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Generalized Minimal Residual Method (GMRes) vs. Tikhonov Regularization

(Ramanathan, Annals of Biomedical Engineering 2003; 31:981) . In the same experimental protocol,
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2.5 cm apart pacing sites were reconstructed with GMRes with 4mm and 6mm localization error;
Tikhonov zero order reconstructed only one minimum. CC during repolarization (the T wave) was
much better for GMRes (0.72) than for Tikhonov regularization (0.57); Tikhonov resulted in much

greater smoothing.

L1– norm Regularization (Ghosh, Annals of Biomedical Engineering 2009; 37:902) 272 .
L1-norm solutions were compared to zero-order and first-order L2-norm Tikhonov solutions and

to a measured “gold standards”. L1 norm resulted in more accurate solutions (average relative
error of 0.36 compared to 0.62) and less smoothing of potentials, preserving details of patterns and
potential gradients. Similar improvement was observed in the presence of an infarct. Morphologies
and multiple deflections of post-infarct electrograms were better preserved with L1-norm

(CC = 0.97 vs. 0.87).

Quadratic vs. Linear Interpolation (Ghosh, Annals of Biomed Eng 2005;33:1187) .
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Quadratic interpolation improves accuracy. It reduces the average relative error between measured

and reconstructed potentials by 25%. It dramatically improved preservation of electrogram
amplitudes over the entire epicardium, with relative error of 0.38 compared to 0.74 for linear inter-
polation; EGM morphologies were slightly improved (CC = 0.97 compared to 0.91). For single site
pacing, quadratic interpolation reduced the error in locating the pacing site from 4 mm to 2 mm.

For dual site pacing (2.5 cm apart), quadratic interpolation was able to differentiate and locate the
2 pacing sites, while linear interpolation failed to do so.

Method of Fundamental Solutions (Wang, Annals of Biomed Eng 2006;34:1272) 274 .

This method does not require meshing the heart and torso surfaces, thereby preventing mesh
related artifacts and errors. For single site pacing (anterior RV), it improves epicardial potentials
reconstruction (CC=0.92 and relative error = 0.47 relative to measured, compared to CC = 0.85 and
relative error = 0.97 with the boundary elements method). Pacing site location was determined

with 3 mm error, compared to 5 mm error with the boundary elements method. Electrograms and
isochrones were also reconstructed with high accuracy.

Incorporating Spatial and Temporal Information. Manual editing of directly recorded or

inverse-reconstructed maps has always been practiced. Determination of far – field influences, of
activation and repolarization times, and of initiation sites involves evaluation of time progression
(an example is the rotation and expansion of the epicardial potential pattern generated by focal
excitation) and of spatial relationships between electrograms in neighboring sites. Taking

advantage of the fact that the process of cardiac excitation is continuous in time, Oster (IEEE
Transactions on Biomedical Engineering 1992;39:65) applied the Twomey technique to
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incorporate information from the time progression of excitation in the regularization procedure