Skip to main content

Advertisement

SpringerLink
Log in

Mathematical modeling of tumor-induced angiogenesis

  • Published:
Journal of Mathematical Biology Aims and scope Submit manuscript

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

References

  1. Adam, J.A., Bellomo, N.: A Survey of Models for Tumor-Immune System Dynamics. Boston: Birkhauser, 1997

  2. Ahmad, S.A., Liu, W., Jung, Y.D., Fan, F., Reinmuth, N., Bucana, C.D., Ellis, L.M.: Differential expression of angiopoietin-1 and angiopoietin-2 in colon carcinoma. A possible mechanism for the initiation of angiogenesis. Cancer 92 (5), 1138–1143 (2001)

    Google Scholar 

  3. Aiello, L.P., Pierce, E.A., Foley, E.D., Takagi, H., Chen, H., Riddle, L., Ferrara, N., King, G.L., Smith, L.E.: Suppression of retinal neovascularization in vivo by inhibition of vascular endothelial growth factor (VEGF) using soluble VEGF-receptor chimeric proteins. Proc. Natl. Acad. Sci. USA 92, 104570–10461 (1995)

    Google Scholar 

  4. Alberts, B., Johnson, A., Lewis, J., Raff, M., Roberts, K., Walter, P.: Molecular Biology of The Cell. Fourth edn. New York and London: Garland, 2002

  5. Allt, G., Lawrenson, J.G.: Pericytes: cell biology and pathology. Cells Tissues Organs 169 (1), 1–11 (2001)

    Article  Google Scholar 

  6. Anderson, A.R.A., Chaplain, M.A.J.: A mathematical model for capillary network formation in the absence of endothelial cell proliferation. Appl. Math. Lett. 11, 109–114 (1998a)

    Google Scholar 

  7. Anderson, A.R.A., Chaplain, M.A.J., Garcia-Reimbert, C., Vargas, C.A.: A gradient driven mathematical model of antiangiogenesis. Math. Comput. Modeling 32, 1141–1152 (2000)

    Article  MATH  Google Scholar 

  8. Anderson, A.R.A., Chaplain, M.A.J.: Continuous and discrete mathematical models of tumor-induced angiogenesis. Bull. Math. Biol. 60 (5), 857–899 (1998b)

    Article  MATH  Google Scholar 

  9. Andreasen, P.A., Kjoller, L., Christensen, L., Duffy, M.J.: The urokinase-type plasminogen activator system in cancer metastasis: a review. Int. J. Cancer 72, 1–22 (1997)

    Article  Google Scholar 

  10. Andres, J.L., Stanley, K., Cheifetz, S., Massague, J.: Membrane-anchored and soluble forms of betaglycan, a polymorphic proteoglycan that binds to transforming growth factor-? J. Cell Biol. 109, 3137–3145 (1989)

    Article  Google Scholar 

  11. Angiolillo, A.L., Sgadari, C., Taub, D.D., Liao, F., Farber, J.M., Maheshwar, S., Kleinman, H.K., Reaman, G.H., Tosato, G.: Human interferon-inducible protein 10 is a potent inhibitor of angiogenesis in vivo. J. Exp. Med. 182, 155–162 (1995)

    Article  Google Scholar 

  12. Asahara, T., Chen, D., Takahashi, T., Fujikawa, K., Kearney, M., Magner, M., Yancopoulos, G.D., Isner, J.M.: Tie2 receptor ligands, angiopoietin-1 and angiopoietin-2, modulate VEGF-induced postnatal neovascularization. Circ. Res. 83 (3), 233–240 (1998)

    Google Scholar 

  13. Assoian, R.K., Komoriya, A., Meyers, C.A., Miller, D.M., Sporn, M.B.: Transforming growth factor-beta in human platelets. J. Biol. Chem. 258, 7155–7160 (1983)

    Google Scholar 

  14. Ausprunk, D.H., Folkman, J.: Migration and proliferation of endothelial cells in preformed and newly-formed blood vessels during tumor angiogenesis. Microvasc. Res. 14, 53–65 (1977)

    Google Scholar 

  15. Bach, T.L., Barsigian, C., Chalupowicz, D.G., Busler, D., Yaen, C.H., Grant, D.S., Martinez, J.: VE-cadherin mediates endothelial cell capillary tube formation in fibrin and collagen gel. Exp. Cell Res. 238, 324–334 (1998)

    Article  Google Scholar 

  16. Baish, J.W., Gazit, Y., Berk, D.A., Nozue, M., Baxter, L.T., Jain, R.K.: Role of tumor vascular architecture in nutrient and drug delivery: An invasion percolation-based network model. Microvasc. Res. 51, 327–346 (1996)

    Article  Google Scholar 

  17. Balding, D., McElwain, D.L.S.: A mathematical model of tumour-induced capillary growth. J. Theor. Biol. 114, 53–73 (1985)

    Google Scholar 

  18. Balsari, A., Maier, J.A.M., Colnaghi, M.I., Menard, S.: Correlation between tumor vascularity, vascular endothelial growth factor production by tumor cells, serum vascular endothelial growth factor levels, and serum angiogenic activity in patients with breat carcinoma. Lab. Invest. 79, 897–902 (1999)

    Google Scholar 

  19. Barleon, B., Sozzani, S., Zhou, D., Weich, H.A., Mantovani, A., Marme, D.: Migration of human monocytes in response to vascular endothelial growth factor (VEGF) is mediated via the VEGF receptor flt-1. Blood 87 (8), 3336–3343 (1996)

    Google Scholar 

  20. Baum, M., Chaplain, M.A.J., Anderson, A.R.A., Douek, M., Vaidya, J.S.: Does breast cancer exist in a state of chaos? Eur. J. Cancer 35, 886–891 (1999)

    Article  Google Scholar 

  21. Bayless, K.J., Salazar, R., Davis, G.E.: RGD-dependent vacuolation and lumen formation observed during endothelial cell morphogenesis in three -dimensional fibrin matrices involves the α v β3 and α5β1 integrins. Am. J. Pathol. 156, 1673–1683 (2000)

    Google Scholar 

  22. Benjamin, L.E., Golijanin, D., Itin, A., Pode, D., Keshet, E.: Selective ablation of immature blood vessels in established human tumors follows vascular endothelial growth factor withdrawal. J. Clin. Invest. 103 (2), 159–165 (1999)

    Google Scholar 

  23. Bicknell, R.J., Lewis, C.E., Ferrara, N., Ferrara, L. (eds.): Tumour Angiogenesis. Oxford: Oxford University Press, 1997

  24. Bingle, L., Brown, N.J., Lewis, C.E.: The role of tumour-associated macrophages in tumour progression: implications for new anticancer therapies. J. Pathol. 196 (3), 254–265 (2002), Review

    Article  Google Scholar 

  25. Bloch, W., Huggel, K., Sasaki, T., Grose, R., Bugnon, P., Addicks, K., Timpl, R., Werner, S.: The angiogenesis inhibitor endostatin impairs blood vessel maturation during wound healing. FASEB J. 14 (15), 2373–2376 (2000)

    Google Scholar 

  26. Bohem, T., Folkman, J., Browder, T., O’Reilly, M.S.: Antiangiogenic therapy of experimental cancer does not acquire dryg resistance. Nature 390, 404–407 (1997)

    Article  CAS  PubMed  Google Scholar 

  27. Bornstein, P.: Diversity of function is inherent in matricellular protein: an appraisal of thrombospondin 1. J. Cell Biol. 130, 503–506 (1995)

    Article  Google Scholar 

  28. Bouck, N., Stellmach, V., Hsu, S.C.: How tumors become angiogenic. Adv. Cancer Res. 69, 135–74 (1996)

    Google Scholar 

  29. Breier, G.: Angiogenesis in embryonic development–a review. Placenta 21, S11–S15 (2000a)

  30. Breier, G.: Endothelial receptor tyrosine kinases involved in blood vessel development and tumor angiogenesis. Adv. Exp. Med. Biol. 476, 57–66 (2000b)

    Google Scholar 

  31. Brooks, P.C., Montgomery, A.M., Rosenfeld, M., Hu, T., Klier, G., Cheresh, D.A.: Integrin α v β3 antagonists promote tumor regression by inducing apoptosis of angiogenic blood vessels. Cell 79, 1157–1164 (1994a)

  32. Brooks, P.C., Clark, R.A., Cheresh, D.A.: Requirement of vascular integrin αvβ 3 for angiogenesis. Science 264, 569–571 (1994b)

    Google Scholar 

  33. Brooks, P.C., Silletti, S., Schalscha, Von, T.L., Friedlander, M., Cheresh, D.A.: Disruption of angiogenesis by PEX, a noncatalytic metalloproteinase fragment with integrin binding activity. Cell 92, 391–400 (1998)

    Article  Google Scholar 

  34. Brouty-Boye, D., Zetter, B.R.: Inhibition of cell motility by interferon. Science 208 (4443), 516–518 (1980)

    Google Scholar 

  35. Brown, L.F., Detmar, M., Claffey, K., Nagy, J.A., Feng, D., Dvorak, A.M., Dvorak, H.F.: VPF/VEGF: A multifunctional angiogenic cytokine. Chap. Regulation of Angiogenesis, 1997

  36. Byrne, H.M., Chaplain, M.A.J.: Mathematical models for tumour angiogenesis: Numerical simulations and nonlinear wave solutions. Bull. Math. Biol. 57, 461–486 (1995)

    MATH  Google Scholar 

  37. Byrne, H.M., Chaplain, M.A.J.: Explicit solutions of a simplified model of capillary sprout growth during tumor angiogenesis. Appl. Math. Lett. 9 (1), 69–74 (1996)

    Article  MATH  Google Scholar 

  38. Byzova, T.V., Goldman, C.K., Pampori, N., Thomas, K.A., Bett, A., Shattil, S.J., Plow, E.F.: A mechanism for modulation of cellular responses to VEGF: activation of the integrins. Mol. Cell 6 (4), 851–860 (2000)

    Google Scholar 

  39. Cao, Y.: Endogenous angiogenesis inhibitors and their therapeutic implications. IJBCB 33, 357–369 (2001)

    Article  Google Scholar 

  40. Cao, Y., Chen, C., Weatherbee, J.A., Tsang, M., Folkman, J.: Gro-beta, a –C-X-C- chemokine, is an angiogenesis inhibitor that suppresses the growth of lewis lung carcinoma in mice. J. Exp. Med. 182, 2069–2077 (1995)

    Article  Google Scholar 

  41. Carlson, T.R., Feng, Y., Maisonpierre, P.C., Mrksich, M., Morla, A.O.: Direct cell adhesion to the angiopoietins mediated by integrins. J. Biol. Chem. 276 (28), 26516–26525 (2001)

    Article  Google Scholar 

  42. Carmeliet, P., Jain, R.K.: Angiogenesis in cancer and other diseases. Nature 407, 249–257 (2000)

    Article  Google Scholar 

  43. Chaplain, M.A.J.: Mathematical modelling of angiogenesis. J. Neuro-Oncology 50, 37–51 (2000)

    Article  Google Scholar 

  44. Chaplain, M.A.J., Anderson, A.R.A.: The mathematical modeling, simulation and prediction of tumor-induced angiogenesis. Invas. Metast. 16, 222–234 (1996)

    Google Scholar 

  45. Chaplain, M.A.J., Anderson, A.R.A.: Modeling the growth and form of capillary networks. Chichester: Wiley. Chap. On Growth and Form: Spatio-Temporal Pattern Formation in Biology, pp. 225–249 (1999)

  46. Chaplain, M. A.J., Orme, M.E.: Mathematical modeling of tumor-induced angiogenesis. Boston: Birkhauser. Chap. Vascular Morphogenesis: In vivo, in vitro, in mente, pp. 205–240 (1998)

  47. Chaplain, M.A.J., Giles, S.M., Sleeman, B.D., Jarvis, R.J.: A mathematical analysis of a model for tumour angiogenesis. J. Math. Biol. 33, 744–770 (1995)

    MATH  Google Scholar 

  48. Chen, C., Parangi, S., Tolentino, M.J., Folkman, J.: A strategy to discover circulating angiogenesis inhibitors generated by human tumors. Cancer Res. 55, 4230–4233 (1995)

    Google Scholar 

  49. Christofori, G.: The Role of Fibroblast Growth Factors in Tumor Progression and Angiogenesis. R. bicknell, ce lewis and n. ferrara edn. Oxford University Press. Chap. Tumor Angiogenesis (1996)

  50. Claesson-Wells, L., Wells, M., Ito, N., Anand-Apte, B., Soker, S., Zetter, B., O’Reilly, S., Folkman, J.: Angiostatin induces endothelial cell apoptosis and activation of focal adhesion kinase independently of the integrin-binding motif RGD. PNAS USA 95, 5579–5583 (1998)

    Google Scholar 

  51. Clapp, C., Martial, J.A., Guzman, R.C., Rentierdelrue, F., Weiner, R.: The 16-kilodalton N-terminal fragment of human prolactin is a potent inhibitor of angiogenesis. Endocrinology 133, 1292–1299 (1993)

    Article  Google Scholar 

  52. Coleman, K.R., Braden, G.A., Willingham, M.C. et~al.: Vitaxin, a humanized monoclonal antibody to the vitronectin receptor (α v β 3), reduces neointimal hyperplasia and total vessel area after balloon injury in hypercholesterolemic rabbits. Circ. Res. 84, 1268–1276 (1999)

    Google Scholar 

  53. Colorado, P.C., Torre, A., Kamphaus, G., Maeshima, Y., Hopfer, H., Takahashi, K., Volk, R., Zamborsky, E.D., Sarkar, S., Herman, P.K., Ericksen, E.M., Dhanabal, M., Simons, M., Post, M., Kufe, D.W., Weichselbaum, R.R., Sukhatme, V.P., Kalluri, R.: Anti-angiogenic cues from vascular basement membrane collagen. Cancer Res. 60, 2520–2526 (2000)

    Google Scholar 

  54. Cory, A.H., Owen, T.C., Barltrop, J.A., Cory, J.G.: Use of an aqueous soluble tetrazolium/formazan assay for cell growth assays in culture. Cancer Commun. 3, 207–212 (1991)

    Google Scholar 

  55. Coussens, L.M., Werb, Z.: Matrix metalloproteinases and the development of cancer. Chem. Biol. 3 (11), 895–904 (1996)

    Google Scholar 

  56. Dallon, J.C., Othmer, H.G.: A discrete cell model with adaptive signalling for aggregation of dictyostelium discoideum. Philos. Trans. R Soc. Lond. B Biol. Sci 352 (1351), 391–417 (1997)

    Article  Google Scholar 

  57. D’Amato, R.J., Loughnan, M.S., et al., Flynn., E.: Thalidomide is an inhibitor of angiogenesis. Proc. Natl. Acad. Sci. USA 91, 4082–4085 (1994)

    Google Scholar 

  58. Dameron, K.M., Volper, O.V., Tainsky, M.A., Bouck, N.: Control of angiogenesis in fibroblasts by p53 regulation of thrombospondin-1. Science 265, 1582–1584 (1994)

    Google Scholar 

  59. Davis, G.E., Camarillo, C.W.: An α2β1 integrin-dependent pinocytic mechanism involving intracellular vacuole formation and coalescence regulates capillary lumen and tube formation in three-dimensional collagen matrix. Exp. Cell Res. 224, 39–51 (1996)

    Article  Google Scholar 

  60. Detmar, M.: The role of VEGF and thrombospondins in skin angiogenesis. J. Dermatol. Sci. 24 (84), S78–S (2000)

    Google Scholar 

  61. Dhanapal, M., Ramchandran, R., Waterman, M.J., Lou, H., Knebelmann, B., Segal, M., Sukhatme, V.P.: Endostatin induces endothelial cell apoptosis. J. Biol. Chem. 274, 11721–11726 (1999)

    Article  Google Scholar 

  62. Doki, Y., Shiozaki, H., Tahara, H., Imoue, M., Iihara, H., Oka, K., Kadowaki, T., Takeichi, M., Takesada, M.: Correlation between E-cadherin expression and invasiveness in vitro in human esophageal cancer cell line. Cancer Res. 53, 3421–3426 (1993)

    Google Scholar 

  63. Dubois-Stringfellow, N., Jonczyk, J., Bautch, V.L.: Perturbations in the fibrinolytic pathway aboliah cyst formation but not capillary-like organization of cultured murine endothelial cells. Blood 83, 3206–3217 (1994)

    Google Scholar 

  64. Dvorak, H.F., Brown, L.F., Detmar, M., Dvorak, A.M.: Vascular permeability factor/vascular endothelail growth factor, microvascular hyperpermeability, and angiogenesis. AM. J. Pathol. 146, 1029–1039 (1995)

    Google Scholar 

  65. Eliceiri, B.P., Paul, R., Schwartzberg, P.L., Hood, J.D., Leng, J., Cheresh, D.A.: Selective requirement for src kinases during VEGF-induced angiogenesis and vascular permeability. Mol. Cell 4 (6), 915–924 (1999)

    Article  Google Scholar 

  66. Enholm, B., Paavonen, K., Ristimaki, A., Kumar, V., Gunji, Y., Klefstrom, J., Kivinen, L., Laiho, M., Olofsson, B., Joukov, V., Eriksson, U., Alitalo, K.: Comparison of VEGF, VEGF-B, VEGF-C and ang-1 mRNA regulation by serum, growth factors, oncoproteins and hypoxia. Oncogene 14 (20), 2475–2483 (1997)

    Article  Google Scholar 

  67. Ergun, S., Kilic, N., Wurmbach, J.H., Ebrahimnejad, A., Fernando, M., Sevinc, S., Kilic, E., Chalajour, F., Fiedler, W., Lauke, H., Lamszus, K., Hammerer, P., Weil, J., Herbst, H., Folkman, J.: Endostatin inhibits angiogenesis by stabilization of newly formed endothelial tubes. Angiogenesis 4 (3), 193–206 (2001)

    Article  Google Scholar 

  68. Etoh, T., Shibuta, K., Barnard, G. G., Kitano, S., Mori, M.: Angiogenin expression in human colorectal cancer: the role of focal macrophage infiltration. Clin. Cancer Res. 6 (9), 3545–3551 (2000)

    Google Scholar 

  69. Ferrara, N.: Role of vascular endothelial growth factor in the regulation of angiogenesis. Kidney Int. 56, 794–814 (1999)

    Article  Google Scholar 

  70. Ferrara, N.: VEGF: an update on biological and therapeutic aspects. Curr. Opin. Biotechnol. 11, 617–624 (2000)

    Article  Google Scholar 

  71. Ferrara, N., Davis-Smyth, T.: The biology of vascular endothelial growth factor. Endocr. Rev. 18, 4–25 (1997)

    Article  Google Scholar 

  72. Ferrara, N., Keyt, B.: VEGF: Basic biology and clinical implications. Chap. Regulation of Angiogenesis, 1997

  73. Flaumenhaft, R., Moscatelli, D., Saksela, O., Rifkin, D.B.: Role of extracellular matrix in the action of basic fibroblast growth factor: matrix as a source of growth factor for long-term stimulation of plasminogen activator production and DNA synthesis. J. Cell Physiol. 75–81 (1989)

  74. Folkman, J.: The vascularization of tumors. Cancer Biology: Readings from Scientific American 115–124 (1986)

  75. Folkman, J.: Therapeutic implications. N. Engl. J. Med. 285, 1182–1186 (1971)

    Google Scholar 

  76. Folkman, J.: The vascularization of tumors. Sci. Am. 234, 58–64 (1976)

    Google Scholar 

  77. Folkman, J.: Angiogenesis in cancer, vascular, rheumatoid and other disease. Nature Med. 1, 27–31 (1995a)

    Google Scholar 

  78. Folkman, J.: Clinical applications of research on angiogenesis. N. Engl. J. Med. 333, 1757–1763 (1995b)

    Google Scholar 

  79. Folkman, J., Haudenschild, C.: Angiogenesis in vitro. Nature 288, 551–556 (1980)

    Google Scholar 

  80. Folkman, J., Klagsbrun, M.: Angiogenic factors. Science 235, 442 (1987)

    Google Scholar 

  81. Folkman, J., Mendelsohn, J., Howley, P.M., Israel, M.A., Liotta, L.A.: Tumor angiogensis. The molecular basis of cancer. Eds. WB Saunders: Philadelphia 206–232 (1995)

  82. Fong, G.H., Rossant, J., Gertenstein, M., Breitman, M.L.: Role of the flt-1 receptor tyrosine kinase in regulating assembly of vascular endothelium. Nature 376, 66–70 (1995)

    Article  Google Scholar 

  83. Fong, T.A., Shawver, L.K., et al., Sun., L.: SU5416 is a potent and selective inhibitor of the vascular endothelial growth factor receptor (flk-1/KDR) that inhibits tyrosine kinase catalysis, tumor vascularization. Cancer Res. 59, 9–106 (1999)

    Google Scholar 

  84. Franz, C.M., Jones, G.E., Ridley, A.J.: Cell migration in development and disease. Dev. Cell. 2 (2), 153–158 (2002)

    Article  Google Scholar 

  85. Frater-Schroeder, M., Mueller, G., Birchmeier, W., Boehlen, P.: Transforming growth factor-β inhibits endothelial cell proliferation. Biochem. Biophys. Res. Commun. 137, 295 (1986)

    Google Scholar 

  86. Frazier, W.A.: Thrombospondin: A modular adhesive glycoprotein of platelets and nucleated cells. J. Cell Biol. 105, 625–632 (1987)

    Article  Google Scholar 

  87. Frolik, C.A., Dart, L.L., Meyers, C.A., Smith, D.M., Sporn, M.B.: Purification and initial characterization of a type beta transforming growth factor from human placenta. Proc. Natl. Acad. Sci. 80, 3676–3680 (1983)

    Google Scholar 

  88. Fukata, Y., Amano, M., Kaibuchi, K.: Rho-rho-kinase pathway in smooth muscle contraction and cytoskeletal reorganization of non-muscle cells. Trends. Pharmacol. Sci. 22 (1), 32–39 (2001)

    Article  Google Scholar 

  89. Funamoto, S., Milan, K., Meili, R., Firtel, R.A.: Role of phosphatidylinositol 3’ kinase and a downstream pleckstrin homology domain-containing protein in controlling chemotaxis in dictyostelium. J. Cell Biol. 153 (4), 795–810 (2001)

    Article  Google Scholar 

  90. Furumatsu, T., Yamaguchi, N., Nishida, K., Kawai, A., Kunisada, T., Namba, M., Inoue, H., Ninomiya, Y.: Endostatin inhibits adhesion of endothelial cells to collagen I via alpha(2)beta(1) integrin, a possible cause of prevention of chondrosarcoma growth. J. Biochem. (Tokyo) 131 (4), 619–626 (2002)

    Google Scholar 

  91. Gamble, J.R., Matthias, L.J., Meyer, G., Kaur, P., Russ, G., Faull, R., Berndt, M.C., Vadas, M.A.: Regulation of in vitro capillary tube formation by anti-integrin antibodies. J. Cell Biol. 121, 931–943 (1993)

    Article  Google Scholar 

  92. Gazit, Y., Berk, D.A., Leunig, M., Jain, R.K., Baxter., L.T.: Scale-invariant behavior and vascular network formation in normal and tumor tissue. Phys. Rev. Lett 75, 2428–2431 (1995)

    Article  Google Scholar 

  93. Gerber, H.P., Hillan, K.J., Ryan, A.M., Kowalski, J.K., Keller, G.A., Rangell, L., Wright, B.D., Radtke, F., Aguet, M., Ferrara, N.: VEGF is required for growth and survival in neonatal mice. Development 126, 1149–1159 (1999)

    Google Scholar 

  94. Gimborne, M.A., Cotran, R.S., Leapman, S.B., Folkman, J.: Tumor growth and neovasularization: An experimental model using the rabbit cornea. J. Nat. Can. Inst. 52, 413–427 (1974)

    Google Scholar 

  95. Goede, V., Brogelli, L., Ziche, M., Augustin, H.G.: Induction of inflammatory angiogenesis by monocyte chemoattractant protein-1. Int. J. Cancer 82 (5), 765–770 (1999)

    Article  Google Scholar 

  96. Good, D.J., Polverini, P.J., Rastinejad, F., Beau, M., Le, M., Lemons, R.S., Frazier, W.A., Bouck, N.P.: A tumor suppressor-dependent inhibitor of angiogenesis is immunologically and functionally indistinguishable from a fragment of thrombospondin. Proc. Natl. Acad. Sci. USA 87, 6624–6628 (1990)

    Google Scholar 

  97. Gospodarowicz, D., Ferrara, N., Schweigerer, L., Neufeld, G.: Structual characterization and biological functions of fibroblast growth factor. Endocr. Rev. 8, 95–113 (1987)

    Google Scholar 

  98. Goto, F., Goto, K., Weindel, K., Folkman, J.: Synergistic effects of vascular endothelial growth factor and basic fibroblast growth factor on the proliferation and cord formation of bovine capillary endothelial cells within collagen gels. Lab. Invest. 69, 508–517 (1993)

    Google Scholar 

  99. Griffioen, A.W., Molema, J.: Angiogenesis: Potentials for pharmacologic intervention in the treatment of cancer, cardiovascular diseases, and chronic inflammation. Pharmaco. Revs. 52 (2), 237–268 (2000), Review

    Google Scholar 

  100. Gupta, S.K., Hassel, T., Singh, J.P.: A potent inhibitor of endothelial cell proliferation is generated by proteolytic cleavage of the chemokine platelet factor 4. Proc. Natl. Acad. Sci. USA 92, 7799–7803 (1995)

    Google Scholar 

  101. Han, Z.C., Liu, Y.: Angiogenesis:state of the art. Int. J. Hematology 70, 68–82 (1999)

    Google Scholar 

  102. Hanahan, D.: Signaling vascular morphogenesis and maintenance. Science 227, 48–50 (1997)

    Article  Google Scholar 

  103. Hanahan, D., Folkman, J.: Patterns and emerging mechanisms of the angiogenic switch during tumorigenesis. Cell 86, 353–364 (1996)

    Article  CAS  PubMed  Google Scholar 

  104. Hanai, J., Dhanabal, M., Karumanchi, S.A., Albanese, C., Waterman, M., Chan., B.: Ramchandran R, pestell R, sukhatme VP. endostatin causes G1 arrest of endothelial cells through inhibition of cyclin D1. J. Biol. Chem. 277 (19), 16464–16469 (2002)

    Google Scholar 

  105. Higgs, H.N., Pollard, T.D.: Regulation of actin filament network formation through ARP2/3 complex: activation by a diverse array of proteins. Annu. Rev. Biochem. 70, 649–676 (2001), Review

    Article  Google Scholar 

  106. Hildenbrand, R., Wolf, G., Bohme, B., Bleyl, U., Steinborn, A.: Urokinase plasminogen activator receptor (CD87) expression of tumor-associated macrophages in ductal carcinoma in situ, breast cancer, and resident macrophages of normal breast tissue. J. Leukoc. Biol. 66 (1), 40–49 (1999)

    Google Scholar 

  107. Hirschi, K.K., D’Amore, P.A.: Pericytes in the microvasculature. Cardiovasc. Res. 32 (4), 687–698 (1996)

    Article  Google Scholar 

  108. Hirschi, K.K., Rohovsky, S.A., D’Amore, P.A.: Cell-cell interactions in vessel assembly: a model for the fundamentals of vascular remodelling. Transpl. Immunol. 3, 177–178 (1997)

    Article  Google Scholar 

  109. Hirschi, K.K., Rohovsky, S.A., Beck, L.H., Smith, S.R., D’Amore, P.A.: Endothelial cells modulate the proliferation of mural cell precursors via platelet-derived growth factor-BB and heterotypic cell contact. Circ. Res. 84 (3), 298–305 (1999)

    Google Scholar 

  110. Holmes, M.J., Sleeman, B.D.: A mathematical model of tumour angiogenesis incorporating cellular traction and viscoelastic effects. J. Theor. Biol. 202 (2), 95–112 (2000)

    Article  Google Scholar 

  111. Homandberg, G.A., Williams, J.E., Grant, D.B.S., Eisenstein, R.: Heparin-binding fragments of fibronectin are potent inhibitors of endothelial cell growth. Am. J. Pathol. 120, 327–332 (1985)

    Google Scholar 

  112. Houck, K.A., Ferrara, N., Winer, J., Li, B., Leung, D.W.: The vascular endothelial growth factor family: identification of a fourth molecular species and characterization of alternative splicing of RNA. Mol. Endocrinol. 5, 1806–1814 (1991)

    Google Scholar 

  113. Houck, K.A., Leung, D.W., Rowland, A.M., Winer, J., Ferrara, N.: Dual regulation of vascular endothelial growth factor bioavailability by genetic and proteolytic mechanisms. J. Biol. Chem. 267, 26031–26037 (1992)

    Google Scholar 

  114. Hynes, R.O.: Integrins: versatility, modulation and signaling in cell adhesion. Cell 69, 11–25 (1992)

    Article  CAS  PubMed  Google Scholar 

  115. Ingber, D., Fujita, T., Kishimoto, S., Sudo, K., Kanamaru, T., Brem, H., Folkman, J.: Synthetic analogues of fumagillin that inhibit angiogenesis and suppress tumour growth. Nature 348, 555–557 (1990)

    Article  Google Scholar 

  116. Inoue, K., Perrotte, P., Wood, C.G., Slaton, J.W., Sweeney, P., Dinney, C.P.: Gene therapy of human bladder cancer with adenovirus-mediated antisense basic fibroblast growth factor. Clin. Cancer Res. 6, 4422–4431 (2000)

    Google Scholar 

  117. Jiang, M.C., Liao, C.F., Lee, P.H.: Aspirin inhibits matrix metalloproteinase-2 activity, increases E-cadherin production, and inhibits in vitro invasion of tumor cells. Biochem. Biophys. Res. Commun. 282, 671–677 (2001)

    Article  Google Scholar 

  118. Jimenez, B., Volpert, O.V.: Mechanistic insights on the inhibition of tumor angiogenesis. J. Mol. Med. 78, 663–672 (2001)

    Article  Google Scholar 

  119. Johnson, D.E., Williams, L.T.: Structural and functional diversity in the FGF receptor multigene family. Adv. Cancer Res. 60, 1–41 (1993), Review

    Google Scholar 

  120. Kamphaus, G.D., Colorado, P.C., Panka, D.J., Hopfer, H., Ramchandran, R., Torre, A., Maeshima, Y., Mier, J.W., Sukhatme, V.P., Kalluri, R.: Canstatin, a novel matrix-derived inhibitor of angiogenesis and tumor growth. J. Biol. Chem. 275, 1209–1215 (2000)

    Article  Google Scholar 

  121. Karihaloo, A., Karumanchi, S.A., Barasch, J., Jha, V., Nickel, C.H., Yang, J., Grisaru, S., Busch, K.T., Nigam, S., Rosenblum, N.D., Sukhatme, V.P., Cantley, L.G.: Endostatin regulates branching morphogenesis of renal epithelial cells and ureteric bud. Proc. Natl. Acad. Sci. USA 98 (22), 12509–12514 (2001)

    Article  Google Scholar 

  122. Kiani, M., Hudetz, A.: Computer simulation of growth of anastomosing microvascular networks. J. Theor. Biol. 150, 547–560 (1991)

    Google Scholar 

  123. Kim, K.J., Li, B., Winer, J., Armanini, M., Gillett, N., Phillips, H.S., HS, Ferrara, N.: Inhibition of vascular endothelial growth factor-induced angiogenesis suppresses tumor growth in vivo. Nature 362, 841–844 (1993)

    Article  Google Scholar 

  124. Kim, Y.M., Jang, J.W., Lee, O.H., Yeon, J., Choi, E.Y., Kim, K.W., Lee, S.T., Kwon, Y.G.: Endostatin inhibits endothelial and tumor cellular invasion by blocking the activation and catalytic activity of matrix metalloproteinase. Cancer Res. 60 (19), 5410–5413 (2000)

    Google Scholar 

  125. Kiosses, W.B., Shattil, S.J., Pampori, N., Schwartz, M.A.: Rac recruits high-affinity integrin alphavbeta3 to lamellipodia in endothelial cell migration. Nat. Cell Biol. 3 (3), 316–320 (2001)

    Article  Google Scholar 

  126. Koblizek, T.I., Weiss, C., Yancopoulos, G.D., Deutsch, U., Risau, W.: Angiopoietin-1 induces sprouting angiogenesis in vitro. Curr. Biol. 8 (9), 529–532 (1998)

    Google Scholar 

  127. Koga, K., Todaka, T., Morioka, M., Hamada, J., Kai, Y., Yano, S., Okamura, A., Takakura, N., Suda, T., Ushio, Y.: Expression of angiopoietin-2 in human glioma cells and its role for angiogenesis. Cancer Res. 61 (16), 6248–6254 (2001)

    Google Scholar 

  128. Konerdig, M.A., Ackern, Van, C.,Steinberg, F., Streffer, C.: The development of the tumoue vascular system: 2-D and 3-D approaches to network formation in human xenografted tumours. M.e. maragoudakis et al edn. New York: Plenum Press. Chap. angiogenesis in health and disease, 1992

  129. Koolwijk, P., Hanemaaijer, R., Van Hinsbergh, V.W.M.: Proteases and angiogenesis: Regulation of plasminogen activators and matrix metalloproteases by endothelial cells. NATO ASI series. Series A, Life sciences 298, 241 (1998)

    Google Scholar 

  130. Kremer, C., Breier, G., Risau, W., Plate, K.H.: Up-regulation of flk-1/vascular endothelial growth factor receptor 2 by its ligand in a cerebral slice culture system. Cancer Res. 57, 3852–3859 (1997)

    Google Scholar 

  131. Kukk, E., Wartiovaara, U., Gunji, Y., Kaukonen, J., Buhring, H.J., Rappold, I.: Matikainen MT, vihko P, partanen J, palotie A, alitalo K, alitalo R. analysis of tie receptor tyrosine kinase in haemopoietic progenitor and leukaemia cells. Br. J. Haematol. 98 (1), 195–203 (1997)

    Google Scholar 

  132. Landini, G., Misson, G.: Simulation of corneal neovascularization by inverted diffusion limited aggregation. Invest. Ophthalmol. Vis. Sci. 34, 1872–1875 (1993)

    Google Scholar 

  133. Lauffenburger, D.A., Horwitz, A.F.: Cell migration: a physically integrated molecular process. Cell 84 (3), 359–369 (1996)

    Article  Google Scholar 

  134. Lauren, J., Gunji, Y., Alitalo, K.: Is angiopoietin-2 necessary for the initiation of tumor angiogenesis? Am. J. Pathol. 5, 1333–1339 (1998), Review

    Google Scholar 

  135. Lawrence, D.A., Pircher, R., Kryceve-Martinerie, C., Petzelbauer, P.: Normal embryo fibroblasts release transforming growth factors in latent form. J. Cell Physiol. 121, 184–188 (1984)

    Google Scholar 

  136. Lee, S.J., Jang, J.W., Kim, Y.M., Lee, H.I., Jeon, J.Y., Kwon, Y.G., Lee, S.T.: Endostatin binds to the catalytic domain of matrix metalloproteinase-2. FEBS Lett 519 (1-3), 147–152 (2002)

    Google Scholar 

  137. Leek, R.D., Lewis, C.E., Whitehouse, R., Greenall, M., Clarke, J., Harris, A.L.: Association of macrophage infiltration with angiogenesis and prognosis in invasive breast carcinoma. Cancer Res. 56 (20), 4625–4629 (1996)

    Google Scholar 

  138. Levine, H.A., Sleeman, B.D., Nilsen-Hamilton, M.: A mathematical model for the roles of pericytes and macrophages in angiogenesis. I. the role of protease inhibitors in preventing angiogenesis. Math. Biosci. 168, 77–115 (2000)

    Article  MATH  Google Scholar 

  139. Levine, H.A., Pamuk, S., Sleeman, B.D., Nilsen-Hamilton, M.: Mathematical modeling of capillary formation and development in tumor angiogenesis: penetration into the stroma. Bull. Math. Biol. 63, 801–863 (2001a)

  140. Levine, H.A., Sleeman, B.D., Nilsen-Hamilton, M.: Mathematical modeling of the onset of capillary formation initiating angiogenesis. J. Math. Biol. 42, 195–238 (2001b)

    Google Scholar 

  141. Levine, H.A., Tucker, A.L., Nilsen-Hamilton, M.: A mathematical model for the role of cell signal transduction in the initiation and inhibition of angiogenesis. Growth Factors 20 (4), 155–175 (2002)

    Article  Google Scholar 

  142. Lewis, J.S., Landers, R.J., Underwood, J.C., Harris, A.L., Lewis, C.E.: Expression of vascular endothelial growth factor by macrophages is up-regulated in poorly vascularized areas of breast carcinomas. J. Pathol. 192 (2), 150–158 (2000)

    Article  Google Scholar 

  143. Liekens, S., De Clercq, E., Neyts, J.: Angiogenesis: regulators and clinical applications. Biochem. Pharmacol. 61, 253–270 (2001)

    Article  Google Scholar 

  144. Liotta, L.A., Stetler-Stevenson, W.G.: Principles of molecular cell biology of cancer: cancer metastasis. Philadelphia: Lippincott. Chap. Cancer: Principles and Practice of Oncology, pp. 134–149 (1993)

  145. Lipponen, P.K.: Expression of cathepsin D in transitional cell bladder tumours. J. Pathol. 178 (1), 59–64 (1996)

    Article  Google Scholar 

  146. Lobov, I.B., Brooks, P.C., Lang, R.A.: Angiopoietin-2 displays VEGF-dependent modula- tion of capillary structure and endothelial cell survival in vivo. Proc. Natl. Acad. Sci. U S A 99 (17), 11205–11210 (2002)

    Article  Google Scholar 

  147. Lowe, P.M., Lee, M.L., Jackson, C.J., To, S.S., Cooper, A.J., Schrieber, L.: The endothelium in psoriasis. Br. J. Dermatol. 132, 497–505 (1995)

    Google Scholar 

  148. Lu, H., Mabilat, C., Yeh, P., Guitton, J.D., Li, H., Pouchelet, M., Shoevaert, D., Legrand, Y., Soria, J., Soria, C.: Blockage of urokinase receptor reduces in vitro the mobility and the deformability of endothelial cells. FEBS Lett 380, 21–24 (1996)

    Article  Google Scholar 

  149. Lyons, R.M., Keski-Oja, J., Moses, H.L.: Proteolytic activation of latent transforming growth factor-Grβ from fibroblast-conditioned medium. J. Cell Physiol. 106, 1659–1665 (1988)

    Article  Google Scholar 

  150. Maeshima, Y., Colorado, P.C., Kalluri, R.: Two RGD-independent alpha vbeta 3 integrin binding sites on tumstatin regulate distinct anti-tumor properties. J. Biol. Chem. 275, 23745–23750 (2000)

    Article  Google Scholar 

  151. Maione, T.E., Gray, G.S., Petro, J., Hunt, A.J., Donner, A.L., Bauer, S.I., Carson, H.F., Sharpe, R.J.: Inhibition of angiogenesis by recombinant human platelet factor-4 and related peptides. Science 247, 77–79 (1990)

    Google Scholar 

  152. Maisonpierre, P.C., Suri, C., Jones, P.F., Bartunkova, S., Wiegand, S.J., Radziejewski, C., Compton, D., McClain, J., Aldrich, T.H., Papadopoulos, N., Daly, T.J., Davis, S., Sato, T.N., Yancopoulos, G.D.: Angiopoietin-2, a natural antagonist for tie2 that disrupts in vivo angiogenesis. Science 277 (5322), 55–60 (1997)

    Article  Google Scholar 

  153. Mandriota, S.J., Pepper, M.S.: Regulation of angiopoietin-2 mRNA levels in bovine microvascular endothelial cells by cytokines and hypoxia. Circ. Res. 83 (8), 852–859 (1998)

    Google Scholar 

  154. Manoussaki, D., Lubkin, S.R., Vernon, R.B., Murray, J.D.: A mathematical model for the formation of vascular networks in vitro. Acta Biotheoretica 44, 271–282 (1996)

    Google Scholar 

  155. Mantovani, A.: Tumor-associated macrophages in neoplastic progression: a paradigm for the in vivo function of chemokines. Lab Invest. 1, 5–16 (1994)

    Google Scholar 

  156. Matsumura, T., Wolff, K., Petzelbauer, P.: Endothelial cell tube formation depends on cadherin 5 and CD31 intercations with filamentous actin. J. Immunol. 158, 3408–3416 (1997)

    Google Scholar 

  157. McDougall, S.R., Anderson, A.R.A., Chaplain, M.A.J., Sherratt, J.A.: Mathematical modelling of flow through vascular networks: Implications for tumour-induced angiogenesis and chemotherapy strategies. Bull. Math. Biol. 64, 673–702 (2002)

    Article  Google Scholar 

  158. Meyer, G.T., Matthias, L.J., Noack, L., Vadas, M.A., Gamble, J.R.: Lumen formation during angiogenesis in vitro involves phagocytic activity, formation and secretion of vacuoles, cell death, and capillary tube remodelling by different populations of endothelial cells. Anat. Record 249 (3), 327–340 (1997)

    Article  Google Scholar 

  159. Mignatti, P., Rifkin, D.B.: Plasminogen activators and matrix metalloproteinases in angiogenesis. Enzyme Protein 117–137 (1996)

  160. Moldovan, N.I.: Role of monocytes and macrophages in adult angiogenesis: A light at the tunnel’s end. J. Hematother. Stem. Cell Res. 11 (2), 179–194 (2002), Review

    Article  Google Scholar 

  161. Monier-Gavelle, F., Duband, J.L.: Control of N-cadherin mediated intercellular adhesion in migrating neural crest cells in vitro. J. Cell Sci. 3839–3853 (1995)

  162. Montesano, R., Pepper, M.S., Mohle-Steinlein, U., Wagner, L., Orci, W., Risau, E.F.: Increased proteolytic activity is responsible for the aberrant morphogenetic behaviour of endothelial cells expressing middle T oncogene. Cell 62, 435–445 (1990)

    Article  Google Scholar 

  163. Moscatelli, D., Rifkin, D.B.: Membrane and matrix localization of proteinases – a common theme in tumor-cell invasion and angiogenesis. Biochem. Biophys. Acta 948 (1), 67–85 (1988)

    Google Scholar 

  164. Moscatelli, D., Presta, M., Joseph-Silverstein, J., Rifkin, D.B.: Both normal and tumor cells produce basic fibroblast growth factor. J. Cell Physiol. 129, 273–276 (1986)

    Google Scholar 

  165. Murray, J.D., Oster, G.F.: Cell traction models for generation of pattern and form in morphogenesis. J. Math. Biol. 19, 265–279 (1984)

    MathSciNet  MATH  Google Scholar 

  166. Murray, J.D., Swanson, K.R.: On Growth and Form: Spatio-Temporal Pattern Formation in Biology. Chichester: Wiley. Chap. On the mechanochemical theory of biological pattern formation with applications to wound healing and angiogenesis, pp. 251–285 (1999)

  167. Murray, J.D., Oster, G.F., Harris, A.K.: A mechanical model for mesenchymal morphogenesis. J. Math. Biol. 17 (1), 125–129 (1983)

    MATH  Google Scholar 

  168. Muthukkaruppan, V.R., Kubai, L., Auerbach, R.: Tumor-induced neovascularization in the mouse eye. J. Natl. Cancer Inst. 69, 699–705 (1982)

    Google Scholar 

  169. Nakahara, H., Howard, L., Thompson, E.W., Seiki, H., Sato, M., Yeh, Y., Chen, W.: Transmembrane/cytoplasmic domain-mediated membrane type 1-matrix metalloproteinase docking to invadopodia is required for cell invasion. Proc. Natl. Acad. Sci. USA 94 (15), 7959–7964 (1997)

    Article  Google Scholar 

  170. Nekka, F., Kyriakos, S., Kerrigan, C., Cartilier, L.: A model of growing vascular structures. Bull. Math. Biol. 58, 409–424 (1996)

    Article  MATH  Google Scholar 

  171. Neufeld, G., Cohen, T., Gengrinovitch, S., Gluzman-Poltorak, Z.: Vascular endothelial growth factor (VEGF) and its receptors. FASEB J. 13, 9–22 (1999)

    Google Scholar 

  172. Norby, K.: Angiogenesis: new aspects relating to its initiation and control. APMIS 105, 417–437 (1997)

    Google Scholar 

  173. Norrby, K.: Mast cells and angiogenesis. APMIS 110 (5), 355–71 (2002)

    Article  Google Scholar 

  174. Olsen, L., Sherratt, J. A., Maini, P. K., Arnold, F.: A mathematical model for the capillary endothelial cell-extracellular matrix interactions in wound-healing angiogenesis. IMA J. Math. Appld. Med. Biol. 14, 261–281 (1997)

    MATH  Google Scholar 

  175. O’Reilly, M.S.: Angiostatin: An endogenous inhibitor of angiogenesis and of tumor growth. Chap. Regulation of Angiogenesis, 1997

  176. O’Reilly, M.S., Holmgren, L., Shing, Y., Chen, C., Rosenthal, R.A., Moses, M., Lane, W.S., Cao, Y., Sage, E.H., Folkman, J.: Angiostatin: a novel angiogenesis inhibitor that mediates the suppression of metastases by a lewis lung carcinoma. Cell 79, 315–328 (1994)

    Article  PubMed  Google Scholar 

  177. O’Reilly, M.S., Boehm, T., Shing, Y., Fukai, N., Vasios, G., Lane, W.S., Flynn, E., Birkhead, J.R., Olsen, J., Folkman, B.R.: Endostatin: An endogenous inhibitor of angiogenesis and tumor growth. Cell 88, 277–285 (1997)

    Article  Google Scholar 

  178. O’Reilly, M.S., Pirie-Shepherd, S., Lane, W.S., Folkman, J.: Antiangiogenic activity of the cleaved conformation of the serpin antithrombin. Science 285, 1926–1928 (1999)

    Article  Google Scholar 

  179. Orlidge, A., D’Amore, P.A.: Inhibition of capillary endothelial cell growth by pericytes and smooth muscle cells. J. Cell Biol. 105 (3), 1455–1462 (1987)

    Article  Google Scholar 

  180. Orme, M.E., Chaplain, M.A.J.: A mathematical model of the first steps of tumour-related angiogenesis: Capillary sprout formation and secondary branching. IMA J. Math. Appld. Med. Biol. 13, 73–98 (1996)

    MATH  Google Scholar 

  181. Orme, M.E., Chaplain, M.A.J.: Two-dimensional models of tumour angiogenesis and anti-angiogenesis strategies. IMA J. of Math. Appld. Med. Biol. 14, 189–205 (1997)

    MATH  Google Scholar 

  182. Oster, G.F., Murray, J.D., Harris, A.K.: Mechanical aspects of mesenchymal morphogenesis. J. Embryol. Exp. Morph. 78, 83–125 (1983)

    Google Scholar 

  183. Othmer, Hans, G., Stevens, Angela: Aggregation, blowup, and collapse: The ABC’s of taxis in reinforced random walks. SIAM J. Appld. Math. 57 (4), 1044–1081 (1997)

    Article  MATH  Google Scholar 

  184. Painter, K.J., Maini, P.K., Othmer, H.G.: Development and applications of a model for cellular response to multiple chemotactic cues. J. Math. Biol. 41 (4), 285–314 (2000)

    Article  MATH  Google Scholar 

  185. Papetti, M., Herman, I.M.: Mechanisms of normal and tumor-derived angiogenesis. Am J. Physiol. Cell Physiol. 282, 5 (970), C947–C970 (2002)

    Google Scholar 

  186. Parent, C.A., Devreotes, P.N.: A cell’s sense of direction. Science 284 (5415), 765–770 (1999)

    Article  Google Scholar 

  187. Patterson, B.C., Sang, Q.A.: Angiostatin-converting enzyme activities of human matrilysin (MMP-7) and gelatinase B/type IV collagenase (MMP-9). J. Biol. Chem. 272 (46), 28823–28825 (1997)

    Article  Google Scholar 

  188. Paweletz, N., Knierim, M.: Tumor-related angiogenesis. Crit. Rev. Onco./Hema. 9, 197–242 (1989)

    Google Scholar 

  189. Pennington, D.W., Lopez, A.R., Thomas, P.S., Ryan, U.S.: Stimulation of rat endothelial cell transforming growth factor-Grβ production by bleomycin. J. Clin. Invest. 83, 148–154 (1991)

    Google Scholar 

  190. Pepper, M.S., Montesano, R.: Proteolytic balance and capillary morphogenesis. Cell Diff. Develop. 32, 319–328 (1990)

    Article  Google Scholar 

  191. Pepper, M.S., Ferrara, N., Orci, L., Montesano, T.: Potent synergism between vascular endothelial growth factor and basic fibroblast growth factor in the induction of angiogenesis in vitro. Biochem. Biophys. Res. Commun. 189, 824–831 (1992)

    Google Scholar 

  192. Pepper, M.S., Montesano, R., Mandriota, S.J., Orci, L., Vassalli, J.: Angiogenesis: a paradigm for balanced extracellular proteolysis during cell migration and morphogenesis. Enzyme Protein 49, 138–162 (1996)

    Google Scholar 

  193. Peters, K.G., Coogan, A., Berry, D., Marks, J., Iglehart, J.D., Kontos, C.D., Rao, P., Sankar,~S., Trogan, E.: Expression of tie2/tek in breast tumour vasculature provides a new marker for evaluation of tumour angiogenesis. Br. J. Cancer 77 (1), 51–56 (1998)

    Google Scholar 

  194. Pettet, G.J., Chaplain, M.A.J., McElwain, D.L.S., M., H., Byrne: A model of wound-healing angiogenesis in soft tissue. Math. Biosc. 136 (1), 35–63 (1996)

    Article  MATH  Google Scholar 

  195. Pike, S.E., Yao, L., Jones, K.D., Cherney, B., Appella, E., Sakaguchi, K., Nakhasi, H., Teruya-Feldstein, J., Wirth, P., Gupta, G., Tosato, G.: Vasostatin, a calreticulin fragment, inhibits angiogenesis and suppresses tumor growth. J. Exp. Med. 188, 2349–2356 (1998)

    Article  Google Scholar 

  196. Pircher, R., Jullien, P., Lawrence, D.: Beta-transforming growth factor is stored in human blood platelets as a latent high molecular weight complex. Biochem. Biophys. Res. Commun 136, 30–37 (1986)

    Google Scholar 

  197. Poltorak, Z., Cohen, T., Neufeld, G.: The VEGF splice variants: properties, receptors, and usage for the treatment of ischemic diseases. Herz 25, 126–129 (2000)

    Google Scholar 

  198. Polverini, P.J.: Cellular adhesion molecules. Newly identified mediators of angiogenesis. Am. J. Pathol. 148, 1023–1029 (1996a)

    Google Scholar 

  199. Polverini, P.J.: How the extracellular matrix and macrophages contribute to angiogenesis-dependent diseases. Eur. J. Cancer 14, 2430–2437 (1996b)

    Google Scholar 

  200. Presta, M., Maier, J.A.M., Ragnotti, G.: The mitogenic signally pathway but not the plasminogen activator-induced pathway of basic fibroblast growth factor is mediated through protein kinase C in fetal bovine aortic endothelial cells. J. Cell Biol. 109, 1877–1884 (1989)

    Article  Google Scholar 

  201. Ramchandran, R., Dhanabal, M., Volk, R., Waterman, W.J., Segal, M., Lu, H., Knebelmann, B., Sukhatme, V.P.: Antiangiogenic activity of restin, NC10 domain of human collagen XV: comparison to endostatin. Biochem. Biophys. Res. Commun. 255, 735–739 (1999)

    Article  Google Scholar 

  202. Rastinejad, F., Polverini, P.J., Bouck, N.P.: Regulation of the activity of a new inhibitor of angiogenesis by a cancer suppressor gene. Cell 56, 345–355 (1989)

    Article  Google Scholar 

  203. Rehn, M., Veikkola, T., Kukk-Valdre, E., Nakamura, H., Ilmonen, M., Lombardo, C.: Pihlajaniemi T, Alitalo K, Vuori K. interaction of endostatin with integrins implicated in angiogenesis. Proc. Natl. Acad. Sci. U S A 98 (3), 1024–1029 (2001)

    Google Scholar 

  204. Rifkin, D.B., Moscatelli, D.: Recent developments in the cell biology of basic fibroblast growth factor. J. Cell Biol. 109, 1–6 (1989)

    Article  Google Scholar 

  205. Ristimaki, A., Narko, K., Enholm, B., Joukov, V., Alitalo, K.: Proinflammatory cytokines regulate expression of the lymphatic endothelial mitogen vascular endothelial growth factor-C. J. Biol. Chem. 273 (14), 8413–8418 (1998)

    Article  Google Scholar 

  206. Roberts, A.B., Sporn, M.B., Assoian, R.K., Smith, J.M., Roche, N.S., Wakefield, L.M., Heine, U.I.: Transforming growth factor type beta: rapid induction of fibrosis and angiogenesis in vivo and stimulation of collagen formation in vitro. Proc. Natl. Acad. Sci. USA 83, 4167 (1986)

    Google Scholar 

  207. Ruoslahti, E.: How cancer spreads. Scientific American 275, 150–154 (1996)

    Google Scholar 

  208. Saelman, E.U.M., Keely, P.J., Santoro, S.A.: Loss of MDCK cell α2β1 integrin expression results in reduced cyst formation, failure of hepatocyte growth factor scatter factor-induced branching morphogenesis, and increased apoptosis. J. Cell Sci. 108, 3531–3540 (1995)

    Google Scholar 

  209. Saksela, O., Rifkin, D.B.: Release of basic fibroblast growth factor-heparan sulfate complexes from endothelial cells by plaminogen activator-mediated proteolytic activity. J. Cell Biol. 110, 767–775 (1990)

    Article  Google Scholar 

  210. Saksela, O., Moscatelli, D., Sommer, A., Rifkin, D.B.: Endothelial cell-derived heparan sulfate binds basic fibroblast growth factor and protects it from proteolytic degradation. J. Cell Biol. 107, 743–751 (1998)

    Article  Google Scholar 

  211. Salcedo, R., Ponce, M.L., Young, H.A., Wasserman, K., Ward, J.M., Kleinman, H.K., Oppenheim, J.J., Murphy, W.J.: Human endothelial cells express CCR2 and respond to MCP-1: direct role of MCP-1 in angiogenesis and tumor progression. Blood 96 (1), 34–40 (2000)

    Google Scholar 

  212. Sato, A., Iwama, A., Takakura, N., Nishio, H., Yancopoulos, G.D., Suda, T.: Characterization of TEK receptor tyrosine kinase and its ligands, angiopoietins, in human hematopoietic progenitor cells. Int. Immunol. 10 (8), 1217–1227 (1998)

    Article  Google Scholar 

  213. Sato, Y., Rifkin, D.B.: Autocrine activities of basic fibroblast growth factor: regulation of endothelial cell movement, plasminogen activator synthesis, and DNA synthesis. J. cell Biol. 107, 1199–1205 (1988)

    Article  Google Scholar 

  214. Sato, Y., Rifkin, D.B.: Inhibition of endothelial cell movement by pericytes and smooth muscle cells: activation of a latent transforming growth factor-beta 1-like molecule by plasmin during co-culture. J. Cell Biol. 109 (1), 309–315 (1989)

    Article  Google Scholar 

  215. Sato, Y., Tsubio, R., Lyons, R., Moses, H., Rifkin, D.B.: Characterization of the activation of latent TGF-β by co-cultures of endothelial cells and pericytes or smooth muscle cells: a self-regulating system. J. Cell Biol. 111, 757–763 (1990)

    Article  Google Scholar 

  216. Savill, Nicholas, J., Hogeweg, Paulien: Modelling morphogenesis: From single cells to crawling slugs. J. Theor. Biol. 184, 229–235 (1997)

    Article  Google Scholar 

  217. Sawano, A., Iwai, S., Sakurai, Y., Ito, M., Shitara, K., Nakahata, T., Shibuya, M.: Flt-1, vascular endothelial growth factor receptor 1, is a novel cell surface marker for the lineage of monocyte-macrophages in humans. Blood 97 (3), 785–791 (2001)

    Article  Google Scholar 

  218. Schlessinger, J., Lax, I., Lemmon, M.: Regulation of growth factor activation by proteoglycans: what is the role of the low affinity receptors? Cell 3, 357–60 (1995), Review

    Google Scholar 

  219. Schwartz, M.A., Ingber, D.E.: Integrating with integrins. Mol. Biol. Cell 5, 389–393 (1994)

    Google Scholar 

  220. Seandel, M., Noack-Kunnmann, K., Zhu, D., Aimes, R.T., Quigley, J.P.: Growth factor-induced angiogenesis in vivo requires specific cleavage of fibrillar type I collagen. Blood 97, 2323–2332 (2001)

    Article  Google Scholar 

  221. Senger, D.R., Claffey, K.P., Benes, J.E., Perruzzi, C.A., Sergiou, A.P., Detmar, M.: Angiogenesis promoted by vascular endothelial growth factor: regulation through alpha1beta1 and alpha2beta1 integrins. Proc. Natl. Acad. Sci. USA 94, 13612–13617 (1997)

    Article  Google Scholar 

  222. Sephy, P.: Angiogenesis inhibitors in oncology: The research continues. Cancer Practice 8 (3), 148–150 (2000)

    Google Scholar 

  223. Servant, G., Weiner, O.D., Herzmark, P., Balla, T., Sedat, J.W., Bourne, H.R.: Polarization of chemoattractant receptor signaling during neutrophil chemotaxis. Science 287 (5455), 1037–1040 (2000)

    Article  Google Scholar 

  224. Sheetz, M.P., Felsenfeld, D., Galbraith, C.G., Choquet, D.: Cell migration as a five-step cycle. Biochem. Soc. Symp. 65, 233–243 (1999)

    Google Scholar 

  225. Shen, B.Q., Lee, D.Y., Gerber. H.P., et al.: Homologous up-regulation of KDR/FLK-1 receptor expression by vascular endothelial growth factor in vitro. J. Biol. Chem. 273, 29979–29985 (1998)

    Article  Google Scholar 

  226. Shichiri, M., Hirata, Y.: Antiangiogenesis signals by endostatin. FASEB J. 15 (6), 1044–1053 (2001)

    Article  Google Scholar 

  227. Sholley, M.M., Ferguson, G.P., Seibel, H.R., Montour, J.L., Wilson, J.D.: Mechanisms of neovascularization. vascular sprouting can occur without proliferation of endothelial cells. Lab. Invest. 51 (6), 624–634 (1984)

    Google Scholar 

  228. Sleeman, B.D., Anderson, A.R.A., Chaplain, M.A.J.: A mathematical analysis of a model for capillary network formation in the absence of endothelial cell proliferation. Appld. Math. Letts. 12, 121–127 (1999)

    Article  MATH  Google Scholar 

  229. Stack, M.S., Gately, S., Bafetti, L.M., Enghild, J.J., Soff, G.A.: Angiostatin inhibits endothelial and melanoma cellular invasion by blocking matrix-enhanced plasminogen activation. J. Biochem. 340, 77–84 (1999)

    Article  Google Scholar 

  230. Stetler-Stevenson, W.G.: Matrix metalloproteinases in angiogenesis: a moving target for therapeutic intervention. J. Clin. Invest. 9, 1237–1241 (1999)

    Google Scholar 

  231. Stokes, C.L., Lauffenburger, D.A.: Analysis of the roles of microvessel endothelial cell random motility and chemotaxis in angiogenesis. J. Theor. Biol. 152, 377–403 (1991)

    Google Scholar 

  232. Stratmann, A., Risau, W., Plate, K.H.: Cell type-specific expression of angiopoietin-1 and angiopoietin-2 suggests a role in glioblastoma angiogenesis. Am. J. Pathol. 153 (5), 1459–1466 (1998)

    Google Scholar 

  233. Tamada, V., Fukiage, C., Boyle, D.L., Azuma, M., Shearer, T.R.: Involvement of cysteine proteases in bFGF-induced angiogenesis in guinea pig and rat cornea. J. Ocular Pharmacol. Therapeutics 16, 271–283 (2000)

    Google Scholar 

  234. Tanaka, S., Mori, M., Sakamoto, Y., Makuuchi, M.N., Sugimachi, K., Wands, J.R.: Biological significance of angiopoietin-2 expression in human hepatocellular carcinoma. J. Clin. Invest. 103, 341–345 (1999)

    Google Scholar 

  235. Taylor, S., Folkman, J.: Protamine is an inhibitor of angiogenesis. Nature 287, 307–312 (1982)

    Google Scholar 

  236. Tennant, T.R., Rinker-Schaeffer, C.W., Stadler, W.M.: Angiogenesis inhibitors. Curr. Onco. Rpts. 2, 11–16 (2000)

    Google Scholar 

  237. Thomas, W.E.: Brain macrophages: on the role of pericytes and perivascular cells. Brain Res. Brain Res. Rev. 31 (1), 42–57 (1999)

    Google Scholar 

  238. Thompson, W.D., Li, W.W., Maragoudakis, M.: The clinical manipulation of angiogenesis: pathology, side-effects, surprises and opportunities with novel human therapies. J. Pathol. 190, 330–337 (2000)

    Article  Google Scholar 

  239. Thurston, G., Suri, C., Smith, K., McClain, J., Sato, T.N., Yancopoulos, G.D., McDonald, D.M.: Leakage-resistant blood vessels in mice transgenically overexpressing angiopoietin-1. Science 286 (5449), 2511–2514 (1999)

    Article  Google Scholar 

  240. Tischer, E., Mitchell, R., Hartman, T., Silva, M., Gospodarowicz, D., Fiddes, J.C., Abraham, J.A.: The human gene for vascular endothelial growth-factor multiple protein forms are encoded through alternative exon splicing. J. Biol. Chem. 266, 11947–11954 (1991)

    Google Scholar 

  241. Toi, M., Inada, K., Suzuki, H., Tominaga, T.: Tumour angiogenesis in breast cancer: its importance as a prognostic indicator and the association with vascular endothelial growth factor expression. Breast Cancer Res. Treat 36, 193–204 (1995)

    Google Scholar 

  242. Tong, S., Yuan, F.: Numerical simulations of angiogenesis in the cornea. Microvasc. Res. 1–14 (2000)

  243. Trinchieri, G.: Interleukin-12: a cytokine at the interface of inflammation and immunity. Adv. Immunol. 70, 83–243 (1998)

    Google Scholar 

  244. Turing, A.M.: The chemical basis of morphogenesis. Philosophical transactions of the Royal Society of London Series B, Biological Sciences 237, 37–72 (1952)

    Google Scholar 

  245. Ueno, T., Toi, M., Saji, H., Muta, M., Bando, H., Kuroi, K., Koike, M., Inadera, H., Matsushima, K.: Significance of macrophage chemoattractant protein-1 in macrophage recruitment, angiogenesis, and survival in human breast cancer. Clin. Cancer Res. 6, 3282–3289 (2000)

    Google Scholar 

  246. Varner, J.A., Brooks, P.C., Cheresh, D.A.: The integrin ανβ3: angiogenesis and apoptosis. Cell Adhes. Commun. 3, 367–374 (1995)

    Google Scholar 

  247. Veikkola, T., Alitalo, K.: VEGF’s, receptors and angiogenesis. Sem. Cancer Biol. 9, 211–220 (1999)

    Article  Google Scholar 

  248. Vernon, R.B., Sage, H.E.: A novel, quantitative model for study of endothelial cell migration and sprout formation within three-dimensional collagen matrices. Microvasc. Res. 57, 118–133 (1999)

    Article  Google Scholar 

  249. Voest, E.E., Kenyon, B.M., O’Reilly, M.S., Truitt, G., D’Amato, R.J., Folkman, J.: Inhibition of angiogenesis in vivo by interleukin 12. Natl. Cancer Inst. 87, 581–586 (1995)

    Google Scholar 

  250. Volpert, O.V., Stellmach, V., Bouck, N.: The modulation of thrombospondin and other naturally occurring inhibitors of angiogenesis during tumor progression. Breast Cancer Res. Treat. 36, 119–126 (1995)

    Google Scholar 

  251. Weninger, W., Pammer, J., Baghestanian, M., Uthman, M., Mildner, A., Ballaun, C., Bankl, H.C., Valent, P.: Expression of vascular endothelial growth factor (VEGF) by human mast cells. J. Vasc. Res. 33, 422 (1996)

    Google Scholar 

  252. Werb, Z.: ECM and cell surface proteolysis: Regulating cellular ecology. Cell 91 (4), 439–442 (1997)

    Article  Google Scholar 

  253. Westermark, B., Siegbahn, A., Heldin, C.H., Claesson-Welsh, L.: B-type receptor for platelet-derived growth factor mediates a chemotactic response by means of ligand-induced activation of the receptor protein-tyrosine kinase. Proc. Natl. Acad. Sci. U S A 87 (1), 128–132 (1990)

    Google Scholar 

  254. Willam, C., Koehne, P., Jurgensen, J.S., Grafe, M., Wagner, K.D., Bachmann, S., Frei, U., Eckardt, K.U.: Tie2 receptor expression is stimulated by hypoxia and proinflammatory cytokines in human endothelial cells. Circ. Res. 87 (5), 370–377 (2000)

    Google Scholar 

  255. Wong, A.L., Haroon, Z.A., Werner, S., Dewhirst, M.W., Greenberg, C.S., Peters, K.G.: Tie-2 expression and phosphorylation in angiogenic and quiescent adult tissues. Circ. Res. 81, 567–574 (1997)

    Google Scholar 

  256. Wong, M.P., Cheung, K.N., Yuen, S.T., Fu, K.H., Chan, A.S., Leung, S.Y., Chung, L.P.: Monocyte chemoattractant protein-1 (MCP-1) expression in primary lymphoepithelioma-like carcinomas (LELCs) of the lung. J. Pathol. 186 (4), 372–377 (1998)

    Article  Google Scholar 

  257. Wu, Pl, Yonekura, H., Li, H., Nozaki, I., Tomono, Y., Naito, I., Ninomyia, Y., Yamamoto, H.: Hypoxia down-regulates endostatin production by human microvascular endothelial cells and pericytes. Biochem. Biophys. Res. Comm. 288, 1149–1154 (2001)

    Article  Google Scholar 

  258. Yamagishi, S., Yonekura, H., Yamamoto, Y., Fujimori, H., Sakurai, S., Tanaka, N., Yamamoto, H.: Vascular endothelial growth factor acts as a pericyte mitogen under hypoxic conditions. Lab. Invest. 79 (4), 501–509 (1999)

    Google Scholar 

  259. Yamagushi, N., Anand-Apte, B., Lee, M., Sasaki, T., Fukai, N., Shapiro, R., Que, I., Lowik, C., Timpl, R., Olsen, B.R.: Endostatin inhibits VEGF-induced endothelial cell migration and tumor growth independently of zinc binding. The EMBO Journal 18 (16), 4414–4423 (1999)

    Article  Google Scholar 

  260. Yancopoulos, G.D., Davis, S., Gale, N.W., Rudge, J.S., Weigand, S.J., Holash, J.: Vascular-specific growth factors and blood-vessel formation. Nature 407 (6801), 242–248 (2000), Review

    Article  Google Scholar 

  261. Yang, S., Graham, J., Kahn, J.W., Schwartz, E.A., Gerritsen, M.E.: Functional roles for PECAM-1 (CD31) and VE-cadherin (CD144) in tube assembly and lumen formation in three-dimensional collagen gels. Am. J. Pathology 155, 887–895 (1999)

    Google Scholar 

  262. Yuan, F., Chen, Y., Dellian, M., Safabakhsh, N., Ferrara, N., Jain, R.K.: Time-dependent vascular regression and permeability changes in established human tumor xenografts induced by an anti-vascular endothelial growth factor/vascular permeability factor antibody. Proc. Natl. Acad. Sci. USA 93, 14765–14770 (1996)

    Article  Google Scholar 

  263. Zawicki, D.F., Jain, R.K., Shmid-Schoenbein, Chiem, S.: Dynamics of neovascularization in normal tissue. Microvasc. Res. 21, 27–47 (1981)

    Article  Google Scholar 

  264. Zhang, Y., Deng, Y., Luther, T., Muller, M., Ziegler, R., Waldherr, R., Stern, D.M.: Nawroth PP. tissue factor controls the balance of angiogenic and antiangiogenic properties of tumor cells in mice. J. Clin. Invest. 94 (3), 1320–1327 (1994)

    Google Scholar 

  265. Zhu, C., Bao, G., Wang, N.: Cell mechanics: mechanical response, cell adhesion, and molecular deformation. Annu. Rev. Biomed. Eng. 2, 189–226 (2000)

    Article  Google Scholar 

  266. Zimmerman, K.: Der peinere bau der blutcapillaren. A. Anat. Entwicklungsgesh. 68, 29–109 (1923)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Mathematics, University of Minnesota, Minneapolis, MN 55455

    Nikos V. Mantzaris, Steve Webb & Hans G. Othmer

  2. Department of Chemical Engineering, Rice University, Houston, TX

    Nikos V. Mantzaris

  3. Department of Mathematical Sciences, Loughborough University, Leicestershire, UK

    Steve Webb

Authors
  1. Nikos V. Mantzaris
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Steve Webb
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Hans G. Othmer
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Hans G. Othmer.

Additional information

All authors contributed equally to this work. Research supported in part by NIH Grant GM29123 and NSF Grants DMS0096312 and DMS0074043.

Revised version: 1 December 2003

Rights and permissions

Reprints and permissions

About this article

Cite this article

Mantzaris, N., Webb, S. & Othmer, H. Mathematical modeling of tumor-induced angiogenesis. J. Math. Biol. 49, 111–187 (2004). https://doi.org/10.1007/s00285-003-0262-2

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00285-003-0262-2

Key words or phrases:

Search

Navigation