메뉴 건너뛰기




Volumn 77, Issue 6, 2012, Pages 729-747

The role of stochasticity in a model of retinal angiogenesis

Author keywords

angiogenesis; complex systems; hybrid models; stochastic differential equations; stochastic processes

Indexed keywords

ANGIOGENESIS; BUILDING BLOCKES; CAPILLARY NETWORK; COMPUTATIONAL ANALYSIS; GEOMETRIC DENSITY; GEOMETRIC PATTERNS; HYBRID MODEL; LAW OF LARGE NUMBERS; LOCAL MEAN; MACRO SCALE; MATHEMATICAL PROBLEMS; MEAN FIELD; MESOSCALE; MICRO-SCALES; MODEL REDUCTION; MULTI-SCALE STRUCTURES; NATURAL PROCESS; STOCHASTIC DIFFERENTIAL EQUATIONS; STOCHASTICITY; STRONG COUPLING; VASCULARIZATION; VASCULARIZATION PROCESS;

EID: 84870198999     PISSN: 02724960     EISSN: 14643634     Source Type: Journal    
DOI: 10.1093/imamat/hxs050     Document Type: Article
Times cited : (9)

References (22)
  • 1
    • 0032170064 scopus 로고    scopus 로고
    • Continuous and discrete mathematical models of tumour-induced angiogenesis
    • Anderson, A. R. A. & Chaplain, M. A. (1998) Continuous and discrete mathematical models of tumour-induced angiogenesis. Bull. Math. Biol., 60, 857-900.
    • (1998) Bull. Math. Biol , vol.60 , pp. 857-900
    • Anderson, A.R.A.1    Chaplain, M.A.2
  • 2
    • 47549094092 scopus 로고    scopus 로고
    • Stochastic geometric models, and related statistical issues in tumour-induced angiogenesis
    • Capasso, V., Micheletti, A. & Morale, D. (2008) Stochastic geometric models, and related statistical issues in tumour-induced angiogenesis. Math. Biosci., 214, 20-31.
    • (2008) Math. Biosci , vol.214 , pp. 20-31
    • Capasso, V.1    Micheletti, A.2    Morale, D.3
  • 3
    • 70449515071 scopus 로고    scopus 로고
    • Asymptotic behavior of a system of stochastic particles subject to nonlocal interactions
    • Capasso, V. & Morale, D. (2009a) Asymptotic behavior of a system of stochastic particles subject to nonlocal interactions. Stochast. Anal. Appl., 27, 574-603.
    • (2009) Stochast. Anal. Appl , vol.27 , pp. 574-603
    • Capasso, V.1    Morale, D.2
  • 4
    • 63249119539 scopus 로고    scopus 로고
    • Stochastic modelling of tumour-induced angiogenesis
    • Capasso, V. & Morale, D. (2009b) Stochastic modelling of tumour-induced angiogenesis. J. Math. Biol., 58, 219-233.
    • (2009) J. Math. Biol , vol.58 , pp. 219-233
    • Capasso, V.1    Morale, D.2
  • 5
    • 34547313699 scopus 로고    scopus 로고
    • Invasion and adaptive evolution for individual-based spatially structured populations
    • Champagnat & Méléard
    • Champagnat & Méléard (2007) Invasion and adaptive evolution for individual-based spatially structured populations. J. Math. Biol., 55, 147-188.
    • (2007) J. Math. Biol , vol.55 , pp. 147-188
  • 7
    • 33947330375 scopus 로고    scopus 로고
    • Development of retinal vasculature
    • Fruttiger, M. (2007) Development of retinal vasculature. Angiogenesis, 10, 177-188.
    • (2007) Angiogenesis , vol.10 , pp. 177-188
    • Fruttiger, M.1
  • 8
    • 0034687236 scopus 로고    scopus 로고
    • Platelet derived growth factor is constituvely secreted from neuronal cells bodies but not from axons
    • Fruttiger, M., Calver, A. R. & Richardson,W. D. (2000) Platelet derived growth factor is constituvely secreted from neuronal cells bodies but not from axons. Curr. Biol., 10, 1283-1286.
    • (2000) Curr. Biol , vol.10 , pp. 1283-1286
    • Fruttiger, M.1    Calver, A.R.2    Richardsonw, D.3
  • 9
    • 30744476478 scopus 로고    scopus 로고
    • Retinal angiogenesis in development and disease
    • Gariano, R. F. & Gardner, T.W. (2003) Retinal angiogenesis in development and disease. Nature, 438, 960-966.
    • (2003) Nature , vol.438 , pp. 960-966
    • Gariano, R.F.1    Gardner, T.W.2
  • 12
    • 13844298300 scopus 로고    scopus 로고
    • An interacting particle system modelling aggregation behavior: From individuals to populations
    • Morale, D., Capasso, V. & Ölschlaeger, K. (2005) An interacting particle system modelling aggregation behavior: from individuals to populations. J. Math. Biol., 50, 49-66.
    • (2005) J. Math. Biol , vol.50 , pp. 49-66
    • Morale, D.1    Capasso, V.2    Ölschlaeger, K.3
  • 13
    • 0005500243 scopus 로고
    • On the derivation of reaction-diffusion equations as lilit dynamics of systems of moderately interacting stochastic processes
    • Oelschläger, K. (1989) On the derivation of reaction-diffusion equations as lilit dynamics of systems of moderately interacting stochastic processes. Probab. Theory Related Fields, 82, 565-586.
    • (1989) Probab. Theory Related Fields , vol.82 , pp. 565-586
    • Oelschläger, K.1
  • 14
    • 0042863949 scopus 로고    scopus 로고
    • A reinforced random walk model of tumour angiogenesis and antiangiogenic strategies
    • Plank, M. J. & Sleeman, B. D. (2003) A reinforced random walk model of tumour angiogenesis and antiangiogenic strategies. IMA Math. Med. Biol., 20, 135-181.
    • (2003) IMA Math. Med. Biol , vol.20 , pp. 135-181
    • Plank, M.J.1    Sleeman, B.D.2
  • 15
    • 7444258529 scopus 로고    scopus 로고
    • Lattice and non-lattice models of tumour angiogenesis
    • Plank, M. J. & Sleeman, B. D. (2004) Lattice and non-lattice models of tumour angiogenesis. Bull. Math. Biol., 66, 1785-1819.
    • (2004) Bull. Math. Biol , vol.66 , pp. 1785-1819
    • Plank, M.J.1    Sleeman, B.D.2
  • 16
    • 79953240058 scopus 로고    scopus 로고
    • Hybrid models of tumor growth Wiley Interdisciplinary Rev
    • doi:10.1002/wsbm.102
    • Rejniak, K. A. & Anderson, A. R. A. (2011) Hybrid models of tumor growth. Wiley Interdisciplinary Rev. Syst. Biol. Med., 3, 115-125. doi:10.1002/wsbm.102
    • (2011) Syst. Biol. Med , vol.3 , pp. 115-125
    • Rejniak, K.A.1    Anderson, A.R.A.2
  • 17
    • 33748070513 scopus 로고    scopus 로고
    • Mathematical modelling of the influence of blood rheological properties upon adaptative tumour-induced angiogenesis
    • Stéphanou, A., McDougall, S. R., Anderson, A. R. A. & Chaplain, M. A. J. (2006) Mathematical modelling of the influence of blood rheological properties upon adaptative tumour-induced angiogenesis. Math. Comput. Modell., 44, 96-123.
    • (2006) Math. Comput. Modell , vol.44 , pp. 96-123
    • Stéphanou, A.1    McDougall, S.R.2    Anderson, A.R.A.3    Chaplain, M.A.J.4
  • 18
    • 0029074024 scopus 로고
    • Development of retinal vasculature is mediated by hypoxia?U induced vascular endothelial growth factor (VEGF)
    • Stone, J., Itin, A., Alon, T., Peter, J., Gnessin, H., Chan-Ling T. & Keshet E. (1995) Development of retinal vasculature is mediated by hypoxia?U induced vascular endothelial growth factor (VEGF). J. Neurosci., 15, 4738-4747.
    • (1995) J. Neurosci , vol.15 , pp. 4738-4747
    • Stone, J.1    Itin, A.2    Alon, T.3    Peter, J.4    Gnessin, H.5    Chan-Ling, T.6    Keshet, E.7
  • 21
    • 0001105004 scopus 로고
    • Topics in propagation of chaos. Ecole d'Ete de Probabilites de Saint-Flour XIX, 1989
    • Berlin Springer
    • Sznitman, A. S. (1991) Topics in propagation of chaos. Ecole d'Ete de Probabilites de Saint-Flour XIX, 1989. Lecture Notes in Mathematics, vol. 1464. Berlin: Springer, pp. 165-251.
    • (1991) Lecture Notes in Mathematics , vol.1464 , pp. 165-251
    • Sznitman, A.S.1
  • 22
    • 18844424905 scopus 로고    scopus 로고
    • Stabilization of the retinal vascular network by reciprocal feedback between blood vessel and astrocytes
    • West, H., Richardson, W. D. & Fruttiger, M. (2005) Stabilization of the retinal vascular network by reciprocal feedback between blood vessel and astrocytes. Development, 132, 1855-1862.
    • (2005) Development , vol.132 , pp. 1855-1862
    • West, H.1    Richardson, W.D.2    Fruttiger, M.3


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.