메뉴 건너뛰기




Volumn 38, Issue 7, 2010, Pages 2331-2345

Adaptive macro finite elements for the numerical solution of monodomain equations in cardiac electrophysiology

Author keywords

Cardiac modeling; Efficient numerical schemes; Macro finite elements; Monodomain equation; Pseudo adaptive meshes; Reaction diffusion equations

Indexed keywords

ADAPTIVE MESHES; CARDIAC MODELING; EFFICIENT NUMERICAL SCHEMES; FINITE ELEMENT; MONODOMAIN EQUATIONS; REACTION DIFFUSION EQUATIONS;

EID: 77954635297     PISSN: 00906964     EISSN: 15739686     Source Type: Journal    
DOI: 10.1007/s10439-010-9997-2     Document Type: Article
Times cited : (113)

References (42)
  • 1
    • 0000157466 scopus 로고    scopus 로고
    • A simple two-variable model of cardiac excitation
    • Aliev, R., and A. Panfilov. A simple two-variable model of cardiac excitation. Chaos Solitons Fractals 7:293-301,1996.
    • (1996) Chaos Solitons Fractals , vol.7 , pp. 293-301
    • Aliev, R.1    Panfilov, A.2
  • 2
    • 20344393858 scopus 로고    scopus 로고
    • A fourth-order accurate localrefinement method for Poisson's equation
    • Barad, M., and P. Colella. A fourth-order accurate localrefinement method for Poisson's equation. J. Comput. Phys. 209:1-18, 2005.
    • (2005) J. Comput. Phys. , vol.209 , pp. 1-18
    • Barad, M.1    Colella, P.2
  • 3
    • 77951132683 scopus 로고    scopus 로고
    • A multiresolutionspace-time adaptive scheme for the bidomain model in electrocardiology
    • doi:10.1002/num.20495
    • Bendahmane, M., R. Bürguer, and R. Ruiz-Baier. A multiresolutionspace-time adaptive scheme for the bidomain model in electrocardiology. Numer. Methods Partial Differ. Equ. 2010. doi:10.1002/num.20495.
    • (2010) Numer. Methods Partial Differ. Equ.
    • Bendahmane, M.1    Bürguer, R.2    Ruiz-Baier, R.3
  • 6
    • 17544388260 scopus 로고    scopus 로고
    • Abstract space-time adaptive method for simulating complex cardiac dynamics
    • Cherry, E. M., H. S. Greenside, and C. S. Henriquez. Abstract space-time adaptive method for simulating complex cardiac dynamics. Phys. Rev. Lett. 84:1343-1346, 2000.
    • (2000) Phys. Rev. Lett. , vol.84 , pp. 1343-1346
    • Cherry, E.M.1    Greenside, H.S.2    Henriquez, C.S.3
  • 7
    • 0141678056 scopus 로고    scopus 로고
    • Efficient simulation of three-dimensional anisotropic cardiac tissue using an adaptive mesh refinement method
    • Cherry, E. M., H. S. Greenside, and C. S. Henriquez.Efficient simulation of three-dimensional anisotropic cardiac tissue using an adaptive mesh refinement method. Chaos. 13(3):853-865, 2003.
    • (2003) Chaos. , vol.13 , Issue.3 , pp. 853-865
    • Cherry, E.M.1    Greenside, H.S.2    Henriquez, C.S.3
  • 8
  • 9
    • 7244242182 scopus 로고    scopus 로고
    • A parallel solver forreaction-diffusion systems in computational electrocardiology
    • Colli-Franzone, P., and L. Pavarino. A parallel solver forreaction-diffusion systems in computational electrocardiology. Math. Models Methods Appl. Sci. 14(6):883-911, 2004.
    • (2004) Math. Models Methods Appl. Sci. , vol.14 , Issue.6 , pp. 883-911
    • Colli-Franzone, P.1    Pavarino, L.2
  • 10
    • 0034026881 scopus 로고    scopus 로고
    • Action potential andcontractility changes in [Na(+)](i) overloaded cardiac myocytes: A simulation study
    • Faber, G. M., and Y. Rudy. Action potential andcontractility changes in [Na(+)](i) overloaded cardiac myocytes: a simulation study. Biophys. J. 78(5):2392-2404, 2000.
    • (2000) Biophys. J. , vol.78 , Issue.5 , pp. 2392-2404
    • Faber, G.M.1    Rudy, Y.2
  • 11
    • 18744390206 scopus 로고    scopus 로고
    • Boulder: Department of Aerospace Engineering Sciences University of Colorado at Boulder
    • Felippa, C. Introduction to Finite Element Methods. Boulder: Department of Aerospace Engineering Sciences, University of Colorado at Boulder, 2007.
    • (2007) Introduction to Finite Element Methods
    • Felippa, C.1
  • 12
    • 17744397787 scopus 로고    scopus 로고
    • Modelling wave propagation in realistic heart geometries using the phase-field method
    • Fenton, F., E. Cherry, A. Karma, and W. Rappel. Modelling wave propagation in realistic heart geometries using the phase-field method. Chaos 15:1-11, 2005.
    • (2005) Chaos , vol.15 , pp. 1-11
    • Fenton, F.1    Cherry, E.2    Karma, A.3    Rappel, W.4
  • 13
    • 12144289223 scopus 로고    scopus 로고
    • Electrical activity and reentry during acute regional myocardial ischemia: Insights from simulations
    • Ferrero, J. M., B. Trenor, B. Rodriguez, and J. Saiz. Electrical activity and reentry during acute regional myocardial ischemia: insights from simulations. Int. J. Bifurcat. Chaos. 13:3703-3715, 2003.
    • (2003) Int. J. Bifurcat. Chaos. , vol.13 , pp. 3703-3715
    • Ferrero, J.M.1    Trenor, B.2    Rodriguez, B.3    Saiz, J.4
  • 15
    • 0021076732 scopus 로고
    • A bidomain modelfor anisotropic cardiac muscle
    • Geselowitz, D. B., and W. T. Miller III. A bidomain modelfor anisotropic cardiac muscle. Ann. Biomed. Eng. 11:315-334, 1983.
    • (1983) Ann. Biomed. Eng. , vol.11 , pp. 315-334
    • Geselowitz, D.B.1    Miller Iii, W.T.2
  • 16
    • 41249085020 scopus 로고    scopus 로고
    • Fourth order compact schemes with adaptive time step for monodomain reaction difusion equations
    • Heidenreich, E. A., J. F. Rodriguez, F. J. Gaspar, and M. Doblare. Fourth order compact schemes with adaptive time step for monodomain reaction difusion equations. J. Comput. Appl. Math. 21:39-55, 2008.
    • (2008) J. Comput. Appl. Math. , vol.21 , pp. 39-55
    • Heidenreich, E.A.1    Rodriguez, J.F.2    Gaspar, F.J.3    Doblare, M.4
  • 18
    • 0027447573 scopus 로고
    • Simulating the electrical behavior of cardiactissue using the bidomain model
    • Henriquez, C. S. Simulating the electrical behavior of cardiactissue using the bidomain model. Crit. Rev. Bioeng. 21:1-77, 1993.
    • (1993) Crit. Rev. Bioeng. , vol.21 , pp. 1-77
    • Henriquez, C.S.1
  • 19
    • 33750471607 scopus 로고    scopus 로고
    • The use of 2d enriched elements with bubble functions for finite element analysis
    • Ho, S. P., and Y. L. Yeh. The use of 2d enriched elements with bubble functions for finite element analysis. Comput. Struct. 84(29-30):2081-2091, 2006.
    • (2006) Comput. Struct. , vol.84 , Issue.29-30 , pp. 2081-2091
    • Ho, S.P.1    Yeh, Y.L.2
  • 22
    • 0004212171 scopus 로고    scopus 로고
    • Philadelphia, USA:Lippincott Williams and Wilkins
    • Katz, A. Physiology of the Heart. Philadelphia, USA:Lippincott Williams and Wilkins, 718 pp., 2001.
    • (2001) Physiology of the Heart
    • Katz, A.1
  • 25
    • 0005181403 scopus 로고    scopus 로고
    • Modeling impulse propagation and extracellular potential distributions in anisotropic cardiac tissue using a finite volume discretization
    • Penland, R. C., D.M.Harrild, and C. S. Heniquez. Modeling impulse propagation and extracellular potential distributions in anisotropic cardiac tissue using a finite volume discretization. Comput. Visualizat. Sci. 4:215-226, 2000.
    • (2000) Comput. Visualizat. Sci. , vol.4 , pp. 215-226
    • Penland, R.C.1    Harrild, D.M.2    Heniquez, C.S.3
  • 26
    • 0032845277 scopus 로고    scopus 로고
    • An advanced algorithm forsolving partial differential equations in cardiac conduction
    • Qu, Z., and A. Garfinkel. An advanced algorithm forsolving partial differential equations in cardiac conduction. IEEE Trans. Biomed. Eng. 46: 1166-1168, 1999.
    • (1999) IEEE Trans. Biomed. Eng. , vol.46 , pp. 1166-1168
    • Qu, Z.1    Garfinkel, A.2
  • 28
    • 0028483993 scopus 로고
    • A collocation-Galerkin finite element model of cardiac action potential propagation
    • Rogers, J. M., and A. D. McCulloch. A collocation-Galerkin finite element model of cardiac action potential propagation. IEEE Trans. Biomed. Eng. 41:743-757, 1994.
    • (1994) IEEE Trans. Biomed. Eng. , vol.41 , pp. 743-757
    • Rogers, J.M.1    McCulloch, A.D.2
  • 29
    • 39749191084 scopus 로고    scopus 로고
    • Heart disease and stroke statistics-2008
    • Rosamond, W., et al. Heart disease and stroke statistics-2008. Circulation 117:e25-e146, 2008.
    • (2008) Circulation , vol.117
    • Rosamond, W.1
  • 30
    • 0033926678 scopus 로고    scopus 로고
    • A numerical efficient method for simulation of defibrillation in an active bidomain sheet of myocardium
    • Skouibine, K., N. Trayanova, and P. Moore. A numerical efficient method for simulation of defibrillation in an active bidomain sheet of myocardium. Math. Biosci. 116:85-100, 2000.
    • (2000) Math. Biosci. , vol.116 , pp. 85-100
    • Skouibine, K.1    Trayanova, N.2    Moore, P.3
  • 31
    • 0035499484 scopus 로고    scopus 로고
    • Extension of high-order compact schemes to time-dependent problems
    • Spotz, W. F., and G. F. Carey. Extension of high-order compact schemes to time-dependent problems. Numer. Methods Partial. Differ. Eq. 17:657-672, 2001.
    • (2001) Numer. Methods Partial. Differ. Eq. , vol.17 , pp. 657-672
    • Spotz, W.F.1    Carey, G.F.2
  • 32
    • 0001518684 scopus 로고
    • On the construction and comparison of difference schemes
    • Strang G. On the construction and comparison of difference schemes. SIAM J. Numer. Anal. 5(3):506-517, 1968.
    • (1968) SIAM J. Numer. Anal. , vol.5 , Issue.3 , pp. 506-517
    • Strang, G.1
  • 33
    • 33746038887 scopus 로고    scopus 로고
    • On the computational complexity of the bidomain and the monodomain models of electrophysiology
    • Sundnes, J., B. F. Nielsen, K. A. Mardal, X. Cai, G. T. Lines, and A. Tveito. On the computational complexity of the bidomain and the monodomain models of electrophysiology. Ann. Biomed. Eng. 34:1088-1097, 2006.
    • (2006) Ann. Biomed. Eng. , vol.34 , pp. 1088-1097
    • Sundnes, J.1    Nielsen, B.F.2    Mardal, K.A.3    Cai, X.4    Lines, G.T.5    Tveito, A.6
  • 34
  • 37
    • 2442572165 scopus 로고    scopus 로고
    • Operator splitting andadaptive mesh refinement for the Luo-Rudy i model
    • Trangenstein, J. A., and C. H. Kim. Operator splitting andadaptive mesh refinement for the Luo-Rudy I model. J. Comput. Phys. 196:645-679, 2004.
    • (2004) J. Comput. Phys. , vol.196 , pp. 645-679
    • Trangenstein, J.A.1    Kim, C.H.2
  • 38
    • 34047149139 scopus 로고    scopus 로고
    • Computer simulations of cardiac defibrillation: A look inside the heart
    • Trayanova, N., J. Eason, and F. Aguel. Computer simulations of cardiac defibrillation: a look inside the heart. Comput. Vis. Sci. 4:259-270, 2002.
    • (2002) Comput. Vis. Sci. , vol.4 , pp. 259-270
    • Trayanova, N.1    Eason, J.2    Aguel, F.3
  • 39
    • 35248866317 scopus 로고    scopus 로고
    • Physiology driven adaptivity for the numerical solution of the bidomain equations
    • Whiteley, J. P. Physiology driven adaptivity for the numerical solution of the bidomain equations. Ann. Biomed. Eng. 35(9):1510-1520, 2007.
    • (2007) Ann. Biomed. Eng. , vol.35 , Issue.9 , pp. 1510-1520
    • Whiteley, J.P.1
  • 40
    • 49049105450 scopus 로고    scopus 로고
    • An efficient technique for the numerical solution of the bidomain equations
    • Whiteley, J. An efficient technique for the numerical solution of the bidomain equations. Ann. Biomed. Eng. 36(8):1398-1408, 2008.
    • (2008) Ann. Biomed. Eng. , vol.36 , Issue.8 , pp. 1398-1408
    • Whiteley, J.1
  • 41
    • 84985376290 scopus 로고
    • The static condensation algorithm
    • Wilson, E. L. The static condensation algorithm. Int. J.Numer. Methods Eng. 8(1):198-203, 1974.
    • (1974) Int. J.Numer. Methods Eng. , vol.8 , Issue.1 , pp. 198-203
    • Wilson, E.L.1
  • 42
    • 0003453202 scopus 로고    scopus 로고
    • Butterworth-Heinemann, Burlington, MA: Elsevier
    • Zienkiewicz, O. C., and R. L. Taylor. Finite Element Method, Vol.1. Butterworth-Heinemann, Burlington, MA: Elsevier, 752 pp., 2005.
    • (2005) Finite Element Method , vol.1
    • Zienkiewicz, O.C.1    Taylor, R.L.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.