A Patchwork Method to Improve the Performance of Current Methods for Solving the Inverse Problem of Electrocardiography.

OBJECTIVE: Noninvasive electrocardiographic imaging (ECGI) reconstructs cardiac electrical activity from body surface potential measurements. However, current methods have demonstrated inaccuracies in reconstructing sinus rhythm, and in particular breakthrough sites. This study aims to combine existing inverse algorithms, making the most of their advantages while minimizing their limitations. METHOD: The "patchwork method" (PM) combines two classical numerical methods for ECGI: the method of fundamental solutions (MFS) and the finite-element method (FEM). We assume that the method with the smallest residual in the predicted torso potentials, computed using the boundary element method (BEM), provides the most accurate solution. The PM selects for each heart node and time step the method whose estimated reconstruction error is smallest. The performance of the PM was evaluated using simulated ectopic and normal ventricular beats. RESULTS: Cardiac potentials and activation maps obtained with the PM (CC = 0.63 ± 0.01 and 0.61 ± 0.05 respectively) were more accurate than MFS (CC = 0.61 ± 0.01 and 0.48 ± 0.05 respectively), FEM (CC = 0.58 ± 0.01 and 0.51 ± 0.02 respectively) or BEM (CC = 0.57 ± 0.02 and 0.49 ± 0.02 respectively). The PM also located all epicardial breakthrough sites, whereas the traditional numerical methods usually missed one. Furthermore, the PM showed its robustness and stability in the presence of Gaussian noise added to the torso potentials. CONCLUSION: The PM overcomes some of the limitations of classical numerical methods, improving the accuracy of mapping important features of activation during sinus rhythm and paced beats. SIGNIFICANCE: This novel method for optimizing ECGI solutions opens a new avenue for improving not only ECGI but also other inverse problems.

"Classical" electropermeabilization modeling at the cell scale.

The aim of this paper is to provide new models of cell electropermeabilization involving only a few parameters. A static and a dynamical model, which are based on the description of the electric potential in a biological cell, are derived. Existence and uniqueness results are provided for each differential system, and an accurate numerical method to compute the solution is described. We then present numerical simulations that corroborate the experimental observations, providing the consistency of the modeling. We emphasize that our new models involve very few parameters, compared with the most achieved models of Neu and Krassowska (Phys Rev E 53(3):3471-3482, 1999) and DeBruin and Krassowska (Biophys J 77:1225-1233, 1999), but they provide the same qualitative results. Thus, these models will facilitate drastically the forthcoming inverse problem solving, which will consist in fitting them with the experiments.