Transfer Learning for Improved Classification of Drivers in Atrial Fibrillation.

"Drivers" are theorized mechanisms for persistent atrial fibrillation. Machine learning algorithms have been used to identify drivers, but the small size of current driver datasets limits their performance. We hypothesized that pretraining with unsupervised learning on a large dataset of unlabeled electrograms would improve classifier accuracy on a smaller driver dataset. In this study, we used a SimCLR-based framework to pretrain a residual neural network on a dataset of 113K unlabeled 64-electrode measurements and found weighted testing accuracy to improve over a non-pretrained network (78.6±3.9% vs 71.9±3.3%). This lays ground for development of superior driver detection algorithms and supports use of transfer learning for other datasets of endocardial electrograms.

Exercise Capacity Correlates With Left Atrial Structural Remodeling as Detected by Late Gadolinium-Enhanced Cardiac Magnetic Resonance in Patients With Atrial Fibrillation.

OBJECTIVES: This study hypothesized that left atrial structural remodeling (LA-TR) correlates with exercise capacity (EC) in a cohort of patients with atrial fibrillation (AF). BACKGROUND: Late gadolinium-enhanced cardiac magnetic resonance (LGE-CMR) imaging provides a method of assessing LA-TR in patients with AF. METHODS: A total of 145 patients (32% female, mean age 63.4 ± 11.6 years of age) with AF (66 paroxysmal, 71 persistent, 8 long-standing persistent) presenting for catheter ablation were included in the study. All patients underwent LGE-CMR imaging as well as maximal exercise test using the Bruce protocol prior to catheter ablation of AF. EC was quantified by minutes of exercise and metabolic equivalent (MET) level achieved. LA-TR was quantified from LGE-CMR imaging and classified according to the Utah classification of LA structural remodeling (Utah stage I: <10% LA wall enhancement; Utah II: 10% to <20%; Utah III: 20% to <30%; and Utah IV: >30%). AF recurrence was assessed at 1 year from the date of ablation. RESULTS: The average duration of exercise was 8 ± 3 min, and the mean MET achieved was 9.7 ± 3.2. METs achieved were inversely correlated with LA-TR (R2 = 0.061; p = 0.003). The duration of exercise was also inversely correlated with LA-TR (R2 = 0.071; p = 0.001). Both EC and LA-TR were associated with AF recurrence post ablation in univariate analysis, but only LA-TR and age were independently predictive of recurrence in multivariate analysis (p = 0.001). For every additional minute on the treadmill, subjects were 13% more likely to be free of AF 1 year post ablation (p = 0.047). CONCLUSIONS: EC is inversely associated with LA-TR in patients with AF and is predictive of freedom from AF post-ablation.

Assessment of regularization techniques for electrocardiographic imaging.

A widely used approach to solving the inverse problem in electrocardiography involves computing potentials on the epicardium from measured electrocardiograms (ECGs) on the torso surface. The main challenge of solving this electrocardiographic imaging (ECGI) problem lies in its intrinsic ill-posedness. While many regularization techniques have been developed to control wild oscillations of the solution, the choice of proper regularization methods for obtaining clinically acceptable solutions is still a subject of ongoing research. However there has been little rigorous comparison across methods proposed by different groups. This study systematically compared various regularization techniques for solving the ECGI problem under a unified simulation framework, consisting of both 1) progressively more complex idealized source models (from single dipole to triplet of dipoles), and 2) an electrolytic human torso tank containing a live canine heart, with the cardiac source being modeled by potentials measured on a cylindrical cage placed around the heart. We tested 13 different regularization techniques to solve the inverse problem of recovering epicardial potentials, and found that non-quadratic methods (total variation algorithms) and first-order and second-order Tikhonov regularizations outperformed other methodologies and resulted in similar average reconstruction errors.

Supplemented standard 12-lead electrocardiogram for optimal diagnosis and reconstruction of significant body surface map patterns.

In this study, based on 120-lead body surface potential maps (BSPMs), we explored the improvement in electrocardiogram (ECG) diagnosis obtained by adding additional leads and using estimation of unmeasured leads. We found that adding a few leads observed to be optimal for diagnosis or signal capture combined with the existing 12-lead ECG improves diagnostic performance. Separately, using reconstruction (estimation) of BSPMs and using diagnostic criteria derived for maps also improve diagnostic performance over that provided by the recorded 12-lead ECG alone. Combining these 2 ideas, namely, addition of optimal leads and estimation of BSPMs improves performance even more.

Application of stochastic finite element methods to study the sensitivity of ECG forward modeling to organ conductivity.

Because numerical simulation parameters may significantly influence the accuracy of the results, evaluating the sensitivity of simulation results to variations in parameters is essential. Although the field of sensitivity analysis is well developed, systematic application of such methods to complex biological models is limited due to the associated high computational costs and the substantial technical challenges for implementation. In the specific case of the forward problem in electrocardiography, the lack of robust, feasible, and comprehensive sensitivity analysis has left many aspects of the problem unresolved and subject to empirical and intuitive evaluation rather than sound, quantitative investigation. In this study, we have developed a systematic, stochastic approach to the analysis of sensitivity of the forward problem of electrocardiography to the parameter of inhomogeneous tissue conductivity. We apply this approach to a two-dimensional, inhomogeneous, geometric model of a slice through the human thorax. We assigned probability density functions for various organ conductivities and applied stochastic finite elements based on the generalized polynomial chaos-stochastic Galerkin (gPC-SG) method to obtain the standard deviation of the resulting stochastic torso potentials. This method utilizes a spectral representation of the stochastic process to obtain numerically accurate stochastic solutions in a fraction of the time required when employing classic Monte Carlo methods. We have shown that a systematic study of sensitivity is not only easily feasible with the gPC-SG approach but can also provide valuable insight into characteristics of the specific simulation.

Epicardial and intramural excitation during ventricular pacing: effect of myocardial structure.

Published studies show that ventricular pacing in canine hearts produces three distinct patterns of epicardial excitation: elliptical isochrones near an epicardial pacing site, with asymmetric bulges; areas with high propagation velocity, up to 2 or 3 m/s and numerous breakthrough sites; and lower velocity areas (<1 m/s), where excitation moves across the epicardial projection of the septum. With increasing pacing depth, the magnitude of epicardial potential maxima becomes asymmetric. The electrophysiological mechanisms that generate the distinct patterns have not been fully elucidated. In this study, we investigated those mechanisms experimentally. Under pentobarbital anesthesia, epicardial and intramural excitation isochrone and potential maps have been recorded from 22 exposed or isolated dog hearts, by means of epicardial electrode arrays and transmural plunge electrodes. In five experiments, a ventricular cavity was perfused with diluted Lugol solution. The epicardial bulges result from electrotonic attraction from the helically shaped subepicardial portions of the wave front. The high-velocity patterns and the associated multiple breakthroughs are due to involvement of the Purkinje network. The low velocity at the septum crossing is due to the missing Purkinje involvement in that area. The asymmetric magnitude of the epicardial potential maxima and the shift of the breakthrough sites provoked by deep stimulation are a consequence of the epi-endocardial obliqueness of the intramural fibers. These results improve our understanding of intramural and epicardial propagation during premature ventricular contractions and paced beats. This can be useful for interpreting epicardial maps recorded at surgery or inversely computed from body surface ECGs.

Ischemic preconditioning protects against arrhythmogenesis through maintenance of both active as well as passive electrical properties in ischemic canine hearts.

BACKGROUND: The mechanisms for the antiarrhythmogenic effects of preconditioning in ischemic hearts, although well demonstrated, are not clear. We measured indices of activation and repolarization using data from a high-resolution epicardial sock electrode array in preconditioned (PC) and non-PC hearts in an attempt to gain further insight into protective mechanisms. METHODS AND RESULTS: Five canine hearts were subjected to a coronary artery occlusion lasting at least 1 hour, and 5 were subjected to a similar occlusion preceded by a preconditioning protocol. Epicardial electrograms were recorded using a 490-electrode sock. Representative beats were selected at intervals of 1 minute for analysis. The mean ST elevation for the PC group both rose slowly after occlusion and also resolved more slowly than the non-PC group. Electrocardiographic markers for propagation such as Total Activation Time, the QRSRMS width, and magnitude of steepest downstroke of the QRS complex all showed that the PC group maintained conduction velocity initially and also varied less dramatically than the control group. The regression line slope computed on a scatter plot of QT width vs cycle length was 0.23 for the PC group and 0.58 for non-PC. During occlusion, the incidence of premature ventricular contractions (PVCs) peaked at approximately 17 minutes followed by a second peak at approximately 27 minutes in the non-PC group, the PC group showed similar peaks at approximately 24 and approximately 53 minutes respectively. CONCLUSION: The slower rate of resolution of ST elevation in PC hearts suggests a delay in gap junction closure, thus maintaining intracellular resistivity and reducing the likelihood of arrhythmia. The speed of conduction is adequately maintained during the early stages of ischemia in PC hearts. The mQTi-mRR regression line, a surrogate measure of rate dependency of repolarization (restitution), has a lower slope in the PC case, thus suggesting a mechanism of reduced arrhythmogenesis. The conclusions are supported by a delay of peak PVCs in PC hearts.

Methods of solving reduced lead systems for inverse electrocardiography.

In the context of inverse electrocardiography, we examine the problem of using measurements from sets of electrocardiographic leads that are smaller than the number of nodes in the associated geometric models of the torso. We compared several methods to estimate the solution from such reduced-lead measurements sets both with and without knowledge of prior statistics of the measurements. We present here simulation results that indicate that deleting rows of the forward matrix corresponding to the unmeasured leads performs best in the absence of prior statistics, and that Bayesian (or least-squares) estimation performs best in the presence of prior statistics.

Generalized training subset selection for statistical estimation of epicardial activation maps from intravenous catheter measurements.

Catheter-based electrophysiological studies of the epicardium are limited to regions near the coronary vessels or require transthoracic access. We have developed a statistical approach by which to estimate high-resolution maps of epicardial activation from very low-resolution multi-electrode venous catheter measurements. This technique uses a linear estimation model that derives a relationship between venous catheter measurements and unmeasured epicardial sites from a set of previously recorded, high-resolution epicardial activation-time maps used as a training data set based on the spatial covariance of the measurement sites. We performed 14 dog experiments with various interventions to create an epicardial activation-time map database. This database included a total of 592 epicardial activation maps which were recorded using a sock array placed on the ventricles of dog hearts. We present five approaches, which examined sequential addition and removal of maps to select a generalized training set for the estimation technique. The selection consisted of choosing a subset of epicardial ectopic activation-time maps from the database of beats which resulted in estimation accuracy levels better than or at least similar to using all the maps in database. Our aim was to minimize the redundancy in the database and to be able to guide the eventual procedures required to obtain training data from open-chest surgery patients. The results from this study illustrated this redundancy and suggested that by including an optimal subset (around 100 maps) of the full database the estimation technique was able to perform as well as and even in some cases better than including all the maps in the database. The results also suggest that such an approach is feasible for providing accurate reconstruction of complete epicardial activation-time maps in a clinical setting and with fewer maps we can obtain similar reconstruction accuracy levels.

Improved performance of bayesian solutions for inverse electrocardiography using multiple information sources.

The usual goal in inverse electrocardiography (ECG) is to reconstruct cardiac electrical sources from body surface potentials and a mathematical model that relates the sources to the measurements. Due to attenuation and smoothing that occurs in the thorax, the inverse ECG problem is ill-posed and imposition of a priori constraints is needed to combat this ill-posedness. When the problem is posed in terms of reconstructing heart surface potentials, solutions have not yet achieved clinical utility; limitations include the limited availability of good a priori information about the solution and the lack of a "good" error metric. We describe an approach that combines body surface measurements and standard forward models with two additional information sources: statistical prior information about epicardial potential distributions and sparse simultaneous measurements of epicardial potentials made with multielectrode coronary venous catheters. We employ a Bayesian methodology which offers a general way to incorporate these information sources and additionally provides statistical performance analysis tools. In a simulation study, we first compare solutions using one or more of these information sources. Then, we study the effects of varying the number of sparse epicardial potential measurements on reconstruction accuracy. To evaluate accuracy, we used the Bayesian error covariance as well as traditional error metrics such as relative error. Our results show that including even sparsely sampled information from coronary venous catheters can substantially improve the reconstruction of epicardial potential distributions and that a Bayesian framework provides a feasible approach to using this information. Moreover, computing the Bayesian error standard deviations offers a means to indicate confidence in the results even in the absence of validation data.

Wavefront-based models for inverse electrocardiography.

We introduce two wavefront-based methods for the inverse problem of electrocardiography, which we term wavefront-based curve reconstruction (WBCR) and wavefront-based potential reconstruction (WBPR). In the WBCR approach, the epicardial activation wavefront is modeled as a curve evolving on the heart surface, with the evolution governed by factors derived phenomenologically from prior measured data. The body surface potential/wavefront relationship is modeled via an intermediate mapping of wavefront to epicardial potentials, again derived phenomenologically. In the WBPR approach, we iteratively construct an estimate of epicardial potentials from an estimated wavefront curve according to a simplified model and use it as an initial solution in a Tikhonov regularization scheme. Initial simulation results using measured canine epicardial data show considerable improvement in reconstructing activation wavefronts and epicardial potentials with respect to standard Tikhonov solutions. In particular the WBCR method accurately finds the anisotropic propagation early after epicardial pacing, and the WBPR method finds the wavefront (regions of sharp gradient of the potential) both accurately and with minimal smoothing.

Instance selection for estimation of epicardial activation sequence from venous catheter measurements.

Catheter-based electrophysiological studies of the outer surface of the heart (epicardium) are limited to regions near the heart vessels or require transthoracic access. We have developed a statistical signal processing approach by which to estimate high-resolution epicardial activation maps from multi-electrode venous catheter measurements. This technique uses a linear minimum mean-squared Bayesian estimation model that derives a relationship between venous catheter measurements and unmeasured epicardial sites from a set of previously recorded, high-resolution epicardial activation-time maps used as a training data set. The training data set selection consisted of choosing a subset of epicardial activation-time maps from a database that could be used in all possible test cases with focal ectopic activity. In this study, our hypothesis was that the number of maps necessary for successful estimation could be reduced without a significant loss of performance. We developed three approaches for this purpose. Our results showed that 100 maps would be sufficient to obtain an estimation accuracy level that was better than all 470 maps paced from all over the epicardium. The results suggest that such an approach is feasible for providing accurate reconstruction of complete epicardial activation-time maps in a clinical setting and with fewer maps we can obtain similar reconstruction accuracy levels.

Venous catheter based mapping of ectopic epicardial activation: training data set selection for statistical estimation.

A source of error in most of the existing catheter cardiac mapping approaches is that they are not capable of acquiring epicardial potentials even though arrhythmic substrates involving epicardial and subepicardial layers account for about 15% of the ventricular tachycardias. In this subgroup of patients, mapping techniques that are limited to the endocardium result in localization errors and failure in subsequent ablation procedures. In addition, catheter-based electrophysiological studies of the epicardium are limited to regions near the coronary vessels or require transthoracic access. We have developed a statistical approach by which to estimate high-resolution maps of epicardial activation from very low-resolution multi-electrode venous catheter measurements. A training set of previously recorded maps is necessary for this technique so that composition of the database becomes an important determinant of accuracy. The specific hypothesis of the study was that estimation accuracy would be best when the training data set matches that of the test beat(s), whereby the matching was according to the site of initiation of the beats. This hypothesis suggests approaches to optimized selection of the training set, three of which we have developed and evaluated. One of these methods, the high-CC refinement method, was able to estimate the earliest activation site of left ventricularly paced maps within an average of 4.67 mm of the true site; in 89% of the cases (a total of 231 cases) the error was smaller than 10 mm. In another method, MHC-Spatial activation, right ventricularly paced maps (239 maps) were estimated with an error of 7.15 mm. The average correlation coefficient between the original and the estimated maps was also very high (0.97), which shows the ability of the training data set refinement methods to estimate the epicardial activation sequence. The results of these tests support the hypothesis and, moreover, suggest that such an approach is feasible for providing accurate reconstruction of complete epicardial activation-time maps in a clinical setting.

Mechanisms of ischemia-induced ST-segment changes.

Many aspects of ischemia-induced changes in the electrocardiogram lack solid biophysical underpinnings although variations in ST segments form the predominant basis for diagnostic and monitoring of patients. This incomplete knowledge certainly plays a role in the poor performance of some forms of electrocardiogram-based detection and characterization of ischemia, especially when it is limited to the subendocardium. The focus of our recent studies has been to develop a comprehensive mechanistic model of the electrocardiographic effects of ischemia. The computational component of this model is based on highly realistic heart geometry with anisotropic fiber structure and allows us to assign ischemic action potentials to contiguous regions that can span a prescribed thickness of the ventricles. A separate, high-resolution model of myocardial tissue provides us with a means of setting electrical characteristics of the heart, including the status of gap junctional coupling between cells. The experimental counterpart of this model consists of dog hearts, either in situ or isolated and perfused with blood, in which we control coronary blood flow by means of a cannula and blood pump. By reducing blood flow through the cannula for various durations, we can replicate any phase of ischemia from hyper acute to early infarction. Based on the results of these models, there is emerging a mechanism of the electrocardiographic response to ischemia that depends strongly on the anisotropic conductivity of the myocardium. Ischemic injury currents flow across the boundary between healthy and ischemic tissue, but it is their interaction with local fiber orientation and the associated conductivity that generates secondary currents that determine epicardial ST-segment potentials. Results from experiments support qualitatively the findings of the simulations and underscore the role of myocardial anisotropy in electrocardiography.

Bayesian solutions and performance analysis in bioelectric inverse problems.

In bioelectric inverse problems, one seeks to recover bioelectric sources from remote measurements using a mathematical model that relates the sources to the measurements. Due to attenuation and spatial smoothing in the medium between the sources and the measurements, bioelectric inverse problems are generally ill-posed. Bayesian methodology has received increasing attention recently to combat this ill-posedness, since it offers a general formulation of regularization constraints and additionally provides statistical performance analysis tools. These tools include the estimation error covariance and the marginal probability density of the measurements (known as the "evidence") that allow one to predictively quantify and compare experimental designs. These performance analysis tools have been previously applied in inverse electroencephalography and magnetoencephalography, but only in relatively simple scenarios. The main motivation here was to extend the utility of Bayesian estimation techniques and performance analysis tools in bioelectric inverse problems, with a particular focus on electrocardiography. In a simulation study we first investigated whether Bayesian error covariance, computed without knowledge of the true sources and based on instead statistical assumptions, accurately predicted the actual reconstruction error. Our study showed that error variance was a reasonably reliable qualitative and quantitative predictor of estimation performance even when there was error in the prior model. We also examined whether the evidence statistic accurately predicted relative estimation performance when distinct priors were used. In a simple scenario our results support the hypothesis that the prior model that maximizes the evidence is a good choice for inverse reconstructions.

The effect of intrathoracic heart position on electrocardiogram autocorrelation maps.

We studied the influence of the heart position in the thorax on the autocorrelation (AC) maps consisting of correlation coefficients between each pair of instantaneous electrocardiogram potential distributions over a time interval. We used a thorax-shaped electrolytic-filled tank with an isolated and perfused dog heart placed at positions spanning 5 cm on each space direction. The correlation coefficient between QRST AC maps was in the range of 0.92 to 0.99, whereas the correlation coefficient between the corresponding QRST integral maps was in the range of 0.55 to 0.87, proving that AC maps are less influenced by the heart position than integral maps. Thus, diagnostic indexes computed from the AC maps can be expected to be more specific to phenomena taking place in the myocardium than to criteria based directly on electrocardiogram amplitudes in various leads.

Venous catheter based mapping of epicardial ectopic activation.

Catheter based electrophysiological studies of the epicardium are limited to regions near the coronary vessels or require transthoracic access. We have developed a statistical approach by which to estimate high-resolution maps of epicardial activation from very low-resolution multielectrode venous catheter measurements. Essential components of this approach are the training data set composition and the catheter electrode locations used to determine the relationship between catheter sites and the remaining measurement sites on the epicardium. We report here on the methods we investigated to show the effect of the content of the training set. Our results showed that the closer the match between features of the maps to be reconstructed and the training data set. the more estimation accurately predicted the earliest site of activation. We also report results from two different approaches to leadset selection by which we obtained similar accuracy levels. The results of this study suggest that reconstructing complete epicardial activation maps from venous catheter based measurements is both feasible and practical for future clinical applications.

Spatial methods of epicardial activation time determination in normal hearts.

The purpose of this study was to demonstrate errors in activation time maps created using the time derivative method on fractionated unipolar electrograms, to characterize the epicardial distribution of those fractionated electrograms, and to investigate spatial methods of activation time determination. Electrograms (EGs) were recorded using uniform grids of electrodes (1 or 2 mm spacing) on the epicardial surface of six normal canine hearts. Activation times were estimated using the time of the minimum time derivative, maximum spatial gradient, and zero Laplacian and compared with the time of arrival of the activation wave front as assessed from a time series of potential maps as the standard. When comparing activation times from the time derivative for the case of epicardial pacing, spatial gradient and Laplacian methods with the standard for EGs without fractionation, correlations were high (R2 = 0.98, 0.98, 0.97, respectively). Similar comparisons using results from only fractionated EGs (R2 = 0.85,0.97,0.95) showed a lower correlation between times from the time derivative method and the standard. The results suggest an advantage of spatial methods over the time derivative method only for the case of epicardial pacing where large numbers of fractionated electrograms are found.

Multielectrode venous catheter mapping as a high quality constraint for electrocardiographic inverse solution.

A persistent challenge in solving inverse problems in electrocardiography is the application of suitable constraints to the calculation of cardiac sources. Whether one formulates the inverse problem in terms of epicardial potentials or activation wavefronts, the problem is physically ill-posed and hence results in numerically unstable computations. Suitable physiological constraints applied with appropriate weighting can recover useful inverse solutions. However, it is often difficult to determine the best possible constraints and their optimal weighting. We have recently begun to use multielectrode catheters as a means of mapping epicardial signals in animal models. To accommodate the sparse sampling of this venous catheter based approach, we have applied statistical signal processing methods to estimate complete epicardial maps of activation time and epicardial potentials. Such measurements--and the estimated maps from them--also have the potential to provide high quality constraints for electrocardiographic inverse problems because they provide direct--albeit sparse--access to the desired solution. In this presentation we describe several approaches we have applied to extract useful constraints from sparsely sampled epicardial signals as well as a training set of epicardial maps, and use them to improve the quality of computed inverse solutions. Results suggest that combining various information sources provides valuable constraint information. Such a multimodal approach to cardiac mapping is clinically and technically viable and offers a possible means to overcome a major remaining limitation of inverse electrocardiography.