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Volumn 10, Issue 3, 2000, Pages 379-407

Advection-diffusion models for solid tumour evolution in vivo and related free boundary problem

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EID: 0034422868     PISSN: 02182025     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0218202500000239     Document Type: Article
Times cited : (89)

References (34)
  • 2
    • 0033422262 scopus 로고    scopus 로고
    • Post-surgical passive response of local environment to primary tumor removal II: Heterogeneous model
    • J. A. Adam and N. Bellomo, Post-surgical passive response of local environment to primary tumor removal II: Heterogeneous model, Math. Models Methods Appl. Sci. 9 (1999) 617-626.
    • (1999) Math. Models Methods Appl. Sci. , vol.9 , pp. 617-626
    • Adam, J.A.1    Bellomo, N.2
  • 3
    • 0008313578 scopus 로고    scopus 로고
    • General aspects of modelling tumor growth and immune response
    • eds. J. A. Adam and N. Bellomo Birkhäuser
    • J. A. Adam, General aspects of modelling tumor growth and immune response, in A Survey of Models on Tumour Immune Systems Dynamics, eds. J. A. Adam and N. Bellomo (Birkhäuser, 1996), pp. 15-87.
    • (1996) A Survey of Models on Tumour Immune Systems Dynamics , pp. 15-87
    • Adam, J.A.1
  • 4
    • 0029294735 scopus 로고
    • Mathematical models for tumour angiogenesis: Numerical simulations and nonlinear wave solutions
    • H. M. Byrne and M. A. Chaplain, Mathematical models for tumour angiogenesis: Numerical simulations and nonlinear wave solutions, Bull. Math. Biol. 57 (1995) 461-486.
    • (1995) Bull. Math. Biol. , vol.57 , pp. 461-486
    • Byrne, H.M.1    Chaplain, M.A.2
  • 5
    • 0030431867 scopus 로고    scopus 로고
    • Modelling the role of cell-cell growth and development of carcinomas
    • H. M. Byrne and M. A. Chaplain, Modelling the role of cell-cell growth and development of carcinomas, Math. Comput. Modelling 24 (1996) 1-17.
    • (1996) Math. Comput. Modelling , vol.24 , pp. 1-17
    • Byrne, H.M.1    Chaplain, M.A.2
  • 6
    • 0003169993 scopus 로고    scopus 로고
    • Necrosis and apoptosis: Distinct cell loss mechanism in a mathematical model of avascular tumour growth
    • H. M. Byrne and M. A. Chaplain, Necrosis and apoptosis: Distinct cell loss mechanism in a mathematical model of avascular tumour growth, J. Theor. Medicine 1 (1997) 223-235.
    • (1997) J. Theor. Medicine , vol.1 , pp. 223-235
    • Byrne, H.M.1    Chaplain, M.A.2
  • 7
    • 0031320752 scopus 로고    scopus 로고
    • Free boundary value problem associated with the growth and development of multicellular spheroids
    • H. M. Byrne and M. A. Chaplain, Free boundary value problem associated with the growth and development of multicellular spheroids, Euro. J. of Appl. Math. 8 (1997) 639-658.
    • (1997) Euro. J. of Appl. Math. , vol.8 , pp. 639-658
    • Byrne, H.M.1    Chaplain, M.A.2
  • 8
    • 0032285146 scopus 로고    scopus 로고
    • Strategies of applied mathematics towards an immunomathematical theory of tumors and immune system interactions
    • N. Bellomo and E. De Angelis, Strategies of applied mathematics towards an immunomathematical theory of tumors and immune system interactions, Math. Models Methods. Appl. Sci. 8 (1998) 1403-1429.
    • (1998) Math. Models Methods. Appl. Sci. , vol.8 , pp. 1403-1429
    • Bellomo, N.1    De Angelis, E.2
  • 9
    • 0031211273 scopus 로고    scopus 로고
    • The role of growth in avascular tumor growth
    • H. M. Byrne and S. A. Gourley, The role of growth in avascular tumor growth, Math. Comp. Modelling 26 (1997) 35-55.
    • (1997) Math. Comp. Modelling , vol.26 , pp. 35-55
    • Byrne, H.M.1    Gourley, S.A.2
  • 10
    • 0030822132 scopus 로고    scopus 로고
    • The effect of time delays on the dynamics of avascular tumour growth
    • H. M. Byrne, The effect of time delays on the dynamics of avascular tumour growth, Math. Biosci. 147 (1997) 83-117.
    • (1997) Math. Biosci. , vol.147 , pp. 83-117
    • Byrne, H.M.1
  • 11
    • 0033417036 scopus 로고    scopus 로고
    • A comparison of the roles of localised and nonlocalised growth factors in solid tumour growth
    • H. M. Byrne, A comparison of the roles of localised and nonlocalised growth factors in solid tumour growth, Math. Models Methods Appl. Sci. 9 (1999) 541-568.
    • (1999) Math. Models Methods Appl. Sci. , vol.9 , pp. 541-568
    • Byrne, H.M.1
  • 12
    • 0030404170 scopus 로고    scopus 로고
    • Mathematical modelling, simulation and prediction of tumour-induced angiogenesis
    • M. A. Chaplain and A. R. A. Anderson, Mathematical modelling, simulation and prediction of tumour-induced angiogenesis, Invasion Metastasis 16 (1996) 222-234.
    • (1996) Invasion Metastasis , vol.16 , pp. 222-234
    • Chaplain, M.A.1    Anderson, A.R.A.2
  • 13
  • 14
    • 0002335219 scopus 로고    scopus 로고
    • From mutation to metastasis: The mathematical modelling of the stages of tumour development
    • eds. J. A. Adam and N. Bellomo Birkhäuser
    • M. A. Chaplain, From mutation to metastasis: The mathematical modelling of the stages of tumour development, in A Survey of Models on Tumour Immune Systems Dynamics, eds. J. A. Adam and N. Bellomo (Birkhäuser, 1996), pp. 187-236.
    • (1996) A Survey of Models on Tumour Immune Systems Dynamics , pp. 187-236
    • Chaplain, M.A.1
  • 15
    • 0008314607 scopus 로고    scopus 로고
    • Mathematical Models for the growth, development and treatment of tumours
    • Ed. M. A. Chaplain, Special Issue on "Mathematical Models for the growth, development and treatment of tumours", Math. Models Methods Appl. Sci. 9 (1999).
    • (1999) Math. Models Methods Appl. Sci. , vol.9 , Issue.SPEC. ISSUE
    • Chaplain, M.A.1
  • 16
    • 0020676758 scopus 로고
    • Growth of mammalian multicellular tumour spheroids
    • A. D. Conger and M. C. Ziskin, Growth of mammalian multicellular tumour spheroids, Cancer Res. 43 (1983) 558-560.
    • (1983) Cancer Res. , vol.43 , pp. 558-560
    • Conger, A.D.1    Ziskin, M.C.2
  • 18
    • 0033467177 scopus 로고    scopus 로고
    • Tumour/immune system competition with medically induced activation/deactivation
    • B. Firmani, L. Guerri and L. Preziosi, Tumour/immune system competition with medically induced activation/deactivation, Math. Models Methods Appl. Sci. 9 (1999) 491-512.
    • (1999) Math. Models Methods Appl. Sci. , vol.9 , pp. 491-512
    • Firmani, B.1    Guerri, L.2    Preziosi, L.3
  • 19
    • 0015804548 scopus 로고
    • Self-regulation of growth in three dimensions
    • J. Folkman and M. Hochberg, Self-regulation of growth in three dimensions, J. Exp. Med. 138 (1973) 745-753.
    • (1973) J. Exp. Med. , vol.138 , pp. 745-753
    • Folkman, J.1    Hochberg, M.2
  • 20
    • 0024543786 scopus 로고
    • Regrowth kinetics of cells from different regions of multicell spheroids of 4-cell-lines
    • J. P. Freyer and P. L. Schor, Regrowth kinetics of cells from different regions of multicell spheroids of 4-cell-lines, J. Cell. Physio. 138 (1989) 384-392.
    • (1989) J. Cell. Physio. , vol.138 , pp. 384-392
    • Freyer, J.P.1    Schor, P.L.2
  • 21
    • 0022642722 scopus 로고
    • Regulation of growth saturation and development of necrosis in EMT6/RO multicellular spheroids glucose and oxygen supply
    • J. P. Freyer and R. M. Sutherland, Regulation of growth saturation and development of necrosis in EMT6/RO multicellular spheroids glucose and oxygen supply, Cancer Res. 46 (1986) 3504-3512.
    • (1986) Cancer Res. , vol.46 , pp. 3504-3512
    • Freyer, J.P.1    Sutherland, R.M.2
  • 22
    • 0030042605 scopus 로고    scopus 로고
    • On the relation between size of necrosis and diameter of tumor spheroids
    • K. Groebe and W. Mueller-Klieser, On the relation between size of necrosis and diameter of tumor spheroids, Internet J. Radiat. Onc. Biol. Phys. 34 (1996) 395-401.
    • (1996) Internet J. Radiat. Onc. Biol. Phys. , vol.34 , pp. 395-401
    • Groebe, K.1    Mueller-Klieser, W.2
  • 23
    • 0017851090 scopus 로고
    • Proliferation and viability in cellular spheroids of human origin
    • M. Haji-Karim and J. Carlsson, Proliferation and viability in cellular spheroids of human origin, Cancer Res. 38 (1978) 1457-1464.
    • (1978) Cancer Res. , vol.38 , pp. 1457-1464
    • Haji-Karim, M.1    Carlsson, J.2
  • 24
    • 0014848047 scopus 로고
    • Growth of modular carcinomas in rodents compared with multicell spheroids in tissue culture
    • W. R. Inch, J. A. McCredie and R. M. Sutherland, Growth of modular carcinomas in rodents compared with multicell spheroids in tissue culture, Growth 34 (1970) 271-282.
    • (1970) Growth , vol.34 , pp. 271-282
    • Inch, W.R.1    McCredie, J.A.2    Sutherland, R.M.3
  • 25
    • 0008408823 scopus 로고    scopus 로고
    • Mathematical modeling in tumor growth and progression
    • Ed. S. Michelson, Mathematical modeling in tumor growth and progression, Invasion Metastasis 16 (1996) 169-268.
    • (1996) Invasion Metastasis , vol.16 , pp. 169-268
    • Michelson, S.1
  • 26
    • 0002670122 scopus 로고    scopus 로고
    • A mathematical model of vascular tumor growth and invasion
    • M. E. Orme and M. A. Chaplain, A mathematical model of vascular tumor growth and invasion, Math. Comp. Model. 23 (1996) 43-60.
    • (1996) Math. Comp. Model. , vol.23 , pp. 43-60
    • Orme, M.E.1    Chaplain, M.A.2
  • 27
    • 0031230846 scopus 로고    scopus 로고
    • Two-dimensional models of tumour angiogenesis and anti-angiogenesis strategies
    • M. E. Orme and M. A. Chaplain, Two-dimensional models of tumour angiogenesis and anti-angiogenesis strategies, IMA J. Math. Appl. Medic. Biol. 14 (1997) 189-205.
    • (1997) IMA J. Math. Appl. Medic. Biol. , vol.14 , pp. 189-205
    • Orme, M.E.1    Chaplain, M.A.2
  • 28
    • 0345881792 scopus 로고    scopus 로고
    • Mathematical modelling of macrophage dynamics in tumours
    • M. R. Owen and J. A. Sherrat, Mathematical modelling of macrophage dynamics in tumours, Math. Model. Methods Appl. Sci. 9 (1999) 513-539.
    • (1999) Math. Model. Methods Appl. Sci. , vol.9 , pp. 513-539
    • Owen, M.R.1    Sherrat, J.A.2
  • 29
    • 0031802840 scopus 로고    scopus 로고
    • Modelling the macrophage invasion of tumours: Effects on growth and composition
    • M. R. Owen and J. A. Sherrat, Modelling the macrophage invasion of tumours: Effects on growth and composition, IMA J. Math. Appl. Med. Biol. 15 (1998) 165-185.
    • (1998) IMA J. Math. Appl. Med. Biol. , vol.15 , pp. 165-185
    • Owen, M.R.1    Sherrat, J.A.2
  • 30
    • 0002498348 scopus 로고    scopus 로고
    • A new approach to modelling the formation of necrotic regions in tumours
    • C. P. Please, G. Pettet and D. L. S. McElwain, A new approach to modelling the formation of necrotic regions in tumours, Appl. Math. Lett. 11 (1998) 89-94.
    • (1998) Appl. Math. Lett. , vol.11 , pp. 89-94
    • Please, C.P.1    Pettet, G.2    McElwain, D.L.S.3
  • 32
    • 0024281372 scopus 로고
    • Cell and environment interaction in tumor microregions: The multicell spheroid model
    • R. M. Sutherland, Cell and environment interaction in tumor microregions: The multicell spheroid model, Science 240 (1988) 177-184.
    • (1988) Science , vol.240 , pp. 177-184
    • Sutherland, R.M.1
  • 33
    • 0031087466 scopus 로고    scopus 로고
    • Mathematical modelling of avascular-tumour growth
    • J. P. Ward and J. R. King, Mathematical modelling of avascular-tumour growth, IMA J. Math. Appl. Med. Biol. 14 (1997) 39-69.
    • (1997) IMA J. Math. Appl. Med. Biol. , vol.14 , pp. 39-69
    • Ward, J.P.1    King, J.R.2
  • 34
    • 0002484583 scopus 로고    scopus 로고
    • Mathematical modelling of avascular-tumour growth II: Modeling growth saturation
    • J. P. Ward and J. R. King, Mathematical modelling of avascular-tumour growth II: Modeling growth saturation, IMA J. Math. Appl. Med. Biol. 15 (1998) 1-42.
    • (1998) IMA J. Math. Appl. Med. Biol. , vol.15 , pp. 1-42
    • Ward, J.P.1    King, J.R.2


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