Akcelik V. (2002). Multiscale Newton-Krylov Methods for inverse acoustic wave propagation PhD Thesis Carnegie Mellon University.
Akcelik V et al. (2006). Parallel algorithms for PDE-constrained optimization Frontiers of parallel computing.
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 [PubMed]
Ascher U, Haber E, Oldenburg D. (2000). On optimization techniques for solving nonlinear inverse problems Inverse Problems. 16
Banks HT, Kunisch K. (1989). Estimation techniques for distributed parameter systems.
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.
Bernus O, Verschelde H, Panfilov AV. (2002). Modified ionic models of cardiac tissue for efficient large scale computations. Physics in medicine and biology. 47 [PubMed]
Biros G, Ghattas O. (2005). Parallel Lagrange Newton-Krylov Schur methods for PDE-constrained optimization. Part I: The Krylov-Schur solver SIAM J Sci Comput. 27
Biros G, Ghattas O. (2005). Parallel Lagrange-ìNewton-Krylov-Schur methods for PDE-constrained optimization. Part II: The Lagrange Newton solver and its application to optimal control of steady viscous flows SIAM J Sci Comp. 27
Brooks DH, Ahmad GF, MacLeod RS, Maratos GM. (1999). Inverse electrocardiography by simultaneous imposition of multiple constraints. IEEE transactions on bio-medical engineering. 46 [PubMed]
Brooks DH, MacLeod RS. (2007). Recent progress in inverse problems in electrocardiology. IEEE Eng Med Biol Mag. 17
Bub G, Shrier A, Glass L. (2002). Spiral wave generation in heterogeneous excitable media. Physical review letters. 88 [PubMed]
Chen X, Oshita Y. (2006). Periodicity and uniqueness of global minimizers of an energy functional containing a long-range interaction SIAM J Math Anal. 37
Cheng LK, Bodley JM, Pullan AJ. (2003). Comparison of potential- and activation-based formulations for the inverse problem of electrocardiology. IEEE transactions on bio-medical engineering. 50 [PubMed]
Colli Franzone P, Pavarino LF, Taccardi B. (2005). Simulating patterns of excitation, repolarization and action potential duration with cardiac Bidomain and Monodomain models. Mathematical biosciences. 197 [PubMed]
Colli-Franzone P, Pavarino LF. (2004). A parallel solver for reaction-diffusion systems in computational electrocardiology Math Mod Methods Appl Sci. 14
Courtemanche M, Winfree AT, Skaggs W. (1990). Stable 3-dimensional action-potential circulation in the FitzHugh-Nagumo model Physica D. 41
Cox SJ. (2006). An adjoint method for channel localization. Mathematical medicine and biology : a journal of the IMA. 23 [PubMed]
Cox SJ, Griffith BE. (2001). Recovering quasi-active properties of dendritic neurons from dual potential recordings. Journal of computational neuroscience. 11 [PubMed]
Cox SJ, Ji L. (2001). Discerning ionic currents and their kinetics from input impedance data. Bulletin of mathematical biology. 63 [PubMed]
Dauby PC, Desaive T, Croisier H, Kolh P. (2006). Standing waves in the FitzHugh-Nagumo model of cardiac electrical activity. Physical review. E, Statistical, nonlinear, and soft matter physics. 73 [PubMed]
Davidenko JM, Pertsov AV, Salomonsz R, Baxter W, Jalife J. (1992). Stationary and drifting spiral waves of excitation in isolated cardiac muscle. Nature. 355 [PubMed]
Dennis JE, Schnabel RB. (1996). Numerical methods for unconstrained optimization and nonlinear equations Classics in Applied Mathematics.
Elmer CE, Van_vleck ES. (2005). Spatially discrete FitzHugh-Nagumo equations SIAM J Appl Math. 65
Engl HW, Hanke M, Neubauer A. (1996). Regularization of inverse problems.
Et al et al. (2007). PETSc Homepage. http:--www.mcs.anl.gov-petsc..
Fitzhugh R. (1961). Impulses and Physiological States in Theoretical Models of Nerve Membrane. Biophysical journal. 1 [PubMed]
Franzone PC, Pennacchio M, Savare G. (2006). Multiscale modeling for the bioelectric activity of the heart SIAM J Math Anal. 37
Ghattas O, Biegler L, Heinkenschloss M, van_Bloemen-Waanders B. (2003). Large-scale PDE-constrained optimization Lecture Notes in Computational Science and Engineering.
Hansen PC, OLeary DP. (1993). The use of L-curve in the regularization of discrete ill-posed problems SIAM J Sci Comput. 14
Hoffman DA, Magee JC, Colbert CM, Johnston D. (1997). K+ channel regulation of signal propagation in dendrites of hippocampal pyramidal neurons. Nature. 387 [PubMed]
Isakov V. (1998). Inverse Problems for Partial Differential Equations.
Keyes DE, Knoll DA. (2004). Jacobian-free Newton-Krylov methods: A survey of approaches and applications J Comp Physiol. 193
Moreau-Villéger V et al. (2006). Building maps of local apparent conductivity of the epicardium with a 2-D electrophysiological model of the heart. IEEE transactions on bio-medical engineering. 53 [PubMed]
Murillo M, Cai XC. (2004). A fully implicit parallel algorithm for simulating the non-linear electrical activity of the heart Numerical Linear Algebra With Applications. 11
Murray JD. (1993). Mathematical Biology.
Nagumo J, Arimoto S, Yoshizawa S. (1962). An Active Pulse Transmission Line Simulating Nerve Axon Proceedings of the IRE. 50
Nii S. (1997). tability of traveling multiple-front (multiple-back) wave solutions of the FitzHugh-Nagumo equations SIAM J Math Anal. 28
Nocedal J, Wright SJ. (1999). Numerical optimization.
Patel SG, Roth BJ. (2005). Approximate solution to the bidomain equations for electrocardiogram problems. Physical review. E, Statistical, nonlinear, and soft matter physics. 72 [PubMed]
Pernarowski M. (2001). Controllability of excitable systems. Bulletin of mathematical biology. 63 [PubMed]
Petersson JH. (2005). On global existence for semilinear parabolic systems Nonlinear Analysis. 60
Riccio ML, Koller ML, Gilmour RF. (1999). Electrical restitution and spatiotemporal organization during ventricular fibrillation. Circulation research. 84 [PubMed]
Roth BJ. (2004). Art Winfree and the bidomain model of cardiac tissue. Journal of theoretical biology. 230 [PubMed]
Saad Y. (2003). Iterative methods for sparse linear systems (2nd ed).
Sandstede B, Szmolyan P, Krupa M. (1997). Fast and slow waves in the FitzHugh-Nagumo equation J Differential Equations. 133
Scott AC. (1975). The electrophysics of a nerve fiber Reviews Of Modern Physics. 47
Shahidi AV, Savard P, Nadeau R. (1994). Forward and inverse problems of electrocardiography: modeling and recovery of epicardial potentials in humans. IEEE transactions on bio-medical engineering. 41 [PubMed]
Sneyd J, Dale PD, Duffy A. (1998). Traveling waves in buffered systems: applications to calcium waves SIAM J Appl Math. 58
Sneyd J, Tsai JC. (2005). Existence and stability of traveling waves in buffered systems SIAM J Appl Math. 66
Suckley R, Biktashev VN. (2003). Comparison of asymptotics of heart and nerve excitability. Physical review. E, Statistical, nonlinear, and soft matter physics. 68 [PubMed]
Vanier MC, Bower JM. (1999). A comparative survey of automated parameter-search methods for compartmental neural models. Journal of computational neuroscience. 7 [PubMed]
Vogel CR. (1996). Non-convergence of the L-curve regularization parameter selection method Inverse Problems. 12
Vogel CR. (2002). Computational methods for inverse problems Frontiers in applied mathematics.
Wagner A, Cox SJ. (2004). Lateral overdetermination of the FitzHugh-Nagumo system Inverse Problems. 20
Walker HF, Eisenstat SC. (1994). Globally Convergent Inexact Newton Methods. 4
Wang J, Gao W. (2004). Existence of wavefronts and impulses to FitzHugh-Nagumo equations Nonlinear Analysis. 57
Weiss JN, Garfinkel A, Karagueuzian HS, Qu Z, Chen PS. (1999). Chaos and the transition to ventricular fibrillation: a new approach to antiarrhythmic drug evaluation. Circulation. 99 [PubMed]
Willms AR, Baro DJ, Harris-Warrick RM, Guckenheimer J. (1999). An improved parameter estimation method for Hodgkin-Huxley models. Journal of computational neuroscience. 6 [PubMed]
Winfree AT. (1990). Stable particle-like solutions to the nonlinear-wave equations of 3-dimensional excitable media SIAM Rev. 32
Yamada H, Nozaki K. (1990). Interaction of pulses in dissipative systems. FitzHugh-Nagumo equations Progress Of Theoretical Physics. 84