A Comparison of Monodomain and Bidomain Reaction-Diffusion Models for Action Potential Propagation in the Human Heart

A bidomain reaction-diffusion model of the human heart was developed, and potentials resulting from normal depolarization and repolarization were compared with results from a compatible monodomain model. Comparisons were made for an empty isolated heart and for a heart with fluid-filled ventricles. Both sinus rhythm and ectopic activation were simulated. The bidomain model took 2 days on 32 processors to simulate a complete cardiac cycle. Differences between monodomain and bidomain results were extremely small, even for the extracellular potentials, which in case of the monodomain model were computed with a high-resolution forward model. Propagation of activation was 2% faster in the bidomain model than in the monodomain model. Electrograms computed with monodomain and bidomain models were visually indistinguishable. We conclude that, in the absence of applied currents, propagating action potentials on the scale of a human heart can be studied with a monodomain model

[1]  Leslie Tung,et al.  A bi-domain model for describing ischemic myocardial d-c potentials , 1978 .

[2]  M. Burgess,et al.  Computer simulations of three-dimensional propagation in ventricular myocardium. Effects of intramural fiber rotation and inhomogeneous conductivity on epicardial activation. , 1993, Circulation research.

[3]  Otto H. Schmitt,et al.  Biological Information Processing Using the Concept of Interpenetrating Domains , 1969 .

[4]  R Hren,et al.  Value of simulated body surface potential maps as templates in localizing sites of ectopic activation for radiofrequency ablation. , 1997, Physiological measurement.

[5]  Natalia A Trayanova,et al.  Differences Between Left and Right Ventricular Chamber Geometry Affect Cardiac Vulnerability to Electric Shocks , 2005, Circulation research.

[6]  Charles Antzelevitch,et al.  Cellular and ionic basis for the sex-related difference in the manifestation of the Brugada syndrome and progressive conduction disease phenotypes. , 2003, Journal of electrocardiology.

[7]  L. Guerri,et al.  Oblique dipole layer potentials applied to electrocardiology , 1983, Journal of mathematical biology.

[8]  Henk A. van der Vorst,et al.  Bi-CGSTAB: A Fast and Smoothly Converging Variant of Bi-CG for the Solution of Nonsymmetric Linear Systems , 1992, SIAM J. Sci. Comput..

[9]  B. Roth Electrical conductivity values used with the bidomain model of cardiac tissue , 1997, IEEE Transactions on Biomedical Engineering.

[10]  Y. Rudy,et al.  Ionic Current Basis of Electrocardiographic Waveforms: A Model Study , 2002, Circulation research.

[11]  D. Durrer,et al.  Total Excitation of the Isolated Human Heart , 1970, Circulation.

[12]  Yousef Saad,et al.  Iterative methods for sparse linear systems , 2003 .

[13]  P. Hunter,et al.  Laminar structure of the heart: a mathematical model. , 1997, The American journal of physiology.

[14]  F. A. Seiler,et al.  Numerical Recipes in C: The Art of Scientific Computing , 1989 .

[15]  B. Roth,et al.  Action potential propagation in a thick strand of cardiac muscle. , 1991, Circulation research.

[16]  Felipe Aguel,et al.  Computer simulations of cardiac defibrillation: a look inside the heart , 2002 .

[17]  A. Tveito,et al.  Modeling the electrical activity of the heart: A Bidomain Model of the ventricles embedded in a torso , 2002 .

[18]  Alexander V Panfilov,et al.  Modified ionic models of cardiac tissue for efficient large scale computations. , 2002, Physics in medicine and biology.

[19]  B M Horácek,et al.  Computer model of excitation and recovery in the anisotropic myocardium. I. Rectangular and cubic arrays of excitable elements. , 1991, Journal of electrocardiology.

[20]  P. Wolf,et al.  Region Specific Modeling of Cardiac Muscle: Comparison of Simulated and Experimental Potentials , 2002, Annals of Biomedical Engineering.

[21]  H. I. Saleheen,et al.  New finite difference formulations for general inhomogeneous anisotropic bioelectric problems , 1997, IEEE Transactions on Biomedical Engineering.

[22]  G. Huiskamp,et al.  A Bidomain Model Based BEM-FEM Coupling Formulation for Anisotropic Cardiac Tissue , 2004, Annals of Biomedical Engineering.

[23]  Marie-Claude Trudel,et al.  Simulation of QRST integral maps with a membrane-based computer heart model employing parallel processing , 2004, IEEE Transactions on Biomedical Engineering.

[24]  A V Panfilov,et al.  Transition from ventricular fibrillation to ventricular tachycardia: a simulation study on the role of Ca(2+)-channel blockers in human ventricular tissue. , 2002, Physics in medicine and biology.

[25]  Andrew C. Zygmunt,et al.  Ionic and Cellular Basis for the Predominance of the Brugada Syndrome Phenotype in Males , 2002, Circulation.

[26]  R M Gulrajani,et al.  A computer heart model incorporating anisotropic propagation. II. Simulations of conduction block. , 1993, Journal of electrocardiology.

[27]  C. Henriquez Simulating the electrical behavior of cardiac tissue using the bidomain model. , 1993, Critical reviews in biomedical engineering.

[28]  Andrew J. Pullan,et al.  Solving the cardiac bidomain equations for discontinuous conductivities , 2006, IEEE Transactions on Biomedical Engineering.

[29]  C.R. Johnson,et al.  The effects of inhomogeneities and anisotropies on electrocardiographic fields: a 3-D finite-element study , 1997, IEEE Transactions on Biomedical Engineering.

[30]  Rodrigo Weber dos Santos,et al.  Parallel multigrid preconditioner for the cardiac bidomain model , 2004, IEEE Transactions on Biomedical Engineering.

[31]  B. Taccardi,et al.  Modeling ventricular excitation: axial and orthotropic anisotropy effects on wavefronts and potentials. , 2004, Mathematical biosciences.

[32]  B M Horácek,et al.  Computer model of excitation and recovery in the anisotropic myocardium. II. Excitation in the simplified left ventricle. , 1991, Journal of electrocardiology.

[33]  C. Henriquez,et al.  Anisotropy, Fiber Curvature, and Bath Loading Effects on Activation in Thin and Thick Cardiac Tissue Preparations: , 1996, Journal of cardiovascular electrophysiology.

[34]  B. Vanrumste,et al.  Comparing iterative solvers for linear systems associated with the finite difference discretisation of the forward problem in electro-encephalographic source analysis , 2006, Medical and Biological Engineering and Computing.

[35]  T. Arts,et al.  Characterization of the normal cardiac myofiber field in goat measured with MR-diffusion tensor imaging. , 2002, American journal of physiology. Heart and circulatory physiology.

[36]  S. Rush,et al.  A Practical Algorithm for Solving Dynamic Membrane Equations , 1978, IEEE Transactions on Biomedical Engineering.

[37]  R Wilders,et al.  A computationally efficient electrophysiological model of human ventricular cells. , 2002, American journal of physiology. Heart and circulatory physiology.

[38]  C. Henriquez,et al.  Paced Activation Mapping Reveals Organization of Myocardial Fibers: , 1997, Journal of cardiovascular electrophysiology.

[39]  B. Taccardi,et al.  The influence of torso inhomogeneities on epicardial potentials , 1994, Computers in Cardiology 1994.

[40]  S. Abboud,et al.  Simulation of cardiac activity and the ECG using a heart model with a reaction-diffusion action potential. , 1996, Medical engineering & physics.

[41]  Andrew J. Pullan,et al.  The effect of torso impedance on epicardial and body surface potentials: a modeling study , 2003, IEEE Transactions on Biomedical Engineering.

[42]  F. Charpentier,et al.  Electrophysiologic characteristics of cells spanning the left ventricular wall of human heart: evidence for presence of M cells. , 1995, Journal of the American College of Cardiology.

[43]  R. Beyar,et al.  A Computer Study of the Left Ventricular Performance Based on Fiber Structure, Sarcomere Dynamics, and Transmural Electrical Propagation Velocity , 1984, Circulation research.

[44]  R. Gulrajani,et al.  A Simulation Study of the Effects of Torso Inhomogeneities on Electrocardiographic Potentials, using Realistic Heart and Torso Models , 1983, Circulation research.

[45]  R M Gulrajani,et al.  A computer heart model incorporating anisotropic propagation. I. Model construction and simulation of normal activation. , 1993, Journal of electrocardiology.

[46]  H. Wellens,et al.  Repolarizing K+ currents ITO1 and IKs are larger in right than left canine ventricular midmyocardium. , 1999, Circulation.

[47]  C. Grimbergen,et al.  Properties of unipolar electrograms recorded with a multielectrode basket catheter. , 2004, Journal of electrocardiology.

[48]  P. Hunter,et al.  A Deformable Finite Element Derived Finite Difference Method for Cardiac Activation Problems , 2003, Annals of Biomedical Engineering.

[49]  Natalia A. Trayanova,et al.  Computational techniques for solving the bidomain equations in three dimensions , 2002, IEEE Transactions on Biomedical Engineering.

[50]  Michael D. Lesh,et al.  Cellular Uncoupling Can Unmask Dispersion of Action Potential Duration in Ventricular Myocardium A Computer Modeling Study , 1989, Circulation research.

[51]  Ingemar Ragnemalm Neighborhoods for distance transformations using ordered propagation , 1992, CVGIP Image Underst..

[52]  R. Barr,et al.  Propagation of excitation in idealized anisotropic two-dimensional tissue. , 1984, Biophysical journal.

[53]  J. Ross,et al.  Fiber Orientation in the Canine Left Ventricle during Diastole and Systole , 1969, Circulation research.

[54]  A. J. Pullan,et al.  Mathematical models and numerical methods for the forward problem in cardiac electrophysiology , 2002 .

[55]  Gernot Plank,et al.  Defibrillation Depends on Conductivity Fluctuations and the Degree of Disorganization in Reentry Patterns , 2005, Journal of cardiovascular electrophysiology.

[56]  R. Lux,et al.  Effect of Myocardial Fiber Direction on Epicardial Potentials , 1994, Circulation.

[57]  C. Luo,et al.  A dynamic model of the cardiac ventricular action potential. I. Simulations of ionic currents and concentration changes. , 1994, Circulation research.

[58]  B. Victorri,et al.  Numerical integration in the reconstruction of cardiac action potentials using Hodgkin-Huxley-type models. , 1985, Computers and biomedical research, an international journal.

[59]  Mirza Faisal Beg,et al.  Computational cardiac anatomy using MRI , 2004, Magnetic resonance in medicine.

[60]  D. Geselowitz,et al.  Simulation Studies of the Electrocardiogram: I. The Normal Heart , 1978, Circulation research.

[61]  Tony F. Chan,et al.  A Quasi-Minimal Residual Variant of the Bi-CGSTAB Algorithm for Nonsymmetric Systems , 1994, SIAM J. Sci. Comput..

[62]  R. Gulrajani Bioelectricity and biomagnetism , 1998 .

[63]  R. Lux,et al.  Epicardial Potential Mapping: Effects of Conducting Media on Isopotential and Isochrone Distributions , 1991, Circulation.

[64]  G. Huiskamp,et al.  Simulation of depolarization in a membrane-equations-based model of the anisotropic ventricle , 1998, IEEE Transactions on Biomedical Engineering.

[65]  C. Henriquez,et al.  Bipolar stimulation of a three-dimensional bidomain incorporating rotational anisotropy , 1998, IEEE Transactions on Biomedical Engineering.

[66]  D. Durrer,et al.  Epicardial and intramural excitation of normal heart in six patients 50 years of age and older. , 1968, British heart journal.

[67]  Bruce Smaill,et al.  A Finite Volume Method for Modeling Discontinuous Electrical Activation in Cardiac Tissue , 2005, Annals of Biomedical Engineering.

[68]  C. Henriquez,et al.  Modeling impulse propagation and extracellular potential distributions in anisotropic cardiac tissue using a finite volume element discretization , 2002 .

[69]  R. Barr,et al.  Relating Epicardial to Body Surface Potential Distributions by Means of Transfer Coefficients Based on Geometry Measurements , 1977, IEEE Transactions on Biomedical Engineering.

[70]  P. Sonneveld CGS, A Fast Lanczos-Type Solver for Nonsymmetric Linear systems , 1989 .

[71]  B. Roth Influence of a perfusing bath on the foot of the cardiac action potential. , 2000, Circulation research.

[72]  William H. Press,et al.  The Art of Scientific Computing Second Edition , 1998 .

[73]  D B Geselowitz,et al.  Simulation Studies of the Electrocardiogram: II. Ischemia and Infarction , 1978, Circulation research.

[74]  I R Efimov,et al.  Virtual Electrodes and Deexcitation: New Insights into Fibrillation Induction and Defibrillation , 2000, Journal of cardiovascular electrophysiology.

[75]  Natalia A Trayanova,et al.  Asymmetry in membrane responses to electric shocks: insights from bidomain simulations. , 2004, Biophysical journal.

[76]  Christopher R. Johnson,et al.  Three-dimensional Propagation in Mathematic Models: Integrative Model of the Mouse Heart , 2004 .