메뉴 건너뛰기




Volumn 58, Issue 1-2, 2009, Pages 219-233

Stochastic modelling of tumour-induced angiogenesis

Author keywords

Angiogenesis; Birth and growth processes; Hybrid models; Stochastic differential equations

Indexed keywords

ANIMAL; ARTICLE; BIOLOGICAL MODEL; COMPUTER SIMULATION; HUMAN; NEOPLASM; NEOVASCULARIZATION (PATHOLOGY); PATHOLOGY; STATISTICS; VASCULARIZATION;

EID: 63249119539     PISSN: 03036812     EISSN: 14321416     Source Type: Journal    
DOI: 10.1007/s00285-008-0193-z     Document Type: Article
Times cited : (74)

References (29)
  • 2
    • 0032170064 scopus 로고    scopus 로고
    • Continuous and discrete mathematical models of tumour-induced angiogenesis
    • Anderson, A.R.A., Chaplain, M.A.J.: Continuous and discrete mathematical models of tumour-induced angiogenesis. Bull. Math. Biol. 60, 857900 (1998)
    • (1998) Bull. Math. Biol. , vol.60 , pp. 857900
    • Anderson, A.R.A.1    Chaplain, M.A.J.2
  • 4
    • 0019334831 scopus 로고
    • Two-dimensional peptide mapping of fibronectin from bovine aortic endothelial cells and bovine plasma
    • Birdwell, C., Brasier, A., Taylor, L.: Two-dimensional peptide mapping of fibronectin from bovine aortic endothelial cells and bovine plasma. Biochem. Biophys. Res. Commun. 97, 574581 (1980)
    • (1980) Biochem. Biophys. Res. Commun. , vol.97 , pp. 574581
    • Birdwell, C.1    Brasier, A.2    Taylor, L.3
  • 6
    • 0029294735 scopus 로고
    • Mathematical models for tumour angiogenesis: Numerical simulations and nonlinear wave solutions
    • Byrne, H., Chaplain, M.: Mathematical models for tumour angiogenesis: numerical simulations and nonlinear wave solutions. Bull. Math. Biol. 57, 461486 (1995)
    • (1995) Bull. Math. Biol. , vol.57 , pp. 461486
    • Byrne, H.1    Chaplain, M.2
  • 8
    • 45749141814 scopus 로고    scopus 로고
    • On mean densities of inhomogeneous geometric processes arising in material science and medicine
    • Capasso, V., Villa, E.: On mean densities of inhomogeneous geometric processes arising in material science and medicine. Image Anal. Stereol. 26, 23-36 (2007)
    • (2007) Image Anal. Stereol. , vol.26 , pp. 23-36
    • Capasso, V.1    Villa, E.2
  • 9
    • 77957176863 scopus 로고
    • A model mechanism for the chemotactic response of endothelial cells to tumour angiogenesis factor
    • Chaplain, M., Stuart, A.: A model mechanism for the chemotactic response of endothelial cells to tumour angiogenesis factor. IMA J. Math. Appl. Med. Biol. 10, 149168 (1993)
    • (1993) IMA J. Math. Appl. Med. Biol. , vol.10 , pp. 149168
    • Chaplain, M.1    Stuart, A.2
  • 10
    • 0029422302 scopus 로고
    • The mathematical modelling of tumour angiogenesis and invasion
    • Chaplain, M.: The mathematical modelling of tumour angiogenesis and invasion. Acta Biotheor. 43, 387402 (1995)
    • (1995) Acta Biotheor. , vol.43 , pp. 387402
    • Chaplain, M.1
  • 15
    • 84863547030 scopus 로고
    • Tumour angiogenesis
    • Folkman, J.: Tumour angiogenesis. Adv. Cancer Res. 19, 331358 (1974)
    • (1974) Adv. Cancer Res. , vol.19 , pp. 331358
    • Folkman, J.1
  • 16
    • 0023157363 scopus 로고
    • Angiogenic factors
    • Folkman, J., Klagsbrun, M.: Angiogenic factors. Science 235, 442-447 (1987)
    • (1987) Science , vol.235 , pp. 442-447
    • Folkman, J.1    Klagsbrun, M.2
  • 17
    • 0035653288 scopus 로고    scopus 로고
    • Vessels of Death or Life
    • Jain, R.K., Carmeliet, P.F.: Vessels of Death or Life. Sci. Am. 285, 38-45 (2001)
    • (2001) Sci. Am. , vol.285 , pp. 38-45
    • Jain, R.K.1    Carmeliet, P.F.2
  • 18
    • 0035287283 scopus 로고    scopus 로고
    • Mathematical modelling of the onset of capillary formation initiating angiogenesis
    • Levine, H.A., Sleeman, B.D., Nilsen-Hamilton, M.: Mathematical modelling of the onset of capillary formation initiating angiogenesis. J. Math. Biol. 42, 195238 (2001)
    • (2001) J. Math. Biol. , vol.42 , pp. 195238
    • Levine, H.A.1    Sleeman, B.D.2    Nilsen-Hamilton, M.3
  • 20
    • 13844298300 scopus 로고    scopus 로고
    • An interacting particle system modelling aggregation behavior: From individuals to populations
    • Morale, D., Capasso, V., Ölschlaeger, K.: An interacting particle system modelling aggregation behavior: from individuals to populations. J. Math. Biol. 50, 49-66 (2005)
    • (2005) J. Math. Biol. , vol.50 , pp. 49-66
    • Morale, D.1    Capasso, V.2    Ölschlaeger, K.3
  • 21
    • 0005500243 scopus 로고
    • On the derivation of reaction-diffusion equations as limit dynamics of systems of moderately interacting stochastic processes
    • Oelschläger, K.: On the derivation of reaction-diffusion equations as limit dynamics of systems of moderately interacting stochastic processes. Probab. Theor. Relat. Fields 82, 565-586 (1989)
    • (1989) Probab. Theor. Relat. Fields , vol.82 , pp. 565-586
    • Oelschläger, K.1
  • 22
    • 0030161443 scopus 로고    scopus 로고
    • A mathematical model of the first steps of tumour-related angiogenesis: Capillary sprout formation and secondary branching
    • Orme, M., Chaplain, M.: A mathematical model of the first steps of tumour-related angiogenesis: capillary sprout formation and secondary branching. IMA J. Math. Appl. Med. 14, 189205 (1996)
    • (1996) IMA J. Math. Appl. Med. , vol.14 , pp. 189205
    • Orme, M.1    Chaplain, M.2
  • 23
    • 0042863949 scopus 로고    scopus 로고
    • A reinforced random walk model of tumour angiogenesis and antiangiogenic strategies
    • Plank, M.J., Sleeman, B.D.: A reinforced random walk model of tumour angiogenesis and antiangiogenic strategies. IMA J. Math. Med. Biol. 20, 135181 (2003)
    • (2003) IMA J. Math. Med. Biol. , vol.20 , pp. 135181
    • Plank, M.J.1    Sleeman, B.D.2
  • 24
    • 7444258529 scopus 로고    scopus 로고
    • Lattice and non-lattice models of tumour angiogenesis
    • Plank, M.J., Sleeman, B.D.: Lattice and non-lattice models of tumour angiogenesis. Bull. Math. Biol. 66(6), 1785-1819 (2004)
    • (2004) Bull. Math. Biol. , vol.66 , Issue.6 , pp. 1785-1819
    • Plank, M.J.1    Sleeman, B.D.2
  • 25
    • 33745918670 scopus 로고    scopus 로고
    • Mathematical modelling of dynamic tumourinduced angiogenesis: Clinical implications and therapeutic targeting strategies
    • McDougall, S.R., Anderson, A.R.A., Chaplain, M.A.J.: Mathematical modelling of dynamic tumourinduced angiogenesis: clinical implications and therapeutic targeting strategies. J. Theor. Biol. 241, 564-589 (2006)
    • (2006) J. Theor. Biol. , vol.241 , pp. 564-589
    • McDougall, S.R.1    Anderson, A.R.A.2    Chaplain, M.A.J.3
  • 27
    • 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.: Mathematical modelling of the influence of blood rheological properties upon adaptative tumour-induced angiogenesis. Math. Comput. Model. 44(1-2), 96-123 (2006)
    • (2006) Math. Comput. Model. , vol.44 , Issue.1-2 , pp. 96-123
    • Stéphanou, A.1    McDougall, S.R.2    Anderson, A.R.A.3    Chaplain, M.A.J.4
  • 28
    • 0025991093 scopus 로고
    • Analysis of the roles of microvessel endothelial cell random motility and chemotaxis in angiogenesis
    • 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)
    • (1991) J. Theor. Biol. , vol.152 , pp. 377-403
    • Stokes, C.L.1    Lauffenburger, D.A.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.