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Volumn 66, Issue 2, 2006, Pages 447-467

A Mixture Theory for the Genesis of Residual Stresses in Growing Tissues II: Solutions to the biphasic equations for a multicell spheroid

Author keywords

Anisotropic growth; Biomechanics; Constitutive equations; Diffusion; Isotropic growth; Linear elasticity; Multicell spheroid; Poroelasticity; Porous media; Residual stresses

Indexed keywords

BIOMECHANICS; DIFFUSION; GROWTH KINETICS; RESIDUAL STRESSES; STRESS RELAXATION; TISSUE;

EID: 33645768942     PISSN: 00361399     EISSN: None     Source Type: Journal    
DOI: 10.1137/040607125     Document Type: Article
Times cited : (48)

References (27)
  • 1
    • 25144517326 scopus 로고    scopus 로고
    • A mixture theory for the genesis of residual stresses in growing tissues I: A general formulation
    • R. P. ARAUJO AND D. L. S. MCELWAIN, A mixture theory for the genesis of residual stresses in growing tissues I: A general formulation, SIAM J. Appl. Math., 65 (2005), pp. 1261-1284.
    • (2005) SIAM J. Appl. Math. , vol.65 , pp. 1261-1284
    • Araujo, R.P.1    Mcelwain, D.L.S.2
  • 2
    • 22344435372 scopus 로고    scopus 로고
    • The nature of the stresses induced during tissue growth
    • R. P. ARAUJO AND D. L. S. MCELWAIN, The nature of the stresses induced during tissue growth, Appl. Math. Lett., 18 (2005), pp. 1081-1085.
    • (2005) Appl. Math. Lett. , vol.18 , pp. 1081-1085
    • Araujo, R.P.1    Mcelwain, D.L.S.2
  • 4
    • 3843061915 scopus 로고    scopus 로고
    • The genesis of residual stresses and vascular collapse in solid tumours
    • R. L. May and W. F. Bluth, eds., Engineering Mathematics Group, ANZIAM, Sydney, Australia
    • R. P. ARAUJO AND D. L. S. MCELWAIN, The genesis of residual stresses and vascular collapse in solid tumours, in Proceedings of the Sixth Engineering Mathematics and Applications Conference, R. L. May and W. F. Bluth, eds., Engineering Mathematics Group, ANZIAM, Sydney, Australia, 2003, pp. 1-6.
    • (2003) Proceedings of the Sixth Engineering Mathematics and Applications Conference , pp. 1-6
    • Araujo, R.P.1    Mcelwain, D.L.S.2
  • 5
    • 3843079723 scopus 로고    scopus 로고
    • A history of the study of solid tumour growth: The contribution of mathematical modelling
    • R. P. ARAUJO AND D. L. S. MCELWAIN, A history of the study of solid tumour growth: The contribution of mathematical modelling, Bull. Math. Biol., 66 (2004), pp. 1039-1091.
    • (2004) Bull. Math. Biol. , vol.66 , pp. 1039-1091
    • Araujo, R.P.1    Mcelwain, D.L.S.2
  • 6
    • 4744337626 scopus 로고    scopus 로고
    • A linear-elastic model of anisotropic tumour growth
    • R. P. ARAUJO AND D. L. S. MCELWAIN, A linear-elastic model of anisotropic tumour growth, European J. Appl. Math., 15 (2004), pp. 365-384.
    • (2004) European J. Appl. Math. , vol.15 , pp. 365-384
    • Araujo, R.P.1    Mcelwain, D.L.S.2
  • 7
    • 2342520039 scopus 로고    scopus 로고
    • New insights into vascular collapse and growth dynamics in solid tumours
    • R. P. ARAUJO AND D. L. S. MCELWAIN, New insights into vascular collapse and growth dynamics in solid tumours, J. Theoret. Biol., 228 (2004), pp. 335-346.
    • (2004) J. Theoret. Biol. , vol.228 , pp. 335-346
    • Araujo, R.P.1    Mcelwain, D.L.S.2
  • 9
    • 0036692144 scopus 로고    scopus 로고
    • The role of cell-cell interactions in a two-phase model for avascular tumour growth
    • 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., 45 (2002), pp. 125-152.
    • (2002) J. Math. Biol. , vol.45 , pp. 125-152
    • Breward, C.J.W.1    Byrne, H.M.2    Lewis, C.E.3
  • 11
    • 0842281982 scopus 로고    scopus 로고
    • Modelling solid tumor growth using the theory of mixtures
    • H. M. BYRNE AND L. PREZIOSI, Modelling solid tumor growth using the theory of mixtures, Math. Med. Biol., 20 (2003), pp. 341-366.
    • (2003) Math. Med. Biol. , vol.20 , pp. 341-366
    • Byrne, H.M.1    Preziosi, L.2
  • 12
    • 0017685313 scopus 로고
    • A proliferation gradient in three-dimensional colonies of cultured human glioma cells
    • J. CARLSSON, A proliferation gradient in three-dimensional colonies of cultured human glioma cells, Int. J. Cancer, 20 (1977), pp. 129-136.
    • (1977) Int. J. Cancer , vol.20 , pp. 129-136
    • Carlsson, J.1
  • 13
    • 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), pp. 745-753.
    • (1973) J. Exp. Med. , vol.138 , pp. 745-753
    • Folkman, J.1    Hochberg, M.2
  • 14
    • 0026033263 scopus 로고
    • Distributions of oxygen, nutrient and metabolic waste concentrations in multicellular spheroids and their dependence on spheroid parameters
    • K. GROEBE AND W. MUELLER-KLIESER, Distributions of oxygen, nutrient and metabolic waste concentrations in multicellular spheroids and their dependence on spheroid parameters, Eur. Biophys. J., 19 (1991), pp. 169-181.
    • (1991) Eur. Biophys. J. , vol.19 , pp. 169-181
    • Groebe, K.1    Mueller-Klieser, W.2
  • 16
    • 0034204267 scopus 로고    scopus 로고
    • A mathematical model of the stress induced during avascular tumour growth
    • A. F. JONES, H. M. BYRNE, J. S. GIBSON, AND J. W. DOLD, A mathematical model of the stress induced during avascular tumour growth, J. Math. Biol., 40 (2000), pp. 473-499.
    • (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
  • 18
    • 0015117787 scopus 로고
    • Shrinkage necrosis: A distinct mode of cellular death
    • J. F. R. KERR, Shrinkage necrosis: A distinct mode of cellular death, J. Path., 105 (1971), pp. 13-20.
    • (1971) J. Path. , vol.105 , pp. 13-20
    • Kerr, J.F.R.1
  • 19
    • 0015383455 scopus 로고
    • Apoptosis: A basic biological phenomenon with wide-ranging implications in tissue kinetics
    • J. F. R. KERR, A. H. WYLLIE, AND A. R. CURRIE, Apoptosis: A basic biological phenomenon with wide-ranging implications in tissue kinetics, Br. J. Cancer, 26 (1972), pp. 239-257.
    • (1972) Br. J. Cancer , vol.26 , pp. 239-257
    • Kerr, J.F.R.1    Wyllie, A.H.2    Currie, A.R.3
  • 21
    • 11144221005 scopus 로고    scopus 로고
    • Residual stress generation and necrosis formation in multi-cell tumour spheroids
    • B. D. MACARTHUR AND C. P. PLEASE, Residual stress generation and necrosis formation in multi-cell tumour spheroids, J. Math. Biol., 49 (2004), pp. 537-552.
    • (2004) J. Math. Biol. , vol.49 , pp. 537-552
    • Macarthur, B.D.1    Please, C.P.2
  • 22
    • 0018774581 scopus 로고
    • A model of vascular compression in solid tumours
    • D. L. S. MCELWAIN, R. CALLCOTT, AND L. E. MORRIS, A model of vascular compression in solid tumours, J. Theoret. Biol., 78 (1979), pp. 405-415.
    • (1979) J. Theoret. Biol. , vol.78 , pp. 405-415
    • Mcelwain, D.L.S.1    Callcott, R.2    Morris, L.E.3
  • 23
    • 0017806209 scopus 로고
    • Apoptosis as a volume loss mechanism in mathematical models of solid tumor growth
    • D. L. S. MCELWAIN AND L. E. MORRIS, Apoptosis as a volume loss mechanism in mathematical models of solid tumor growth, Math. Biosci., 39 (1978), pp. 147-157.
    • (1978) Math. Biosci. , vol.39 , pp. 147-157
    • Mcelwain, D.L.S.1    Morris, L.E.2
  • 24
    • 0002498348 scopus 로고    scopus 로고
    • A new approach to modelling the formation of necrotic regions in tumours
    • C. P. PLEASE, G. J. PETTET, AND D. L. S. MCELWAIN, A new approach to modelling the formation of necrotic regions in tumours, Appl. Math. Lett., 11 (1998), pp. 89-94.
    • (1998) Appl. Math. Lett. , vol.11 , pp. 89-94
    • Please, C.P.1    Pettet, G.J.2    Mcelwain, D.L.S.3
  • 26
    • 0001773156 scopus 로고
    • Growth as a finite displacement field
    • D. E. Carlson and R. T. Shield, eds., Martinus Nijhoff, The Hague, The Netherlands
    • R. SKALAK, Growth as a finite displacement field, in Proceedings of the IUTAM Symposium on Finite Elasticity, D. E. Carlson and R. T. Shield, eds., Martinus Nijhoff, The Hague, The Netherlands, 1981, pp. 347-355.
    • (1981) Proceedings of the IUTAM Symposium on Finite Elasticity , pp. 347-355
    • Skalak, R.1
  • 27
    • 0015592636 scopus 로고
    • Hypoxic cells in an in vitro tumour model
    • R. M. SUTHERLAND AND R. E. DURAND, Hypoxic cells in an in vitro tumour model, Int. J. Radiat. Biol., 23 (1973), pp. 235-246.
    • (1973) Int. J. Radiat. Biol. , vol.23 , pp. 235-246
    • Sutherland, R.M.1    Durand, R.E.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.