Models of cardiac tissue electrophysiology: Progress, challenges and open questions

Progress in Biophysics and Molecular Biology - Tập 104 - Trang 22-48 - 2011
R.H. Clayton1, O. Bernus2, E.M. Cherry3, H. Dierckx4, F.H. Fenton3, L. Mirabella5,6, A.V. Panfilov7, F.B. Sachse8, G. Seemann9, H. Zhang10
1Department of Computer Science, University of Sheffield, Regent Court, 211 Portobello Street, Sheffield S1 4DP, UK
2Institute of Membrane and Systems Biology, Multidisciplinary Cardiovascular Research Centre, University of Leeds, UK
3Department of Biomedical Sciences, Cornell University, Ithaca, NY, USA
4Department of Physics and Astronomy, University of Ghent, Belgium
5Department of Mathematics and Computer Science, Emory University, USA
6Dipartimento di Matematica, Politecnico di Milano, Italy
7Department of Theoretical Biology, Utrecht University, The Netherlands
8Bioengineering Department and Nora Eccles Harrison Cardiovascular Research and Training Institute, University of Utah, USA
9Institute of Biomedical Engineering, Karlsruhe Institute of Technology, Germany
10Department of Physics, University of Manchester, UK

Tài liệu tham khảo

Abildskov, 1976, Effects of activation sequence on the local recovery of ventricular excitability in the dog, Circulation Research, 38, 240, 10.1161/01.RES.38.4.240 Abrahams, 1987, Myocardial hypertrophy in Macaca fascicularis. Structural remodeling of the collagen matrix, Laboratory Investigation, 56, 676 Adler, 1981, [DNA content and cell number in heart and liver of children. Comparable biochemical, cytophotometric and histological investigations (author’s transl)], Pathology, Research and Practice, 172, 25, 10.1016/S0344-0338(81)80120-3 Akar, 2001, Optical measurement of cell-to-cell coupling in intact heart using subthreshold electrical stimulation, American Journal of Physiology, Heart Circulatory Physiology, 281, H533, 10.1152/ajpheart.2001.281.2.H533 Allexandre, 2002, Accuracy and speed considerations of a new numerical method for modeling cardiac excitation, Computers in Cardiology, 29, 9, 10.1109/CIC.2002.1166694 Anderson, 1998, The architecture of the sinus node, the atrioventricular conduction axis, and the internodal atrial myocardium, Journal of Cardiovascular Electrophysiology, 9, 1233, 10.1111/j.1540-8167.1998.tb00097.x Austin, 2006, Solving the cardiac bidomain equations for discontinuous conductivities, IEEE Transactions on Biomedical Engineering, 53, 1265, 10.1109/TBME.2006.873750 Banerjee, 2006, Dynamic interactions between myocytes, fibroblasts, and extracellular matrix, Annals of New York Academy Sciences, 1080, 76, 10.1196/annals.1380.007 Banerjee, 2007, Determination of cell types and numbers during cardiac development in the neonatal and adult rat and mouse, American Journal of Physiology, Heart Circulatory Physiology, 293, H1883, 10.1152/ajpheart.00514.2007 Barr, 1984, Propagation of excitation in an idealized anisotropic two-dimensional tissue, Biophysical Journal, 45, 1191, 10.1016/S0006-3495(84)84268-X Beeler, 1977, Reconstruction of the action potential of ventricular myocardial fibres, Journal of Physiology, 268, 177, 10.1113/jphysiol.1977.sp011853 Belhamadia, 2009, Towards accurate numerical method for monodomain models using a realistic heart geometry, Mathematical Biosciences, 220, 89, 10.1016/j.mbs.2009.05.003 Bernus, 2002, A computationally efficient electrophysiological model of human ventricular cells, Americal Journal of Physiology (Heart and Circulatory Physiology), 282, H2296, 10.1152/ajpheart.00731.2001 Bernus, 2004, Intramural wave propagation in cardiac tissue: asymptotic solutions and cusp waves, Physical Review E, 70, 061913, 10.1103/PhysRevE.70.061913 Bers, 2008 Bondarenko, 2004, Computer model of action potential of mouse ventricular myocytes, American Journal of Physiology (Heart and Circulatory Physiology), 287, H1378, 10.1152/ajpheart.00185.2003 Bordas, 2009, Simulation of cardiac electrophysiology on next-generation high-performance computers, Philosophical Transactions of the Royal Society A, 367, 1951, 10.1098/rsta.2008.0298 Bourgault, 2003, Simulation of electrophysiological waves with an unstructured finite element method, M2AN, 37, 649, 10.1051/m2an:2003051 Boyett, 2009, The sinoatrial node:Its complex structure and unique ion channel gene program, 127 Brette, 2003, T-tubule function in mammalian cardiac myocytes, Circualtion Research, 92, 1182, 10.1161/01.RES.0000074908.17214.FD Bub, 2002, Spiral wave generation in heterogenous excitable media, Physical Review Letters, 88, 058101-1, 10.1103/PhysRevLett.88.058101 Bueno-Orovio, 2006, Spectral methods for partial differential equations in irregular domains: the spectral smoothed boundary method, SIAM Journal on Scientific Computing, 28, 886, 10.1137/040607575 Bueno-Orovio, 2008, Minimal model for human ventricular action potentials in tissue, Journal of Theoretical Biology, 253, 544, 10.1016/j.jtbi.2008.03.029 Burton, 2006, 3-Dimensional models of individual cardiac histo-anatomy: tools and challenges, Annals of the New York Academy of Sciences, 1380, 301, 10.1196/annals.1380.023 Cabo, 1994, Wavefront curvature as a cause of slow conduction and block in isolated cardiac muscle, Circulation Research, 75, 1014, 10.1161/01.RES.75.6.1014 Cabrera, 1998, The architecture of the atrial musculature between the orifice of the inferior caval vein and the tricuspid valve: the anatomy of the isthmus, Jouranl of Cardiovascular Electrophysiology, 9, 1186, 10.1111/j.1540-8167.1998.tb00091.x Caldwell, 2009, Three distinct directions of intramural activation reveal nonuniform side-to-side electrical coupling of ventricular myocytes, Circulation Arrhythmia and Electrophysiology, 2, 433, 10.1161/CIRCEP.108.830133 Camelliti, 2005, Structural and functional characterisation of cardiac fibroblasts, Cardiovascuar Research, 65, 40, 10.1016/j.cardiores.2004.08.020 Campbell, 1987, Comparison of regional differences in cardiac myocyte dimensions in rats, hamsters, and guinea pigs, Anatomical Record, 219, 53, 10.1002/ar.1092190110 Chen, 2009, Nerve sprouting and cardiac arrhythmias, 381 Cherry, 2008, Properties of two human atrial cell models in tissue: restitution, memory, propagation, and reentry, Journal of Theoretical Biology, 254, 674, 10.1016/j.jtbi.2008.06.030 Cherry, 2004, Suppression of alternans and conduction blocks despite steep APD restitution: electrotonic, memory, and conduction velocity restitution effects, American Journal of Physiology (Heart and Circulatory Physiology), 286, 2332, 10.1152/ajpheart.00747.2003 Cherry, 2007, A tale of two dogs: analyzing two models of canine ventricular electrophysiology, American Journal of Physiology (Heart and Circulatory Physiology), 292, H43, 10.1152/ajpheart.00955.2006 Cherry, 2008, Visualization of spiral and scroll waves in simulated and experimental cardiac tissue, New Journal of Physics, 10, 125016, 10.1088/1367-2630/10/12/125016 Cherry, 2000, A space-time adaptive method for simulating complex cardiac dynamics, Physical Review Letters, 84, 1343, 10.1103/PhysRevLett.84.1343 Cherry, 2003, Efficient simulation of three-dimensional anisotropic cardiac tissue using an adaptive mesh refinement method, Chaos, 13, 853, 10.1063/1.1594685 Cherry, 2008, Dynamics of human atrial cell models: restitution, memory, and intracellular calcium dynamics in single cells, Progress in Biophysics & Molecular Biology, 98, 24, 10.1016/j.pbiomolbio.2008.05.002 Chialvo, 1990, Supernormal excitability as a mechanism of chaotic dynamics of activation in cardiac Purkinje fibers, Cardiovascular Research, 66, 525 Chinchapatnam, 2009, Voxel based adaptive meshless method for cardiac eletrophysiology simulation, LNCS Functional Imaging and Modeling of the Heart, 5528, 10.1007/978-3-642-01932-6_20 Clayton, 2008, A guide to modelling cardiac electrical activity in anatomically detailed ventricles, Progress in Biophysics & Molecular Biology, 96, 19, 10.1016/j.pbiomolbio.2007.07.004 Colli Franzone, 2004, A parallel solver for reaction-diffusion systems in computational electrocardiology, Mathematical Models and Methods in Applied Sciences, 14, 883, 10.1142/S0218202504003489 Colli Franzone, 1998, Spread of excitation in 3-D models of the anisotropic cardiac tissue. II. Effects of fiber architecture and ventricular geometry, Mathematical Biosciences, 147, 131, 10.1016/S0025-5564(97)00093-X Colli Franzone, 2006, Adaptivity in space and time for reaction-diffusion systems in electrocardiology, SIAM Journal on Scientific Computing, 28, 942, 10.1137/050634785 Colli Franzone, 2005, Simulating patterns of excitation, repolarization and action potential duration with cardiac Bidomain and Monodomain models, Mathematical Biosciences, 197, 35, 10.1016/j.mbs.2005.04.003 Conrath, 2004, Intercellular coupling through gap junctions masks M cells in the human heart, Cardiovascular Research, 62, 407, 10.1016/j.cardiores.2004.02.016 Cooper, 2006, On the application of partial evaluation to the optimisation of cardiac eletrophysiological simulations, 12 Courdiere, 2006, Stability and convergence of a finite volume method for two systems of reaction-diffusion equations in electro-cardiology, Nonlinear Analysis: Real World Applications, 7, 916, 10.1016/j.nonrwa.2005.02.006 Courtemanche, 1998, Ionic mechanisms underlying human atrial action potential properties: insights from a mathematical model, American Journal of Physiology (Heart and Circulatory Physiology), 275, H301, 10.1152/ajpheart.1998.275.1.H301 Courtemanche, 1996, Complex spiral wave dynamics in a spatially distributed ionic model of cardiac electrical activity, Chaos, 6, 579, 10.1063/1.166206 Curtis, 1938, Transverse electrical impedance of the squid giant axon, Journal of General Physiology, 21, 757, 10.1085/jgp.21.6.757 Davies, 2009, Hemodynamic shear stress and the endothelium in cardiovascular pathophysiology, Nature Clinical Practice Cardiovascular Medicine, 6, 16, 10.1038/ncpcardio1397 Delmar, 2009, Molecular organization and regulation of the cardiac gap junction channel connexin 43, 85 Demmel, 1997 Deuflhard, 2009, Adaptive finite element simulation of ventricular fibrillation dynamics, Computing and Visualization in Science, 12, 201, 10.1007/s00791-008-0088-y Dierckx, 2009, Intravoxel fibre structure of the left ventricular free wall and posterior left-right ventricular insertion site in canine myocardium using Q-ball imaging, Lecture Notes in Computer Science, 5528, 495, 10.1007/978-3-642-01932-6_53 Dobrzynski, 2005, Computer three-dimensional reconstruction of the sinoatrial node, Circulation, 111, 846, 10.1161/01.CIR.0000152100.04087.DB Durrer, 1970, Total excitation of the isolated human heart, Circulation, 41, 899, 10.1161/01.CIR.41.6.899 Efimov, 2004, Optical imaging of the heart, Circulation Research, 286, H2183 Endresen, 1989, Electrical restitution and conduction intervals of ventricular premature beats in man: influence of heart rate, PACE, 12, 1347, 10.1111/j.1540-8159.1989.tb05048.x Endresen, 1987, Monophasic action potentials in patients with coronary artery disease: reproducibility and electrical restitution and conduction at different stimulation rates, Cardiovascular Research, 21, 696, 10.1093/cvr/21.9.696 Ethier, 2008, Semi-implicit time-discretization schemes for the bidomain model, SIAM Journal on Numerical Analysis, 46, 2443, 10.1137/070680503 Faber, 2000, Action potential and contractility changes in Na+ (i) overloaded cardiac myocytes: a simulation study, Biophysical Journal, 78, 2392, 10.1016/S0006-3495(00)76783-X Fast, 1993, Macroscopic conduction in cultured strands of neonatal rat heart cells measured with voltage-sensitive dyes, Circulation Research, 73, 914, 10.1161/01.RES.73.5.914 Fawcett, 1969, The ultrastructure of the cat myocardium. I. Ventricular papillary muscle, Journal of Cell Biology, 42, 1, 10.1083/jcb.42.1.1 Fenton, 1998, Vortex dynamics in three-dimensional continuous myocardium with fibre rotation: filament instability and fibrillation, Chaos, 8, 20, 10.1063/1.166311 Fenton, 2002, Multiple mechanisms of spiral wave breakup in a model of cardiac electrical activity, Chaos, 12, 852, 10.1063/1.1504242 Fenton, 2005, Modeling wave propagation in realistic heart geometries using the phase-field method, Chaos, 15, 013502, 10.1063/1.1840311 Fischer, 2000, A bidomain model based BEM-FEM coupling formulation for anisotropic cardiac tissue, Annals of Biomedical Engineering, 28, 1229, 10.1114/1.1318927 Fitzhugh, 1961, Impulses and physiological states in theoretical models of nerve membrane, Biophysical Journal, 1, 445, 10.1016/S0006-3495(61)86902-6 Fox, 2002, Ionic mechanism of electrical alternans, American Journal of Physiology (Heart and Circulatory Physiology), 282, H516, 10.1152/ajpheart.00612.2001 Fozzard, 1972, Strength–duration curves in cardiac Purkinje fibres: effects of liminal length and charge distribution, Journal of Physiology, 226, 593, 10.1113/jphysiol.1972.sp009999 Fozzard, 1966, Membrane capacity of the cardiac Purkinje fibre, Journal of Physiology, 182, 255, 10.1113/jphysiol.1966.sp007823 Gerardo-Giorda, 2009, A model-based block-triangular preconditioner for the bidomain system in electrocardiology, Journal of Computational Physics, 228, 3625, 10.1016/j.jcp.2009.01.034 Gerdes, 1986, Regional differences in myocyte size in normal rat heart, Anatomical Record, 215, 420, 10.1002/ar.1092150414 Gerhardt, 1990, A cellular automaton model of excitable media including curvature and dispersion, Science, 247, 1563, 10.1126/science.2321017 Gerneke, 2007, Surface imaging microscopy using an ultramiller for large volume 3D reconstruction of wax- and resin-embedded tissues, Microscopy Research and Technique, 70, 886, 10.1002/jemt.20491 Gilbert, 2007, Regional localisation of left ventricular sheet structure: integration with current models of cardiac fibre, sheet and band structure, European Journal of Cardiothoracic Surgery, 32, 231, 10.1016/j.ejcts.2007.03.032 Gilbert, 2009, A quantitative comparison of the myocardial fibre orientation in the rabbit as determined by histology and by diffusion Tensor-MRI, Lecture Notes in Computer Science, 5528, 49, 10.1007/978-3-642-01932-6_6 Girouard, 1996, Optical mapping in a new guinea pig model of ventricular tachycardia reveals mechanisms for multiple wavelengths in a single reentrant circuit, Circulation, 93, 603, 10.1161/01.CIR.93.3.603 Goldsmith, 2004, Organization of fibroblasts in the heart, Developmental Dynamics, 230, 787, 10.1002/dvdy.20095 Gray, 1998, Spatial and temporal organization during cardiac fibrillation, Nature, 392, 75, 10.1038/32164 Greenberg, 1978, Spatial patterns for discrete models of diffusion in excitablemedia, SIAM Journal on Applied Mathematics, 34, 515, 10.1137/0134040 Gumbiner, 1996, Cell adhesion: the molecular basis of tissue architecture and morphogenesis, Cell, 84, 345, 10.1016/S0092-8674(00)81279-9 Hackbusch, 1985 Hall Barbosa, 2003, Simulation of a plane wavefront propagating in cardiac tissue using a cellular automata model, Physics in Medicine and Biology, 48, 4151, 10.1088/0031-9155/48/24/012 Hanson, 2009, Interaction of activation-repolarization coupling and restitution properties in humans, Circulation Arrhythmia and Electrophysiology, 2, 162, 10.1161/CIRCEP.108.785352 Harrild, 1997, A finite volume model of cardiac propagation, Annals of Biomedical Engineering, 28, 315, 10.1007/BF02648046 Helm, 2005, Measuring and mapping cardiac fiber and laminar architecture using diffusion tensor imaging, Annals of the New York Academy of Sciences, 1047, 296, 10.1196/annals.1341.026 Henriquez, 1996, Using computer models to understand the roles of tissue structure and membrane dynamics in arrhythmogenesis, Proceedings of the IEEE, 84, 334, 10.1109/5.486738 Henriquez, 1990, Simulation of propagation along a cylindrical bundle of cardiac tissue. II. Results of simulation, IEEE Transactions on Biomedical Engineering, 37, 861, 10.1109/10.58597 Henriquez, 1993, Simulating the electrical behavior of cardiac tissue using the bidomain model, Critical Reviews in Biomedical Engineering, 21, 1 Henry, 2004, The role of M cells and the long QT syndrome in cardiac arrhythmias: simulation studies of reentrant excitations using a detailed electrophysiological model, Chaos, 14, 172, 10.1063/1.1636272 Hinch, 2004, A mathematical analysis of the generation and termination of calcium sparks, Biophysical Journal, 86, 1293, 10.1016/S0006-3495(04)74203-4 Hodgkin, 1952, A quantitative description of membrane current and its application to conduction and excitation in nerve, Journal of Physiology (London), 117, 500, 10.1113/jphysiol.1952.sp004764 Holden, 1993, Modelling propagation and re-entry in anisotropic and smooth heterogeneous cardiac tissue, Journal of the Chemical Society Faraday Transactions, 89, 2833, 10.1039/ft9938902833 Holmes, 2000, Direct histological validation of diffusion tensor MRI in formaldehyde-fixed myocardium, Magnetic Resonance in Medicine, 44, 157, 10.1002/1522-2594(200007)44:1<157::AID-MRM22>3.0.CO;2-F Hooke, 1994, Linear algebraic transformations of the bidomain equations: implications for numerical methods, Mathematical Biosciences, 120, 127, 10.1016/0025-5564(94)90049-3 Hort, 1957, [Micrometric examination of guinea pig hearts of different width.], Verh Dtsch Ges Kreislaufforsch, 23, 343 Hort, 1957, [Research on muscle fiber dilation and the structure of the right heart chamber wall in a guinea pig.], Virchows Archiv, 329, 694, 10.1007/BF00955111 Hort, 1960, [Macroscopic and micrometric research on the myocardium of the left ventricle filled to varying degrees.], Virchows Archives of Pathology Anatomy and Physiology and Clinical Medicine, 333, 523, 10.1007/BF00956322 Hoyt, 1989, Distribution and three-dimensional structure of intercellular junctions in canine myocardium, Circulation Research, 64, 563, 10.1161/01.RES.64.3.563 Hsu, 1998, Magnetic resonance myocardial fiber-orientation mapping with direct histological correlation, American Journal of Physiology (Heart and Circulatory Physiology), 274, 1627, 10.1152/ajpheart.1998.274.5.H1627 Hucker, 2008, Bimodal biophotonic imaging of the structure-function relationship in cardiac tissue, Journal of Biomedical Optics, 13, 054012, 10.1117/1.2975826 Hucker, 2009, Mechanisms of atrioventricular Nodal excitability and propagation, 249 Hund, 2004, Rate dependence and regulation of action potential and calcium transient in a canine cardiac ventricular cell model, Circulation, 110, 4008, 10.1161/01.CIR.0000147231.69595.D3 Iyer, 2004, A computational model of the human left-ventricular epicardial myocyte, Biophysical Journal, 87, 1507, 10.1529/biophysj.104.043299 Jacquemet, 2005, Finite volume stiffness matrix for solving anisotropic cardiac propagation in 2-D and 3-D unstructured meshes, IEEE Transactions on Biomedical Engineering, 52, 1490, 10.1109/TBME.2005.851459 Jie, 2010, Mechanisms of mechanically induced spontaneous arrhythmias in acute regional ischaemia, Circulation Research, 106, 185, 10.1161/CIRCRESAHA.109.210864 Jongsma, 2000, Gap junctions in cardiovascular disease, Circulation Research, 86, 1193, 10.1161/01.RES.86.12.1193 Ju, 1996, Extracellular matrix and cardiovascular diseases, Canadian Journal of Cardiology, 12, 1259 Keener, 1998, A numerical method for the solution of the bidomain equations in cardiac tissue, Chaos, 8, 234, 10.1063/1.166300 Keener, 1998 Kleber, 2004, Basic mechanisms of cardiac impulse propagation and associated arrhythmias, Physiological Reviews, 84, 431, 10.1152/physrev.00025.2003 Kohl, 1994, Mechanosensitive fibroblasts in the sino-atrial node region of rat heart: interaction with cardiomyocytes and possible role, Experimental Physiology, 79, 943, 10.1113/expphysiol.1994.sp003819 Kohl, 2005, Electrical coupling of fibroblasts and myocytes: relevance for cardiac propagation, Journal of Electrocardiology, 38, 45, 10.1016/j.jelectrocard.2005.06.096 Lampe, 2009, Gap junction distribution and regulation in the heart, 307 Lasher, 2009, Towards modeling of cardiac micro-structure with catheter-based confocal microscopy: a novel approach for dye delivery and tissue characterization, IEEE Transactions on Medical Imaging, 28, 1156, 10.1109/TMI.2009.2017376 Le Novere, 2005, Minimum information requested in the annotation of biochemical models (MIRIAM), Nature Biotechnology, 23, 1509, 10.1038/nbt1156 LeGrice, 1995, Laminar structure of the heart: ventricular myocyte arrangement and connective tissue architecture in the dog, American Journal of Physiology (Heart and Circulatory Physiology), 269, 571, 10.1152/ajpheart.1995.269.2.H571 Li, 2008, Computer three-dimensional reconstruction of the atrioventricular node, Circulation Research, 102, 975, 10.1161/CIRCRESAHA.108.172403 Lindemans, 1979, Acute voltage, charge, and energy thresholds as functions of electrode size for electrical stimulation of the canine heart, Cardiovascular Research, 13, 383, 10.1093/cvr/13.7.383 Lodish, 2003 Lunkenheimer, 2006, Three-dimensional architecture of the left ventricular myocardium, The Anatomical Record. Part A, Discoveries in Molecular, Cellular, and Evolutionary Biology, 288, 565, 10.1002/ar.a.20326 Luo, 1991, A model of the ventricular cardiac action potential. Depolarization, repolarization and their interaction, Circulation, 68, 1501, 10.1161/01.RES.68.6.1501 Maclachlan, 2007, A comparison of non-standard solvers for ODEs describing cellular reactions in the heart, Computer Methods in Biomechanics and Biomedical Engineering, 10, 317, 10.1080/10255840701259301 Mahajan, 2008, A rabbit ventricular action potential model replicating cardiac dynamics at rapid heart rates, Biophysical Journal, 94, 392, 10.1529/biophysj.106.98160 Mironov, 2008, Role of conduction velocity restitution and short-term memory in the development of action potential duration alternans in isolated rabbit hearts, Circulation, 118, 17, 10.1161/CIRCULATIONAHA.107.737254 Moe, 1964, A computer model of atrial fibrillation, American Heart Journal, 67, 200, 10.1016/0002-8703(64)90371-0 Munteanu, 2009, A scalable Newton-Krylov-Schwarz method for the bidomain reaction–diffusion system, SIAM Journal on Scientific Computing, 31, 3861, 10.1137/08074355X Murillo, 2004, A fully implicit parallel algorithm for simulating the non-linear electrical activity of the heart, Numerical Linear Algebra with Applications, 11, 261, 10.1002/nla.381 Nash, 2006, Whole heart action potential duration restitution properties in cardiac patients: a combined clinical and modelling study, Experimental Physiology, 91, 339, 10.1113/expphysiol.2005.031070 Neal, 2010, Current progress in patient-specific modeling, Breifings in Bioinformatics, 11, 111, 10.1093/bib/bbp049 Nerbonne, 2002, Heterogeneous expression of voltage-gated potassium channels in the heart: roles in normal excitation and arrhythmias, Journal of Cardiovascular Electrophysiology, 13, 406, 10.1046/j.1540-8167.2002.00406.x Neu, 1993, Homogenization of syncytial tissues, Critical Reviews in Biomedical Engineering, 21, 137 Nickerson, 2006, Computational multiscale modeling in the physiome project: modeling cardiac electromechanics, IBM Journal of Research and Development, 50, 617, 10.1147/rd.506.0617 Niederer, 2007, An improved numerical method for strong coupling of excitation and contraction models in the heart, Progress in Biophysics & Molecular Biology, 96, 90, 10.1016/j.pbiomolbio.2007.08.001 Nielsen, 1991, Mathematical model of geometry and fibrous structure of the heart, American Journal of Physiology (Heart and Circulatory Physiology), 260, H1365, 10.1152/ajpheart.1991.260.4.H1365 Noble, 1998, Improved guinea pig ventricular cell model incorporating a dyadic space, IKr and IKs, and length and tension dependent processes, Canadian Journal of Cardiology, 14, 123 Noble, 1972, The relation of Rushton’s ‘liminal length’ for excitation to the resting and active conductances of excitable cells, Journal of Physiology, 226, 573, 10.1113/jphysiol.1972.sp009998 Noble, 1979 Nygren, 1998, Mathematical model of an adult human atrial cell: the role of K+ currents in repolarization, Circulation Research, 82, 63, 10.1161/01.RES.82.1.63 Olivetti, 1991, Cardiomyopathy of the aging human heart: myocyte loss and reactive cellular hypertrophy, Circulation Research, 68, 1560, 10.1161/01.RES.68.6.1560 Olivetti, 1996, Aging, cardiac hypertrophy and ischemic cardiomyopathy do not affect the proportion of mononucleated and multinucleated myocytes in the human heart, Journal of Molecular and Cellular Cardiology, 28, 1463, 10.1006/jmcc.1996.0137 Osaka, 1987, Effects of activation sequence and anisotropic cellular geometry on the repolarization phase of action potential in the dog ventricles, Circulation, 76, 226, 10.1161/01.CIR.76.1.226 Owens, 2007, A survey of general-purpose computation on graphics hardware, Computer Graphics Forum, 26, 80, 10.1111/j.1467-8659.2007.01012.x Pandit, 2001, A mathematical model of action potential heterogeneity in adult rat left ventricular myocytes, Biophysical Journal, 81, 3029, 10.1016/S0006-3495(01)75943-7 Panfilov, 1995, Re-entry in three-dimensional Fitzhugh-Nagumo medium with rotational anisotropy, Physica D, 84, 545, 10.1016/0167-2789(95)00059-D Panfilov, 2007, Drift and breakup of spiral waves in reaction-diffusion-mechanics systems, Proceedings of the National Academy of Sciences of the United States of America, 104, 7922, 10.1073/pnas.0701895104 Panfilov, 2002, Sprial breakup in an array of coupled cells: the role of the intercellular conductance, Physical Review Letters, 88, 118101, 10.1103/PhysRevLett.88.118101 Pavarino, 2008, Multilevel additive Schwarz preconditioners for the bidomain reaction–diffusion system, SIAM Journal on Scientific Computing, 31, 420, 10.1137/070706148 Penland, 2002, Modeling impulse propagation and extracellular potential distributions in anisotropic cardiac tissue using a finite volume element discretization, Computing and Visualization in Science, 4, 215, 10.1007/s00791-002-0078-4 Pennacchio, 2009, Algebraic multigrid preconditioners for the bidomain reaction-diffusion system, Applied Numerical Mathematics, 59, 3033, 10.1016/j.apnum.2009.08.001 Pennacchio, 2004, The mortar finite element method for the cardiac “bidomain” model of extracellular potential, Journal of Scientific Computing, 20, 191, 10.1023/B:JOMP.0000008720.85771.d0 Peskin, 1989, Fiber architecture of the left ventricular wall: an asymptotic analysis, Communications in Pure and Applied Mathematics, 42, 79, 10.1002/cpa.3160420106 Plank, 2007, Algebraic multigrid preconditioner for the cardiac bidomain model, IEEE Transactions on Biomedical Engineering, 54, 585, 10.1109/TBME.2006.889181 Plank, 2008, From mitochondrial ion channels to arrhythmias in the heart: computational techniques to bridge the spatio-temporal scales, Philosophical Transactions of the Royal Society A, 366, 3381, 10.1098/rsta.2008.0112 Plank, 2009, Generation of histo-anatomically representative models of the individual heart: tools and application, Philosophical Transactions of the Royal Society A, 367, 2257, 10.1098/rsta.2009.0056 Plonsey, 2000 Poelzing, 2004, Heterogeneous connexin43 expression produces electrophysiological heteroegeneities across the ventricular wall, American Journal of Physiology (Heart and Circulatory Physiology), 296, H2001, 10.1152/ajpheart.00987.2003 Poelzing, 2005, Optical measurements reveal nature of intercellular coupling across ventricular wall, American Journal of Physiology (Heart and Circulatory Physiology), 289, H1428, 10.1152/ajpheart.01245.2004 Pollard, 1991, Computer simulations of activation in an anatomically based model of the human ventricular conduction system, IEEE Transactions on Biomedical Engineering, 38, 982, 10.1109/10.88444 Pop, 2009, Fusion of optical imaging and MRI for the evaluation and adjustment of macroscopic models of cardiac electrophysiology: a feasibility study, Medical Image Analysis, 13, 370, 10.1016/j.media.2008.07.002 Pope, 2008, Three-dimensional transmural organization of perimysial collagen in the heart, American Journal of Physiology (Heart and Circulatory Physiology), 295, H1243, 10.1152/ajpheart.00484.2008 Potse, 2006, A comparison of monodomain and bidomain reaction-diffusion models for action potential propagation in the human heart, IEEE Transactions on Biomedical Engineering, 53, 2425, 10.1109/TBME.2006.880875 Prassl, 2009, Automatically generated, anatomically accurate meshes for cardiac electrophysiology problems, IEEE Transactions on Biomedical Engineering, 53, 2425 Press, 1992 Priebe, 1998, Simulation study of cellular electrical properties in heart failure, Circulation Research, 82, 1206, 10.1161/01.RES.82.11.1206 Pullan, 2005 Qu, 1999, An advanced algorithm for solving partial differential equation in cardiac conduction, IEEE Transactions on Biomedical Engineering, 46, 1166, 10.1109/10.784149 Quan, 1998, Efficient integration of a realistic two-dimensional cardiac tissue model by domain decomposition, IEEE Transactions on Biomedical Engineering, 45, 372, 10.1109/10.661162 Roberts, 2008, Effect of nonuniform interstitial space properties on impulse propagation: a discrete multidomain model, Biophysical Journal, 95, 3724, 10.1529/biophysj.108.137349 Robinson, 1983, Skeletal framework of mammalian heart muscle. Arrangement of inter- and pericellular connective tissue structures, Laboratory Investigation, 49, 482 Rodriguez, 2005, Differences between left and right ventricular chamber geometry affect cardiac vulnerability to electric shocks, Circulation Research, 97, 168, 10.1161/01.RES.0000174429.00987.17 Rook, 1992, Differences in gap junction channels between cardiac myocytes, fibroblasts, and heterologous pairs, American Journal Physiology, 263, C959, 10.1152/ajpcell.1992.263.5.C959 Roth, 1994, Electrical stimulation of cardiac tissue: a bidomain model with active membrane properties, IEEE Transactions on Biomedical Engineering, 41, 232, 10.1109/10.284941 Roth, 1991, Action potential propagation in a thick strand of cardiac muscle, Circulation Research, 68, 162, 10.1161/01.RES.68.1.162 Roth, 1997, Electrical conductivity values used with the bidomain model of cardiac tissue, IEEE Transactions on Biomedical Engineering, 44, 326, 10.1109/10.563303 Roth, 2001, Meandering of spiral waves in anisotropic cardiac tissue, Physica D, 150, 127, 10.1016/S0167-2789(01)00145-2 Rudy, 1995, Reentry – insights from theoretical simulations in a fixed Pathway, Journal of Cardiovascular Electrophysiology, 6, 294, 10.1111/j.1540-8167.1995.tb00402.x Rush, 1978, A practical algorithm for solving dynamic membrane equations, IEEE Transactions on Biomedical Engineering, 25, 389, 10.1109/TBME.1978.326270 Rushton, 1937, Initiation of the propagated disturbance, Proceedings of the Royal Society of London B, 124, 210, 10.1098/rspb.1937.0083 Saad, 2003 Sachse, 2009, A model of electrical conduction in cardiac tissue including fibroblasts, Annals of Biomedical Engineering, 37, 874, 10.1007/s10439-009-9667-4 Sambelashvilli, 2004, Dynamics of virtual electrode-induced scroll-wave reentry in a 3D bidomain model, American Journal of Physiology (Heart and Circulatory Physiology), 287, H1570, 10.1152/ajpheart.01108.2003 Sampson, 2005, Electrotonic influences on action potential duration dispersion in small hearts: a simulation study, American Journal of Physiology (Heart and Circulatory Physiology), 289, H350, 10.1152/ajpheart.00507.2004 Sands, 2005, Automated imaging of extended tissue volumes using confocal microscopy, Microscopy Research and Technique, 67, 227, 10.1002/jemt.20200 Sato, 2009, Acceleration of cardiac tissue simulations with graphic processing units, Medical and Biological Engineering and Computing, 47, 1011, 10.1007/s11517-009-0514-4 Satoh, 1996, Surface:volume relationship in cardiac myocytes studied with confocal microscopy and membrane capacitance measurements: species-dependence and developmental effects, Biophysical Journal, 70, 1494, 10.1016/S0006-3495(96)79711-4 Savio-Galimberti, 2008, Novel features of the rabbit transverse tubular system revealed by quantitative analysis of three-dimensional reconstructions from confocal images, Biophysical Journal, 95, 2053, 10.1529/biophysj.108.130617 Schoenberg, 1975, Effect of diameter on membrane capacity and conductance of sheep cardiac Purkinje fibres, Journal of General Physiology, 65, 441, 10.1085/jgp.65.4.441 Scollan, 2000, Reconstruction of cardiac ventricular geometry and fibre orientation using magnetic resonance imaging, Annals of Biomedical Engineering, 28, 934, 10.1114/1.1312188 Seemann, 2006, Heterogeneous three-dimensional anatomical and electrophysiological model of human atria, Philosophical Transactions of the Royal Society A, 364, 1465, 10.1098/rsta.2006.1781 Seemann, G., Sachse, F.B., Karl, K., Weiss, D.L., Heuveline, V. and Dössel, O. Framework for modular, flexible and efficient solving the cardiac bidomain equation using PETSc. Progress in Industrial Mathematics at ECMI 2008, in press. Shannon, 2004, A mathematical treatment of integrated Ca dynamics within the ventricular myocyte, Biophysical Journal, 87, 3351, 10.1529/biophysj.104.047449 Shaw, 1995, The vulnerable window for unidirectional block in cardiac tissue: characterisation and dependence on membrane excitability and intercellular coupling, Journal of Cardiovascular Electrophysiology, 6, 115, 10.1111/j.1540-8167.1995.tb00763.x Shaw, 1997, Electrophysiologic effects of acute myocardial ischemia – a mechanistic investigation of action potential conduction and conduction failure, Circulation Research, 80, 124, 10.1161/01.RES.80.1.124 Shaw, 1997, Ionic mechanisms of propagation in cardiac tissue – roles of the sodium and L-type calcium currents during reduced excitability and decreased gap junction coupling, Circulation Research, 81, 727, 10.1161/01.RES.81.5.727 Smith, 1984, Simple finite-element model accounts for a wide range of cardiac dysrhythmias, Proceedings of the National Acadamy of Sciences, 81, 233, 10.1073/pnas.81.1.233 Smith, 2007, Computational biology of cardiac myocytes: proposed standards for the physiome, Journal of Experimental Biology, 210, 1576, 10.1242/jeb.000133 Smith, 2008, Nondestructive optical determination of fiber organization in intact myocardial wall, Microsc Res Tech, 71, 510, 10.1002/jemt.20579 Spach, 1992, Cellular Vmax reflects both membrane properties and the load presented by adjoining cells, American Journal of Physiology (Heart and Circulatory Physiology), 263, H1855, 10.1152/ajpheart.1992.263.6.H1855 Spach, 2000, Electrophysiological effects of remodeling cardiac gap junctions and cell size: experimental and model studies of normal cardiac growth, Circulation Research, 86, 302, 10.1161/01.RES.86.3.302 Spach, 2004, Cell size and communication: role in structural and electrical development and remodeling of the heart, Heart Rhythm, 1, 500, 10.1016/j.hrthm.2004.06.010 Stevens, 2003, Sarcomere length changes in a 3D mathematical model of the pig ventricles, Progress in Biophysics and Molecular Biology, 82, 229, 10.1016/S0079-6107(03)00023-3 Stinstra, 2005, On the passive cardiac conductivity, Annals of Biomedical Engineering, V33, 1743, 10.1007/s10439-005-7257-7 Stinstra, 2006, A model of 3D propagation in discrete cardiac tissue, Computers in Cardiology, 33, 41 Strang, 1968, On the construction and comparison of difference schemes, SIAM Journal on Numerical Analysis, 5, 506, 10.1137/0705041 Streeter, 1969, Fiber orientation in the canine left ventricle during diastole and systole, Circulation Research, 24, 339, 10.1161/01.RES.24.3.339 Sundnes, 2002, Multigrid block preconditioning for a coupled system of partial differential equations modeling the electrical activity in the heart, Computer Methods in Biomechanics and Biomedical Engineering, 5, 397, 10.1080/1025584021000025023 Sundnes, 2005, An operator splitting method for solving the bidomain equations coupled to a volume conductor model for the torso, Mathematical Biosciences, 194, 233, 10.1016/j.mbs.2005.01.001 Sundnes, 2009, A second-order algortihm for solving dynamic cell membrane equations, IEEE Transactions on Biomedical Engineering, 56, 10.1109/TBME.2009.2014739 Szentadrassy, 2005, Apico–basal inhomogeneity in distribution of ion channels in canine and human ventricular myocardium, Cardiovascular Research, 65, 851, 10.1016/j.cardiores.2004.11.022 Ten Tusscher, 2006, Comparison of electrophysiological models for human ventricular cells and tissues, Progress in Biophysics & Molecular Biology, 90, 326, 10.1016/j.pbiomolbio.2005.05.015 Ten Tusscher, 2009, Organization of ventricular fibrillation in the human heart: experiments and models, Experimental Physiology, 94, 553, 10.1113/expphysiol.2008.044065 TenTusscher, 2004, A model for human ventricular tissue, American Journal of Physiology (Heart and Circulatory Physiology), 286, H1573, 10.1152/ajpheart.00794.2003 Trangenstein, 2004, Operator splitting and adaptive mesh refinement for the Luo-Rudy I model, Journal of Computational Physics, 196, 645, 10.1016/j.jcp.2003.11.014 Trayanova, 2006, Defibrillation of the heart: insights into mechanisms from modelling studies, Experimental Physiology, 91, 323, 10.1113/expphysiol.2005.030973 Trew, 2005, A finite volume method for modeling discontinuous electrical activation in cardiac tissue, Annals of Biomedical Engineering, V33, 590, 10.1007/s10439-005-1434-6 Trew, 2005, A generalized finite difference method for modeling cardiac electrical activation on arbitrary, irregular computational meshes, Mathematical Biosciences, 198, 169, 10.1016/j.mbs.2005.07.007 van Kempen, 1991, Spatial distribution of connexin43, the major cardiac gap junction protein, in the developing and adult rat heart, Circulation Research, 68, 1638, 10.1161/01.RES.68.6.1638 Vetter, 1998, Three dimensional analysis of regional cardiac function: a model of rabbit ventricular anatomy, Progress in Biophysics & Molecular Biology, 69, 157, 10.1016/S0079-6107(98)00006-6 Victorri, 1985, Numerical integration in the reconstruction of cardiac action potentials using Hodgkin-Huxley-type models, Computers and Biomedical Research, 18, 10, 10.1016/0010-4809(85)90003-5 Vigmond, 1999, Computationally efficient model for simulating electrical activity in cardiac tissue with fiber rotation, Annals of Biomedical Engineering, 27, 160, 10.1114/1.160 Vigmond, 2002, Computational techniques for solving the bidomain equations in three dimensions, IEEE Transactions on Biomedical Engineering, 49, 1260, 10.1109/TBME.2002.804597 Vigmond, 2008, Solvers for the cardiac bidomain equations, Progress in Biophysics & Molecular Biology, 96, 3, 10.1016/j.pbiomolbio.2007.07.012 Vigmond, 2009, Near-real-time simulations of bioelectric activity in small mammalian hearts using graphical processing units, Conference Proceedings: IEEE Engineering in Medicine and Biology Society, 1, 3290 Viswanathan, 1999, Effects of I-Kr and I-Ks heterogeneity on action potential duration and its rate dependence – a simulation study, Circulation, 99, 2466, 10.1161/01.CIR.99.18.2466 Waller, 1984, Spatial and temporal structure in systems of couple nonlinear oscillators, Physical Review A, 30, 2047, 10.1103/PhysRevA.30.2047 Weber dos Santos, 2004, Parallel multigrid preconditioner for the cardiac bidomain model, IEEE Transactions on Biomedical Engineering, 51, 1960, 10.1109/TBME.2004.834275 Weber dos Santos, 2004, Preconditioning techniques for the bidomain equations, Lecture Notes in Computational Science and Engineering, 40, 571, 10.1007/3-540-26825-1_60 Weber, 1994, Collagen network of the myocardium: function, structural remodeling and regulatory mechanisms, Journal of Molecular and Cellular Cardiology, 26, 279, 10.1006/jmcc.1994.1036 Whiteley, 2006, An efficient numerical technique for the solution of the monodomain and bidomain equations, IEEE Transactions on Biomedical Engineering, 53, 2139, 10.1109/TBME.2006.879425 Whiteley, 2008, An efficient technique for the numerical solution of the bidomain equations, Annals of Biomedical Engineering, 36, 1398, 10.1007/s10439-008-9513-0 Wiener, 1946, The mathematical formations of the problem of conduction of impulse in a network of connected elements, specifically in cardiac muscle, Archivos del Instituto de Cardiologa de Mexico, 16, 205 Wikswo, 1995, Virtual electrodes in cardiac tissue: a common mechanism for anodal and cathodal stimulation, Biophysical Journal, 73, 2195, 10.1016/S0006-3495(95)80115-3 Winfree, 1998, A spatial scale factor for electrophysiological models of myocardium, Progress in Biophysics & Molecular Biology, 69, 185, 10.1016/S0079-6107(98)00007-8 Winslow, 1993, Generation and propagation of ectopic beats induced by spatially localized Na–K pump inhibition in atrial network models, Proceedings of the Royal Society of London B, 254, 55, 10.1098/rspb.1993.0126 Winslow, 1999, Mechanisms of altered excitation-contraction coupling in canine tachycardia-induced heart failure, II: model studies, Circulation Research, 84, 571, 10.1161/01.RES.84.5.571 Xu, 1998, Two forms of spiral-wave re-entry in an ionic model of ischaemic myocardium, Chaos, 8, 157, 10.1063/1.166286 Yue, 2005, Global endocardial electrical restitution in human right and left ventricles determined by noncontact mapping, Journal of the American College of Cardiology, 46, 1067, 10.1016/j.jacc.2005.05.074