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Volumn 37, Issue 11, 2003, Pages 1163-1175

Individual-based approaches to birth and death in avascular tumors

Author keywords

Avascular growth; Individual based modelling; Off lattice approach; Quantitative comparison; Tumor spheroids

Indexed keywords


EID: 0037898943     PISSN: 08957177     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0895-7177(03)00128-6     Document Type: Article
Times cited : (104)

References (54)
  • 1
    • 0022351061 scopus 로고
    • A reduction in the in situ rates of oxygen and glucose consumption of cells in EMT6/Ro spheroids during growth
    • J.P. Freyer and R.M. Sutherland, A reduction in the in situ rates of oxygen and glucose consumption of cells in EMT6/Ro spheroids during growth, J. Cell. Physiol. 124, 516-524 (1985).
    • (1985) J. Cell. Physiol. , vol.124 , pp. 516-524
    • Freyer, J.P.1    Sutherland, R.M.2
  • 2
    • 0023093713 scopus 로고
    • A review on cellular aggregates in cancer research
    • W.J. Müller-Klieser, A review on cellular aggregates in cancer research, Cancer. Res. Clin. Oncol. 113 (2), 101-122 (1987).
    • (1987) Cancer. Res. Clin. Oncol. , vol.113 , Issue.2 , pp. 101-122
    • Müller-Klieser, W.J.1
  • 3
    • 0024281372 scopus 로고
    • Cell and environment interactions in tumor microregions: The multicell spheroid model
    • R.M. Sutherland, Cell and environment interactions in tumor microregions: The multicell spheroid model, Science 140, 177-184 (1988).
    • (1988) Science , vol.140 , pp. 177-184
    • Sutherland, R.M.1
  • 4
    • 0003293418 scopus 로고
    • On the nature of the function expressive of the law of mortality
    • B. Gompertz, On the nature of the function expressive of the law of mortality, Phil. Trans. Roy. Soc. (London) 27, 513-585 (1825).
    • (1825) Phil. Trans. Roy. Soc. (London) , vol.27 , pp. 513-585
    • Gompertz, B.1
  • 5
    • 0037701951 scopus 로고
    • Quantitative theories of carcinogenesis
    • Edited by J.R. Thompson and B.W. Brown, Marcel Decker, New York
    • D.J. Murdoch, D.R. Krewski and K.S. Crump, Quantitative theories of carcinogenesis, In Cancer Modelling, (Edited by J.R. Thompson and B.W. Brown), pp. 61-90, Marcel Decker, New York, (1987).
    • (1987) Cancer Modelling , pp. 61-90
    • Murdoch, D.J.1    Krewski, D.R.2    Crump, K.S.3
  • 6
    • 51249194974 scopus 로고
    • Outline of a mathematical approach to the cancer problem
    • N. Rashevsky, Outline of a mathematical approach to the cancer problem, Bull. Math. Biophysics 7, 69 (1945).
    • (1945) Bull. Math. Biophysics , vol.7 , pp. 69
    • Rashevsky, N.1
  • 7
    • 0000500154 scopus 로고
    • A two-dimensional growth process
    • Edited by J. Neyman, University of California Press
    • th Berkeley Symposium on Mathematics and Probability, (Edited by J. Neyman), pp. 223-239, University of California Press, (1961).
    • (1961) th Berkeley Symposium on Mathematics and Probability , pp. 223-239
    • Eden, M.1
  • 8
    • 0015492587 scopus 로고
    • Stochastic model for abnormal clone spread through epithelial basal layer
    • T. Williams and R. Bjerknes, Stochastic model for abnormal clone spread through epithelial basal layer, Nature 236, 19-21 (1972).
    • (1972) Nature , vol.236 , pp. 19-21
    • Williams, T.1    Bjerknes, R.2
  • 9
    • 84971848028 scopus 로고
    • Random growth in a tessellation
    • D. Richardson, Random growth in a tessellation, Proc. Camb. Phil. Soc. 74, 515-528 (1973).
    • (1973) Proc. Camb. Phil. Soc. , vol.74 , pp. 515-528
    • Richardson, D.1
  • 10
    • 0017198676 scopus 로고
    • On the growth and stability of cell cultures and solid tumors
    • H.P. Greenspan, On the growth and stability of cell cultures and solid tumors, J. Theor. Biol. 56, 229-242 (1976).
    • (1976) J. Theor. Biol. , vol.56 , pp. 229-242
    • Greenspan, H.P.1
  • 11
    • 0026784087 scopus 로고
    • A mathematical model for the growth and classification of a solid tumour: A new approach via nonlinear elasticity theory using strain-energy functions
    • M.A.J. Chaplain and B.D. Sleeman, A mathematical model for the growth and classification of a solid tumour: A new approach via nonlinear elasticity theory using strain-energy functions, Math. Biosc. 111, 169-217 (1992).
    • (1992) Math. Biosc. , vol.111 , pp. 169-217
    • Chaplain, M.A.J.1    Sleeman, B.D.2
  • 12
    • 0028790729 scopus 로고
    • Growth of nonnecrotic tumours in the presence and absence of inhibitors
    • H.M. Byrne and M.A.J. Chaplain, Growth of nonnecrotic tumours in the presence and absence of inhibitors, Math. Biosci. 130, 151-181 (1995).
    • (1995) Math. Biosci. , vol.130 , pp. 151-181
    • Byrne, H.M.1    Chaplain, M.A.J.2
  • 13
    • 0001177693 scopus 로고
    • A Monte Carlo model to tissue cell populations
    • D. Drasdo, R. Kree and J.S. McCaskill, A Monte Carlo model to tissue cell populations, Phys. Rev. E 52 (6), 6635-6657 (1995).
    • (1995) Phys. Rev. E , vol.52 , Issue.6 , pp. 6635-6657
    • Drasdo, D.1    Kree, R.2    McCaskill, J.S.3
  • 14
    • 0002113460 scopus 로고    scopus 로고
    • Different growth regimes found in a Monte Carlo model of growing tissue cell populations
    • Edited by F. Schweitzer, Gordon and Breach, London
    • D. Drasdo, Different growth regimes found in a Monte Carlo model of growing tissue cell populations, In Self Organization of Complex Structures: From Individual to Collective Dynamics, (Edited by F. Schweitzer), pp. 281-292, Gordon and Breach, London, (1996).
    • (1996) Self Organization of Complex Structures: From Individual to Collective Dynamics , pp. 281-292
    • Drasdo, D.1
  • 15
    • 0002964937 scopus 로고    scopus 로고
    • Avascular growth, angiogenesis and vascular growth in solid tumours: The mathematical modelling of the stages of tumour development
    • M.A.J. Chaplain, Avascular growth, angiogenesis and vascular growth in solid tumours: The mathematical modelling of the stages of tumour development, Mathl. Comp. Modelling 23 (6), 47-87 (1996).
    • (1996) Mathl. Comp. Modelling , vol.23 , Issue.6 , pp. 47-87
    • Chaplain, M.A.J.1
  • 16
    • 0033199022 scopus 로고    scopus 로고
    • Stochastic simulation of benign avascular tumor growth using the Potts model
    • E.L. Stott, N.F. Britton, J.A. Glazier and M. Zajac, Stochastic simulation of benign avascular tumor growth using the Potts model, Mathl, Comput. Modelling 30 (5/6), 183-198 (1999).
    • (1999) Mathl, Comput. Modelling , vol.30 , Issue.5-6 , pp. 183-198
    • Stott, E.L.1    Britton, N.F.2    Glazier, J.A.3    Zajac, M.4
  • 17
    • 0034204267 scopus 로고    scopus 로고
    • A mathematical model of the stress induced during avascular tumor growth
    • A.F. Jones, H.M. Byrne, J.S. Gibson and J.W. Dold, A mathematical model of the stress induced during avascular tumor growth, J. Math. Biol. 40, 473-499 (2000).
    • (2000) J. Math. Biol. , vol.40 , pp. 473-499
    • Jones, A.F.1    Byrne, H.M.2    Gibson, J.S.3    Dold, J.W.4
  • 19
    • 0035480791 scopus 로고    scopus 로고
    • A new mathematical model for avascular tumour growth
    • J.A. Sherratt and M.A.J. Chaplain, A new mathematical model for avascular tumour growth, J. Math. Biol. 43, 291-312 (2001).
    • (2001) J. Math. Biol. , vol.43 , pp. 291-312
    • Sherratt, J.A.1    Chaplain, M.A.J.2
  • 21
    • 0038716149 scopus 로고
    • Explicit solutions of a simplified model of capillary sprout growth during tumour angiogenesis
    • H.M. Byrne and M.A.J. Chaplain, Explicit solutions of a simplified model of capillary sprout growth during tumour angiogenesis, Appl. Math. Letters 8 (5), 71-76 (1995).
    • (1995) Appl. Math. Letters , vol.8 , Issue.5 , pp. 71-76
    • Byrne, H.M.1    Chaplain, M.A.J.2
  • 22
    • 0029422302 scopus 로고
    • The mathematical modelling of tumour angiogenesis and invasion
    • M.A.J. Chaplain, The mathematical modelling of tumour angiogenesis and invasion, Acta Biotheor. 43, 387-402 (1995).
    • (1995) Acta Biotheor. , vol.43 , pp. 387-402
    • Chaplain, M.A.J.1
  • 23
    • 37649028647 scopus 로고    scopus 로고
    • Emergence of taxis and synergy in angiogenesis
    • B.C. Sansone, M. Scalerandi and C.A. Condat, Emergence of taxis and synergy in angiogenesis, Phys. Rev. Lett. 87, 128102-128104 (2001).
    • (2001) Phys. Rev. Lett. , vol.87 , pp. 128102-128104
    • Sansone, B.C.1    Scalerandi, M.2    Condat, C.A.3
  • 24
    • 0026289268 scopus 로고
    • A mathematical model for the interaction between cytotoxic T lymphocytes and tumour cells. Analysis of the growth, stabilization, and regression of a B-cell lymphona in mice chimeric with respect to the major histocompatibility complex
    • V.A. Kuznetsov, A mathematical model for the interaction between cytotoxic T lymphocytes and tumour cells. Analysis of the growth, stabilization, and regression of a B-cell lymphona in mice chimeric with respect to the major histocompatibility complex, Biomed. Sci. 2 (5), 465-476 (1991).
    • (1991) Biomed. Sci. , vol.2 , Issue.5 , pp. 465-476
    • Kuznetsov, V.A.1
  • 25
    • 0031558747 scopus 로고    scopus 로고
    • Pattern formation and spatiotemporal irregularity in a model for macrophage-tumor interactions
    • M.R. Owen and J.A. Sherratt, Pattern formation and spatiotemporal irregularity in a model for macrophage-tumor interactions, J. Theor. Biol. 189, 63-80 (1997).
    • (1997) J. Theor. Biol. , vol.189 , pp. 63-80
    • Owen, M.R.1    Sherratt, J.A.2
  • 27
    • 0010853793 scopus 로고
    • Modelling resistance to cancer chemotherapeutic agents
    • Edited by J.R. Thompson and B.W. Brown, Marcel Decker, New York
    • A.J. Coldman and J.H. Goldie, Modelling resistance to cancer chemotherapeutic agents, In Cancer Modelling, (Edited by J.R. Thompson and B.W. Brown), pp. 315-364, Marcel Decker, New York, (1987).
    • (1987) Cancer Modelling , pp. 315-364
    • Coldman, A.J.1    Goldie, J.H.2
  • 28
    • 0038377873 scopus 로고
    • Repair of radiation injury and the time factor in radiotherapy
    • Edited by J.R. Thompson and B.W. Brown, Marcel Decker, New York
    • H.D. Thames, Repair of radiation injury and the time factor in radiotherapy, In Cancer Modelling, (Edited by J.R. Thompson and B.W. Brown), pp. 269-314, Marcel Decker, New York, (1987).
    • (1987) Cancer Modelling , pp. 269-314
    • Thames, H.D.1
  • 29
    • 0343010451 scopus 로고    scopus 로고
    • Cancer: A challenge for control theory and computer modelling
    • W. Düchting, W. Ulmer and T. Ginsberg, Cancer: A challenge for control theory and computer modelling, Europ. J. Cancer 32A (8), 1283-1292 (1996).
    • (1996) Europ. J. Cancer , vol.32 A , Issue.8 , pp. 1283-1292
    • Düchting, W.1    Ulmer, W.2    Ginsberg, T.3
  • 30
    • 0034697619 scopus 로고    scopus 로고
    • Cell kinetics in a tumour cord
    • A. Bertuzzi and A. Gandolfi, Cell kinetics in a tumour cord, J. Theor. Biol. 204, 587-599 (2000).
    • (2000) J. Theor. Biol. , vol.204 , pp. 587-599
    • Bertuzzi, A.1    Gandolfi, A.2
  • 31
    • 0033752019 scopus 로고    scopus 로고
    • A quantitative model for differential motility of gliomas in grey and white matter
    • K.R. Swanson, E.C. Alvord Jr. and J.D. Murray, A quantitative model for differential motility of gliomas in grey and white matter, Cell Prolif. 33, 317-329 (2000).
    • (2000) Cell Prolif. , vol.33 , pp. 317-329
    • Swanson, K.R.1    Alvord E.C., Jr.2    Murray, J.D.3
  • 32
    • 0036692144 scopus 로고    scopus 로고
    • The role of cell-cell interactions in a two-phase model for avascular tumour growth
    • to appear
    • C.J.W. Breward, H.M. Byrne and C.E. Lewis, The role of cell-cell interactions in a two-phase model for avascular tumour growth, J. Math. Biol. (to appear).
    • J. Math. Biol.
    • Breward, C.J.W.1    Byrne, H.M.2    Lewis, C.E.3
  • 33
    • 0001119103 scopus 로고
    • Notice sur la loi la population suit dans son accroissement
    • P.F. Verhulst, Notice sur la loi la population suit dans son accroissement, Corr. Math. et. Phys 10, 113-121 (1838).
    • (1838) Corr. Math. et. Phys , vol.10 , pp. 113-121
    • Verhulst, P.F.1
  • 34
    • 0000268135 scopus 로고
    • The wave of advance of advantage genes
    • R.A. Fisher, The wave of advance of advantage genes, Ann. Eugenics. 7, 353-369 (1937).
    • (1937) Ann. Eugenics. , vol.7 , pp. 353-369
    • Fisher, R.A.1
  • 35
    • 0002722044 scopus 로고
    • Study of the diffusion equation with growth of the quantity of matter and its application to a biological problem
    • in Russian
    • A. Kolmogorov, I. Petrovsky and N. Piscounov, Study of the diffusion equation with growth of the quantity of matter and its application to a biological problem, Moscow Univ. Bull. Math., (in Russian) 1, 1-25 (1937).
    • (1937) Moscow Univ. Bull. Math. , vol.1 , pp. 1-25
    • Kolmogorov, A.1    Petrovsky, I.2    Piscounov, N.3
  • 36
    • 0034206088 scopus 로고    scopus 로고
    • Front propagation in heterogeneous media
    • J. Xin, Front propagation in heterogeneous media, SIAM Review 42 (2), 161-230 (2000).
    • (2000) SIAM Review , vol.42 , Issue.2 , pp. 161-230
    • Xin, J.1
  • 37
    • 0038716136 scopus 로고    scopus 로고
    • On selected individual based models to the dynamics of tissue organization
    • (Edited by W. Alt et al.), Birkhäuser, (in press)
    • D. Drasdo, On selected individual based models to the dynamics of tissue organization, In Polymer and Cell Dynamics, (Edited by W. Alt et al.), Birkhäuser, (in press).
    • Polymer and Cell Dynamics
    • Drasdo, D.1
  • 38
    • 0037701926 scopus 로고
    • Fractal fragmentation in replicative systems
    • G. Landini and J.W. Rippin, Fractal fragmentation in replicative systems, Fractals 1 (2), 239-246 (1993).
    • (1993) Fractals , vol.1 , Issue.2 , pp. 239-246
    • Landini, G.1    Rippin, J.W.2
  • 39
    • 0012575045 scopus 로고
    • Kinetic roughening phenomena, stochastic growth, directed polymers and all that
    • T. Halpin-Healy and Y.C. Zhang, Kinetic roughening phenomena, stochastic growth, directed polymers and all that, Phys. Rep. 254, 215 (1995).
    • (1995) Phys. Rep. , vol.254 , pp. 215
    • Halpin-Healy, T.1    Zhang, Y.C.2
  • 41
    • 33646972262 scopus 로고
    • Selected topics in fluctuation kinetics of reactions
    • A.S. Mikhailov, Selected topics in fluctuation kinetics of reactions, Phys. Reports 307 (5/6) (1989).
    • (1989) Phys. Reports , vol.307 , Issue.6-35
    • Mikhailov, A.S.1
  • 44
    • 0000104017 scopus 로고
    • Structure of water: A Monte Carlo calculation
    • J.A. Baxker and R.O. Watts, Structure of water: A Monte Carlo calculation, Chem. Phys. Lett. 3, 144-145 (1969).
    • (1969) Chem. Phys. Lett. , vol.3 , pp. 144-145
    • Baxker, J.A.1    Watts, R.O.2
  • 45
    • 35949007530 scopus 로고
    • Random walk and directed movement: Comparison between inert particles and self-organized molecular machines
    • M. Schienbein, K. Franke and H. Gruler, Random walk and directed movement: Comparison between inert particles and self-organized molecular machines, Phys. Rev. E 49 (6), 5462-5471 (1994).
    • (1994) Phys. Rev. E , vol.49 , Issue.6 , pp. 5462-5471
    • Schienbein, M.1    Franke, K.2    Gruler, H.3
  • 46
    • 0000313998 scopus 로고
    • Quantitative comparison between differential adhesion models and cell sorting in the presence and absence of fluctuations
    • J.C.M. Mombach, J.A. Glazier, R.C. Raphael and M. Zajak, Quantitative comparison between differential adhesion models and cell sorting in the presence and absence of fluctuations, Phys. Rev. Lett. 75 (11), 2244-2247 (1995).
    • (1995) Phys. Rev. Lett. , vol.75 , Issue.11 , pp. 2244-2247
    • Mombach, J.C.M.1    Glazier, J.A.2    Raphael, R.C.3    Zajak, M.4
  • 47
    • 0034662976 scopus 로고    scopus 로고
    • Cell sorting is analogous to phase ordering in fluids
    • D. Beysens, G. Forgacs and J.A. Glazier, Cell sorting is analogous to phase ordering in fluids, PNAS 97 (17), 9647-9471 (2000).
    • (2000) PNAS , vol.97 , Issue.17 , pp. 9647-9471
    • Beysens, D.1    Forgacs, G.2    Glazier, J.A.3
  • 49
    • 0029005577 scopus 로고
    • How do sea urchins invaginate? Using bio-mechanics to distinguish between mechanisms of primary invagination
    • L.A. Davidson, M.A.R. Koehl, R. Keller and G.F. Oster, How do sea urchins invaginate? Using bio-mechanics to distinguish between mechanisms of primary invagination, Development 121, 2005-2018 (1995).
    • (1995) Development , vol.121 , pp. 2005-2018
    • Davidson, L.A.1    Koehl, M.A.R.2    Keller, R.3    Oster, G.F.4
  • 50
    • 0034180349 scopus 로고    scopus 로고
    • Buckling instabilities in one-layered growing tissues
    • D. Drasdo, Buckling instabilities in one-layered growing tissues, Phys. Rev. Lett. 84, 4424-4427 (2000).
    • (2000) Phys. Rev. Lett. , vol.84 , pp. 4424-4427
    • Drasdo, D.1
  • 51
    • 0033778696 scopus 로고    scopus 로고
    • Modelling generic and genetic interactions in cleavage, blastulation and gastrulation
    • D. Drasdo and G. Forgacs, Modelling generic and genetic interactions in cleavage, blastulation and gastrulation, Dev. Dyn. 219 (2), 182-191 (2000).
    • (2000) Dev. Dyn. , vol.219 , Issue.2 , pp. 182-191
    • Drasdo, D.1    Forgacs, G.2
  • 53
    • 34250246792 scopus 로고
    • On the nonequilibrium phase transition in reaction-diffusion system with an absorbing state
    • H.K. Jansen, On the nonequilibrium phase transition in reaction-diffusion system with an absorbing state, Z. Phys. B 42, 151-154 (1981).
    • (1981) Z. Phys. B , vol.42 , pp. 151-154
    • Jansen, H.K.1
  • 54
    • 0031845830 scopus 로고    scopus 로고
    • The growth law of primary breast cancer as inferred from mamography screening trials data
    • D. Hart, E. Shochat and Z. Agur, The growth law of primary breast cancer as inferred from mamography screening trials data, Br. J. Cancer 78 (3), 382-387 (1998).
    • (1998) Br. J. Cancer , vol.78 , Issue.3 , pp. 382-387
    • Hart, D.1    Shochat, E.2    Agur, Z.3


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