Lattice and non-lattice models of tumour angiogenesis

Bulletin of Mathematical Biology

Volumn 66, Issue 6, 2004, Pages 1785-1819

  Plank, M J ^a,b   Sleeman, B D ^a  

^a UNIVERSITY OF LEEDS   (United Kingdom)

^b UNIVERSITY OF CANTERBURY   (New Zealand)

Author keywords

[No Author keywords available]

Indexed keywords

ANGIOGENESIS INHIBITOR;

ANIMAL; ARTICLE; BIOLOGICAL MODEL; CAPILLARY; COMPUTER SIMULATION; HUMAN; NEOPLASM; NEOVASCULARIZATION (PATHOLOGY); PATHOLOGY; PATHOPHYSIOLOGY; STATISTICS; VASCULAR ENDOTHELIUM; VASCULARIZATION;

ANGIOGENESIS INHIBITORS; ANIMALS; CAPILLARIES; COMPUTER SIMULATION; ENDOTHELIUM, VASCULAR; HUMANS; MODELS, BIOLOGICAL; MODELS, CARDIOVASCULAR; NEOPLASMS; NEOVASCULARIZATION, PATHOLOGIC; STOCHASTIC PROCESSES;

EID: 7444258529     PISSN: 00928240     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.bulm.2004.04.001     Document Type: Article

References (55)

1. Anderson A.R.A., Chaplain M.A.J. Continuous and discrete mathematical models of tumour-induced angiogenesis. Bull. Math. Biol. 60:1998;857-900
2. Anderson A.R.A., Chaplain M.A.J., Newman E.L., Steele R.J.C., Thompson A.M. Mathematical modelling of tumour invasion and metastasis. J. Theor. Med. 2:2000;129-154
3. Anderson A.R.A., Sleeman B.D., Young I.M., Griffiths B.S. Nematode movement along a chemical gradient in a structurally heterogeneous environment. 2. Theory. Fundan. Appl. Nematol. 20:1997;165-172
4. Ausprunk D.H., Folkman J. Migration and proliferation of endothelial cells in preformed and newly formed blood vessels during tumour angiogenesis. Microvasc. Res. 14:1977;53-65
5. Balding D., McElwain D.L.S. Mathematical modelling of tumour-induced capillary growth. J. Theor. Biol. 114:1985;53-73
6. Bowersox J.C., Sorgente N. Chemotaxis of aortic endothelial cells in response to fibronectin. Cancer Res. 42:1982;2547-2551
7. Brem H., Folkman J. Inhibition of tumour angiogenesis mediated by cartilage. J. Exp. Med. 141:1975;427-439
8. Burn, D.S., (2000). Gene flow in agricultural systems and angiogenesis in tumour growth. PhD thesis, School of Mathematics, University of Leeds
9. Carmeliet P., Jain R.K. Angiogenesis in cancer and other diseases. Nature. 407:2000;249-257
10. Carter S.B. Principles of cell motility: the direction of cell movement and cancer invasion. Nature. 208:1965;1183-1187
11. Chaplain M.A.J., Giles S.M., Sleeman B.D., Jarvis R.J. A mathematical model for tumour angiogenesis. J. Math. Biol. 33:1995;744-770
12. Chaplain M.A.J., Stuart A.M. A model mechanism for the chemotactic response of endothelial cells to tumour angiogenesis factor. IMA J. Math. Appl. Med. Biol. 10:1993;149-168
13. Clark R.A.F., Dvorak H.F., Colvin R.B. Fibronectin in delayed-type hyper-sensitivity skin reactions: associations with vessel permeability and endothelial cell activation. J. Immunol. 126:1981;787-793
14. Dallon J.C., Othmer H.G. A discrete cell model with adaptive signalling for aggregation of Dictyostelium discoideum. Phil. Trans. R. Soc. Lond. B. 352:1997;391-417
15. Davis B. Reinforced random walk. Prob. Theor. Rel. Fields. 84:1990;203-229
16. Denekamp J., Hobson B. Endothelial cell proliferation in experimental tumours. Br. J. Cancer. 46:1982;711-720
17. Folkman J. Tumour angiogenesis: therapeutic implications. New Engl. J. Med. 285:1971;1182-1186
18. Folkman J. Tumour angiogenesis. Adv. Cancer Res. 19:1974;331-358
19. Folkman J., Klagsbrun M. Angiogenic factors. Science. 235:1987;442-447
20. Han Z.C., Liu Y. Angiogenesis: state of the art. Int. J. Haematol. 70:1999;68-82
21. Hanahan D., Folkman J. Patterns and emerging mechanisms of the angiogenic switch during tumourigenesis. Cell. 86:1996;353-364
22. Hashizume H., Baluk P., Morikawa S., McLean J.W., Thurston G., Roberge S., Jain R.K., McDonald D.M. Openings between defective endothelial cells explain tumour vessel leakiness. Am. J. Path. 156:2000;1363-1380
23. Hill N.A., Häder D.P. A biased random walk model for the trajectories of swimming micro-organisms. J. Theor. Biol. 186:1997;503-526
24. Hunt T.K., Knighton D.R., Thakral K.K., Goodson W.H., Andrews W.S. Studies on inflammation and wound healing: angiogenesis and collagen synthesis stimulated in vivo by resident and activated macrophages. Surgery. 96:1984;48-54
25. Klagsbrun M., D'Amore P.A. Vascular endothelial growth factor and its receptors. Cytokine Growth Factor Rev. 7:1996;259-270
26. Konerding M.A., Malkusch W., Klapthor B., van Ackern C., Fait E., Hill S.A., Parkins C., Chaplin D.J., Presta M., Denekamp J. Evidence for characteristic vascular patterns in solid tumours: quantitative studies using corrosion casts. Br. J. Cancer. 80:1999;724-732
27. Konerding M.A., van Ackern C., Steinberg F., Streffer C. Combined morphological approaches in the study of network formation in tumour angiogenesis. Steiner R., Weisz P.B., Langer R. Angiogenesis: Key Principles - Science - Technology - Medicine. 1992;40-58 Birkhauser, Basel
28. Less J.R., Skalak T.C., Sevick E.M., Jain R.K. Microvascular architecture in a mammary carcinoma: branching patterns and vessel dimensions. Cancer Res. 51:1991;265-273
29. Leung D.W., Cachianes G., Kuang W.J., Goeddel D.V., Ferrara N. Vascular endothelial growth factor is a secreted angiogenic mitogen. Science. 246:1989;1306-1309
30. Levine H.A., Pamuk S., Sleeman B.D., Nilsen-Hamilton M. A mathematical model of capillary formation and development in tumour angiogenesis: penetration into the stroma. Bull. Math. Biol. 63:2001;801-863
31. Levine H.A., Sleeman B.D. A system of reaction diffusion equations arising in the theory of reinforced random walks. SIAM J. Appl. Math. 57:1997;683-730
32. Levine H.A., Sleeman B.D., Nilsen-Hamilton M. Mathematical modelling of the onset of capillary formation initiating angiogenesis. J. Math. Biol. 42:2001;195-238
33. Liotta L.A., Steeg P.S., Stetler-Stevenson W.G. Cancer metastasis and angiogenesis: an imbalance of positive and negative regulation. Cell. 64:1991;327-336
34. Moses M.A., Langer R. Metalloproteinase inhibition as a mechanism for the inhibition of angiogenesis. Steiner R., Weisz P.B., Langer R. Angiogenesis: Key Principles - Science - Technology - Medicine. 1992;146-151 Birkhauser, Basel
35. Muthukkaruppan V.R., Auerbach R. Angiogenesis in the mouse cornea. Science. 205:1979;1416-1418
36. Muthukkaruppan V.R., Kubai L., Auerbach R. Tumour-induced neovascularisation in the mouse eye. J. Natl. Cancer Inst. 69:1982;699-708
37. Nicosia R.F., Bonanno E., Smith M. Fibronectin promotes the elongation of microvessels during angiogenesis in vitro. J. Cell Physiol. 154:1993;654-661
38. Othmer H.G., Stevens A. Aggregation, blowup and collapse: the ABC's of taxis and reinforced random walks. SIAM J. Appl. Math. 57:1997;1044-1081
39. Paweletz N., Kneirim M. Tumour-related angiogenesis. Crit. Rev. Oncol. Haematol. 9:1989;197-242
40. Pepper M.S. Manipulating angiogenesis. Arterioscter Thromb. Vasc. Biol. 17:1997;605-619
41. Pepper M.S. Extracellular proteolysis and angiogenesis. Thromb. Haemost. 86:2001;346-355
42. Pepper M.S., Belin D., Montesano R., Orci L., Vassalli J.D. Transforming growth factor- β1 modulates basic fibroblast growth factor-induced proteolytic and angiogenic properties of endothelial cells in vitro. J. Cell Biol. 111:1990;743-755
43. Plank M.J., Sleeman B.D. A reinforced random walk model of tumour angiogenesis and anti-angiogenic strategies. IMA J. Math. Med. Biol. 20:2003;135-181
44. Plank M.J., Sleeman B.D., Jones P.F. A mathematical model of an in vitro experiment to investigate endothelial cell migration. J. Theor. Med. 4:2003;251-270
45. Reynolds L.P., Killilea S.D., Redmer D.A. Angiogenesis in the female reproductive cycle. FASEB J. 6:1992;886-892
46. Risau V. Mechanisms of angiogenesis. Nature. 386:1997;671-674
47. Schirrmacher V. Cancer metastasis: experimental approaches, theoretical concepts and impacts for treatment strategies. Adv. Cancer Res. 43:1985;1-73
48. Sholley M.M., Ferguson G.P., Seibel H.R., Montour J.L., Wilson J.D. Mechanisms of neovascularisation. Lab. Invest. 51:1984;624-634
49. Shweiki D., Itin A., Soffer D., Keshet E. Vascular endothelial growth factor induced by hypoxia may mediate hypoxia-initiated angiogenesis. Nature. 359:1992;843-845
50. Sleeman B.D., Wallis I.P. Tumour induced angiogenesis as a reinforced random walk: modelling capillary network formation without endothelial cell proliferation. J. Math. Comp. Modelling. 36:2002;339-358
51. Stokes C.L., Lauffenburger D.A. Analysis of the roles of microvessel endothelial cell random motility and chemotaxis in angiogenesis. J. Theor. Biol. 152:1991;377-403
52. Unemori E.N., Ferrara N., Bauer E.A., Amento E.P. Vascular endothelial growth factor induces interstitial collagenase expression in human endothelial cells. J. Cell Physiol. 153:1992;557-562
53. Vajkoczy P., Farhadi M., Gaumann A., Heidenreich R., Erber R., Wunder A., Tonn J.C., Menger M.D., Breier G. Microtumour growth initiates angiogenic sprouting with simultaneous expression of VEGF, VEGF receptor-2 and angiopoietin-2. J. Clin. Invest. 109:2002;777-785
54. Vernon R.B., Sage E.H. A novel, quantitative model for study of endothelial cell migration and sprout formation within three-dimensional collagen matrices. Microvasc. Res. 57:1999;118-133
55. Yancopoulos G.D., Davis S., Gale N.W., Rudge J.S., Wiegand S.J., Holash J. Vascular-specific growth factors and blood vessel formation. Nature. 407:2000;242-249