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. Author manuscript; available in PMC: 2018 Aug 1.
Published in final edited form as: Heart Rhythm. 2017 Apr 10;14(8):1224–1233. doi: 10.1016/j.hrthm.2017.04.017

Highest dominant frequency and rotor positions are robust markers of driver location during noninvasive mapping of atrial fibrillation: A computational study

Miguel Rodrigo *, Andreu M Climent *,†,‡, Alejandro Liberos *,†,‡, Francisco Fernández-Avilés †,‡,§, Omer Berenfeld , Felipe Atienza †,‡,§, Maria S Guillem *
PMCID: PMC5568422  NIHMSID: NIHMS888347  PMID: 28408329

Abstract

BACKGROUND

Dominant frequency (DF) and rotor mapping have been proposed as noninvasive techniques to guide localization of drivers maintaining atrial fibrillation (AF).

OBJECTIVE

The purpose of this study was to evaluate the robustness of both techniques in identifying atrial drivers noninvasively under the effect of electrical noise or model uncertainties.

METHODS

Inverse-computed DFs and phase maps were obtained from 30 different mathematical AF simulations. Epicardial highest dominant frequency (HDF) regions and rotor location were compared with the same inverse-computed measurements after addition of noise to the ECG, size variations of the atria, and linear or angular deviations in the atrial location inside the thorax.

RESULTS

Inverse-computed electrograms (EGMs) individually correlated poorly with the original EGMs in the absence of induced uncertainties (0.45 ± 0.12) and were worse with 10-dB noise (0.22 ± 0.11), 3-cm displacement (0.01 ± 0.02), or 36° rotation (0.02 ± 0.03). However, inverse-computed HDF regions showed robustness against induced uncertainties: from 82% ± 18% match for the best conditions, down to 73% ± 23% for 10-dB noise, 77% ± 21% for 5-cm displacement, and 60% ± 22% for 36° rotation. The distance from the inverse-computed rotor to the original rotor was also affected by uncertainties: 0.8 ± 1.61 cm for the best conditions, 2.4 ± 3.6 cm for 10-dB noise, 4.3 ± 3.2 cm for 4-cm displacement, and 4.0 ± 2.1 cm for 36° rotation. Restriction of rotor detections to the HDF area increased rotor detection accuracy from 4.5 ± 4.5 cm to 3.2 ± 3.1 cm (P <.05) with 0-dB noise.

CONCLUSION

The combination of frequency and phase-derived measurements increases the accuracy of noninvasive localization of atrial rotors driving AF in the presence of noise and uncertainties in atrial location or size.

Keywords: Electrocardiographic imaging, Inverse problem, Dominant frequency, Rotor, Dominant region

Introduction

Personalized characterization of patterns of activation in patients with atrial fibrillation (AF) using the novel noninvasive electrocardiographic imaging (ECGI) method has been reported with successful ablation rates.1 The method has been used to identify the hierarchy of dominant AF regions by noninvasively measuring dominant frequencies (DFs)2 or rotors on the epicardial wall of the atria.1 However, the propagation patterns that result from the inverse problem solution during AF seem to be simpler1,3 than those obtained using intracardiac contact electrodes and optical mapping experiments,4,5 with less and smoother simultaneous wavefronts. These discrepancies between contact and noncontact mapping techniques raise some skepticism regarding the accuracy of the method in characterizing the true propagation patterns and rotors during AF and in understanding AF mechanisms despite successful AF ablation guided by inverse solution mapping.1

In this study, we used multiple computer simulations to quantify the accuracy of ECGI-based AF driver detection under uncertainties that are relevant to its usage in the clinical setting. Variations in the geometry of the computer model, including location, orientation and size of the atria, and varying electrical noise, are introduced into the inverse problem solution of body surface potentials to assess the accuracy of the solutions relative to the atrial activity used to generate the surface potentials.

Methods

Mathematical models

A realistic 3-dimensional model of the atrial anatomy was used to simulate atrial electrical activity. Heterogeneity in the electrophysiologic properties of the atrial myocardium was introduced as changes in ionic currents and fibrosis distribution to generate AF maintained by rotors and fibrillatory activity exhibiting nonuniform propagation patterns and different shapes and extensions of the dominant region (see Mathematical Models section in the Supplementary Material). An ensemble of 30 different AF episodes driven by a single rotor at varying locations was simulated (see Supplemental Figures 1 through 4).

For each simulation, a uniform mesh of unipolar electrograms (EGMs) was calculated surrounding the epicardial surface. The ECG potentials on the torso model were calculated by solving the forward problem, and then the inverse-computed EGMs (icEGMs) were reconstructed on the atrial surface by solving the inverse problem using the zero-order Tikhonov and L-curve methods. Temporal series of EGMs and icEGMs were compared in terms of correlation coefficients.

Addition of model and signal uncertainties for the inverse problem solution

To evaluate the robustness of the inverse solution approach against model uncertainties, we evaluated the accuracy of the solution under 4 uncertainty conditions: (1) noise, (2) error in atrial size, (3) error in atrial location, and (4) error in atrial orientation inside the torso volume. Those uncertainties were generated by (1) white Gaussian noise added to the surface ECG signals with a signal-to-noise ratio (SNR) between 60 dB (low noise) and 0 dB (high noise); (2) deviations in atrial size from −20% to +20% (80%–120% of its original dimension in each axis); (iii) displacements in atrial position from 0 to 5 cm in the lateral axis (x-axis in Figure 1A); and (iv) atrial rotations from 0° to 45° around the lateral axis.

Figure 1.

Figure 1

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Numerical setup and examples of uncertainties in inverse-computed maps. A: Schematic view of the torso (green) and the reference atrial (red) surface at its original position. B: Original potential map for an episode of atrial fibrillation maintained by a rotor in the left atrium. C: Inverse-computed potential map for the simulation in shown in panel B. Inverse-computed potential maps for the simulation in panel A solved (D) with 10 dB of signal-to-noise ratio, (E) with a 20% enlarged atrium, (F) at displaced (2 cm) position, and (G) at rotated (27°) position. EGM = electrogram; icEGM = inverse-computed electrogram.

Rotor and DF identification

Rotor localization was automated based on identification of singularity points (SPs) in the phase signal map obtained with the Hilbert transform. Only long-lasting SPs (>1 rotation) were considered rotors, and other SPs were discarded.6 Histograms of atrial rotors presence were obtained by counting the number of rotors in each atrial model node, and the node with the highest SP presence was considered the rotor place.

For DF analysis, the power spectral density of all signals was computed using Welch periodograms to determine local DFs.7 Because a spatial correlation in our unstructured mesh does not accurately account for the discrete metric in the DF maps, we compared inverse-computed DF maps with the original DF maps in terms of the concordance of their highest dominant frequency (HDF) regions, defined as the intersection between HDF regions (or regions within 0.5 Hz from the HDF) over the original HDF region. The distance between the barycenters of the original and the inverse-computed HDF regions was also calculated.

Results

Illustrating sample cases

Epicardial maps based on inverse-computed potentials always differed from those computed from the original EGMs. Figure 1A shows a schematic view of the 3-dimensional torso model used for the inverse solution and the atrial surface at its reference position. The potential distributions for an AF episode driven by a stable rotor is shown in Figure 1B. Figure 1C shows the inverse-computed voltage map following the inverse solution under the best possible conditions, that is, with no added electrical noise to the ECGs and with the atria at their reference position. As shown, the inverse-computed voltage map is smoother than the original EGMs due to the inability of the inverse solution to reconstruct the wavefront irregularity produced by the fibrotic tissue.6 However, the activating wavefront (transition from blue to red color) around the rotor is at the same place.

Figure 1D shows the inverse-computed maps after the inverse solution with noise added to the ECG (10-dB SNR). As expected, the inverse-computed voltage map differed from the original map to a greater extent than those computed with no addition of uncertainties, but the potential map still retained some similarity with the original map. The inverse solution based on a mismatch in the atrial size used in the inverse solution (120%) (Figure 1E) presented a potential distribution similar to that obtained under the best conditions. Inverse-computed potential map with atrial displacement of 2 cm (Figure 1F) and rotation of 27° (Figure 1G) relative to the reference position and orientation also retained the main features of the original map, although some other incorrect wavefronts appeared on the icEGM map.

EGM signal correlation

Figure 2A shows the original (blue) and inverse-computed (red) EGM signals from a point near the rotor core of the simulation in Figure 1 for 2 inverse solutions: with no noise (60-dB SNR) and under noisy conditions (0-dB SNR). Even for the best scenario (no noise), the inverse-computed signal notability differed from the original EGM signal, although it still retained the main activation sequence showing a correlation coefficient of 0.61. However, the addition of noise reduced the similarity between the original and inverse-computed signals, showing a correlation of 0.27. A summary of the measured correlation coefficients in the whole database is given in Figure 2, showing that the correlation coefficient for EGM signals (0.45 ± 0.12) was poor even in the absence of noise or model uncertainties. Addition of white noise to the surface ECGs before computing the inverse solution decreased this correlation coefficient to 0.18 ± 0.1 for 0-dB SNR. Uncertainties in atrial size moderately decreased the correlation coefficient down to 0.33 ± 0.10 for 80% (Figure 2C). Uncertainties in the location or orientation of the atria inside the torso volume, however, had a large impact on the correlation coefficients, as shown in Figures 2D and 2E. Correlation coefficients decreased from 0.41 ± 0.13 for 0 cm down to 0.01 ± 0.02 for a 3-cm displacement, and down to 0.03 ± 0.05 for 27° of rotation.

Figure 2.

Figure 2

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Correlation of inverse-computed electrogram (icEGMs) with original electrograms (EGMs). A: Comparison between original (EGM) and inverse-computed signals (icEGM) from a point in the posterior left atrial wall (PLAW) under 2 levels of ECG noise. Average correlation coefficients under variations in (B) ECG noise, (C) size, (D) displacement, and (E) rotation.

Notably, the correlation coefficient between icEGMs and original EGMs showed significantly higher values in the HDF regions than in the rest of the passively activated atrial tissue (see Supplemental Figure 5). This trend was observed for all scenarios in which the general correlation coefficient was significantly different from 0: for 60-, 30-, 20-, and 10-dB SNR in the ECG; for all atrial sizes; for 1-cm, 2-cm, and 3-cm displacement; and for rotations of 0°, 9°, and 18°. These values could be explained by the more stable propagation patterns in the area of the rotor, where the propagation had clear wavefronts, relative to the peripheral passive tissue where there was fibrillatory conduction.

HDF regions

Although the morphology of icEGMs and their original EGMs has been shown to be poorly related, they do allow for robust estimation of the local activation rate (or DF) against signal or model uncertainties (Figure 3). Inverse-computed DF map (Figure 3B) presented a high correlation with the original DF map (Figure 3) in the absence of ECG noise, and the extent and position of the HDF region were preserved following the inverse solution. In the presence of ECG noise (Figure 3C), identification of the HDF region was accomplished with a concordance >75% for SNRs as low as 10 dB that decreased to 56.5% ± 32.3% for 0 dB. Changes in atrial size did not result in noticeable changes in HDF region concordance, which remained stable around 85% ± 10%. Notably, identification of the HDF region was very robust against uncertainties in the atrial location, with mean concordance values above 75.9% ± 11.9% for uncertainty of 3 cm in location. Inverse-computed DF maps were more sensitive to angular deviations (but less sensitive than the EGMs), where the concordance of the HDF progressively decreased from 84.5% ± 10.6% for 0° down to 56.2% ± 23.0% for 45°.

Figure 3.

Figure 3

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Concordance of inverse-computed highest dominant frequency (HDF) region with original HDF region. A: Original DF map. B: Inverse-computed DF map solved with 60 dB of noise-to-signal ratio. Average concordance values under variations in (C) ECG noise, (D) size, (E) displacement, and (F) rotation. EGM = electrogram; icEGM = inverse-computed electrogram.

The rationale behind the ability of the inverse solution to locate correctly HDF regions can be understood from the data shown in Supplemental Figure 6 showing that the HDF region is generally wider in the inverse-computed data compared to the original HDF region. Indeed, the addition of noise increased the size of the HDF region by 26.8% ± 32.2% for 60 dB up to 36.7% ± 35.1% for 20 dB, followed by a decrease down to −4.8% ± 53.0% for the largest level of noise at 0 dB. Decreases in atrial size also increased the HDF region (−10.4% ± 83.6% for 80% size), whereas atrial enlargement did not significantly alter HDF area size (15.2% ± 27.3% for 120% size). In contrast, displacement of atrial position resulted in a considerably higher increase in HDF area, up to 202.1% ± 169.9% for 5 cm, whereas an angular deviation provoked a maximum increase of 59.0% ± 78.6% for 45°.

Complementary to the data presented in Figure 3, the center of the original HDF maps and their inverse-computed counterparts were compared. Figure 4A shows the original DF map with its barycenter (black cross), which suffered a displacement (black dot, Figure 4B) compared with the barycenter of the HDF region of the inverse-computed DF map with a displacement of 2 cm in the atrial position. As can be seen in Figure 4C, this deviation for the entire database presented values <4 cm for every level of electrical noise added to the ECG, with an average value of 1.36 ± 0.78 cm for 0-dB SNR. Changes in atrial size increased the error in the HDF region center location to 1.67 ± 0.94 cm for 80% and 0.81 ± 0.56 cm for 120%. When atrial displacements were present in the inverse calculation, the distance between HDF region centers increased gradually with displacement, up to 3.12 ± 1.11 cm for 5 cm (Figure 4E). Finally, the angular deviations also showed a constant increment in the error of HDF center region location, which reached 3.15 ± 1.05 cm for 45°.

Figure 4.

Figure 4

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Error in noninvasive highest dominant frequency (HDF) center identification. A: Original DF map with the barycenter of the HDF (black cross). B: Inverse-computed DF map solved with 60 dB of noise-to-signal ratio with the barycenter of the HDF (black dot). Error average under variations in (C) ECG noise, (D) size, (E) displacement, and (F) rotation. EGM = electrogram; icEGM = inverse-computed electrogram.

Incidence of SP detections

The low accuracy and tendency for simplification of propagation patterns by the inverse solution did not allow full estimation of the complexity of the electrical patterns during our simulated AF. The original EGM maps presented more simultaneous nondriving, short-lasting rotors (8.5 ± 5.3) than their inverse-computed counterparts, even for high SNRs (e.g., 4.4 ± 2.5 for 60-dB SNR), and this number further gradually decreased down to 1.4 ± 0.3 for 0-dB SNR (see Supplemental Figure 7). Uncertainties in atrial location or orientation, however, had the opposite effect on the detected number of nondriving rotors, with up to 5.6 ± 2.6 for 1 cm and 14.6 ± 1.1 for 5-cm displacements and 4.6 ± 2.4 for 9° and 12.3 ± 4.7 for 45° rotations.

However, despite the sensitivity of rotor detection to signal or model uncertainties, driving rotor identification, defined as the region with the most frequently detected rotations, was robust. Figure 5 shows the phase map (top) and rotor location maps (bottom) for the original and the inverse-computed signals (Figures 5A and 5B, respectively). Due to the smoothing effect of the inverse solution, rotors tended to cluster in stable sites, and the rotor position (in red) was easily identified. In Figures 5C through 5F, the accuracy of this estimation is presented for the entire database. Figure 5C shows this error for both the original phase maps (0.7 ± 0.7 cm) and the inverse-computed maps under the effect of electrical noise. These average errors remained stable around 1 to 1.5 cm from 60 to 20 dB. For higher noise levels of 10 and 0 dB, the average value of the error in rotor location increased to 2.4 ± 3.6 cm and 4.5 ± 4.5 cm, respectively, but in both cases 50% of rotors were localized to <2 cm from their original location. Variations in atrial size (Figure 5D) did not result in significant variations with respect to the original location. Displacements in atrial position provoked a similar error in the inverse-computed rotor position: from 0.9 ± 1.3 cm for a 1-cm displacement to 4.7 ± 3.3 cm for a 5-cm displacement (Figure 5E). Rotations of the atria inside the thorax also resulted in incremental errors in the inverse-computed rotor position: from 1.2 ± 1.3 cm for 9° to 4.9 ± 2.6 cm for 45° (Figure 5F).

Figure 5.

Figure 5

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Error in noninvasive rotor position identification. A: Original EGM phase map for an episode of atrial fibrillation maintained by a rotor in the left atrium (top) and the histogram quantifying the rotor presence (bottom). B: Noninvasive electrocardiographic imaging phase map with 60-dB signal-to-noise ratio for the simulation in panel A (top) and the histogram quantifying the rotor presence (bottom). Error average under variations in (C) ECG noise, (D) size, (E) displacement, and (F) rotation. EGM = electrogram; icEGM = inverse-computed electrogram.

Inverse identification of the driving atrium

Next, the overall ability of the inverse solution in identifying the dominant atrium responsible for AF maintenance was also evaluated by both SP and HDF analysis. The atrial surface was divided into 2 anatomic regions (left atrium and right atrium), and the match between the original and inverse-estimated dominant atrium was quantified. As shown in Figure 6A, there was a good match in SP detection and rotor site (>90%) for all SNRs except for the most noisy case, for which the matching ratio decreased to 73% for 0 dB. Atrial size again had little effect on rotor region identification. Rotor region identification was also accurate (>80%) for deviations <4 cm or 36°.

Figure 6.

Figure 6

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Noninvasive identification of the dominant atrium by rotor histogram under variations in (A) ECG noise, (B) size, (C) displacement, and (D) rotation.

The ability to identify the dominant atrium by measuring the extension of the HDF region was evaluated (Figure 7). There was a good match (>90%) for all SNRs except for the most noisy case, for which the match ratio decreased to 87% for 0 dB, results that outperform SP-alone identification. Analysis of the inverse-computed HDF region was able to properly identify the dominant atrium for >90% of cases when changes in blood conductance (see Supplementary Material) or atrial location were present. However, changes in atrial orientation decreased this match ratio down to 80% for angular deviations >27°.

Figure 7.

Figure 7

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Noninvasive identification of the dominant atrium by highest dominant frequency (HDF) region analysis under variations in (A) ECG noise, (B) size, (C) displacement, and (D) rotation.

Combined SP and HDF approach for driver identification

Because driving rotors activate at the fastest rates in the atria and both DF and rotor measurements and localizations were robust against inverse problem uncertainties, these 2 parameters were combined to improve driver location. Figure 8 shows the error in atrial rotor location considering only those inverse-computed rotors present in the HDF region, compared to the error when all inverse-computed rotors were considered. As shown, the combination of information from both measurements can reduce the average error in the driver location. However, this reduction in the inverse-computed rotor location error is significant only for the extreme cases, as in the sample case shown in Figures 8A and 8B.

Figure 8.

Figure 8

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Rotor identification in the highest dominant frequency (HDF) region. Noninvasive rotor histogram (A) with 0-dB signal-to-noise ratio (SNR) and (B) with 0-dB SNR with only rotors inscribed inside the HDF region. Error in noninvasive rotor position identification by rotational activity (blue) and by rotational activity plus dominant frequency (red) under variations in (C) ECG noise, (D) size, (E) displacement, and (F) rotation. icEGM = inverse-computed electrogram.

Discussion

Main findings

In this work, we used mathematical models of the human torso and AF propagation to demonstrate that inverse-computed maps allow for accurate identification of atrial drivers, even in the presence of noise or model uncertainties. Despite limited accuracy in the morphology of the inverse-computed epicardial potentials caused by noise and uncertainties in heart position and orientation, atrial drivers can still be identified with significant accuracy because the predominant activation patterns and their frequencies are preserved. Overall, the identification of atrial drivers by localization of SPs confined to HDF regions outperforms driver identification based on SP localization alone.

Accuracy of the inverse problem solution in AF

We recently showed that icEGMs are poorly related to intracardiac contact EGMs (either measured experimentally or simulated), with large relative errors in the instantaneous phases.2 In the present study, we demonstrated that errors in reconstruction of epicardial potentials can be mostly attributed to a loss of complexity in the surface potentials relative to the original epicardial potentials, quantified in terms of the number of simultaneous phase singularities. This loss of complexity is consistent with a mutual cancellation of extracellular potentials of propagating wavefronts with opposed directions6 that is not retrievable by solving the inverse problem.

Despite this loss of information at the body surface level, surface potentials have been shown to keep some relevant attributes of AF drivers in terms of both their activation frequency7 and rotor location.6 However, other uncertainties may add computational errors to the inverse problem solution, which may restrict the validity of such an approach in the context of AF. These uncertainties include the presence of electrical noise up to 32 dB or the inaccuracies in the geometric model used up to 3 cm,8 due to inaccurate volume segmentation, changes in chamber size due to treatment up to ±40%,8 or use of a static torso model that does not account for the dynamic position of the atria inside the thorax during heart contraction and respiration.9 Although previous studies concluded that these uncertainties have a limited impact on inverse problem solutions in the context of nonfibrillating ventricular activity, they did not account for the more complex scenario of AF, with multiple simultaneous activation wavefronts and lower SNRs (which can reach 0 dB in clinical settings).8–10 Moreover, the impact of anticipated atrial surface acquisition by image techniques could also have a significant impact on the position of the atria inside the thorax.1

We also found that the addition of electrical noise to the surface recordings resulted in additional smoothening of the surface potentials, already smoothened by the inverse problem solution in the absence of noise, which results in a further decrease in the number of simultaneous phase singularities. However, despite the non-negligible effect of signal or noise inaccuracies on the reconstructed propagation patterns, we found that activation-based parameters, such as activation frequency or rotor location, are robust against both signal and model uncertainties, with errors that allow identification of the AF driving atrium and mean errors in the location of drivers <2 cm for up to 20 dB of SNR or 2-cm displacement. This driver identification accuracy can also be expected for reduced and irregular geometries on the atrial shell or a reduced amount of sensing surface electrodes (see Supplemental Figures 8 and 9). The good performance of activation-based parameters suggests that the information underlying key features of propagation patterns reach the torso surface and can be inverse-reconstructed, whereas the fibrillatory conduction that surrounds the main rotational activity cancels out, as we previously described.6

Targeting drifting rotors for ablation with some inaccuracy (comparable to rotor drift, 1.18 ± 0.55 cm in our population of models) may result in successful AF termination because the rotational path can be interrupted by ablation (see Supplementary Movie 1, with an error in rotor location of 1.7 cm). In contrast, ablation strategies based on larger identification errors may not result in AF termination (see Supplemental Movie 2, with an error in rotor location of 3.3 cm).

A combination of rotor and DF measurements, however, allows for improved rotor identification in the most extreme cases of noise or displacement.

Inverse problem and AF mechanisms

There is still no agreement on which mechanisms are responsible for AF maintenance.11,12 A growing body of experimental and clinical evidence including rotor-guided ablation strategies suggest that drivers in the form of electrical reentries are responsible for AF maintenance.1,13–15 Nevertheless, other investigators disagree about rotors driving AF.4,12 Indeed, even clinical reports suggesting that rotors play a driving role in AF differ in their details. Whereas Haissaguerre et al1 have reported on the identification of driving rotors by solving the inverse problem of electrocardiography, their activation maps were simpler and with fewer and less stable rotors compared to the intracardiac panoramic contact activation maps by Narayan et al.13 Neither of these 2 systems has been independently validated for AF wave detection, so we cannot know for sure which results are closer to being true, but those differences could be explained based on the present study. According to our results, reconstructed epicardial potentials using the inverse solution present a simplified version of the original epicardial potentials; however, the presence of key patterns and rotors is preserved, albeit affected by secondary epicardial patterns as well.6

Study limitations

We used mathematical models to validate the noninvasive estimation of atrial drivers during AF because current technology does not allow validating such an approach in a physiologically realistic scenario. An accurate validation would require precise simultaneous measurements of the transmembrane voltage in the entire atrial tissue (i.e., as optical mapping recordings) with simultaneous torso potentials, which is unattainable.

The mathematical models used a simplistic representation of the torso and the atrial surface, with no intrastructural heterogeneities. Inclusion of uncertainties in the conductance of inner organs may add further errors in the estimation of AF driver locations (i.e., added errors up to 1 cm for 100% error in lungs conductivity) (see Supplemental Figure 10).

Finally, although our population of models may not represent all possible atrial substrates during AF, we used a set of 30 different simulations to enhance the relevance of the study to the general AF population.

Conclusion

AF driver identification based on the inverse problem solution is possible despite the overall simplification of calculated epicardial potentials. The identification of drivers based on a combination of frequency and phase-derived measurements outperforms the identification of drivers based on rotor location only, especially under noise conditions.

Supplementary Material

Supplement

Acknowledgments

This work was supported in part by grants from Generalitat Valenciana (ACIF/2013/021); Instituto de Salud Carlos III-FEDER (Fondo Europeo de Desarrollo Regional) and Ministerio de Ciencia e Innovación (PI13-01882, PI13-00903, PI14/00857, PI16/01123, IJCI-2014- 22178, DTS16/00160 and Red RIC RD12.0042.0001); Spanish Society of Cardiology (Clinical Research Grant 2015); and the National Heart, Lung, and Blood Institute (P01-HL039707, P01-HL087226, and Q1 R01-HL118304). Dr. Atienza served on the advisory board of Medtronic and Sorin. Dr. Berenfeld received research support from Medtronic and St. Jude Medical; and is a cofounder and Scientific Officer of Rhythm Solutions, Inc., Research and Development Director for S.A.S. Volta Medical, and consultant to Acutus Medical.

Footnotes

All other authors have reported that they have no relationships relevant to the contents of this paper to disclose.

Appendix

Supplementary data

Supplementary data associated with this article can be found in the online version at http://dx.doi.org/10.1016/j.hrthm.2017.04.017.

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