메뉴 건너뛰기




Volumn 17, Issue 1, 2009, Pages 1-25

Angiogenesis model with carrying capacity depending on vessel density

Author keywords

Angiogenesis; Antiangiogenic therapy; Cusp catastrophe; Hysteresis effect; Local stability; Ordinary and delay differential equations; Steady states; Vascular and avascular tumor

Indexed keywords


EID: 65249153022     PISSN: 02183390     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0218339009002739     Document Type: Article
Times cited : (20)

References (37)
  • 1
    • 85013312416 scopus 로고
    • Tumor angiogenesis: Therapeutic implications
    • Folkman J, Tumor angiogenesis: Therapeutic implications, N Engl J Med 285:1182-1186, 1971.
    • (1971) N Engl J Med , vol.285 , pp. 1182-1186
    • Folkman, J.1
  • 2
    • 32944463899 scopus 로고    scopus 로고
    • Folkman J, Angiogenesis, Ann Rev Med 57:1-18, 2006.
    • Folkman J, Angiogenesis, Ann Rev Med 57:1-18, 2006.
  • 3
    • 0027970092 scopus 로고
    • Agiostatin: A novel angiogenesis inhibitor that mediates the suppression of metastases by a Lewis lung carcinoma
    • O'Reilly MS et al., Agiostatin: A novel angiogenesis inhibitor that mediates the suppression of metastases by a Lewis lung carcinoma, Cell 79:315-328, 1994.
    • (1994) Cell , vol.79 , pp. 315-328
    • O'Reilly, M.S.1
  • 4
    • 0031454617 scopus 로고    scopus 로고
    • Endostatin: An endogenous inhibitor of angiogenesis and tumor growth
    • O'Reilly MS et al., Endostatin: An endogenous inhibitor of angiogenesis and tumor growth, Cell 88:277-285, 1997.
    • (1997) Cell , vol.88 , pp. 277-285
    • O'Reilly, M.S.1
  • 5
    • 0028929803 scopus 로고
    • Agiogenesis in cancer, vascular, rheumatoid and other disease
    • Folkman J, Agiogenesis in cancer, vascular, rheumatoid and other disease, Nat Med 1(1):27-31, 1995.
    • (1995) Nat Med , vol.1 , Issue.1 , pp. 27-31
    • Folkman, J.1
  • 6
    • 0034648765 scopus 로고    scopus 로고
    • Angiogenesis in cancer and other diseases
    • Carmeliet P, Jain RK, Angiogenesis in cancer and other diseases, Nature 407:249-257, 2000.
    • (2000) Nature , vol.407 , pp. 249-257
    • Carmeliet, P.1    Jain, R.K.2
  • 7
    • 0034648793 scopus 로고    scopus 로고
    • Vascular-specific growth factors and blood vessel formation
    • Yangopoulos CD, Davis S, Gale NW et al., Vascular-specific growth factors and blood vessel formation, Nature 407:242-248, 2000.
    • (2000) Nature , vol.407 , pp. 242-248
    • Yangopoulos, C.D.1    Davis, S.2    Gale, N.W.3
  • 8
    • 0033588842 scopus 로고    scopus 로고
    • New model of tumor angiogenesis: Dynamic balance between vessel regression and growth mediated by angiopoietins and VEGF
    • Holash SJ, Wiegandand GD, Yancopoulos GD, New model of tumor angiogenesis: Dynamic balance between vessel regression and growth mediated by angiopoietins and VEGF, Oncogene 18:5356-5362, 1999.
    • (1999) Oncogene , vol.18 , pp. 5356-5362
    • Holash, S.J.1    Wiegandand, G.D.2    Yancopoulos, G.D.3
  • 10
    • 0037840352 scopus 로고    scopus 로고
    • A computer algorithm describing the process of vessel formation and maturation, and its use for predicting the effects of anti-angiogenic and anti-maturation therapy on vascular tumor growth
    • Arakelyan L, Vainstein V, Agur Z, A computer algorithm describing the process of vessel formation and maturation, and its use for predicting the effects of anti-angiogenic and anti-maturation therapy on vascular tumor growth, Angiogenesis 5:203-214, 2002.
    • (2002) Angiogenesis , vol.5 , pp. 203-214
    • Arakelyan, L.1    Vainstein, V.2    Agur, Z.3
  • 11
    • 16644400591 scopus 로고    scopus 로고
    • Mathematical modeling of tumor-induced angiogenesis
    • Mantzaris NV,Webb S, Othmer HG, Mathematical modeling of tumor-induced angiogenesis, J Math Biol 49(2):111-187, 2004.
    • (2004) J Math Biol , vol.49 , Issue.2 , pp. 111-187
    • Mantzaris, N.V.1    Webb, S.2    Othmer, H.G.3
  • 12
  • 13
    • 0033213978 scopus 로고    scopus 로고
    • A dynamical theory of tumor growth, treatment response and postvascular dormancy
    • Tumor development under angiogenic signaling
    • Hahnfeldt P, Panigrahy D, Folkman J, Hlatky L, Tumor development under angiogenic signaling: A dynamical theory of tumor growth, treatment response and postvascular dormancy, Cancer Res 59:4770-4775, 1999.
    • (1999) Cancer Res , vol.59 , pp. 4770-4775
    • Hahnfeldt, P.1    Panigrahy, D.2    Folkman, J.3    Hlatky, L.4
  • 14
    • 85120211136 scopus 로고    scopus 로고
    • d'Onofrio A, Gandolfi A, Tumor eradication by antiangiogenic therapy: Analysis and extensions of the model by Hahnfeldt et al. (1999), Math Biosci 191:159-184, 2004.
    • d'Onofrio A, Gandolfi A, Tumor eradication by antiangiogenic therapy: Analysis and extensions of the model by Hahnfeldt et al. (1999), Math Biosci 191:159-184, 2004.
  • 15
    • 85121095960 scopus 로고    scopus 로고
    • A family of models of angiogenesis and antiangiogensis anticancer therapy
    • accepted
    • d'Onofrio A, Gandolfi A, A family of models of angiogenesis and antiangiogensis anticancer therapy, Math Med Biol, accepted.
    • Math Med Biol
    • d'Onofrio, A.1    Gandolfi, A.2
  • 16
    • 33750446670 scopus 로고    scopus 로고
    • The response to antiangiogenic anticancer drugs that inhibit endothelial cell proliferation
    • d'Onofrio A, Gandolfi A, The response to antiangiogenic anticancer drugs that inhibit endothelial cell proliferation, Appl Math Comput 181(2):1155-1162, 2006.
    • (2006) Appl Math Comput , vol.181 , Issue.2 , pp. 1155-1162
    • d'Onofrio, A.1    Gandolfi, A.2
  • 17
    • 0037406640 scopus 로고    scopus 로고
    • Optimal scheduling of radiotherapy and angiogenic inhibitors
    • Ergun A, Camphausen K, Wein LM, Optimal scheduling of radiotherapy and angiogenic inhibitors, Bull Math Biol 65:407-424, 2003.
    • (2003) Bull Math Biol , vol.65 , pp. 407-424
    • Ergun, A.1    Camphausen, K.2    Wein, L.M.3
  • 18
    • 40449120191 scopus 로고    scopus 로고
    • Analysis of a mathematical model for tumor antiangiogenesis
    • Ledzewicz U, Scḧattler H, Analysis of a mathematical model for tumor antiangiogenesis, Opt Control Appl Meth 29:41-57, 2008.
    • (2008) Opt Control Appl Meth , vol.29 , pp. 41-57
    • Ledzewicz, U.1    Scḧattler, H.2
  • 19
    • 42749090784 scopus 로고    scopus 로고
    • Antiangiogenic therapy in cancer treatment as an optimal control problem
    • Ledzewicz U, Scḧattler H, Antiangiogenic therapy in cancer treatment as an optimal control problem, SIAM J Contr Optim 46(3):1052- 1079, 2007.
    • (2007) SIAM J Contr Optim , vol.46 , Issue.3 , pp. 1052-1079
    • Ledzewicz, U.1    Scḧattler, H.2
  • 20
    • 42749096482 scopus 로고    scopus 로고
    • Optimal and suboptimal protocols for a class of mathematical models for tumor anti-angiogenesis
    • Ledzewicz U, Scḧattler H, Optimal and suboptimal protocols for a class of mathematical models for tumor anti-angiogenesis, J Theor Biol 252(2):295-312, 2008.
    • (2008) J Theor Biol , vol.252 , Issue.2 , pp. 295-312
    • Ledzewicz, U.1    Scḧattler, H.2
  • 21
    • 65249089139 scopus 로고    scopus 로고
    • Comparison of six models of antiangiogenic therapy
    • accepted
    • Świerniak A, Comparison of six models of antiangiogenic therapy, Appl Math, accepted.
    • Appl Math
    • Świerniak, A.1
  • 22
  • 24
    • 0033170748 scopus 로고    scopus 로고
    • Dynamic remodeling of the vascular bed precedes tumor growth: MLS ovarian carcinoma spheroids implanted in nude mice
    • Gilead A, Neeman M, Dynamic remodeling of the vascular bed precedes tumor growth: MLS ovarian carcinoma spheroids implanted in nude mice, Neoplasia 1:226-230, 1999.
    • (1999) Neoplasia , vol.1 , pp. 226-230
    • Gilead, A.1    Neeman, M.2
  • 25
    • 34247401423 scopus 로고    scopus 로고
    • Critical point analysis for three-variable cancer angiogenesis models
    • Foryś U, Kheifetz Y, Kogan Y, Critical point analysis for three-variable cancer angiogenesis models, Math Biosci Eng 2(3):511-525, 2005.
    • (2005) Math Biosci Eng , vol.2 , Issue.3 , pp. 511-525
    • Foryś, U.1    Kheifetz, Y.2    Kogan, Y.3
  • 26
    • 11144315531 scopus 로고    scopus 로고
    • Vessel maturation effects on tumour growth: Validation of a computer model in implanted human ovarian carcinoma spheroids
    • Arakelyan L,Merbl Y, Agur Z, Vessel maturation effects on tumour growth: Validation of a computer model in implanted human ovarian carcinoma spheroids, Eur J Cancer 41:159-167, 2005.
    • (2005) Eur J Cancer , vol.41 , pp. 159-167
    • Arakelyan, L.1    Merbl, Y.2    Agur, Z.3
  • 27
    • 33746260079 scopus 로고    scopus 로고
    • Vascular network remodeling via vessel cooption, regression and growth in tumors
    • Bartha K, Rieger H, Vascular network remodeling via vessel cooption, regression and growth in tumors, J Theor Biol 241(4):903-918, 2006.
    • (2006) J Theor Biol , vol.241 , Issue.4 , pp. 903-918
    • Bartha, K.1    Rieger, H.2
  • 28
    • 37349011512 scopus 로고    scopus 로고
    • Emergent vascular network inhomogeneities and resulting blood flow patterns in a growing tumor
    • Welter M, Bartha K, Rieger H, Emergent vascular network inhomogeneities and resulting blood flow patterns in a growing tumor, J Theor Biol 250(2):257-280, 2008.
    • (2008) J Theor Biol , vol.250 , Issue.2 , pp. 257-280
    • Welter, M.1    Bartha, K.2    Rieger, H.3
  • 29
    • 0000128125 scopus 로고
    • Models for the growth of solid tumour by diffusion
    • Greenspan HP, Models for the growth of solid tumour by diffusion, Stud Appl Math 52:317-340, 1972.
    • (1972) Stud Appl Math , vol.52 , pp. 317-340
    • Greenspan, H.P.1
  • 32
    • 0028133084 scopus 로고
    • Comparative Gompertzian analysis of alterations of tumor growth patterns
    • Bassukas ID, Comparative Gompertzian analysis of alterations of tumor growth patterns, Cancer Res 54:4385-4392, 1994.
    • (1994) Cancer Res , vol.54 , pp. 4385-4392
    • Bassukas, I.D.1
  • 34
    • 0021858751 scopus 로고
    • Zur praxis der anpassung der logistichen function an das wachstum exprerimenteller tumoren
    • Krug H, Taubert G, Zur praxis der anpassung der logistichen function an das wachstum exprerimenteller tumoren, Arch Geschwulstforsch 55:235-244, 1985.
    • (1985) Arch Geschwulstforsch , vol.55 , pp. 235-244
    • Krug, H.1    Taubert, G.2
  • 35
    • 84966166281 scopus 로고
    • Dynamics of tumour growth
    • Laird AK, Dynamics of tumour growth, Br J Cancer 18:490-502, 1964.
    • (1964) Br J Cancer , vol.18 , pp. 490-502
    • Laird, A.K.1
  • 36
    • 0001315130 scopus 로고
    • Dynamics of tumour growth: Comparison of growth rates and extrapolation of growth curve to one cell
    • Laird AK, Dynamics of tumour growth: Comparison of growth rates and extrapolation of growth curve to one cell, Br J Cancer 19:278-291, 1965.
    • (1965) Br J Cancer , vol.19 , pp. 278-291
    • Laird, A.K.1
  • 37
    • 0039403613 scopus 로고
    • Reconstruction models for the Ehrlich Ascites Tumor for the mouse
    • eds, Wuertz, Winnipeg, Canada
    • Schuster R, Schuster H, Reconstruction models for the Ehrlich Ascites Tumor for the mouse, in Arino O, Axelrod D, Kimmel M (eds.) Mathematical Population Dynamics, Vol. 2, pp. 335-348, Wuertz, Winnipeg, Canada, 1995.
    • (1995) Mathematical Population Dynamics , vol.2 , pp. 335-348
    • Schuster, R.1    Schuster, H.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.