Noninvasive electrocardiographic imaging (ECGI): application of the generalized minimal residual (GMRes) method

Abstract

Electrocardiographic imaging (ECGI) is a developing imaging modality for cardiac electrophysiology and arrhythmias. It reconstructs epicardial potentials, electrograms, and isochrones from electrocardiographic body-surface potentials noninvasively. Current ECGI methodology employs Tikhonov regularization, which imposes constraints on the reconstructed potentials or their derivatives. This approach can sometimes reduce spatial resolution by smoothing the solution. Accuracy depends on a priori knowledge of solution characteristics and determination of an optimal regularization parameter. These properties led us to implement an independent, iterative approach for ECGI--the generalized minimal residual (GMRes) method--which does not apply constraints. GMRes was applied to experimental data during activation/repolarization of normal and infarcted hearts. GMRes reconstructions were compared to Tikhonov reconstructions and to measured "gold standards" in isolated hearts. Overall, the accuracy of GMRes solutions was similar to Tikhonov regularization. However, in certain cases GMRes recovered localized potential features (e.g., multiple potential minima), which were lost in the Tikhonov solution. Simultaneous use of these two complementary methods in clinical ECGI will ensure reliability and maximal extraction of diagnostic information in the absence of a priori information about a patient's condition.

FIGURE 1

Condition-L curves and L curves. Panel A: curves for single-site pacing data 25 ms (left) and 50 ms (right) after pacing. Top row: condition-L curve for GMRes. Second row: L curve for GMRes. Bottom row: L curve for Tikhonov regularization. Panel B: curves for dual-site pacing data. Same format as panel A. Note that the condition-L curves are in semilog scale and the L curves are log-log scale.

FIGURE 2

Epicardial potential maps 25 ms after pacing from a single site (indicated by the asterisk). Measured potentials (left), GMRes reconstruction (middle), and Tikhonov reconstruction (right) are shown on an anterior view of the epicardial envelope. + and - indicate potential maxima and minima, respectively. Potential values (in microvolts) are displayed using a color scale. Inset shows a simplified (approximate) equivalent source configuration consisting of two opposing dipoles along the major axis of an elliptical wave front propagating from the pacing site. The major axis of the wave front is oriented along local fiber orientation (indicated by gray lines). This generates a potential pattern of a central negative region containing two minima and two flanking maxima oriented along the fiber direction, which is reconstructed by both GMRes and Tikhonov.

FIGURE 3

Simultaneous dual-site pacing. Top row: potential maps during activation (25 ms after pacing). Left-most column shows the body surface potential map (BSPM). Second column shows directly measured epicardial potentials. Third column shows the GMRes reconstruction. Right-most column shows corresponding Tikhonov reconstruction. Insets A and B show Tikhonov reconstructions for time frames 23 and 27 ms, respectively. Asterisks in each epicardial potential map indicate the location of the pacing sites. Bottom row: potential maps during repolarization (90 ms after pacing). Bottom row follows the same format from left to right as the top row. Insets C and D show Tikhonov reconstructions for time frames 88 and 92 ms. + and - signs indicate potential maxima and minima, respectively. Lead II of the ECG is provided for timing purposes.

FIGURE 4

Epicardial electrograms and potential maps pre- and postinfarction. The left column in panels A, B, and C shows the measured electrogram, the middle column the GMRes reconstruction, and the third column the Tikhonov reconstruction. Numbers in boxes indicated epicardial sites. Panels A and B: electrogram from site 1, located remote to the infarct. Panel A shows electrogram preinfarction. Panel B shows electrograms from the same site, postinfarction. Panels C and D, top row: electrograms from site 2, located inside the infarct region. Bottom row: electrograms from site 3, also located inside the infarct region. Panel C, preinfarction; panel D, postinfarction. CC: correlation coefficient relative to the measured electrogram. Panel E: diagram of the epicardial surface of the heart showing the infarct region (dashed line) and the locations of electrograms 1, 2, and 3. Panel F, top row: epicardial potential maps for the preinfarction heart (time frame of 48 ms after pacing). Measured (left), GMRes reconstruction (middle), and Tikhonov reconstruction (right). Bottom row: corresponding epicardial potential maps for the infarcted heart.

FIGURE 5

Isochrone maps during monomorphic ventricular tachycardia (VT). Two consecutive cycles are shown. Top row: first cycle. On the left are directly measured isochrone maps. The GMRes and Tikhonov reconstructions are shown in the middle and right columns, respectively. White arrows indicate direction of wave front propagation. Black lines indicate conduction block. Blue region at the base is late activation from the previous cycle that occurs about the same time as the beginning of the present cycle at the entrance to the common pathway between the lines of block. Bottom row: second cycle. Same format as the top row.

FIGURE 6

Measured (left), GMRes reconstruction (middle), Tikhonov reconstruction (right) of epicardial QRST integral maps during enhanced regional dispersion of repolarization induced by localized cooling. Dotted rectangular box in the measured map shows the shape and location of the cooling probe.

FIGURE 7

Tikhonov-GMRes hybrid method for the dual-site pacing data of Fig. 3. Tikhonov zero order provided the initial values for the GMRes iterative procedure. Measured epicardial potentials (left) and Tikhonov-GMRes reconstructed images (right).

FIGURE 8

Potential maps for progressive numbers of GMRes iterations (dual-site pacing, 25 ms). Condition-L curve corner is at iteration 19 (dark box indicates chosen solution). Note moderate change in solution between 17 and 21 iterations and clear deterioration of solution for iteration ≥22.

FIGURE 9

CC of reconstructed potential maps as a function of number of GMRes iterations for all data sets. CC were calculated with respect to measured epicardial potentials and averaged over the entire cardiac cycle. The CC values are bell shaped, with a “plateau region” near the peak value. The iteration corresponding to the solution chosen by the condition-L-curve criterion is in this region and is indicated by the corresponding enlarged symbol shaded black.