Total Variation Regularization in Electrocardiographic Mapping

Electrocardiographic mapping (ECGM) is to estimate the cardiac activities from the measured body surface potentials (BSPs), in which the epicardial potentials (EPs) is often reconstructed. One of the challenges in ECGM problem is its ill-posedness, and regularization techniques are needed to obtain the clinically reasonable solutions. The total variation (TV) method has been validated in keeping the sharp edges and has found some preliminary applications in ECG inverse problem. In this study, we applied and compared two algorithms: lagged diffusivity (LD) fixed point iteration and primal dual-interior point method (PD-IPM), to implement TV regularization method in ECGM problem. With a realistic heart-lung-torso model, the TV methods are tested and compared to the L2-norm regularization methods in zero- and first-order. The simulation results demonstrate that the TV method can generate better EPs compared to the zero-order Tikhonov method. Compared to the first-order Tikhonov method, the TV's results are much sharper. For the two algorithms in TV method, the LD algorithm seems more robust than the PD-IPM in ECGM problem, though the PD-IPM converges faster.

[1]  S Crozier,et al.  Electrodynamic Heart Model Construction and ECG Simulation , 2006, Methods of Information in Medicine.

[2]  Joakim Sundnes,et al.  A Computationally Efficient Method for Determining the Size and Location of Myocardial Ischemia , 2009, IEEE Transactions on Biomedical Engineering.

[3]  A. N. Tikhonov,et al.  Solutions of ill-posed problems , 1977 .

[4]  Andrea Borsic,et al.  Regularisation methods for imaging from electrical measurements. , 2002 .

[5]  Andy Adler,et al.  In Vivo Impedance Imaging With Total Variation Regularization , 2010, IEEE Transactions on Medical Imaging.

[6]  Y Rudy,et al.  The inverse problem in electrocardiography: solutions in terms of epicardial potentials. , 1988, Critical reviews in biomedical engineering.

[7]  Lei Ding,et al.  Sparse source imaging in electroencephalography with accurate field modeling , 2008, Human brain mapping.

[8]  L. Xia,et al.  Combination of the LSQR method and a genetic algorithm for solving the electrocardiography inverse problem. , 2007, Physics in medicine and biology.

[9]  Michael L. Overton,et al.  An Efficient Primal-Dual Interior-Point Method for Minimizing a Sum of Euclidean Norms , 2000, SIAM J. Sci. Comput..

[10]  Ling Xia,et al.  Solving the ECG Forward Problem by Means of Standard h- and h-Hierarchical Adaptive Linear Boundary Element Method: Comparison With Two Refinement Schemes , 2009, IEEE Transactions on Biomedical Engineering.

[11]  L. Weixue,et al.  Computer simulation of epicardial potentials using a heart-torso model with realistic geometry. , 1996, IEEE transactions on bio-medical engineering.

[12]  P. Hansen.  Rank-Deficient and Discrete Ill-Posed Problems: Numerical Aspects of Linear Inversion , 1987 .

[13]  L. Rudin,et al.  Nonlinear total variation based noise removal algorithms , 1992 .

[14]  Ling Xia,et al.  Truncated Total Least Squares: A New Regularization Method for the Solution of ECG Inverse Problems , 2008, IEEE Transactions on Biomedical Engineering.

[15]  R. Throne,et al.  A comparison of spatial regularization with zero and first order Tikhonov regularization for the inverse problem of electrocardiography , 2000, Computers in Cardiology 2000. Vol.27 (Cat. 00CH37163).

[16]  Y. Rudy,et al.  Application of L1-Norm Regularization to Epicardial Potential Solution of the Inverse Electrocardiography Problem , 2009, Annals of Biomedical Engineering.

[17]  Y. Rudy,et al.  Noninvasive electrocardiographic imaging for cardiac electrophysiology and arrhythmia , 2004, Nature Medicine.