메뉴 건너뛰기




Volumn 17, Issue SUPPL. 1, 2007, Pages 1721-1750

Modelling scaffold occupation by a growing, nutrient-rich tissue

Author keywords

Asymptotic analysis; Moving boundary problem; Tissue engineering

Indexed keywords


EID: 35348866705     PISSN: 02182025     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0218202507002455     Document Type: Article
Times cited : (14)

References (61)
  • 1
    • 0142248828 scopus 로고    scopus 로고
    • A cellular automaton model for tumour growth in inhomogeneous environment
    • T. Alarcón, H. M. Byrne and P. K. Maini, A cellular automaton model for tumour growth in inhomogeneous environment, J. Theor. Biol. 225 (2003) 257-274.
    • (2003) J. Theor. Biol , vol.225 , pp. 257-274
    • Alarcón, T.1    Byrne, H.M.2    Maini, P.K.3
  • 2
    • 35348922631 scopus 로고
    • Variational inequalities and free boundary problems
    • R.W. Cottle, F. Giannessi and J.-L. Lions, eds, Wiley
    • C. Baiocchi, Variational inequalities and free boundary problems, in Variational Inequalities and Complementarity Problems, R.W. Cottle, F. Giannessi and J.-L. Lions, eds. (Wiley, 1980) pp. 25-33.
    • (1980) Variational Inequalities and Complementarity Problems , pp. 25-33
    • Baiocchi, C.1
  • 3
    • 27644540984 scopus 로고    scopus 로고
    • A mathematical model for tumor cords incorporating the flow of interstitial fluid
    • A. Bertuzzi, A. Fasano and A. Gandolfi, A mathematical model for tumor cords incorporating the flow of interstitial fluid, Math. Mod. Meth. Appl Sci. 15 (2005) 1735-1779.
    • (2005) Math. Mod. Meth. Appl Sci , vol.15 , pp. 1735-1779
    • Bertuzzi, A.1    Fasano, A.2    Gandolfi, A.3
  • 4
    • 33750078422 scopus 로고    scopus 로고
    • Modelling the response of vascular tumours to chemotherapy: A multiscale approach
    • H. M. Byrne, T. Alarcón, M. R. Owen, J. Murphy and P. K. Maini, Modelling the response of vascular tumours to chemotherapy: A multiscale approach, Math. Mod. Meth. Appl. Sci. 16 (2006) 1219-1241.
    • (2006) Math. Mod. Meth. Appl. Sci , vol.16 , pp. 1219-1241
    • Byrne, H.M.1    Alarcón, T.2    Owen, M.R.3    Murphy, J.4    Maini, P.K.5
  • 6
    • 0842281982 scopus 로고    scopus 로고
    • Modelling solid tumour growth using the theory of mixtures
    • H. M. 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.M.1    Preziosi, L.2
  • 7
    • 84988072922 scopus 로고
    • Modeling of contact-inhibited animal cell growth on flat surfaces and spheres
    • R. S. Cherry and E. T. Papoutsakis, Modeling of contact-inhibited animal cell growth on flat surfaces and spheres, Biotech. Bioeng. 33 (1989) 300-305.
    • (1989) Biotech. Bioeng , vol.33 , pp. 300-305
    • Cherry, R.S.1    Papoutsakis, E.T.2
  • 8
    • 0015111628 scopus 로고
    • The solution of a quadratic programming problem using systematic overrelaxation
    • C. W. Cryer, The solution of a quadratic programming problem using systematic overrelaxation, SIAM J. Control 9 (1971) 385-392.
    • (1971) SIAM J. Control , vol.9 , pp. 385-392
    • Cryer, C.W.1
  • 16
    • 12144264054 scopus 로고    scopus 로고
    • Analysis of a mathematical model for tumor lymphangiogenesis
    • A. Friedman and G. Lolas, Analysis of a mathematical model for tumor lymphangiogenesis, Math. Mod. Meth. Appl. Sci. 15 (2005) 95-109.
    • (2005) Math. Mod. Meth. Appl. Sci , vol.15 , pp. 95-109
    • Friedman, A.1    Lolas, G.2
  • 18
    • 0343145707 scopus 로고    scopus 로고
    • Analysis of cell growth in a polymer scaffold using a moving boundary approach
    • C. J. Galban and B. R. Locke, Analysis of cell growth in a polymer scaffold using a moving boundary approach, Biotech. Bioeng. 56 (1997) 422-432.
    • (1997) Biotech. Bioeng , vol.56 , pp. 422-432
    • Galban, C.J.1    Locke, B.R.2
  • 19
    • 0033589363 scopus 로고    scopus 로고
    • Analysis of cell growth kinetics and substrate diffusion in a polymer scaffold
    • C. J. Galban and B. R. Locke, Analysis of cell growth kinetics and substrate diffusion in a polymer scaffold, Biotech. Bioeng. 65 (1999) 121-132.
    • (1999) Biotech. Bioeng , vol.65 , pp. 121-132
    • Galban, C.J.1    Locke, B.R.2
  • 20
    • 0033588792 scopus 로고    scopus 로고
    • Effects of spatial variation of cells and nutrient and product concentrations coupled with product inhibition on cell growth in a polymer scaffold
    • C. J. Galban and B. R. Locke, Effects of spatial variation of cells and nutrient and product concentrations coupled with product inhibition on cell growth in a polymer scaffold, Biotech. Bioeng. 64 (1999) 633-643.
    • (1999) Biotech. Bioeng , vol.64 , pp. 633-643
    • Galban, C.J.1    Locke, B.R.2
  • 21
    • 33646364803 scopus 로고    scopus 로고
    • Fluid flow increases type II collagen deposition and tensile mechanical properties in bioreactor-grown tissue-engineered cartilage
    • March 1
    • C. V. Gemmiti, R. E. Guldberg, Fluid flow increases type II collagen deposition and tensile mechanical properties in bioreactor-grown tissue-engineered cartilage, Tissue Eng. (2006) March 1.
    • (2006) Tissue Eng
    • Gemmiti, C.V.1    Guldberg, R.E.2
  • 22
    • 0017198676 scopus 로고
    • On the growth and stability of cell cultures and solid tumours
    • H. P. Greenspan, On the growth and stability of cell cultures and solid tumours, J. Theor. Biol. 56 (1976) 229-242.
    • (1976) J. Theor. Biol , vol.56 , pp. 229-242
    • Greenspan, H.P.1
  • 23
    • 0032053771 scopus 로고    scopus 로고
    • A mixture theory for charge-hydrated soft tissues containing multi-electrolytes: Passive transport and swelling behaviours
    • W. Y. Gu, W. M. Lai and V. G. Mow, A mixture theory for charge-hydrated soft tissues containing multi-electrolytes: Passive transport and swelling behaviours, J. Biotnech. Eng. 120 (1998) 169-180.
    • (1998) J. Biotnech. Eng , vol.120 , pp. 169-180
    • Gu, W.Y.1    Lai, W.M.2    Mow, V.G.3
  • 25
    • 4744350838 scopus 로고    scopus 로고
    • Mathematical analysis of some multi-dimensional tissue-growth models
    • J. R. King and S. J. Franks, Mathematical analysis of some multi-dimensional tissue-growth models, Eur. J. Appl. Math. 15 (2004) 273-295.
    • (2004) Eur. J. Appl. Math , vol.15 , pp. 273-295
    • King, J.R.1    Franks, S.J.2
  • 26
    • 0026203776 scopus 로고
    • A triphasic theory for the welling and deformation behaviours of articular cartilage
    • W. M. Lai, J. S. Hou and V. G. Mow, A triphasic theory for the welling and deformation behaviours of articular cartilage, J. Biomech. Eng. 113 (1991) 245-258.
    • (1991) J. Biomech. Eng , vol.113 , pp. 245-258
    • Lai, W.M.1    Hou, J.S.2    Mow, V.G.3
  • 27
    • 0027595948 scopus 로고
    • Tissue engineering
    • R. Langer and J. P. Vacanti, Tissue engineering, Sci. 260 (1993) 920-926.
    • (1993) Sci , vol.260 , pp. 920-926
    • Langer, R.1    Vacanti, J.P.2
  • 28
    • 0033114043 scopus 로고    scopus 로고
    • Tissue engineering: The challenges ahead
    • R. S. Langer and J. P. Vacanti, Tissue engineering: The challenges ahead, Sci. Am. 280 (1999) 86-89.
    • (1999) Sci. Am , vol.280 , pp. 86-89
    • Langer, R.S.1    Vacanti, J.P.2
  • 29
    • 0242386325 scopus 로고    scopus 로고
    • Organic tissues in rotating bioreactors: Fluid-mechanical aspects, dynamical growth models, and morphological evolution
    • M. Lappa, Organic tissues in rotating bioreactors: Fluid-mechanical aspects, dynamical growth models, and morphological evolution, Biotech. Bioeng. 84 (2003) 518-532.
    • (2003) Biotech. Bioeng , vol.84 , pp. 518-532
    • Lappa, M.1
  • 30
    • 33645957316 scopus 로고    scopus 로고
    • Multiphase modelling of tissue growth using the theory of mixtures
    • G. Lemon, J. R. King, H. M. Byrne, O. E. Jensen and K. E. Shakesheff, Multiphase modelling of tissue growth using the theory of mixtures, J. Math. Biol. 52 (2006) 571-594.
    • (2006) J. Math. Biol , vol.52 , pp. 571-594
    • Lemon, G.1    King, J.R.2    Byrne, H.M.3    Jensen, O.E.4    Shakesheff, K.E.5
  • 31
    • 33847651698 scopus 로고    scopus 로고
    • Multiphase modelling of cell behaviour on artificial scaffolds: Effects of nutrient depletion and spatially nonuniform porosity
    • G. Lemon and J. R. King, Multiphase modelling of cell behaviour on artificial scaffolds: Effects of nutrient depletion and spatially nonuniform porosity, Math. Med. Biol. 24 (2007) 57-83.
    • (2007) Math. Med. Biol , vol.24 , pp. 57-83
    • Lemon, G.1    King, J.R.2
  • 32
    • 25144444761 scopus 로고    scopus 로고
    • Heterogeneous proliferation within engineered cartilaginous tissue: The role of oxygen tension
    • M. C. Lewis, B. D. Macarthur, J. Malda, G. Pettet and C. P. Please, Heterogeneous proliferation within engineered cartilaginous tissue: The role of oxygen tension, Biotech. Bioeng. 91 (2005) 607-615.
    • (2005) Biotech. Bioeng , vol.91 , pp. 607-615
    • Lewis, M.C.1    Macarthur, B.D.2    Malda, J.3    Pettet, G.4    Please, C.P.5
  • 33
    • 0036737932 scopus 로고    scopus 로고
    • On the mechanics of solids with a growing mass
    • V. A. Lubarda, and A. Hoger, On the mechanics of solids with a growing mass, Int. J. Solids. Struct. 39 (2002) 4627-1664.
    • (2002) Int. J. Solids. Struct , vol.39 , pp. 4627-1664
    • Lubarda, V.A.1    Hoger, A.2
  • 34
    • 1542722131 scopus 로고    scopus 로고
    • Extinction behaviour for two-dimensional inward-solidification problems
    • S. W. McCue, J. R. King and D. S. Riley, Extinction behaviour for two-dimensional inward-solidification problems, Proc. Roy. Soc. Lond. Ser. A 459 (2003) 977-999.
    • (2003) Proc. Roy. Soc. Lond. Ser. A , vol.459 , pp. 977-999
    • McCue, S.W.1    King, J.R.2    Riley, D.S.3
  • 35
    • 0038383162 scopus 로고    scopus 로고
    • Extinction behaviour of contracting bubbles in porous media
    • S. W. McCue, J. R. King and D. S. Riley, Extinction behaviour of contracting bubbles in porous media, Quart. J. Mech. Appl. Math. 56 (2003) 455-482.
    • (2003) Quart. J. Mech. Appl. Math , vol.56 , pp. 455-482
    • McCue, S.W.1    King, J.R.2    Riley, D.S.3
  • 37
    • 0033106488 scopus 로고    scopus 로고
    • Growing new organs
    • D. J. Mooney and A. G. Mikos, Growing new organs, Sci. Am. 280 (1999) 60-65.
    • (1999) Sci. Am , vol.280 , pp. 60-65
    • Mooney, D.J.1    Mikos, A.G.2
  • 38
    • 0017427064 scopus 로고
    • Theoretical derivation of Darcy's Law
    • S. P. Neuman, Theoretical derivation of Darcy's Law, Acta Mech. 25 (1975) 153-170.
    • (1975) Acta Mech , vol.25 , pp. 153-170
    • Neuman, S.P.1
  • 39
    • 0034282186 scopus 로고    scopus 로고
    • Glycosaminoglycan deposition in engineered cartilage: Experiments and mathematical model
    • B. Obradovic, J. H. Meldon, L. E. Freed and G. Vunjak-Novakovic, Glycosaminoglycan deposition in engineered cartilage: Experiments and mathematical model, AIChE J. 46 (2000) 1860-1871.
    • (2000) AIChE J , vol.46 , pp. 1860-1871
    • Obradovic, B.1    Meldon, J.H.2    Freed, L.E.3    Vunjak-Novakovic, G.4
  • 40
    • 0028485195 scopus 로고
    • Numerical and asymptotic solutions to a model for the waterproofing of telecommunications cables
    • S. B. G. O'Brien and P. J. Slikkerveer, Numerical and asymptotic solutions to a model for the waterproofing of telecommunications cables, Int. J. Engg. Sci. 32 (1994) 1283-1301.
    • (1994) Int. J. Engg. Sci , vol.32 , pp. 1283-1301
    • O'Brien, S.B.G.1    Slikkerveer, P.J.2
  • 41
    • 0035824717 scopus 로고    scopus 로고
    • Cellular automaton model of early tumour growth and invasion: The effects of native tissue vascularity and increased anaerobic tumour metabolism
    • A. A. Patel, E. T. Gawlinsky, S. K. Lemieux and R. A. Gatenby, Cellular automaton model of early tumour growth and invasion: The effects of native tissue vascularity and increased anaerobic tumour metabolism, J. Theor. Biol. 213 (2001) 315-331.
    • (2001) J. Theor. Biol , vol.213 , pp. 315-331
    • Patel, A.A.1    Gawlinsky, E.T.2    Lemieux, S.K.3    Gatenby, R.A.4
  • 43
    • 33645560618 scopus 로고    scopus 로고
    • Oxygen gradients correlate with cell density and cell viability in engineered cardiac tissue
    • M. Radisic, J. Malda, E. Epping, W. Geng, R. Langer and G. Vunjak-Novakovic, Oxygen gradients correlate with cell density and cell viability in engineered cardiac tissue, Biotech. Bioeng. 93 (2006) 332-343.
    • (2006) Biotech. Bioeng , vol.93 , pp. 332-343
    • Radisic, M.1    Malda, J.2    Epping, E.3    Geng, W.4    Langer, R.5    Vunjak-Novakovic, G.6
  • 44
  • 45
    • 33646249607 scopus 로고    scopus 로고
    • A multiscale mathematical model of cancer and its use in analyzing irradiation therapies
    • B. Ribba, T. Colin and S. Schnell, A multiscale mathematical model of cancer and its use in analyzing irradiation therapies, Theor. Biol. Med. Model. 3 (2006) 7.
    • (2006) Theor. Biol. Med. Model , vol.3 , pp. 7
    • Ribba, B.1    Colin, T.2    Schnell, S.3
  • 47
    • 0036680533 scopus 로고    scopus 로고
    • Tissue engineering: Advances in in vitro cartilage generation
    • M. V. Risbud and R. Sittinger, Tissue engineering: Advances in in vitro cartilage generation, Trends Biotech. 20 (2002) 351-356.
    • (2002) Trends Biotech , vol.20 , pp. 351-356
    • Risbud, M.V.1    Sittinger, R.2
  • 48
    • 0035129867 scopus 로고    scopus 로고
    • Tissue engineering: Current state and prospects
    • U. A. Stock and J. P. Vacanti, Tissue engineering: Current state and prospects, Annu. Rev. Med. 52 (2001) 443-451.
    • (2001) Annu. Rev. Med , vol.52 , pp. 443-451
    • Stock, U.A.1    Vacanti, J.P.2
  • 49
    • 0036192178 scopus 로고    scopus 로고
    • Proliferating cells versus differentiated cells in tissue engineering
    • R. Strehl, K. Schumacher, U. Vries and W. W. Minuth, Proliferating cells versus differentiated cells in tissue engineering, Tiss. Eng. 8 (2002) 37-42.
    • (2002) Tiss. Eng , vol.8 , pp. 37-42
    • Strehl, R.1    Schumacher, K.2    Vries, U.3    Minuth, W.W.4
  • 51
    • 0036304182 scopus 로고    scopus 로고
    • Intercellular adhesion and cancer invasion: A discrete simulation using the extended Potts model
    • S. Turner and J. A. Sherratt, Intercellular adhesion and cancer invasion: A discrete simulation using the extended Potts model, J. Theor. Biol. 216 (2002) 85-100.
    • (2002) J. Theor. Biol , vol.216 , pp. 85-100
    • Turner, S.1    Sherratt, J.A.2
  • 53
    • 0033859614 scopus 로고    scopus 로고
    • The science of tissue engineering
    • C. A. Vacanti and J. P. Vacanti, The science of tissue engineering, Orth. Clin. N. Am. 31 (2000) 351-355.
    • (2000) Orth. Clin. N. Am , vol.31 , pp. 351-355
    • Vacanti, C.A.1    Vacanti, J.P.2
  • 57
    • 33845414425 scopus 로고    scopus 로고
    • Tissue growth in a rotating bioreactor: Part I: Mechanical stability
    • S. L. Waters, L. J. Cummings, K. M. Shakesheff and F. Rose, Tissue growth in a rotating bioreactor: Part I: Mechanical stability, Math. Med. Biol. 23 (2006) 311-337.
    • (2006) Math. Med. Biol , vol.23 , pp. 311-337
    • Waters, S.L.1    Cummings, L.J.2    Shakesheff, K.M.3    Rose, F.4
  • 58
    • 34547816696 scopus 로고    scopus 로고
    • Tissue growth in a rotating bioreactor: Part II: Fluid flow and nutrient transport problems
    • S. L. Waters and L. J. Cummings, Tissue growth in a rotating bioreactor: Part II: Fluid flow and nutrient transport problems, Math. Med. Biol. (2007).
    • (2007) Math. Med. Biol
    • Waters, S.L.1    Cummings, L.J.2
  • 59
    • 0036910980 scopus 로고    scopus 로고
    • Modeling the dynamic composition of engineered cartilage
    • C. G. Wilson, L. J. Bonassar and S. S. Kohles, Modeling the dynamic composition of engineered cartilage, Arch. Biochem. Biophys. 408 (2002) 246-254.
    • (2002) Arch. Biochem. Biophys , vol.408 , pp. 246-254
    • Wilson, C.G.1    Bonassar, L.J.2    Kohles, S.S.3
  • 61
    • 0026204950 scopus 로고
    • Proliferation of anchorage-dependent contact-inhibited cells: 1. development of theoretical models based on cellular automata
    • K. Zygourakis, R. Bizios and P. Markenscoff, Proliferation of anchorage-dependent contact-inhibited cells: 1. development of theoretical models based on cellular automata, Biotech. Bioeng. 38 (1991) 459-470.
    • (1991) Biotech. Bioeng , vol.38 , pp. 459-470
    • Zygourakis, K.1    Bizios, R.2    Markenscoff, P.3


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.