Computational and Mathematical Modeling of Angiogenesis

References

• Anderson AR, Chaplain MA. Continuous and discrete mathematical models of tumor-induced angiogenesis. Bull Math Biol 1998; 60(5)857–99
   PubMed Web of Science ®Google Scholar
• Arakelyan L, Vainstein V, Agur Z. 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 2002; 5(3)203–14
   Google Scholar
• Auerbach R, Auerbach W, Polakowski I. Assays for angiogenesis: A review. Pharmacol Ther 1991; 51(1)1–11
   Google Scholar
• Baish JW, Gazit Y, Berk DA, Nozue M, Baxter LT, Jain RK. Role of tumor vascular architecture in nutrient and drug delivery: An invasion percolation-based network model. Microvasc Res 1996; 51(3)327–46
   PubMed Web of Science ®Google Scholar
• Bauer AL, Jackson TL, Jiang Y. A cell-based model exhibiting branching and anastomosis during tumor-induced angiogenesis. Biophys J 2007; 92(9)3105–21
   Google Scholar
• Capogrosso Sansone B, Scalerandi M, Condat CA. Emergence of taxis and synergy in angiogenesis. Phys Rev Lett 2001; 87(12)128102
   Google Scholar
• Chaplain MA. The mathematical modelling of tumour angiogenesis and invasion. Acta Biotheor 1995; 43(4)387–402
   Google Scholar
• Chaplain MA, McDougall SR, Anderson AR. Mathematical modeling of tumor-induced angiogenesis. Annu Rev Biomed Eng 2006; 8: 233–57
   PubMed Web of Science ®Google Scholar
• Clark ER, Clark EL. Microscopic observations on the extra-endothelial cells of living mammalian blood vessels. AmerJ Anatomy 1940; 66: 1–49
   Google Scholar
• Drake CJ, LaRue A, Ferrara N, Little CD. VEGF regulates cell behavior during vasculogenesis. Dev Biol 2000; 224(2)178–88
   Google Scholar
• Gevertz JL, Torquato S. Modeling the effects of vasculature evolution on early brain tumor growth. J Theor Biol 2006; 243(4)517–31
   Google Scholar
• Godde R, Kurz H. Structural and biophysical simulation of angiogenesis and vascular remodeling. Dev Dyn 2001; 220(4)387–401
   Google Scholar
• Hogea CS, Murray BT, Sethian JA. Simulating complex tumor dynamics from avascular to vascular growth using a general level-set method. J Math Biol 2006; 53(1)86–134
   PubMed Web of Science ®Google Scholar
• Jabbarzadeh E, Abrams CF. Strategies to enhance capillary formation inside biomaterials: A computational study. Tissue Eng 2007; 13(8)2073–86
   Google Scholar
• Jain RK, Tong RT, Munn LL. Effect of vascular normalization by antiangiogenic therapy on interstitial hypertension, peritumor edema, and lymphatic metastasis: Insights from a mathematical model. Cancer Res 2007; 67(6)2729–35
   PubMed Web of Science ®Google Scholar
• Ji JW, Tsoukias NM, Goldman D, Popel AS. A computational model of oxygen transport in skeletal muscle for sprouting and splitting modes of angiogenesis. J Theor Biol 2006; 241(1)94–108
   Google Scholar
• Komarova NL, Mironov V. On the role of endothelial progenitor cells in tumor neovascularization. J Theor Biol 2005; 235(3)338–49
   Google Scholar
• Levine HA, Sleeman BD, Nilsen-Hamilton M. A mathematical model for the roles of pericytes and macrophages in the initiation of angiogenesis. I. The role of protease inhibitors in preventing angiogenesis. Math Biosci 2000; 168(1)77–115
   PubMed Web of Science ®Google Scholar
• Mac Gabhann F, Ji JW, Popel AS. Multi-scale computational models of pro-angiogenic treatments in peripheral arterial disease. Ann Biomed Eng 2007; 35(6)982–94
   PubMed Web of Science ®Google Scholar
• Mac Gabhann F, Ji JW, Popel AS. VEGF gradients, receptor activation, and sprout guidance in resting and exercising skeletal muscle. J Appl Physiol 2007; 102(2)722–34
   Google Scholar
• Mac Gabhann F, Popel AS. Targeting neuropilin-1 to inhibit VEGF signaling in cancer: Comparison of therapeutic approaches. PLoS Comput Biol 2006; 2(12)180
   Google Scholar
• McDougall SR, Anderson AR, Chaplain MA. Mathematical modelling of dynamic adaptive tumour-induced angiogenesis: Clinical implications and therapeutic targeting strategies. J Theor Biol 2006; 241(3)564–89
   PubMed Web of Science ®Google Scholar
• Merks RM, Brodsky SV, Goligorksy MS, Newman SA, Glazier JA. Cell elongation is key to in silico replication of in vitro vasculogenesis and subsequent remodeling. Dev Biol 2006; 289(1)44–54
   PubMed Web of Science ®Google Scholar
• Oh H, Takagi H, Otani A, Koyama S, Kemmochi S, Uemura A, Honda Y. Selective induction of neuropilin-1 by vascular endothelial growth factor (VEGF): A mechanism contributing to VEGF-induced angiogenesis. Proc Natl Acad Sci U S A 2002; 99(1)383–8
   PubMed Web of Science ®Google Scholar
• Peirce SM, Van Gieson EJ, Skalak TC. Multicellular simulation predicts microvascular patterning and in silico tissue assembly. FASEB J 2004; 18(6)731–3
   PubMedGoogle Scholar
• Pettet GJ, Byrne HM, McElwain DL, Norbury J. A model of wound-healing angiogenesis in soft tissue. Math Biosci 1996; 136(1)35–63
   Google Scholar
• Scalerandi M, Sansone BC, Condat CA. Diffusion with evolving sources and competing sinks: Development of angiogenesis. Phys Rev E Stat Nonlin Soft Matter Phys 65 (1 Pt 2002; 1): 011902
   Google Scholar
• Shiba Y, Takahashi M, Ikeda U. Models for the study of angiogenesis. Curr Pharm Des 2008; 14(4)371–7
   Google Scholar
• Stokes CL, Lauffenburger DA. Analysis of the roles of microvessel endothelial cell random motility and chemotaxis in angiogenesis. J Theor Biol 1991; 152(3)377–403
   Google Scholar
• Stokes CL, Lauffenburger DA, Williams SK. Migration of individual microvessel endothelial cells: Stochastic model and parameter measurement. J Cell Sci 1991; 99(Pt 2)419–30
   Google Scholar
• Szczerba D, Szekely G. Computational model of flow-tissue interactions in intussusceptive angiogenesis. J Theor Biol 2005; 234(1)87–97
   Google Scholar
• Tong S, Yuan F. Numerical simulations of angiogenesis in the cornea. Microvasc Res 2001; 61(1)14–27
   Google Scholar
• Zaman MH, Kamm RD, Matsudaira P, Lauffenburger DA. Computational model for cell migration in three-dimensional matrices. Biophys J 2005; 89(2)1389–97
   PubMed Web of Science ®Google Scholar