin of Mathematical Biology

Volumn 67, Issue 2, 2005, Pages 313-337

  Sun, Shuyu ^a   Wheeler, Mary F ^a   Obeyesekere, Mandri ^b   Patrick Jr , Charles W ^b  

^a UNIVERSITY OF TEXAS AT AUSTIN   (United States)

^b UNIVERSITY OF TEXAS   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 13744260837     PISSN: 00928240     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.bulm.2004.07.004     Document Type: Article

References (27)

1. A. Anderson, and M. Chaplain Continuous and discrete mathematical models of tumor-induced angiogenesis Bull. Math. Biol. 60 1998 857 900
2. T. Arbogast, C. Dawson, P. Keenan, M. Wheeler, and L. Yotov Enhanced cell-centered finite differences for elliptic equations on general geometry SIAM J. Sci. Comput. 19 1998 404 425
3. T. Arbogast, M. Wheeler, and L. Yotov Mixed finite elements for elliptic problems with tensor coefficients as cell-centered finite differences SIAM J. Sci. Comput. 34 1997 828 852
4. F. Arnold, and D. West Angiogenesis in wound healing Pharmacol. Ther. 52 1991 407 422
5. D. Balding, and D. McElwain A mathematical model of tumour-induced capillary growth J. Theor. Biol. 114 1985 53 73
6. C. Birdwell, A. Brasier, and L. Taylor Two-dimensional peptide mapping of fibronectin from bovine aortic endothelial cells and bovine plasma Biochem. Biophys. Res. Commun. 97 1980 574 581
7. H. Byrne, and M. Chaplain Mathematical models for tumour angiogenesis: Numerical simulations and nonlinear wave solutions Bull. Math. Biol. 57 1995 461 486
8. M. Chaplain The mathematical modelling of tumour angiogenesis and invasion Acta Biotheor. 43 1995 387 402
9. M. Chaplain, and A. Stuart A model mechanism for the chemotactic response of endothelial cells to tumour angiogenesis factor IMA J. Math. Appl. Med. Biol. 10 1993 149 168
10. J. Folkman Angiogenesis in cancer, vascular, rheumatoid and other disease Nat. Med. 1 1995 21 23
11. C. Frye, and C. Patrick Jr. Isolation and culture of rat microvascular endothelial cells J. In Vitro Cell. Dev. Biol. 38 2002 208 212
12. C. Graham, and P. Lala Mechanisms of placental invasion of the uterus and their control Biochem. Cell Biol. 70 1992 867 874
13. R. Kendall, R. Rutledge, X. Mao, A. Tebben, R. Hungate, and K. Thoma Vascular endothelial growth factor receptor KDR tyrosine kinase activity is increased by autophosphorylation of two activation loop tryosine residues Biol. Chem. 274 1999 6453 6460
14. W. Korohoda, and J. Czyz Efficacy of the Frame and Hu mathematical model for the quantitative analysis of agents influencing growth of chick embryo fibroblasts Folia Histochem. Cytobiol. 32 1994 113 118
15. H. Levine, S. Pamuk, B. Sleeman, and M. Nilsen-Hamilton Mathematical modeling of capillary formation and development in tumor angiogenesis: Penetration into stroma Bull. Math. Biol. 63 2001 801 863
16. L. Liotta, G. Saidel, and J. Kleinerman Diffusion model of tumor vascularization Bull. Math. Biol. 39 1977 117 128
17. S. Maggelakis, and A. Savakis A mathematical model of growth factor induced capillary growth in the retina Math. Comput. Modelling 24 1996 33 41
18. S. Maggelakis, and A. Savakis A mathematical model of retinal neovascularization Math. Comput. Modelling 29 1999 91 97
19. S. McDougall, A. Anderson, M. Chaplain, and J. Sheratt Mathematical modelling of flow through vascular networks: Implications for tumour-induced angiogenesis and chemotherapy strategies Bull. Math. Biol. 64 2002 673 702
20. M. Orme, and M. Chaplain A mathematical model of the first steps of tumour-related angiogenesis: capillary sprout formation and secondary branching IMA J. Math. Appl. Med. 14 1996 189 205
21. S. Paku, and N. Paweletz First steps of tumor-related angiogenesis Lab. Invest. 65 1991 334 346
22. G. Petter, M. Chaplain, D. McElwain, and H. Byrne On the role of angiogenesis in wound healing Proc. R. Soc. Lond. 1996 1487 1493
23. D. Shweiki, A. Itin, D. Soffer, and E. Keshet Vascular endothelial growth factor induced by hypoxia may mediate hypoxia-initiated angiogenesis Nature 359 1992 843 845
24. R. Spooner, F. Friedlos, K. Maycroft, S. Stribbling, J. Rousse, J. Brueggen, B. Stolz, T. O'Reilly, J. Wood, A. Matter, R. Marais, and C. Springer A novel vascular endothelial growth factor-directed therapy that selectively activates cytotoxic prodrug Br. J. Cancer 88 2003 1622 1630
25. C. Stokes, and D. Lauffenburger Analysis of the roles of microvessel endothelial cell random motility and chemotaxis in angiogenesis J. Theor. Biol. 152 1991 377 403
26. C. Stokes, D. Lauffenburger, and S. Williams Migration of individual microvessel endothelial cells: stochastic model and parameter measurement J. Cell Sci. 99 1991 419 430
27. D. Zawicki, R. Jain, G. Schmid-Schoenbein, and S. Chien Dynamics of neovascularization in normal tissue Microvasc. Res. 21 1981 27 47