Estimation of the Bidomain Conductivity Parameters of Cardiac Tissue From Extracellular Potential Distributions Initiated by Point Stimulation

A method for determining the bidomain conductivity values is developed. The study was generated because the different sets of measured conductivity values reported in the literature each produce significantly different bidomain simulation results. The method involves mapping the propagation of the electrical activation of cardiac tissue, initiated by point stimulation, via extracellular electrodes. A time-dependent bidomain model is used to simulate the electrical phenomena. The optimum set of conductivity values is achieved by minimizing the difference between the bidomain model output and the measured extracellular potential, by means of inverse techniques in parameter estimation least-squares and singular value decomposition. The method is validated with synthetic data with added random noise. Other parameters in the model such as membrane capacitance and fiber angle can also be estimated. The method takes a different approach to the conventional four-electrode technique, as it does not require the small electrode separation needed to separate the extracellular current from the intracellular.

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

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

[3]  Peter R. Johnston,et al.  The importance of anisotropy in modeling ST segment shift in subendocardial ischaemia , 2001, IEEE Transactions on Biomedical Engineering.

[4]  C. Li A computer simulation of ST segment shift in myocardial ischaemia , 1998 .

[5]  Xuyao Zheng Inversion for elastic parameters in weakly anisotropic media , 2004 .

[6]  D. Marquardt An Algorithm for Least-Squares Estimation of Nonlinear Parameters , 1963 .

[7]  P. C. Franzone,et al.  Wavefront propagation in an activation model of the anisotropic cardiac tissue: asymptotic analysis and numerical simulations , 1990, Journal of mathematical biology.

[8]  Richard L. Cooley,et al.  Simultaneous confidence and prediction intervals for nonlinear regression models with application to a groundwater flow model , 1987 .

[9]  R. C. Susil,et al.  A generalized activating function for predicting virtual electrodes in cardiac tissue. , 1997, Biophysical journal.

[10]  B. Roth,et al.  The effect of externally applied electrical fields on myocardial tissue , 1996, Proc. IEEE.

[11]  Peter R. Johnston,et al.  The effect of conductivity values on ST segment shift in subendocardial ischaemia , 2003, IEEE Transactions on Biomedical Engineering.

[12]  A. M. Scher,et al.  Effect of Tissue Anisotropy on Extracellular Potential Fields in Canine Myocardium in Situ , 1982, Circulation research.

[13]  Kenneth Levenberg A METHOD FOR THE SOLUTION OF CERTAIN NON – LINEAR PROBLEMS IN LEAST SQUARES , 1944 .

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

[15]  Bradley J. Roth,et al.  The effect of plunge electrodes during electrical stimulation of cardiac tissue , 2001, IEEE Transactions on Biomedical Engineering.

[16]  C. Henriquez,et al.  Estimation of Cardiac Bidomain Parameters from Extracellular Measurement: Two Dimensional Study , 2006, Annals of Biomedical Engineering.

[17]  J. Stinstra,et al.  On the Passive Cardiac Conductivity , 2005, Annals of Biomedical Engineering.

[18]  Gui-rong Liu,et al.  Computational Inverse Techniques in Nondestructive Evaluation , 2003 .

[19]  C. Luo,et al.  A model of the ventricular cardiac action potential. Depolarization, repolarization, and their interaction. , 1991, Circulation research.

[20]  N. G. Sepulveda,et al.  Current injection into a two-dimensional anisotropic bidomain. , 1989, Biophysical journal.

[21]  B. Taccardi,et al.  Spread of Excitation in a Myocardial Volume: , 1993, Journal of cardiovascular electrophysiology.

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

[23]  B. Taccardi,et al.  Anisotropic Mechanisms for Multiphasic Unipolar Electrograms: Simulation Studies and Experimental Recordings , 2000, Annals of Biomedical Engineering.

[24]  A. M. Scher,et al.  Influence of Cardiac Fiber Orientation on Wavefront Voltage, Conduction Velocity, and Tissue Resistivity in the Dog , 1979, Circulation research.

[25]  B. Taccardi,et al.  Potential Distributions Generated By Point Stimulation in a Myocardial Volume: , 1993, Journal of cardiovascular electrophysiology.

[26]  Rob S. MacLeod,et al.  A Mechanism for ST Depression Associated with Contiguous Subendocardial Ischemia Short title: Mechanism for ST Depression , 2004 .

[27]  N. Sun Inverse problems in groundwater modeling , 1994 .

[28]  J. Stinstra,et al.  Using models of the passive cardiac conductivity and full heart anisotropic bidomain to study the epicardial potentials in ischemia , 2004, The 26th Annual International Conference of the IEEE Engineering in Medicine and Biology Society.

[29]  Wanda Krassowska,et al.  Theoretical versus experimental estimates of the effective conductivities of cardiac muscle , 1992, Proceedings Computers in Cardiology.

[30]  M. C. Hill Methods and guidelines for effective model calibration; with application to UCODE, a computer code for universal inverse modeling, and MODFLOWP, a computer code for inverse modeling with MODFLOW , 1998 .

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

[32]  C. Luo,et al.  A dynamic model of the cardiac ventricular action potential. II. Afterdepolarizations, triggered activity, and potentiation. , 1994, Circulation research.

[33]  Peter Rex Johnston Tissue conductivity and ST depression in a cylindrical left ventricle. , 2002 .

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

[35]  B. Babbitt,et al.  METHODS AND GUIDELINES FOR EFFECTIVE MODEL CALIBRATION , 2001 .

[36]  L. Clerc Directional differences of impulse spread in trabecular muscle from mammalian heart. , 1976, The Journal of physiology.

[37]  Y. Shoham,et al.  Inversion of anisotropic magnetotelluric data , 1977 .

[38]  Craig S. Henriquez,et al.  Using computer models to understand the roles of tissue structure and membrane dynamics in arrhythmogenesis , 1996, Proc. IEEE.

[39]  B. Taccardi,et al.  Multiple Components in the Unipolar Electrogram: A Simulation Study in a Three‐Dimensional Model of Ventricular Myocardium , 1998, Journal of cardiovascular electrophysiology.

[40]  F. J. Claydon,et al.  Patterns of and mechanisms for shock-induced polarization in the heart: a bidomain analysis , 1999, IEEE Transactions on Biomedical Engineering.

[41]  G. W. Beeler,et al.  Reconstruction of the action potential of ventricular myocardial fibres , 1977, The Journal of physiology.

[42]  F. Trelles,et al.  Measurement of myocardial conductivities with a four-electrode technique in the frequency domain , 1997, Proceedings of the 19th Annual International Conference of the IEEE Engineering in Medicine and Biology Society. 'Magnificent Milestones and Emerging Opportunities in Medical Engineering' (Cat. No.97CH36136).

[43]  J. Keener,et al.  A numerical method for the solution of the bidomain equations in cardiac tissue. , 1998, Chaos.

[44]  J. Doherty,et al.  A hybrid regularized inversion methodology for highly parameterized environmental models , 2005 .

[45]  I W Hunter,et al.  An anatomical heart model with applications to myocardial activation and ventricular mechanics. , 1992, Critical reviews in biomedical engineering.

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

[47]  Robert Plonsey,et al.  Quantitative Formulations of Electrophysiological Sources of Potential Fields in Volume Conductors , 1984, IEEE Transactions on Biomedical Engineering.

[48]  Pierre Savard,et al.  Measurement of myocardial conductivities with an eight-electrode technique in the frequency domain , 1995, Proceedings of 17th International Conference of the Engineering in Medicine and Biology Society.

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

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

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

[52]  R. Lux,et al.  High-density epicardial mapping during current injection and ventricular activation in rat hearts. , 1998, American journal of physiology. Heart and circulatory physiology.

[53]  P. Hunter,et al.  Mathematical model of geometry and fibrous structure of the heart. , 1991, The American journal of physiology.

[54]  John A. Board,et al.  A modular simulation system for the bidomain equations , 1999 .