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Volumn 8, Issue 1, 2007, Pages 45-60

An age and spatially structured model of tumor invasion with haptotaxis

Author keywords

Diffusion; Haptotaxis; Semigroups of operators; Tumor model

Indexed keywords


EID: 34548670516     PISSN: 15313492     EISSN: None     Source Type: Journal    
DOI: 10.3934/dcdsb.2007.8.45     Document Type: Article
Times cited : (23)

References (45)
  • 1
    • 0023518620 scopus 로고
    • A mathematical model tumor growth. II: Effects of geometry and spatial non uniformity on stability
    • J. Adam, A mathematical model tumor growth. II: Effects of geometry and spatial non uniformity on stability, Math. Biosci, 86 (1987), 183-211.
    • (1987) Math. Biosci , vol.86 , pp. 183-211
    • Adam, J.1
  • 2
    • 0025068944 scopus 로고
    • Diffusion related growth characteristics of a spherical prevascular carcinoma
    • J. Adam and S. Maggelakis, Diffusion related growth characteristics of a spherical prevascular carcinoma, Bull. Math. Biol, 52 (1990), 549-582.
    • (1990) Bull. Math. Biol , vol.52 , pp. 549-582
    • Adam, J.1    Maggelakis, S.2
  • 3
    • 0035998604 scopus 로고    scopus 로고
    • On the closure of mass balance models for tumor growth
    • D. Ambrosi and L. Preziosi, On the closure of mass balance models for tumor growth, Math. Mod. Meth. Appl. Sci, 12 (2002), 737-754.
    • (2002) Math. Mod. Meth. Appl. Sci , vol.12 , pp. 737-754
    • Ambrosi, D.1    Preziosi, L.2
  • 4
    • 51249186677 scopus 로고
    • Dual semigroups and second order linear elliptic boundary value problems
    • Herbert Amann, Dual semigroups and second order linear elliptic boundary value problems Israel J. Math, 45 (1983), 225-254.
    • (1983) Israel J. Math , vol.45 , pp. 225-254
    • Amann, H.1
  • 5
    • 53349128723 scopus 로고    scopus 로고
    • Strongly continuous dual semigroups
    • Herbert Amann and Joachim Escher, Strongly continuous dual semigroups Ann. Mat. Pura Appl., 171 (1996), 41-62.
    • (1996) Ann. Mat. Pura Appl , vol.171 , pp. 41-62
    • Amann, H.1    Escher, J.2
  • 6
    • 25144494216 scopus 로고    scopus 로고
    • A hybrid mathematical model of solid tumour invasion: The importance of cell adhesion
    • A. Anderson, A hybrid mathematical model of solid tumour invasion: The importance of cell adhesion, Math. Med. Biol. IMA Journal, 22 (2005), 163-186.
    • (2005) Math. Med. Biol. IMA Journal , vol.22 , pp. 163-186
    • Anderson, A.1
  • 7
    • 0030404170 scopus 로고    scopus 로고
    • Mathematical modelling, simulation and prediction of tumour-induced angiogenesis
    • A.R.A. Anderson and M. Chaplain, Mathematical modelling, simulation and prediction of tumour-induced angiogenesis, Invasion and Metastasis 16 (1996), 222-234.
    • (1996) Invasion and Metastasis , vol.16 , pp. 222-234
    • Anderson, A.R.A.1    Chaplain, M.2
  • 8
    • 0032170064 scopus 로고    scopus 로고
    • Continuous and discrete mathematical models of tumorinduced angiogenesis
    • A.R.A. Anderson and M. Chaplain, Continuous and discrete mathematical models of tumorinduced angiogenesis, Bull. Math. Biol, 60 (1998), 857-899.
    • (1998) Bull. Math. Biol , vol.60 , pp. 857-899
    • Anderson, A.R.A.1    Chaplain, M.2
  • 9
    • 33847793521 scopus 로고    scopus 로고
    • Computational methods and results for structured multiscale models of tumor invasion
    • B. Ayati, A.R.A. Anderson and G.F. Webb, Computational methods and results for structured multiscale models of tumor invasion, SIAM Multiscale Mod. Simul., 5 (2006), 1-20.
    • (2006) SIAM Multiscale Mod. Simul , vol.5 , pp. 1-20
    • Ayati, B.1    Anderson, A.R.A.2    Webb, G.F.3
  • 11
    • 0036234535 scopus 로고    scopus 로고
    • Cell kinetics in tumour cords studied by a model with variable cell cycle length
    • A. Bertuzzi, A. Fasano, A. Gandolfi and D. Marangi, Cell kinetics in tumour cords studied by a model with variable cell cycle length, Math. Biosci, 177 (2002), 103-125.
    • (2002) Math. Biosci , vol.177 , pp. 103-125
    • Bertuzzi, A.1    Fasano, A.2    Gandolfi, A.3    Marangi, D.4
  • 12
    • 0034697619 scopus 로고    scopus 로고
    • Cell kinetics in a tumor cord
    • A. Bertuzzi and A. Gandolfi, Cell kinetics in a tumor cord, J. Theor. Biol, 204 (2000), 587-599.
    • (2000) J. Theor. Biol , vol.204 , pp. 587-599
    • Bertuzzi, A.1    Gandolfi, A.2
  • 14
    • 0842281982 scopus 로고    scopus 로고
    • Modelling solid tumour growth using the theory of mixtures
    • H. Byrne and L. Preziosi, Modelling solid tumour growth using the theory of mixtures, Math. Med. Biol, 20 (2003), 341-366.
    • (2003) Math. Med. Biol , vol.20 , pp. 341-366
    • Byrne, H.1    Preziosi, L.2
  • 15
    • 0031320752 scopus 로고    scopus 로고
    • Free boundary value problems associated with the growth and development of multicellular spheroids
    • H. Byrne and M. Chaplain, Free boundary value problems associated with the growth and development of multicellular spheroids, Eur. J. Appl. Math, 8 (1997), 639-658.
    • (1997) Eur. J. Appl. Math , vol.8 , pp. 639-658
    • Byrne, H.1    Chaplain, M.2
  • 16
    • 26844499863 scopus 로고    scopus 로고
    • Global solutions of some Chemotaxis and angiogenesis systems in high space dimensions
    • L. Corrias, B. Perthame and H. Zaag, Global solutions of some Chemotaxis and angiogenesis systems in high space dimensions, Milan J. Math, 72 (2004), 159-186.
    • (2004) Milan J. Math , vol.72 , pp. 159-186
    • Corrias, L.1    Perthame, B.2    Zaag, H.3
  • 17
    • 0035869870 scopus 로고    scopus 로고
    • Analysis of a mathematical model of the growth of necrotic tumors
    • S. Cui and A. Friedman, Analysis of a mathematical model of the growth of necrotic tumors, J. Math. Anal. Appl, 255 (2001), 636-677.
    • (2001) J. Math. Anal. Appl , vol.255 , pp. 636-677
    • Cui, S.1    Friedman, A.2
  • 19
    • 4944259840 scopus 로고
    • Diffusive epidemic models with spatial and age dependent heterogeneity
    • W.E. Fitzgibbon, M.E. Parrot and G.F. Webb, Diffusive epidemic models with spatial and age dependent heterogeneity, Discr. Cont. Dyn. Sys 1 (1995), 35-57.
    • (1995) Discr. Cont. Dyn. Sys , vol.1 , pp. 35-57
    • Fitzgibbon, W.E.1    Parrot, M.E.2    Webb, G.F.3
  • 20
    • 0036433997 scopus 로고    scopus 로고
    • Mathematical analysis of a model for the initiation of angiogenesis
    • M. Fontelos, A. Friedman and B. Hu., Mathematical analysis of a model for the initiation of angiogenesis, SIAM J. Math. Anal, 33 (2002), 1330-1355.
    • (2002) SIAM J. Math. Anal , vol.33 , pp. 1330-1355
    • Fontelos, M.1    Friedman, A.2    Hu, B.3
  • 23
    • 1042298945 scopus 로고    scopus 로고
    • On the existence of spatially patterned dormant malignancies in a model for the growth of non-necrotic vascular tumors
    • A. Friedman and R. Reitich, On the existence of spatially patterned dormant malignancies in a model for the growth of non-necrotic vascular tumors, Math. Mod. Meth. Appl. Sci., 77 (2001), 1-25.
    • (2001) Math. Mod. Meth. Appl. Sci , vol.77 , pp. 1-25
    • Friedman, A.1    Reitich, R.2
  • 24
    • 0029751950 scopus 로고    scopus 로고
    • A reaction-diffusion model of cancer invasion
    • R. Gatenby and E. Gawlinski, A reaction-diffusion model of cancer invasion, Can. Res, 56 (2006), 5745-5753.
    • (2006) Can. Res , vol.56 , pp. 5745-5753
    • Gatenby, R.1    Gawlinski, E.2
  • 25
    • 0000128125 scopus 로고
    • Models for the growth of solid tumor by diffusion
    • H. Greenspan, Models for the growth of solid tumor by diffusion, Stud. Appl. Math, 51 (1972), 317-340.
    • (1972) Stud. Appl. Math , vol.51 , pp. 317-340
    • Greenspan, H.1
  • 26
    • 84972570248 scopus 로고    scopus 로고
    • 1, Osaka J. Math, 30 (1993), 397-429.
    • 1, Osaka J. Math, 30 (1993), 397-429.
  • 27
    • 84935021209 scopus 로고
    • American Mathematical Society Colloquium Publications, Providence
    • E. Hille and R. S. Phillips, "Functional Analysis and Semigroups," American Mathematical Society Colloquium Publications, Vol. 31, Providence, 1957.
    • (1957) Functional Analysis and Semigroups , vol.31
    • Hille, E.1    Phillips, R.S.2
  • 28
    • 4744373150 scopus 로고    scopus 로고
    • From 1970 until present: The Keller-Segal model in Chemotaxis and its consequences I
    • D. Horstmann, From 1970 until present: The Keller-Segal model in Chemotaxis and its consequences I., Jahresberict Deutscher Math. Verein, 105 (2004), 103-165.
    • (2004) Jahresberict Deutscher Math. Verein , vol.105 , pp. 103-165
    • Horstmann, D.1
  • 29
    • 0034845581 scopus 로고    scopus 로고
    • H. Levine and S. Pamuk, Sleeman, B., Nilsen-Hamilton, M., Mathematical modeling of capillary formation and development in tumor angiogenesis: Penetration into the stroma, Bull. Math. Biol, 63 (2001), 801-863.
    • H. Levine and S. Pamuk, Sleeman, B., Nilsen-Hamilton, M., Mathematical modeling of capillary formation and development in tumor angiogenesis: Penetration into the stroma, Bull. Math. Biol, 63 (2001), 801-863.
  • 30
    • 14044275152 scopus 로고    scopus 로고
    • Modelling tumor-induced angiogenesis
    • ed. L. Preziosi, Chapman and Hall/CRC, Boca Raton
    • H. Levine and B.Sleeman, Modelling tumor-induced angiogenesis, in "Cancer Modelling and Simulation" (ed. L. Preziosi), Chapman and Hall/CRC, Boca Raton, 2003.
    • (2003) Cancer Modelling and Simulation
    • Levine, H.1    Sleeman, B.2
  • 32
    • 0003207468 scopus 로고
    • One-parameter Semigroups of Positive Operators
    • Springer-Verlag, Berlin
    • R. Nagel, "One-parameter Semigroups of Positive Operators," Lecture Notes in Mathematics, 1184. Springer-Verlag, Berlin, 1986.
    • (1986) Lecture Notes in Mathematics , vol.1184
    • Nagel, R.1
  • 34
    • 0035480791 scopus 로고    scopus 로고
    • A new mathematical model for avascular tumour growth
    • J. Sherratt and M. Chaplain, A new mathematical model for avascular tumour growth, J. Math. Biol, 43 (2001), 291-312.
    • (2001) J. Math. Biol , vol.43 , pp. 291-312
    • Sherratt, J.1    Chaplain, M.2
  • 35
    • 0000189791 scopus 로고    scopus 로고
    • A mathematical analysis of a model for capillary network formation in the absence of endothelial cell proliferation
    • B. Sleeman, A. Anderson and M. Chaplain, A mathematical analysis of a model for capillary network formation in the absence of endothelial cell proliferation, Appl. Math. Let, 12 (1999), 121-127.
    • (1999) Appl. Math. Let , vol.12 , pp. 121-127
    • Sleeman, B.1    Anderson, A.2    Chaplain, M.3
  • 36
    • 84967800047 scopus 로고
    • Generation of analytic semigroups by strongly elliptic operators
    • H. B. Stewart, Generation of analytic semigroups by strongly elliptic operators, Trans. Amer. Math. Soc, 199 (1974), 141-162.
    • (1974) Trans. Amer. Math. Soc , vol.199 , pp. 141-162
    • Stewart, H.B.1
  • 37
    • 84967728255 scopus 로고
    • Generation of analytic semigroups by strongly elliptic operators under general boundary conditions
    • H. B. Stewart, Generation of analytic semigroups by strongly elliptic operators under general boundary conditions, Trans. Amer. Math. Soc, 259 (1980), 299-310.
    • (1980) Trans. Amer. Math. Soc , vol.259 , pp. 299-310
    • Stewart, H.B.1
  • 39
    • 34548690412 scopus 로고    scopus 로고
    • H. Triebel, Theory of function spaces, Mathematik und ihre Anwendungen in Physik und Technik, [Mathematics and its Applications in Physics and Technology], 38. Akademische Verlagsgesellschaft Geest & Portig K.-G., Leipzig, 1983.
    • H. Triebel, "Theory of function spaces, Mathematik und ihre Anwendungen in Physik und Technik," [Mathematics and its Applications in Physics and Technology], 38. Akademische Verlagsgesellschaft Geest & Portig K.-G., Leipzig, 1983.
  • 41
    • 34548693955 scopus 로고    scopus 로고
    • Global existence of classical solutions for a haptotaxis model
    • Ch. Walker and G. F. Webb, Global existence of classical solutions for a haptotaxis model, SIAM J. Math. Anal. 38 (2007), 1694-1712.
    • (2007) SIAM J. Math. Anal , vol.38 , pp. 1694-1712
    • Walker, C.1    Webb, G.F.2
  • 42
    • 84972506905 scopus 로고
    • Exponential representation of solutions to an abstract semi-linear differential equation
    • G. F. Webb, Exponential representation of solutions to an abstract semi-linear differential equation, Pacific J. Math, 70 (1977), 269-279.
    • (1977) Pacific J. Math , vol.70 , pp. 269-279
    • Webb, G.F.1
  • 43
    • 23644457494 scopus 로고
    • An age-dependent epidemic model with spatial diffusion
    • G. F. Webb, An age-dependent epidemic model with spatial diffusion, Arch. Rat. Mech. Anal, 75 (1980), 91-102
    • (1980) Arch. Rat. Mech. Anal , vol.75 , pp. 91-102
    • Webb, G.F.1


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