메뉴 건너뛰기




Volumn 23, Issue 2, 2007, Pages 251-264

Reconstructing parameters of the FitzHugh-Nagumo system from boundary potential measurements

Author keywords

Electrocardiology; FitzHugh Nagumo model; Inverse problems; KKTsystem; Newton Krylov method; Parameter identification; PDE constrained optimization

Indexed keywords

CONSTRAINED OPTIMIZATION; INVERSE PROBLEMS; NUMERICAL METHODS; PARAMETER ESTIMATION;

EID: 34548243980     PISSN: 09295313     EISSN: None     Source Type: Journal    
DOI: 10.1007/s10827-007-0035-9     Document Type: Article
Times cited : (21)

References (61)
  • 1
    • 34548231957 scopus 로고    scopus 로고
    • Multiscale Newton-Krylov Methods for inverse acoustic wave propagation
    • Ph.D. thesis, Carnegie Mellon University, Pittsburgh, Pennsylvania
    • Akcelik, V. (2002). Multiscale Newton-Krylov Methods for inverse acoustic wave propagation. Ph.D. thesis, Carnegie Mellon University, Pittsburgh, Pennsylvania.
    • (2002)
    • Akcelik, V.1
  • 3
    • 0034616964 scopus 로고    scopus 로고
    • Head-on collisions of waves in an excitable FitzHugh-Nagumo system: A transition from wave annihilation to classical wave behavior
    • Argentina, M., Coullet, P., & Krinsky, V. (2000). Head-on collisions of waves in an excitable FitzHugh-Nagumo system: A transition from wave annihilation to classical wave behavior. Journal of Theoretical Biology, 205, 47-52.
    • (2000) Journal of Theoretical Biology , vol.205 , pp. 47-52
    • Argentina, M.1    Coullet, P.2    Krinsky, V.3
  • 6
    • 34548259620 scopus 로고    scopus 로고
    • Multilevel algorithms for large-scale Interior point methods in bound constrained optimization
    • Technical Report TR-2006-002-A, Department of Mathematics and Computer Science, Emory University. 16p
    • Benzi, M., Haber, E., & Hanson, L. (2006). Multilevel algorithms for large-scale interior point methods in bound constrained optimization. Technical Report TR-2006-002-A, Department of Mathematics and Computer Science, Emory University. 16p.
    • (2006)
    • Benzi, M.1    Haber, E.2    Hanson, L.3
  • 7
    • 0037035845 scopus 로고    scopus 로고
    • Modified ionic models of cardiac tissue for efficient large scale computations
    • Bernus, O., Verschelde, H., & Panfilov, A. V. (2002). Modified ionic models of cardiac tissue for efficient large scale computations. Physics in Medicine and Biology, 47, 1947-1959.
    • (2002) Physics in Medicine and Biology , vol.47 , pp. 1947-1959
    • Bernus, O.1    Verschelde, H.2    Panfilov, A.V.3
  • 8
    • 2942631643 scopus 로고    scopus 로고
    • Large-scale PDE-constrained optimization
    • Biegler L. Ghattas O. Heinkenschloss M. Bloemen-Waanders B. v. (Eds.) In Berlin: Springer-Verlag
    • Biegler, L., Ghattas, O., Heinkenschloss, M., & Bloemen-Waanders, B. v. (Eds.) (2003). Large-scale PDE-constrained optimization. In Lecture Notes in Computational Science and Engineering. Berlin: Springer-Verlag.
    • (2003) Lecture Notes in Computational Science and Engineering
  • 9
    • 33644934079 scopus 로고    scopus 로고
    • Parallel Lagrange-Newton-Krylov-Schur methods for PDE-constrained optimization. Part I: The Krylov-Schur solver
    • Biros, G., & Ghattas, O. (2005a). Parallel Lagrange-Newton-Krylov-Schur methods for PDE-constrained optimization. Part I: The Krylov-Schur solver. SIAM Journal on Scientific Computing, 27, 687-713.
    • (2005) SIAM Journal on Scientific Computing , vol.27 , pp. 687-713
    • Biros, G.1    Ghattas, O.2
  • 10
    • 33644965417 scopus 로고    scopus 로고
    • Parallel Lagrange-Newton-Krylov-Schur methods for PDE-constrained optimization. Part II: The Lagrange-Newton solver and its application to optimal control of steady viscous flows
    • Biros, G., & Ghattas, O. (2005b). Parallel Lagrange-Newton-Krylov-Schur methods for PDE-constrained optimization. Part II: The Lagrange-Newton solver and its application to optimal control of steady viscous flows. SIAM Journal on Scientific Computing, 27, 714-739.
    • (2005) SIAM Journal on Scientific Computing , vol.27 , pp. 714-739
    • Biros, G.1    Ghattas, O.2
  • 12
    • 0037017199 scopus 로고    scopus 로고
    • Spiral wave generation in heterogeneous excitable media
    • Bub, G., Shrier, A., & Glass, L. (2002). Spiral wave generation in heterogeneous excitable media. Physical Review Letters, 88, 058101.
    • (2002) Physical Review Letters , vol.88 , pp. 058101
    • Bub, G.1    Shrier, A.2    Glass, L.3
  • 13
    • 33746145553 scopus 로고    scopus 로고
    • Periodicity and uniqueness of global minimizers of an energy functional containing a long-range interaction
    • Chen, X., & Oshita, Y. (2006). Periodicity and uniqueness of global minimizers of an energy functional containing a long-range interaction. SIAM Journal on Mathematical Analysis, 37, 1299-1332.
    • (2006) SIAM Journal on Mathematical Analysis , vol.37 , pp. 1299-1332
    • Chen, X.1    Oshita, Y.2
  • 14
    • 0037281306 scopus 로고    scopus 로고
    • Comparison of potential- and activation-based formulations for the inverse problem of electrocardiology
    • Cheng, L. K., Bodley, J. M., & Pullan, A. J. (2003). Comparison of potential- and activation-based formulations for the inverse problem of electrocardiology. IEEE Transactions on Biomedical Engineering, 50, 11-22.
    • (2003) IEEE Transactions on Biomedical Engineering , vol.50 , pp. 11-22
    • Cheng, L.K.1    Bodley, J.M.2    Pullan, A.J.3
  • 16
    • 0000292491 scopus 로고
    • Stable 3-dimensional action-potential circulation in the FitzHugh-Nagumo model
    • Courtemanche, M., Skaggs, W., & Winfree, A. T. (1990). Stable 3-dimensional action-potential circulation in the FitzHugh-Nagumo model. Physica D, 41, 173-182.
    • (1990) Physica D , vol.41 , pp. 173-182
    • Courtemanche, M.1    Skaggs, W.2    Winfree, A.T.3
  • 17
    • 33745618422 scopus 로고    scopus 로고
    • An adjoint method for channel localization
    • Cox, S. J. (2006). An adjoint method for channel localization. Mathematical Medicine and Biology, 23, 139-152.
    • (2006) Mathematical Medicine and Biology , vol.23 , pp. 139-152
    • Cox, S.J.1
  • 18
    • 0035687005 scopus 로고    scopus 로고
    • Recovering quasi-active properties of dendritic neurons from dual potential recordings
    • Cox, S. J., & Griffith, B. E. (2001). Recovering quasi-active properties of dendritic neurons from dual potential recordings. Journal of Computational Neuroscience, 11, 95-110.
    • (2001) Journal of Computational Neuroscience , vol.11 , pp. 95-110
    • Cox, S.J.1    Griffith, B.E.2
  • 19
    • 0034845037 scopus 로고    scopus 로고
    • Discerning ionic currents and their kinetics from input impedance data
    • Cox S. J., & Ji, L. (2003) Discerning ionic currents and their kinetics from input impedance data. Bulletin of Mathematical Biology, 63, 909-932.
    • (2003) Bulletin of Mathematical Biology , vol.63 , pp. 909-932
    • Cox, S.J.1    Ji, L.2
  • 20
    • 6344280486 scopus 로고    scopus 로고
    • Lateral overdetermination of the FitzHugh-Nagumo system
    • Cox, S. J., & Wagner, A. (2004). Lateral overdetermination of the FitzHugh-Nagumo system. Inverse Problems, 20, 1639-1647.
    • (2004) Inverse Problems , vol.20 , pp. 1639-1647
    • Cox, S.J.1    Wagner, A.2
  • 21
    • 33344474187 scopus 로고    scopus 로고
    • Standing waves in the FitzHugh-Nagumo model of cardiac electrical activity
    • Dauby, P. C., Desaive, T., & Croisier, H. (2006). Standing waves in the FitzHugh-Nagumo model of cardiac electrical activity. Physical Review E, 73, 021908.
    • (2006) Physical Review E , vol.73 , pp. 021908
    • Dauby, P.C.1    Desaive, T.2    Croisier, H.3
  • 22
    • 0026507547 scopus 로고
    • Stationary and drifting spiral waves of excitation in isolated cardiac-muscle
    • Davidenko, J. M., Pertsov, A. V., Salomonsz, R., Baxter, W., & Jalefe, J. (1992). Stationary and drifting spiral waves of excitation in isolated cardiac-muscle. Nature, 355, 349-351.
    • (1992) Nature , vol.355 , pp. 349-351
    • Davidenko, J.M.1    Pertsov, A.V.2    Salomonsz, R.3    Baxter, W.4    Jalefe, J.5
  • 23
    • 0003315567 scopus 로고    scopus 로고
    • Numerical methods for unconstrained optimization and nonlinear equations
    • In Philadelphia: SIAM
    • Dennis, Jr J. E., & Schnabel, R. B. (1996). Numerical methods for unconstrained optimization and nonlinear equations. In Classics in Applied Mathematics. Philadelphia: SIAM.
    • (1996) Classics in Applied Mathematics
    • Dennis Jr., J.E.1    Schnabel, R.B.2
  • 24
  • 27
    • 53349102813 scopus 로고
    • Impulses and physiological states in theoretical models of nerve membrane
    • FitzHugh, R. (1961). Impulses and physiological states in theoretical models of nerve membrane. Biophysical Journal, 1, 445-466.
    • (1961) Biophysical Journal , vol.1 , pp. 445-466
    • FitzHugh, R.1
  • 28
    • 26444455786 scopus 로고    scopus 로고
    • Simulating patterns of excitation, repolarization and action potential duration with cardiac bidomain and monodomain models
    • Franzone, P. C., Pavarino, L. F., & Taccardi, B. (2005). Simulating patterns of excitation, repolarization and action potential duration with cardiac bidomain and monodomain models. Mathematical Biosciences, 197, 35-66.
    • (2005) Mathematical Biosciences , vol.197 , pp. 35-66
    • Franzone, P.C.1    Pavarino, L.F.2    Taccardi, B.3
  • 29
    • 2542500467 scopus 로고    scopus 로고
    • Existence of wavefronts and impulses to FitzHugh-Nagumo equations
    • Gao, W., & Wang, J. (2004). Existence of wavefronts and impulses to FitzHugh-Nagumo equations. Nonlinear Analysis, 57, 667-676.
    • (2004) Nonlinear Analysis , vol.57 , pp. 667-676
    • Gao, W.1    Wang, J.2
  • 30
    • 0000183429 scopus 로고    scopus 로고
    • On optimization techniques for solving nonlinear inverse problems
    • Haber, E., Ascher, U., & Oldenburg, D. (2000). On optimization techniques for solving nonlinear inverse problems. Inverse Problems, 16, 1263-1280.
    • (2000) Inverse Problems , vol.16 , pp. 1263-1280
    • Haber, E.1    Ascher, U.2    Oldenburg, D.3
  • 31
    • 0001632418 scopus 로고
    • The use of L-curve in the regularization of discrete ill-posed problems
    • Hansen, P. C., & O'Leary, D. P. (1993). The use of L-curve in the regularization of discrete ill-posed problems. SIAM Journal on Scientific Computing, 14, 1487-1503.
    • (1993) SIAM Journal on Scientific Computing , vol.14 , pp. 1487-1503
    • Hansen, P.C.1    O'Leary, D.P.2
  • 32
    • 0030855840 scopus 로고    scopus 로고
    • + Channel regulation of signal propagation in dendrites of hippocampal pyramidal neurons
    • + Channel regulation of signal propagation in dendrites of hippocampal pyramidal neurons. Nature, 387, 869-875.
    • (1997) Nature , vol.387 , pp. 869-875
    • Hoffman, D.A.1    Magee, J.C.2    Colbert, C.M.3    Johnston, D.4
  • 34
    • 0348198275 scopus 로고    scopus 로고
    • Jacobian-free Newton-Krylov methods: A survey of approaches and applications
    • Knoll, D. A., & Keyes, D. E. (2004). Jacobian-free Newton-Krylov methods: A survey of approaches and applications. Journal of Comparative Physiology, 193, 357-397.
    • (2004) Journal of Comparative Physiology , vol.193 , pp. 357-397
    • Knoll, D.A.1    Keyes, D.E.2
  • 38
    • 10044241890 scopus 로고    scopus 로고
    • A fully implicit parallel algorithm for simulating the non-linear electrical activity of the heart
    • Murillo, M., & Cai, X.-C. (2004). A fully implicit parallel algorithm for simulating the non-linear electrical activity of the heart. Numerical Linear Algebra with Applications, 11, 261-277.
    • (2004) Numerical Linear Algebra With Applications , vol.11 , pp. 261-277
    • Murillo, M.1    Cai, X.-C.2
  • 41
    • 3042538112 scopus 로고    scopus 로고
    • Stability of traveling multiple-front (multiple-back) wave solutions of the FitzHugh-Nagumo equations
    • Nii, S. (1997). Stability of traveling multiple-front (multiple-back) wave solutions of the FitzHugh-Nagumo equations. SIAM Journal on Mathematical Analysis, 28, 1094-1112.
    • (1997) SIAM Journal on Mathematical Analysis , vol.28 , pp. 1094-1112
    • Nii, S.1
  • 43
    • 28844445663 scopus 로고    scopus 로고
    • Approximate solution to the bidomain equations for electrocardiogram problems
    • Patel, S. G., & Roth, B. J. (2005). Approximate solution to the bidomain equations for electrocardiogram problems. Physical Review E, 72, 051931.
    • (2005) Physical Review E , vol.72 , pp. 051931
    • Patel, S.G.1    Roth, B.J.2
  • 46
    • 10044239256 scopus 로고    scopus 로고
    • On global existence for semilinear parabolic systems
    • Petersson, J. H. (2005). On global existence for semilinear parabolic systems. Nonlinear Analysis, 60, 337-347.
    • (2005) Nonlinear Analysis , vol.60 , pp. 337-347
    • Petersson, J.H.1
  • 47
    • 0033617107 scopus 로고    scopus 로고
    • Electrical restitution and spatiotemporal organization during ventricular fibrillation
    • Riccio, M. L., Koller, M. L., & Gilmour, P. F. (1999). Electrical restitution and spatiotemporal organization during ventricular fibrillation. Circulation Research, 84, 955- 963.
    • (1999) Circulation Research , vol.84 , pp. 955-963
    • Riccio, M.L.1    Koller, M.L.2    Gilmour, P.F.3
  • 48
    • 4444265502 scopus 로고    scopus 로고
    • Art Winfree and the bidomain model of cardiac tissue
    • Roth, B. J. (2004). Art Winfree and the bidomain model of cardiac tissue. Journal of Theoretical Biology, 230, 445-449.
    • (2004) Journal of Theoretical Biology , vol.230 , pp. 445-449
    • Roth, B.J.1
  • 50
    • 35949037602 scopus 로고
    • The electrophysics of a nerve fiber
    • Scott, A. C. (1975). The electrophysics of a nerve fiber. Reviews of Modern Physics, 47, 487-533.
    • (1975) Reviews of Modern Physics , vol.47 , pp. 487-533
    • Scott, A.C.1
  • 51
    • 0028233213 scopus 로고
    • Forward and inverse problem of electrocardiography: Modeling and recovery of epicardial potentials in humans
    • Shahidi, V., Savard, P., & Nadeau, R. (1994). Forward and inverse problem of electrocardiography: Modeling and recovery of epicardial potentials in humans. IEEE Transactions on Biomedical Engineering, 41, 249-256.
    • (1994) IEEE Transactions on Biomedical Engineering , vol.41 , pp. 249-256
    • Shahidi, V.1    Savard, P.2    Nadeau, R.3
  • 52
    • 0032141593 scopus 로고    scopus 로고
    • Traveling waves in buffered systems: Applications to calcium waves
    • Sneyd, J., Dale, P. D., & Duffy, A. (1998). Traveling waves in buffered systems: Applications to calcium waves. SIAM Journal on Applied Mathematics, 58, 1178-1192.
    • (1998) SIAM Journal on Applied Mathematics , vol.58 , pp. 1178-1192
    • Sneyd, J.1    Dale, P.D.2    Duffy, A.3
  • 53
    • 84891949264 scopus 로고    scopus 로고
    • Comparison of asymptotics of heart and nerve excitability
    • Suckley, R., & Biktashev, V. N. (2003). Comparison of asymptotics of heart and nerve excitability. Physical Review E, 68, 011902.
    • (2003) Physical Review E , vol.68 , pp. 011902
    • Suckley, R.1    Biktashev, V.N.2
  • 54
    • 33644603823 scopus 로고    scopus 로고
    • Existence and stability of traveling waves in buffered systems
    • Tsai, J.-C., & Sneyd, J. (2005). Existence and stability of traveling waves in buffered systems. SIAM Journal on Applied Mathematics, 66, 237-265.
    • (2005) SIAM Journal on Applied Mathematics , vol.66 , pp. 237-265
    • Tsai, J.-C.1    Sneyd, J.2
  • 55
    • 0032875742 scopus 로고    scopus 로고
    • A comparative survey of automated parameter-search methods for compartmental neural models
    • Vanier, M. C., & Bower, J.-M. (1999). A comparative survey of automated parameter-search methods for compartmental neural models. Journal of Computational Neuroscience, 7, 149-171.
    • (1999) Journal of Computational Neuroscience , vol.7 , pp. 149-171
    • Vanier, M.C.1    Bower, J.-M.2
  • 56
    • 0001041472 scopus 로고    scopus 로고
    • Non-convergence of the L-curve regularization parameter selection method
    • Vogel, C. R. (1996). Non-convergence of the L-curve regularization parameter selection method. Inverse Problems, 12, 535-547.
    • (1996) Inverse Problems , vol.12 , pp. 535-547
    • Vogel, C.R.1
  • 57
    • 4043182719 scopus 로고    scopus 로고
    • Computational methods for inverse problems
    • In Philadelphia: SIAM
    • Vogel, C. R. (2002). Computational methods for inverse problems. In Frontiers in applied mathematics. Philadelphia: SIAM.
    • (2002) Frontiers in Applied Mathematics
    • Vogel, C.R.1
  • 58
    • 0033151558 scopus 로고    scopus 로고
    • Chaos and the transition to ventricular fibrillation - A new approach to antiarrhythmic drug evaluation
    • Weiss, J. N., Garfinkel, A., Karagueuzian, H. S., Qu, Z., & Chen, P. S. (1999). Chaos and the transition to ventricular fibrillation - A new approach to antiarrhythmic drug evaluation. Circulation, 99, 2819-2826.
    • (1999) Circulation , vol.99 , pp. 2819-2826
    • Weiss, J.N.1    Garfinkel, A.2    Karagueuzian, H.S.3    Qu, Z.4    Chen, P.S.5
  • 60
    • 0002564681 scopus 로고
    • Stable particle-like solutions to the nonlinear-wave equations of 3-dimensional excitable media
    • Winfree, A. T. (1990). Stable particle-like solutions to the nonlinear-wave equations of 3-dimensional excitable media. SIAM Review, 32, 1-53.
    • (1990) SIAM Review , vol.32 , pp. 1-53
    • Winfree, A.T.1
  • 61
    • 0012719476 scopus 로고
    • Interaction of pulses in dissipative systems. FitzHugh-Nagumo equations
    • Yamada, H., & Nozaki, K. (1990). Interaction of pulses in dissipative systems. FitzHugh-Nagumo equations. Progress of Theoretical Physics, 84, 801-809.
    • (1990) Progress of Theoretical Physics , vol.84 , pp. 801-809
    • Yamada, H.1    Nozaki, K.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.