A Multiscale Approach Leading to Hybrid Mathematical Models for Angiogenesis: Role of Randomness - Mathematical Methods and Models in Biomedicine - page 110

29. Oelschlager, K.: On the derivation of reaction-diffusion equations as lilit dynamics of systems
of moderately interacting stochastic processes. Prob. Th. Rel. Fields 82 , 565-586 (1989)
30. Okubo, A.: Dynamical aspects of animal grouping: Swarms, school, flocks and herds. Adv.
BioPhys. 22 , 1-94 (1986)
31. Okubo, A., Levin, S.: Diffusion and ecological problems: Modern Perspectives. Springer,
Heidelberg (2002)
32. Orme, M., Chaplain, M.: A mathematical model of the first steps of tumour-related angio-
genesis: Capillary sprout formation and secondary branching. IMA J. Math. Appl. Med. 14 ,
189-205 (1996)
33. Plank, M.J., Sleeman, B.D.: A reinforced random walk model of tumour angiogenesis and
anti-angiogenic strategies. IMA J. Math. Med. Biol. 20 , 135-181 (2003)
34. Plank, M.J., Sleeman, B.D.: Lattice and non-lattice models of tumour angiogenesis. Bull. Math.
Biol. 66 (6), 1785-1819 (2004)
35. Rejniak, K.A., Anderson, A.R.A.: Hybrid models of tumor growth. Wiley Interdiscipl. Rev.
Syst. Biol. Med. 3 , 115-125 (2011) doi: 10.1002/wsbm.102
36. Stephanou, A., McDougall, S.R., Anderson, A.R.A., Chaplain, M.A.J.: Mathematical mod-
elling of the influence of blood rheological properties upon adaptative tumour-induced
angiogenesis. Math. Comput. Model. 44 , 96-123 (2006)
37. 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)
38. Stone, J., Itin, A., Alon, T., Peter, J., Gnessin, H., Chan-Ling, T., Keshet, E.: Development of
retinal vasculature is mediated by hypoxia induced vascular endothelial growth factor (VEGF).
J. Neurosci. 15 , 4738-4747 (1995)
39. Sznitman, A.S.: Topics in propagation of chaos. Ecole d'Ete de Probabilites de Saint-Flour
XIX, 1989. In: Lecture Notes in Mathematics, vol. 1464, pp. 165-251. Springer, Berlin (1991)
40. Sun, S., Wheeler, M.F., Obeyesekere, M., Patrick, C.W. Jr.: A deterministic model of growth
factor-induced angiogenesis. Bull. Math. Biol. 67 , 313-337 (2005)
41. Sun, S., Wheeler, M.F., Obeyesekere, M., Patrick, C.W. Jr.: A Multiscale angiogene-
sis modeling using mixed finite element methods. SIAM Multiscale Model. Simul. 4 ,
1137-1167 (2005)
42. West, H., Richardson, W.D., Fruttiger, M.: Stabilization of the retinal vascular network by
reciprocal feedback between blood vessel and astrocytes. Development 132 , 1855-1862 (2005)