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Volumn 203, Issue 1, 2005, Pages 191-220

Evolving interfaces via gradients of geometry-dependent interior Poisson problems: Application to tumor growth

Author keywords

Curvature discretization; Finite differences; Gaussian filter; Ghost fluid method; Interior Poisson problem; Level set method; Moving boundary problems; Second order accuracy; Tumor growth; Velocity extension

Indexed keywords

BOUNDARY CONDITIONS; CURVE FITTING; EVOLUTIONARY ALGORITHMS; IMAGE ENHANCEMENT; NUMERICAL METHODS; POISSON EQUATION;

EID: 10844239997     PISSN: 00219991     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jcp.2004.08.010     Document Type: Article
Times cited : (87)

References (38)
  • 1
    • 0002108952 scopus 로고    scopus 로고
    • The fast construction of extension velocities in level set methods
    • D. Adalsteinsson J.A. Sethian The fast construction of extension velocities in level set methods J. Comput. Phys. 148 1 1999 2-22
    • (1999) J. Comput. Phys. , vol.148 , Issue.1 , pp. 2-22
    • Adalsteinsson, D.1    Sethian, J.A.2
  • 2
    • 0008313578 scopus 로고    scopus 로고
    • General aspects of modeling tumor growth and immune response
    • J. Adam N. Bellomo (Eds.) Birkhauser Boston
    • J. Adam General aspects of modeling tumor growth and immune response in: J. Adam N. Bellomo (Eds.) A Survey of Models on Tumor Immune Systems Dynamics 1996 Birkhauser Boston 15-87
    • (1996) A Survey of Models on Tumor Immune Systems Dynamics , pp. 15-87
    • Adam, J.1
  • 3
    • 0030586186 scopus 로고    scopus 로고
    • Growth of necrotic tumors in the presence and absence of inhibitors
    • H.M. Byrne M.A.J. Chaplain Growth of necrotic tumors in the presence and absence of inhibitors Math. Biosci. 135 1996 187-216
    • (1996) Math. Biosci. , vol.135 , pp. 187-216
    • Byrne, H.M.1    Chaplain, M.A.J.2
  • 4
    • 0030431867 scopus 로고    scopus 로고
    • Modelling the role of cell-cell adhesion in the growth and development of carcinomas
    • H.M. Byrne M.A.J. Chaplain Modelling the role of cell-cell adhesion in the growth and development of carcinomas Math. Comput. Model. 24 1996 1-17
    • (1996) Math. Comput. Model. , vol.24 , pp. 1-17
    • Byrne, H.M.1    Chaplain, M.A.J.2
  • 6
    • 0002631224 scopus 로고    scopus 로고
    • A simple level set method for solving Stefan problems
    • S. Chen B. Merriman S. Osher P. Smereka A simple level set method for solving Stefan problems J. Comput. Phys. 135 1 1997 8-29
    • (1997) J. Comput. Phys. , vol.135 , Issue.1 , pp. 8-29
    • Chen, S.1    Merriman, B.2    Osher, S.3    Smereka, P.4
  • 7
  • 9
    • 0346837922 scopus 로고    scopus 로고
    • A non-oscillatory Eulerian approach to interfaces in multimaterial flows (the ghost fluid method)
    • R.P. Fedkiw T. Aslam B. Merriman S. Osher A non-oscillatory Eulerian approach to interfaces in multimaterial flows (the ghost fluid method) J. Comput. Phys. 152 2 1999 457-492
    • (1999) J. Comput. Phys. , vol.152 , Issue.2 , pp. 457-492
    • Fedkiw, R.P.1    Aslam, T.2    Merriman, B.3    Osher, S.4
  • 10
    • 9144233185 scopus 로고    scopus 로고
    • Diffusional instability as a mechanism for glioblastoma growth and invasion
    • (in preparation)
    • H. Frieboes, C.-H. Sun, B. Tromberg, V. Cristini, Diffusional instability as a mechanism for glioblastoma growth and invasion, 2004 (in preparation)
    • (2004)
    • Frieboes, H.1    Sun, C.-H.2    Tromberg, B.3    Cristini, V.4
  • 11
    • 10244220985 scopus 로고    scopus 로고
    • A fourth order accurate discretization for the Laplace and heat equations on arbitrary domains, with applications to the Stefan problem
    • in press
    • F. Gibou, R. Fedkiw, A fourth order accurate discretization for the Laplace and heat equations on arbitrary domains, with applications to the Stefan problem, J. Comput. Phys. 202 (2) (2005), in press
    • (2005) J. Comput. Phys. , vol.202 , Issue.2
    • Gibou, F.1    Fedkiw, R.2
  • 12
    • 0042164092 scopus 로고    scopus 로고
    • A level set approach for the numerical simulation of dendritic growth
    • F. Gibou R. Fedkiw R. Caflisch S. Osher A level set approach for the numerical simulation of dendritic growth J. Sci. Comput. 19 2003 183-199
    • (2003) J. Sci. Comput. , vol.19 , pp. 183-199
    • Gibou, F.1    Fedkiw, R.2    Caflisch, R.3    Osher, S.4
  • 13
    • 0037050814 scopus 로고    scopus 로고
    • A second order accurate symmetric discretization of the Poisson equation on irregular domains
    • F. Gibou R. Fedkiw L.T. Cheng M. Kang A second order accurate symmetric discretization of the Poisson equation on irregular domains J. Comput. Phys. 176 1 2002 205-227
    • (2002) J. Comput. Phys. , vol.176 , Issue.1 , pp. 205-227
    • Gibou, F.1    Fedkiw, R.2    Cheng, L.T.3    Kang, M.4
  • 14
    • 0019392895 scopus 로고
    • A numerical-method for 2 phase flow with an unstable interface
    • J. Glimm D. Marchesin O. McBryan A numerical-method for 2 phase flow with an unstable interface J. Comp. Phys. 39 1981 179-200
    • (1981) J. Comp. Phys. , vol.39 , pp. 179-200
    • Glimm, J.1    Marchesin, D.2    McBryan, O.3
  • 16
    • 0032345207 scopus 로고    scopus 로고
    • Total variation diminishing Runge-Kutta schemes
    • S. Gottlieb, C.W. Shu, Total variation diminishing Runge-Kutta schemes, Math. Comp. 67 (1998) 73-85
    • (1998) Math. Comp. , vol.67 , pp. 73-85
    • Gottlieb, S.1    Shu, C.W.2
  • 17
    • 0035273564 scopus 로고    scopus 로고
    • Strong stability-preserving high-order time discretization methods
    • S. Gottlieb C.W. Shu E. Tadmor Strong stability-preserving high-order time discretization methods SIAM Rev. 43 1 2001 89-112
    • (2001) SIAM Rev. , vol.43 , Issue.1 , pp. 89-112
    • Gottlieb, S.1    Shu, C.W.2    Tadmor, E.3
  • 18
    • 0034503787 scopus 로고    scopus 로고
    • Weighted ENO schemes for multi-dimensional Hamilton-Jacobi equations
    • G.S. Jiang D. Peng Weighted ENO schemes for multi-dimensional Hamilton-Jacobi equations SIAM J. Sci. Comput. 21 6 2000 2126-2143
    • (2000) SIAM J. Sci. Comput. , vol.21 , Issue.6 , pp. 2126-2143
    • Jiang, G.S.1    Peng, D.2
  • 19
    • 0030161771 scopus 로고    scopus 로고
    • Efficient implementation of weighted ENO schemes
    • G.S. Jiang C.W. Shu Efficient implementation of weighted ENO schemes J. Comput. Phys. 126 2 1996 202-228
    • (1996) J. Comput. Phys. , vol.126 , Issue.2 , pp. 202-228
    • Jiang, G.S.1    Shu, C.W.2
  • 21
    • 0001491689 scopus 로고    scopus 로고
    • A boundary condition capturing method for Poisson's equation on irregular domains
    • X.D. Liu R. Fedkiw M. Kang A boundary condition capturing method for Poisson's equation on irregular domains J. Comput. Phys. 160 1 2000 151-178
    • (2000) J. Comput. Phys. , vol.160 , Issue.1 , pp. 151-178
    • Liu, X.D.1    Fedkiw, R.2    Kang, M.3
  • 22
    • 10844232858 scopus 로고    scopus 로고
    • Numerical simulation of tumor growth and chemotherapy
    • M.S. Thesis, University of Minnesota School of Mathematics, September
    • P. Macklin, Numerical simulation of tumor growth and chemotherapy, M.S. Thesis, University of Minnesota School of Mathematics, September 2003
    • (2003)
    • Macklin, P.1
  • 23
    • 85190261945 scopus 로고    scopus 로고
    • Nonlinear simulations of tumor response to chemotherapy
    • (in preparation)
    • P. Macklin, J. Lowengrub, Nonlinear simulations of tumor response to chemotherapy, 2004 (in preparation)
    • (2004)
    • Macklin, P.1    Lowengrub, J.2
  • 25
    • 0030173610 scopus 로고    scopus 로고
    • A fast level set based algorithm for topology-independent shape modeling
    • R. Malladi J.A. Sethian B.C. Vemuri A fast level set based algorithm for topology-independent shape modeling J. Math. Imaging Vision 6 1996 269-289
    • (1996) J. Math. Imaging Vision , vol.6 , pp. 269-289
    • Malladi, R.1    Sethian, J.A.2    Vemuri, B.C.3
  • 27
    • 0017806209 scopus 로고
    • Apoptosis as a volume loss mechanism in mathematical models of solid tumor growth
    • D.L.S. McElwain L.E. Morris Apoptosis as a volume loss mechanism in mathematical models of solid tumor growth Math. Biosci. 39 1978 147-157
    • (1978) Math. Biosci. , vol.39 , pp. 147-157
    • McElwain, D.L.S.1    Morris, L.E.2
  • 28
    • 44749084234 scopus 로고
    • Fronts propagating with curvature-dependent speed: Algorithms based on Hamilton-Jacobi formulations
    • S. Osher J.A. Sethian Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations J. Comput. Phys. 79 1988 12-49
    • (1988) J. Comput. Phys. , vol.79 , pp. 12-49
    • Osher, S.1    Sethian, J.A.2
  • 33
    • 85190265517 scopus 로고    scopus 로고
    • Department of Pharmacology, University of Minnesota, Personal Communication
    • S. Ramakrishnan, Department of Pharmacology, University of Minnesota, Personal Communication
    • Ramakrishnan, S.1
  • 35
    • 0033279022 scopus 로고    scopus 로고
    • An efficient, interface preserving level set re-distancing algorithm and its application to interfacial incompressible fluid flow
    • M. Sussman E. Fatemi An efficient, interface preserving level set re-distancing algorithm and its application to interfacial incompressible fluid flow SIAM J. Sci. Comput. 20 4 1999 1165-1191
    • (1999) SIAM J. Sci. Comput. , vol.20 , Issue.4 , pp. 1165-1191
    • Sussman, M.1    Fatemi, E.2
  • 36
    • 0032100281 scopus 로고    scopus 로고
    • An improved level set method for incompressible two-phase flows
    • M. Sussman E. Fatemi P. Smereka S. Osher An improved level set method for incompressible two-phase flows Comput. Fluids 27 5-6 1998 663-680
    • (1998) Comput. Fluids , vol.27 , Issue.5-6 , pp. 663-680
    • Sussman, M.1    Fatemi, E.2    Smereka, P.3    Osher, S.4
  • 38
    • 85190289678 scopus 로고    scopus 로고
    • Nonlinear simulation of tumor necrosis, neo-vascularization and tissue invation via an adaptive finite-element/level-set method
    • (in press)
    • X. Zheng, S.M. Wise, V. Cristini, Nonlinear simulation of tumor necrosis, neo-vascularization and tissue invation via an adaptive finite-element/level-set method, B. Math. Biol. (in press)
    • B. Math. Biol.
    • Zheng, X.1    Wise, S.M.2    Cristini, V.3


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.