Free Access
Issue
Math. Model. Nat. Phenom.
Volume 5, Number 1, 2010
Cell migration
Page(s) 163 - 202
DOI https://doi.org/10.1051/mmnp/20105108
Published online 03 February 2010
  1. T. Alarcon, H.M. ByrneP.K. Maini. A cellular automaton model for tumour growth in inhomogeneous environment. J. Theor. Biol., 225 (2003), 257–274 [CrossRef] [PubMed] [Google Scholar]
  2. A.R.A. AndersonM.A.J. Chaplain. Continuous and discrete mathematical models of tumor-induced angiogenesis. Bull. Math. Biol., 60 (1998), 857–899 [Google Scholar]
  3. A. Armulik, A. Abramsson, C. Betsholtz. (2005). Endothelial/pericyte interactions. Circulation Research, 97 (2005), 512–523 [Google Scholar]
  4. D.H. AusprunkJ. Folkman. Migration and proliferation of endothelial cells in preformed and newly formed blood vessels during tumour angiogenesis. Microvasc. Res., 14 (1977), 53–65 [Google Scholar]
  5. R.G. Bagley. Pericytes from human non-small cell lung carcinomas: An attractive target for anti-angiogenic therapy. Microvascular Res., 71 (2006), 163–174 [CrossRef] [Google Scholar]
  6. J.W. Baish, Y. Gazit, D.A. Berk, M. Nozue, L.T. BaxterR.K. Jain. Role of tumor vascular architecture in nutrient and drug delivery: an invasion percolation-based network model. Microvasc. Res., 51 (1996), 327–346 [CrossRef] [PubMed] [Google Scholar]
  7. L.E. Benjamin, I. HemoE. Keshet. A plasticity window for blood vessel remodelling is defined by pericyte coverage of the preformed endothelial network and is regulated by PDGF-B and VEGF. Development, 125 (1998), 1591–1598 [PubMed] [Google Scholar]
  8. D. Bray. Cell Movements. New-York: Garland Publishing, 1992. [Google Scholar]
  9. R.A. Brekken, P.E. Thorpe. Vascular endothelial growth factor and vascular targeting of solid tumors. 21 (2001), 4221–4229. [Google Scholar]
  10. C.F. Chantrain, P. Henriet, S. Jodele, H. Emonard, O. Feron, P.J. Courtoy, Y.A. DeClerck, E. Marbaix (2006). Mechanisms of pericyte recruitment in tumour angiogenesis: A new role for metalloproteinases. European J. Cancer, 42 (2006), 310–318 [CrossRef] [Google Scholar]
  11. M.A.J. ChaplainG. Lolas. Mathematical modelling of cancer cell invasion of tissue: The role of the urokinase plasminogen activator system. Math. Mod. Meth. Appl. Sci., 11 (2005), 1685–1734 [Google Scholar]
  12. M. Ciofalo, M.W. Collins, T.R. Hennessy. “Microhydrodynamics phenomena in the circulation.” In: Nanoscale fluid dynamics in physiological processes: A review study. WIT Press, Southampton, 1999, pp 219–236. [Google Scholar]
  13. G.E. Davis, K.A. Pintar Allen, R. SalazarS.A. Maxwell. Matrix metalloproteinase-1 and –9 activation by plasmin regulates a novel endothelial cell-mediated mechanism of collagen gel contraction and capillary tube regression in three-dimensional collagen matrices. J. Cell Sci., 114 (2000), 917–930 [Google Scholar]
  14. A.W. El-KarehT.W. Secomb Theoretical models for drug delivery to solid tumours. Crit. Rev. Biomed. Eng., 25 (1997), 503–571 [PubMed] [Google Scholar]
  15. J. FolkmanM. Klagsbrun. Angiogenic factors. Science, 235 (1987), 442–447 [CrossRef] [PubMed] [Google Scholar]
  16. Y.C. Fung. Biomechanics. Springer-Verlag, New-York, 1993. [Google Scholar]
  17. M.S. Gee, W.N. Procopio, S. Makonnen, M.D. Feldman, N.W. YeildingW.M.F. Lee. Tumor vessel development and maturation impose limits on the effectiveness of anti-vascular therapy. Am. J. Path., 162 (2003), 183–193 [Google Scholar]
  18. R. GöddeH. Kurz. Structural and biophysical simulation of angiogenesis and vascular remodeling. Developmental Dynamics, 220 (2001), 387–401 [Google Scholar]
  19. M. HidalgoS.G. Eckkhardt. Development of matrix metalloproteinase inhibitors in cancer therapy. Journal of the National Cancer Institute, 93 (2001), 178–193 [CrossRef] [PubMed] [Google Scholar]
  20. S. Hughes, T. Gardiner, P. Hu, L. Baxter, E. RosinovaT. Chan-Ling. Altered pericyte-endothelial relations in the rat retina during aging: Implications for vessel stability. Neurobiology of Aging, 27 (2006), 1838–1847 [CrossRef] [PubMed] [Google Scholar]
  21. Y. Izumi. Tumour biology: herceptin acts as an antiangiogenic cocktail. Nature 416 (2002), 279–280. [CrossRef] [Google Scholar]
  22. T.L. Jackson, S.R. Lubkin, J.D. Murray. Theoretical analysis of conjugate localization in two-step cancer chemotherapy. J. Math. Biol. 39 (1999), 353–376. [CrossRef] [PubMed] [Google Scholar]
  23. R.K. Jain. (2003) Molecular regulation of vessel maturation. Nat. Med., 9 (2003), 685–93 [CrossRef] [PubMed] [Google Scholar]
  24. A. Kamiya, R. Bukhari, T. Togawa. Adaptive regulation of wall shear stress optimizing vascular tree function. Bull. Math. Biology. 46 (1984), 127–137. [Google Scholar]
  25. G.S. KrenzC.A. Dawson. Vessel distensibility and flow distribution in vascular trees. J. Math. Biol., 44 (2002), 360–374 [CrossRef] [MathSciNet] [PubMed] [Google Scholar]
  26. C.C. Kumar. Targeting integrins αvβ3 and αvβ5 for blocking tumour-induced angiogenesis. Adv. Exp. Med. Biol., 476 (2000), 169–180 [PubMed] [Google Scholar]
  27. H.A. Levine, S. Pamuk, B.D. SleemanM. Nielsen-Hamilton. Mathematical modeling of the capillary formation and development in tumor angiogenesis: penetration into the stroma. Bull. Math. Biol., 63 (2001), 801–863 [Google Scholar]
  28. S.R. McDougall, A.R.A. Anderson, M.A.J. ChaplainJ.A. Sherratt. Mathematical modelling of flow through vascular networks: implications for tumour-induced angiogenesis and chemotherapy strategies. Bull. Math. Biol., 64 (2002), 673–702 [CrossRef] [PubMed] [Google Scholar]
  29. S.R. McDougall, A.R.A. AndersonM.A.J. Chaplain. Mathematical modelling of dynamic adaptive tumour-induced angiogenesis: clinical implications and therapeutic targeting strategies. J. Theor. Biol., 241 (2006), 564–589 [CrossRef] [PubMed] [Google Scholar]
  30. J.A. Madri, B.M. Pratt. Endothelial cell-matrix interactions: in vitro models of angiogenesis. J. Histochem. Cytochem. 34 (1986), 85–91. [PubMed] [Google Scholar]
  31. M.R. Mancuso et al.Rapid vascular regrowth in tumors after reversal of VEGF inhibition. J. Clin. Investigation, 116 (2006), 2610–2621 [CrossRef] [Google Scholar]
  32. S. Morikawa, P. Baluk, T. Kaidoh, A. Haskell, R.K. JainD.M. McDonald. Abnormalities in pericytes on blood vessels and endothelial sprouts in tumors. Am. J. Path., 160 (2002), 985–1000 [Google Scholar]
  33. L.L. Munn. Aberrant vascular architecture in tumors and its importance in drug-based therapies. Drug Discovery Today, 8 (2003), 396–403 [CrossRef] [PubMed] [Google Scholar]
  34. N. Paweletz, M. Knierim. Tumor-related angiogenesis. Crit. Rev. Oncol. Hematol. 9 (1989), 197–242. [CrossRef] [PubMed] [Google Scholar]
  35. A.R. Pries, T.W. SecombP. Gaehtgens. Biophysical aspects of blood flow in the microvasculature. Cardiovasc. Res., 32 (1996), 654–667 [PubMed] [Google Scholar]
  36. A.R. Pries, T.W. SecombP. Gaehtgens. Structural adaptation and stability of microvascular networks: theory and simulation. Am. J. Physiol., 275 (1998), H349–H360 [PubMed] [Google Scholar]
  37. A.R. Pries, B. ReglinT.W. Secomb. Structural adaptation of microvascular networks: functional roles of adaptive responses. Am. J. Physiol., 281 (2001), H1015–H1025 [Google Scholar]
  38. A.R. Pries, B. ReglinT.W. Secomb. Structural adaptation of vascular networks: role of the pressure response. Hypertension, 38 (2001), 1476–1479 [CrossRef] [PubMed] [Google Scholar]
  39. A. Quarteroni, M. TuveriA. Veneziani. Computational vascular fluid dynamics: problems, models and methods. Comput. Visual. Sci., 2 (2000), 163–197 [Google Scholar]
  40. S. Rafil. Vascular and haematopoietic stem cells: novel targets for anti-angiogenesis therapy? Nature Reviews Cancer, 2 (2002), 826–835. [CrossRef] [PubMed] [Google Scholar]
  41. C. Rouget. Memoire sur le developpement, la structure et les proprietes physiologiques des capillaires sanguins et lymphatiques. Arch. Physiol. Norm. Pathol., 5 (1873), 603–663 [Google Scholar]
  42. T.W. Secomb. Mechanics of blood flow in the microcirculation. In “Biological Fluid Dynamics.” eds. C.P. Ellington and T.J. Pedley. Company of Biologists, Cambridge, 1995, pp. 305-321. [Google Scholar]
  43. G.I. Schoefl. Studies of inflammation III. Growing capillaries: Their structure and permeability. Virchows Arch. Path. Anat., 337 (1963), 97–141 [CrossRef] [Google Scholar]
  44. M.M. Sholley, G.P. Ferguson, H.R. Seibel, J.L. MontourJ.D. Wilson. Mechanisms of neovascularization. Vascular sprouting can occur without proliferation of endothelial cells. Lab. Invest., 51 (1984), 624–634 [PubMed] [Google Scholar]
  45. A. Stéphanou, S.R. McDougall, A.R.A. AndersonM.A.J. Chaplain. Mathematical modelling of flow in 2D and 3D vascular networks: applications to anti-angiogenic and chemotherapeutic drug strategies. Math. Comp. Model., 41 (2005), 1137–1156 [CrossRef] [Google Scholar]
  46. A. Stéphanou, S.R. McDougall, A.R.A. AndersonM.A.J. Chaplain. Mathematical modelling of the influence of blood rheological properties upon adaptive tumour-induced angiogenesis. Math. Comp. Model., 44 (2005), 96–123 [Google Scholar]
  47. M.D. SternlichtZ. Werb. How matrix metalloproteinases regulate cell behavior. Annu. Rev. Cell Dev. Biol., 17 (2001), 463–516 [Google Scholar]
  48. G.M. Tozer, C. KanthouB.C. Baguley. Disrupting tumour blood vessels. Nature Reviews Cancer, 5 (2005), 423–433 [Google Scholar]
  49. L. Yan, M.A. Moses, S. Huang, D. Ingber (2000) Adhesion-dependent control of matrix metalloproteinase-2 activation in human capillary endothelial cells. J. Cell Sci., 113 (2000), 3979–3987. [PubMed] [Google Scholar]

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