메뉴 건너뛰기




Volumn 9, Issue 3, 2006, Pages 127-138

Angiogenesis - Understanding the mathematical challenge

Author keywords

Angiogenesis; Angiopoietins; Mathematical modelling; VEGF

Indexed keywords

ANGIOGENESIS; BIOCHEMISTRY; CAPILLARY; CELL FUNCTION; MATHEMATICAL MODEL; MEDICAL RESEARCH; PRIORITY JOURNAL; REVIEW; SCIENTIST; SIMULATION; SPROUTING;

EID: 33846894490     PISSN: 09696970     EISSN: None     Source Type: Journal    
DOI: 10.1007/s10456-006-9039-8     Document Type: Review
Times cited : (15)

References (38)
  • 1
    • 0018656345 scopus 로고
    • Population biology of infectious diseases: Part I
    • Anderson R, May RM (1979) Population biology of infectious diseases: Part I. Nature 280:361-367
    • (1979) Nature , vol.280 , pp. 361-367
    • Anderson, R.1    May, R.M.2
  • 2
    • 1542319131 scopus 로고    scopus 로고
    • Disease control: Virtual plagues get real
    • Gewin V (2004) Disease control: virtual plagues get real. Nature 427:774-775
    • (2004) Nature , vol.427 , pp. 774-775
    • Gewin, V.1
  • 3
    • 0030952289 scopus 로고    scopus 로고
    • Mechanisms of angiogenesis
    • Risau W (1997) Mechanisms of angiogenesis. Nature 386:671-674
    • (1997) Nature , vol.386 , pp. 671-674
    • Risau, W.1
  • 4
    • 2342430184 scopus 로고    scopus 로고
    • Vasculogenesis and angiogenesis
    • Patan S (2004) Vasculogenesis and angiogenesis. Cancer Treat Res 117:3-32
    • (2004) Cancer Treat Res , vol.117 , pp. 3-32
    • Patan, S.1
  • 6
    • 0025882274 scopus 로고
    • Migration of individual microvessel endothelial cells: Stochastic model and parameter measurement
    • Stokes CL, Lauffenburger DA, Williams SK (1991) Migration of individual microvessel endothelial cells: stochastic model and parameter measurement. J Cell Sci 99:419-430
    • (1991) J Cell Sci , vol.99 , pp. 419-430
    • Stokes, C.L.1    Lauffenburger, D.A.2    Williams, S.K.3
  • 7
    • 0025991093 scopus 로고
    • Analysis of the roles of microvessel endothelial cell random motility and chemotaxis in angiogenesis
    • Stokes CL, Lauffenburger DA (1991) Analysis of the roles of microvessel endothelial cell random motility and chemotaxis in angiogenesis. J Theor Biol 152:377-403
    • (1991) J Theor Biol , vol.152 , pp. 377-403
    • Stokes, C.L.1    Lauffenburger, D.A.2
  • 8
    • 0000622777 scopus 로고    scopus 로고
    • Modelling the growth and form of capillary networks
    • Chaplain MAJ, Singh GD McLachlan JC eds, Wiley, pp
    • Chaplain MAJ, Anderson ARA (1999) Modelling the growth and form of capillary networks. In: Chaplain MAJ, Singh GD McLachlan JC (eds) On growth and form. Wiley, pp 225-249
    • (1999) On growth and form , pp. 225-249
    • Chaplain, M.A.J.1    Anderson, A.R.A.2
  • 9
    • 0036664608 scopus 로고    scopus 로고
    • Mathematical modelling of flow through vascular networks: Implication for tumour induced angiogenesis and chemotherapy strategies
    • McDougall SR, Anderson ARA, Chaplain MAJ, Sherratt JA (2002) Mathematical modelling of flow through vascular networks: implication for tumour induced angiogenesis and chemotherapy strategies. Bull Math Biol 24:673-702
    • (2002) Bull Math Biol , vol.24 , pp. 673-702
    • McDougall, S.R.1    Anderson, A.R.A.2    Chaplain, M.A.J.3    Sherratt, J.A.4
  • 10
    • 26844479092 scopus 로고    scopus 로고
    • Mathematical modelling of flow in 2D and 3D vascular networks: Applications to anti-angiogenic and chemotherapeutic drug strategies
    • Stéphanou A, McDougall SR, Anderson ARA, Chaplain MAJ (2005) Mathematical modelling of flow in 2D and 3D vascular networks: applications to anti-angiogenic and chemotherapeutic drug strategies. Math Comput Model 41:1137-1156
    • (2005) Math Comput Model , vol.41 , pp. 1137-1156
    • Stéphanou, A.1    McDougall, S.R.2    Anderson, A.R.A.3    Chaplain, M.A.J.4
  • 11
    • 0031852651 scopus 로고    scopus 로고
    • Structural adaptation and stability of microvascular networks: Theory and simulations
    • Pries AR, Secomb TW, Gaehtgens P (1998) Structural adaptation and stability of microvascular networks: theory and simulations. Am J Physiol 275:H349-360
    • (1998) Am J Physiol , vol.275
    • Pries, A.R.1    Secomb, T.W.2    Gaehtgens, P.3
  • 13
    • 0034845581 scopus 로고    scopus 로고
    • Mathematical modeling of capillary formation and development in tumor angiogenesis: Penetration into the stroma
    • Levine HA, Pamuk S, Sleeman BD, Nilsen-Hamilton M (2001) Mathematical modeling of capillary formation and development in tumor angiogenesis: penetration into the stroma. Bull Math Biol 63:801-863
    • (2001) Bull Math Biol , vol.63 , pp. 801-863
    • Levine, H.A.1    Pamuk, S.2    Sleeman, B.D.3    Nilsen-Hamilton, M.4
  • 14
    • 0142248828 scopus 로고    scopus 로고
    • A cellular automaton model for tumour growth in inhomogeneous environment
    • Alarcon T, Byrne HM, Maini PK (2003) A cellular automaton model for tumour growth in inhomogeneous environment. J Theor Biol 225:257-274
    • (2003) J Theor Biol , vol.225 , pp. 257-274
    • Alarcon, T.1    Byrne, H.M.2    Maini, P.K.3
  • 15
    • 0037699954 scopus 로고    scopus 로고
    • The biology of VEGF and its receptors
    • Ferrara N, Gerber HP, LeCouter J (2003) The biology of VEGF and its receptors. Nat Med 9:669-676
    • (2003) Nat Med , vol.9 , pp. 669-676
    • Ferrara, N.1    Gerber, H.P.2    LeCouter, J.3
  • 16
    • 0032907687 scopus 로고    scopus 로고
    • Vascular endothelial growth factor (VEGF) and its receptors
    • Neufeld G, Cohen T, Gengrinovitch S, Poltorak Z (1999) Vascular endothelial growth factor (VEGF) and its receptors. FASEB J 13:9-22
    • (1999) FASEB J , vol.13 , pp. 9-22
    • Neufeld, G.1    Cohen, T.2    Gengrinovitch, S.3    Poltorak, Z.4
  • 17
    • 10444255566 scopus 로고    scopus 로고
    • Angiogenesis: Now and then
    • Costa C, Soares R, Schmitt F (2004) Angiogenesis: now and then. APMIS 112:402-412
    • (2004) APMIS , vol.112 , pp. 402-412
    • Costa, C.1    Soares, R.2    Schmitt, F.3
  • 18
    • 19944402914 scopus 로고    scopus 로고
    • Endothelial cell regulation of matrix metalloproteinases
    • Haas TL (2005) Endothelial cell regulation of matrix metalloproteinases. Can J Physiol Pharmacol 83:1-7
    • (2005) Can J Physiol Pharmacol , vol.83 , pp. 1-7
    • Haas, T.L.1
  • 20
    • 24044459285 scopus 로고    scopus 로고
    • Matrix metalloproteinases and angiogenesis
    • Rundhaug JE (2005) Matrix metalloproteinases and angiogenesis. J Cell Mol Med 9:267-285
    • (2005) J Cell Mol Med , vol.9 , pp. 267-285
    • Rundhaug, J.E.1
  • 21
    • 0037112468 scopus 로고    scopus 로고
    • Mechanical signaling and the cellular response to extracellular matrix in angiogenesis and cardiovascular physiology
    • Ingber DE (2002) Mechanical signaling and the cellular response to extracellular matrix in angiogenesis and cardiovascular physiology. Circ Res 91:877-887
    • (2002) Circ Res , vol.91 , pp. 877-887
    • Ingber, D.E.1
  • 22
    • 0032538279 scopus 로고    scopus 로고
    • Cells' perception of position in a concentration gradient
    • Gurdon JB, Dyson S, St Johnston D (1998) Cells' perception of position in a concentration gradient. Cell 95:159-162
    • (1998) Cell , vol.95 , pp. 159-162
    • Gurdon, J.B.1    Dyson, S.2    St Johnston, D.3
  • 23
    • 0042863949 scopus 로고    scopus 로고
    • A reinforced random walk model of tumour angiogenesis and anti-angiogenic strategies
    • Plank MJ, Sleeman BD (2003) A reinforced random walk model of tumour angiogenesis and anti-angiogenic strategies. Math Med Biol 20:135-181
    • (2003) Math Med Biol , vol.20 , pp. 135-181
    • Plank, M.J.1    Sleeman, B.D.2
  • 24
    • 0033525530 scopus 로고    scopus 로고
    • Vascular endothelial growth factor receptor KDR tyrosine kinase activity is increased by autophosphorylation of two activation loop tyrosine residues
    • Kendall RL, Rutledge RZ, Mao X, Tebben AJ, Hungate RW, Thomas KA (1999) Vascular endothelial growth factor receptor KDR tyrosine kinase activity is increased by autophosphorylation of two activation loop tyrosine residues. J Biol Chem 274:6453-6460
    • (1999) J Biol Chem , vol.274 , pp. 6453-6460
    • Kendall, R.L.1    Rutledge, R.Z.2    Mao, X.3    Tebben, A.J.4    Hungate, R.W.5    Thomas, K.A.6
  • 25
    • 0033176048 scopus 로고    scopus 로고
    • Angiogenesis: State of the art
    • Han ZC, Liu Y (1999) Angiogenesis: state of the art. Int J Haematol 70:68-82
    • (1999) Int J Haematol , vol.70 , pp. 68-82
    • Han, Z.C.1    Liu, Y.2
  • 26
    • 0017370183 scopus 로고
    • Migration and proliferation of endothelial cells in preformed and newly formed blood vessels during tumor angiogenesis
    • Ausprunk DH, Folkman J (1977) Migration and proliferation of endothelial cells in preformed and newly formed blood vessels during tumor angiogenesis. Microvasc Res 14:53-65
    • (1977) Microvasc Res , vol.14 , pp. 53-65
    • Ausprunk, D.H.1    Folkman, J.2
  • 27
    • 0034076189 scopus 로고    scopus 로고
    • Mechanisms of angiogenesis and arteriogenesis
    • Carmeliet P (2000) Mechanisms of angiogenesis and arteriogenesis. Nat Med 6:389-395
    • (2000) Nat Med , vol.6 , pp. 389-395
    • Carmeliet, P.1
  • 28
    • 0031207030 scopus 로고    scopus 로고
    • Aggregation, blowup and collapse: The ABCs of taxis and reinforced random walks
    • Othmer HG, Stevens A (1997) Aggregation, blowup and collapse: the ABCs of taxis and reinforced random walks. SIAM J Appl Math 57:1044-1081
    • (1997) SIAM J Appl Math , vol.57 , pp. 1044-1081
    • Othmer, H.G.1    Stevens, A.2
  • 29
    • 7444258529 scopus 로고    scopus 로고
    • Lattice and non-lattice models of tumour angiogenesis
    • Plank MJ, Sleeman BD (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
  • 30
    • 0036984640 scopus 로고    scopus 로고
    • Role of angiogenesis in tumor growth and metastasis
    • Folkman J (2002) Role of angiogenesis in tumor growth and metastasis. Semin Oncol 29(Suppl 16):15-18
    • (2002) Semin Oncol , vol.29 , Issue.SUPPL. 16 , pp. 15-18
    • Folkman, J.1
  • 31
    • 1342312142 scopus 로고    scopus 로고
    • Not just angiogenesis-wider roles for the angiopoietins
    • Jones PF (2003) Not just angiogenesis-wider roles for the angiopoietins. J Pathol 201:515-527
    • (2003) J Pathol , vol.201 , pp. 515-527
    • Jones, P.F.1
  • 35
    • 0033588842 scopus 로고    scopus 로고
    • New model of tumor angiogenesis: Dynamic balance between vessel regression and growth mediated by angiopoietins and VEGF
    • Holash J, Wiegand SJ, Yancopoulos GD (1999) New model of tumor angiogenesis: dynamic balance between vessel regression and growth mediated by angiopoietins and VEGF. Oncogene 18:5356-5362
    • (1999) Oncogene , vol.18 , pp. 5356-5362
    • Holash, J.1    Wiegand, S.J.2    Yancopoulos, G.D.3
  • 36
    • 2442692715 scopus 로고    scopus 로고
    • The role of the angiopoietins in tumour angiogenesis
    • Plank MJ, Sleeman BD, Jones PF (2004) The role of the angiopoietins in tumour angiogenesis. Growth Factors 22:1-11
    • (2004) Growth Factors , vol.22 , pp. 1-11
    • Plank, M.J.1    Sleeman, B.D.2    Jones, P.F.3
  • 38
    • 0036780251 scopus 로고    scopus 로고
    • Clinical translation of angiogenesis inhibitors
    • Kerbel R, Folkman J (2002) Clinical translation of angiogenesis inhibitors. Nat Rev Cancer 2:727-739
    • (2002) Nat Rev Cancer , vol.2 , pp. 727-739
    • Kerbel, R.1    Folkman, J.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.