Noninvasive reconstruction of cardiac electrical activity: update on current methods, applications and challenges

Evaluation of five methods for the interpolation of bad leads in the solution of the inverse electrocardiography problem

Objective.This study aims to assess the sensitivity of epicardial potential-based electrocardiographic imaging (ECGI) to the removal or interpolation of bad leads.Approach.We utilized experimental data from two distinct centers. Langendorff-perfused pig (n= 2) and dog (n= 2) hearts were suspended in a human torso-shaped tank and paced from the ventricles. Six different bad lead configurations were designed based on clinical experience. Five interpolation methods were applied to estimate the missing data. Zero-order Tikhonov regularization was used to solve the inverse problem for complete data, data with removed bad leads, and interpolated data. We assessed the quality of interpolated ECG signals and ECGI reconstructions using several metrics, comparing the performance of interpolation methods and the impact of bad lead removal versus interpolation on ECGI.Main results.The performance of ECG interpolation strongly correlated with ECGI reconstruction. The hybrid method exhibited the best performance among interpolation techniques, followed closely by the inverse-forward and Kriging methods. Bad leads located over high amplitude/high gradient areas on the torso significantly impacted ECGI reconstructions, even with minor interpolation errors. The choice between removing or interpolating bad leads depends on the location of missing leads and confidence in interpolation performance. If uncertainty exists, removing bad leads is the safer option, particularly when they are positioned in high amplitude/high gradient regions. In instances where interpolation is necessary, the inverse-forward and Kriging methods, which do not require training, are recommended.Significance.This study represents the first comprehensive evaluation of the advantages and drawbacks of interpolating versus removing bad leads in the context of ECGI, providing valuable insights into ECGI performance.

Direct Estimation of Equivalent Bioelectric Sources Based on Huygens' Principle

An estimation of the electric sources in the heart was conducted using a novel method, based on Huygens' Principle, aiming at a direct estimation of equivalent bioelectric sources over the heart's surface in real time. The main scope of this work was to establish a new, fast approach to the solution of the inverse electrocardiography problem. The study was based on recorded electrocardiograms (ECGs). Based on Huygens' Principle, measurements obtained from the surfaceof a patient's thorax were interpolated over the surface of the employed volume conductor model and considered as secondary Huygens' sources. These sources, being non-zero only over the surface under study, were employed to determine the weighting factors of the eigenfunctions' expansion, describing the generated voltage distribution over the whole conductor volume. With the availability of the potential distribution stemming from measurements, the electromagnetics reciprocity theorem is applied once again to yield the equivalent sources over the pericardium. The methodology is self-validated, since the surface potentials calculated from these equivalent sources are in very good agreement with ECG measurements. The ultimate aim of this effort is to create a tool providing the equivalent epicardial voltage or current sources in real time, i.e., during the ECG measurements with multiple electrodes.

Comparison of dipole-based and potential-based ECGI methods for premature ventricular contraction beat localization with clinical data

Introduction: Localization of premature ventricular contraction (PVC) origin to guide the radiofrequency ablation (RFA) procedure is one of the prominent clinical goals of non-invasive electrocardiographic imaging. However, the results reported in the literature vary significantly depending on the source model and the level of complexity in the forward model. This study aims to compare the paced and spontaneous PVC localization performances of dipole-based and potential-based source models and corresponding inverse methods using the same clinical data and to evaluate the effects of torso inhomogeneities on these performances. Methods: The publicly available EP solution data from the EDGAR data repository (BSPs from a maximum of 240 electrodes) with known pacing locations and the Bratislava data (BSPs in 128 leads) with spontaneous PVCs from patients who underwent successful RFA procedures were used. Homogeneous and inhomogeneous torso models and corresponding forward problem solutions were used to relate sources on the closed epicardial and epicardial-endocardial surfaces. The localization error (LE) between the true and estimated pacing site/PVC origin was evaluated. Results: For paced data, the median LE values were 25.2 and 13.9 mm for the dipole-based and potential-based models, respectively. These median LE values were higher for the spontaneous PVC data: 30.2-33.0 mm for the dipole-based model and 28.9-39.2 mm for the potential-based model. The assumption of inhomogeneities in the torso model did not change the dipole-based solutions much, but using an inhomogeneous model improved the potential-based solutions on the epicardial-endocardial ventricular surface. Conclusion: For the specific task of localization of pacing site/PVC origin, the dipole-based source model is more stable and robust than the potential-based source model. The torso inhomogeneities affect the performances of PVC origin localization in each source model differently. Hence, care must be taken in generating patient-specific geometric and forward models depending on the source model representation used in electrocardiographic imaging (ECGI).

Finite velocity of ECG signal propagation: preliminary theory, results of a pilot experiment and consequences for medical diagnosis

A satisfactory model of the biopotentials propagating through the human body is essential for medical diagnostics, particularly for cardiovascular diseases. In our study, we develop the theory, that the propagation of biopotential of cardiac origin (ECG signal) may be treated as the propagation of low-frequency endogenous electromagnetic wave through the human body. We show that within this approach, the velocity of the ECG signal can be theoretically estimated, like for any other wave and physical medium, from the refraction index of the tissue in an appropriate frequency range. We confirm the theoretical predictions by the comparison with a direct measurement of the ECG signal propagation velocity and obtain mean velocity as low as v=1500 m/s. The results shed new light on our understanding of biopotential propagation through living tissue. This propagation depends on the frequency band of the signal and the transmittance of the tissue. This finding may improve the interpretation of the electric measurements, such as ECG and EEG when the frequency dependence of conductance and the phase shift introduced by the tissue is considered. We have shown, that the ECG propagation modifies the amplitude and phase of signal to a considerable extent. It may also improve the convergence of inverse problem in electrocardiographic imaging.

Influence of the Tikhonov Regularization Parameter on the Accuracy of the Inverse Problem in Electrocardiography

The electrocardiogram (ECG) is the standard method in clinical practice to non-invasively analyze the electrical activity of the heart, from electrodes placed on the body's surface. The ECG can provide a cardiologist with relevant information to assess the condition of the heart and the possible presence of cardiac pathology. Nonetheless, the global view of the heart's electrical activity given by the ECG cannot provide fully detailed and localized information about abnormal electrical propagation patterns and corresponding substrates on the surface of the heart. Electrocardiographic imaging, also known as the inverse problem in electrocardiography, tries to overcome these limitations by non-invasively reconstructing the heart surface potentials, starting from the corresponding body surface potentials, and the geometry of the torso and the heart. This problem is ill-posed, and regularization techniques are needed to achieve a stable and accurate solution. The standard approach is to use zero-order Tikhonov regularization and the L-curve approach to choose the optimal value for the regularization parameter. However, different methods have been proposed for computing the optimal value of the regularization parameter. Moreover, regardless of the estimation method used, this may still lead to over-regularization or under-regularization. In order to gain a better understanding of the effects of the choice of regularization parameter value, in this study, we first focused on the regularization parameter itself, and investigated its influence on the accuracy of the reconstruction of heart surface potentials, by assessing the reconstruction accuracy with high-precision simultaneous heart and torso recordings from four dogs. For this, we analyzed a sufficiently large range of parameter values. Secondly, we evaluated the performance of five different methods for the estimation of the regularization parameter, also in view of the results of the first analysis. Thirdly, we investigated the effect of using a fixed value of the regularization parameter across all reconstructed beats. Accuracy was measured in terms of the quality of reconstruction of the heart surface potentials and estimation of the activation and recovery times, when compared with ground truth recordings from the experimental dog data. Results show that values of the regularization parameter in the range (0.01-0.03) provide the best accuracy, and that the three best-performing estimation methods (L-Curve, Zero-Crossing, and CRESO) give values in this range. Moreover, a fixed value of the regularization parameter could achieve very similar performance to the beat-specific parameter values calculated by the different estimation methods. These findings are relevant as they suggest that regularization parameter estimation methods may provide the accurate reconstruction of heart surface potentials only for specific ranges of regularization parameter values, and that using a fixed value of the regularization parameter may represent a valid alternative, especially when computational efficiency or consistency across time is required.

Solving the inverse problem in electrocardiography imaging for atrial fibrillation using various time-frequency decomposition techniques based on empirical mode decomposition: A comparative study

Electrocardiographic imaging (ECGI) can aid in identifying the driving sources that cause and sustain atrial fibrillation (AF). Traditional regularization strategies for addressing the ECGI inverse problem are not currently concerned about the multi-scale analysis of the inverse problem, and these techniques are not clinically reliable. We have previously investigated the solution based on uniform phase mode decomposition (UPEMD-based) to the ECGI inverse problem. Numerous other methods for the time-frequency analysis derived from empirical mode decomposition (EMD-based) have not been applied to the inverse problem in ECGI. By applying many EMD-based solutions to the ECGI inverse problem and evaluating the performance of these solutions, we hope to find a more efficient EMD-based solution to the ECGI inverse problem. In this study, five AF simulation datasets and two real datasets from AF patients derived from a clinical ablation procedure are employed to evaluate the operating efficiency of several EMD-based solutions. The Pearson's correlation coefficient (CC), the relative difference measurement star (RDMS) of the computed epicardial dominant frequency (DF) map and driver probability (DP) map, and the distance (Dis) between the estimated and referenced most probable driving sources are used to evaluate the application of various EMD-based solutions in ECGI. The results show that for DF maps on all simulation datasets, the CC of UPEMD-based and improved UPEMD (IUPEMD)-based techniques are both greater than 0.95 and the CC of the empirical wavelet transform (EWT)-based solution is greater than 0.889, and the RDMS of UPEMD-based and IUPEMD-based approaches is less than 0.3 overall and the RDMS of EWT-based method is less than 0.48, performing better than other EMD-based solutions; for DP maps, the CC of UPEMD-based and IUPEMD-based techniques are close to 0.5, the CC of EWT-based is 0.449, and the CC of the remaining EMD-based techniques on the SAF and CAF is all below 0.1; the RDMS of UPEMD-based and IUPEMD-based are 0.06∼0.9 less than that of other EMD-based methods for all the simulation datasets overall. On two authentic AF datasets, the Dis between the first 10 real and estimated maximum DF positions of UPEMD-based and EWT-based methods are 212∼1440 less than that of others, demonstrating these two EMD-based solutions are superior and are suggested for clinical application in solving the ECGI inverse problem. On all datasets, EWT-based algorithms deconstruct the signal in the shortest time (no more than 0.12s), followed by UPEMD-based solutions (less than 0.81s), showing that these two schemes are more efficient than others.

Electrocardiographic imaging for cardiac arrhythmias and resynchronization therapy

Use of the 12-lead electrocardiogram (ECG) is fundamental for the assessment of heart disease, including arrhythmias, but cannot always reveal the underlying mechanism or the location of the arrhythmia origin. Electrocardiographic imaging (ECGi) is a non-invasive multi-lead ECG-type imaging tool that enhances conventional 12-lead ECG. Although it is an established technology, its continuous development has been shown to assist in arrhythmic activation mapping and provide insights into the mechanism of cardiac resynchronization therapy (CRT). This review addresses the validity, reliability, and overall feasibility of ECGi for use in a diverse range of arrhythmias. A systematic search limited to full-text human studies published in peer-reviewed journals was performed through Medline via PubMed, using various combinations of three key concepts: ECGi, arrhythmia, and CRT. A total of 456 studies were screened through titles and abstracts. Ultimately, 42 studies were included for literature review. Evidence to date suggests that ECGi can be used to provide diagnostic insights regarding the mechanistic basis of arrhythmias and the location of arrhythmia origin. Furthermore, ECGi can yield valuable information to guide therapeutic decision-making, including during CRT. Several studies have used ECGi as a diagnostic tool for atrial and ventricular arrhythmias. More recently, studies have tested the value of this technique in predicting outcomes of CRT. As a non-invasive method for assessing cardiovascular disease, particularly arrhythmias, ECGi represents a significant advancement over standard procedures in contemporary cardiology. Its full potential has yet to be fully explored.

Spatial-Temporal Signals and Clinical Indices in Electrocardiographic Imaging (II): Electrogram Clustering and T-wave Alternans

During the last years, attention and controversy have been present for the first commercially available equipment being used in Electrocardiographic Imaging (ECGI), a new cardiac diagnostic tool which opens up a new field of diagnostic possibilities. Previous knowledge and criteria of cardiologists using intracardiac Electrograms (EGM) should be revisited from the newly available spatial-temporal potentials, and digital signal processing should be readapted to this new data structure. Aiming to contribute to the usefulness of ECGI recordings in the current knowledge and methods of cardiac electrophysiology, we previously presented two results: First, spatial consistency can be observed even for very basic cardiac signal processing stages (such as baseline wander and low-pass filtering); second, useful bipolar EGMs can be obtained by a digital processing operator searching for the maximum amplitude and including a time delay. In addition, this work aims to demonstrate the functionality of ECGI for cardiac electrophysiology from a twofold view, namely, through the analysis of the EGM waveforms, and by studying the ventricular repolarization properties. The former is scrutinized in terms of the clustering properties of the unipolar an bipolar EGM waveforms, in control and myocardial infarction subjects, and the latter is analyzed using the properties of T-wave alternans (TWA) in control and in Long-QT syndrome (LQTS) example subjects. Clustered regions of the EGMs were spatially consistent and congruent with the presence of infarcted tissue in unipolar EGMs, and bipolar EGMs with adequate signal processing operators hold this consistency and yielded a larger, yet moderate, number of spatial-temporal regions. TWA was not present in control compared with an LQTS subject in terms of the estimated alternans amplitude from the unipolar EGMs, however, higher spatial-temporal variation was present in LQTS torso and epicardium measurements, which was consistent through three different methods of alternans estimation. We conclude that spatial-temporal analysis of EGMs in ECGI will pave the way towards enhanced usefulness in the clinical practice, so that atomic signal processing approach should be conveniently revisited to be able to deal with the great amount of information that ECGI conveys for the clinician.

Reduced leadset selection and performance evaluation in the inverse problem of electrocardiography for reconstructing the ventricularly paced electrograms

OBJECTIVE

Noninvasive electrocardiographic imaging (ECGI) is used for obtaining high-resolution images of the electrical activity of the heart, and is a powerful method with the potential to detect certain arrhythmias. However, there is no 'best' lead configuration in the literature to measure the torso potentials. This paper evaluates ECGI reconstructions using various reduced leadset configurations, explores whether one can find a common reduced leadset configuration that can accurately reconstruct the electrograms for datasets with different pacing sites, and compares two activation time estimation methods.

APPROACH

We used 23 ventricularly-paced datasets with pacing sites on different regions of the epicardium. Starting with a full 192‑leadset, we found "optimized" reduced leadsets specific to each dataset; we considered 64‑lead and 32‑lead configurations. Based on the histogram of individual "optimized" lead selections, we found a common reduced leadset. We compared the ECGI reconstructions and activation times of the individually optimized lead configurations with the common lead configurations.

RESULTS

Both 64‑lead configurations had similar performances to the 192‑leadset. 32‑leadset configurations, on the other hand, yielded noisy reconstructions, which affected their performance.

SIGNIFICANCE

There are no statistically significant differences in the performance of the inverse solutions when a 64‑lead common reduced leadset is used to estimate the electrograms and their respective pacing sites compared to using the full leadset. 32‑lead configurations, on the other hand, require a more careful study to improve their performance. The activation time method used significantly affects the pacing site estimation performance, especially with fewer electrodes.

Effects of Interpolation on the Inverse Problem of Electrocardiography

Electrocardiographic Imaging (ECGI) aims to reconstruct electrograms from the body surface potential measurements. Bad leads are usually excluded from the inverse problem solution. Alternatively, interpolation can be applied. This study explores how sensitive ECGI is to different bad-lead configurations and interpolation methods. Experimental data from a Langendorff-perfused pig heart suspended in a human-shaped torso-tank was used. Epicardial electrograms were acquired during 30 s (31 beats) of RV pacing using a 108-electrode array, simultaneously with torso potentials from 128 electrodes embedded in the tank surface. Six different bad lead cases were designed based on clinical experience. Inverse problem was solved by applying Tikhonov regularization i) using the complete data, ii) bad-leads-removed data, and iii) interpolated data, with 5 different methods. Our results showed that ECGI accuracy of an interpolation method highly depends on the location of the bad leads. If they are in the high-potential-gradient regions of the torso, a highly accurate interpolation method is needed to achieve an ECGI accuracy close to using complete data. If the BSP reconstruction of the interpolation method is poor in these regions, the reconstructed electrograms also have lower accuracy, suggesting that bad leads should be removed instead of interpolated. The inverse-forward method was found to be the best among all interpolation methods applied in this study in terms of both missing BSP lead reconstruction and ECGI accuracy, even for the bad leads located over the chest.

Novel use of repolarization parameters in electrocardiographic imaging to uncover arrhythmogenic substrate

BACKGROUND

Measuring repolarization characteristics is challenging and has been reserved for experienced physicians. In electrocardiographic imaging (ECGI), activation-recovery interval (ARI) is used as a measure of local cardiac repolarization duration. We hypothesized that repolarization characteristics, such as local electrogram morphology and local and global dispersion of repolarization timing and duration could be of significance in ECGI.

OBJECTIVE

To further explore their potential in arrhythmic risk stratification we investigated the use of novel repolarization parameters in ECGI.

MATERIALS AND METHODS

We developed and compared methods for T-peak and T-end detection in reconstructed potentials. All methods were validated on annotated reconstructed electrograms (EGMs). Characteristics of the reconstructed EGMs and epicardial substrate maps in IVF patients were analyzed by using data recorded during sinus rhythm. The ECGI data were analyzed for EGM morphology, conduction, and repolarization.

RESULTS

We acquired ECGI data from 8 subjects for this study. In all patients we evaluated four repolarization parameters: Repolarization time, T-wave area, Tpeak-Tend interval, and T-wave alternans. Most prominent findings were steep repolarization time gradients in regions with flat EGMs. These regions were also characterized by low T-wave area and large differences in Tpeak-Tend interval.

CONCLUSIONS

Measuring novel repolarization parameters in reconstructed electrograms acquired with ECGI is feasible, can be done in a fully automated manner and may provide additional information on underlying arrhythmogenic substrate for risk stratification. Further studies are needed to investigate their potential use and clinical application.

Novel experimental model for studying the spatiotemporal electrical signature of acute myocardial ischemia: a translational platform

Myocardial ischemia is one of the most common cardiovascular pathologies and can indicate many severe and life threatening diseases. Despite these risks, current electrocardiographic detection techniques for ischemia are mediocre at best, with reported sensitivity and specificity ranging from 50%-70% and 70%-90%, respectively.

OBJECTIVE

To improve this performance, we set out to develop an experimental preparation to induce, detect, and analyze bioelectric sources of myocardial ischemia and determine how these sources reflect changes in body-surface potential measurements.

APPROACH

We designed the experimental preparation with three important characteristics: (1) enable comprehensive and simultaneous high-resolution electrical recordings within the myocardial wall, on the heart surface, and on the torso surface; (2) develop techniques to visualize these recorded electrical signals in time and space; and (3) accurately and controllably simulate ischemic stress within the heart by modulating the supply of blood, the demand for perfusion, or a combination of both.

MAIN RESULTS

To achieve these goals we designed comprehensive system that includes (1) custom electrode arrays (2) signal acquisition and multiplexing units, (3) a surgical technique to place electrical recording and myocardial ischemic control equipment, and (4) an image based modeling pipeline to acquire, process, and visualize the results. With this setup, we are uniquely able to capture simultaneously and continuously the electrical signatures of acute myocardial ischemia within the heart, on the heart surface, and on the body surface.

SIGNIFICANCE

This novel experimental preparation enables investigation of the complex and dynamic nature of acute myocardial ischemia that should lead to new, clinically translatable results.

Evaluation of ECG Imaging to Map Hemodynamically Stable and Unstable Ventricular Arrhythmias

BACKGROUND

ECG imaging (ECGI) has been used to guide treatment of ventricular ectopy and arrhythmias. However, the accuracy of ECGI in localizing the origin of arrhythmias during catheter ablation of ventricular tachycardia (VT) in structurally abnormal hearts remains to be fully validated.

METHODS

During catheter ablation of VT, simultaneous mapping was performed using electroanatomical mapping (CARTO, Biosense-Webster) and ECGI (CardioInsight, Medtronic) in 18 patients. Sites of entrainment, pace-mapping, and termination during ablation were used to define the VT site of origin (SoO). Distance between SoO and the site of earliest activation on ECGI were measured using co-registered geometries from both systems. The accuracy of ECGI versus a 12-lead surface ECG algorithm was compared.

RESULTS

A total of 29 VTs were available for comparison. Distance between SoO and sites of earliest activation in ECGI was 22.6, 13.9 to 36.2 mm (median, first to third quartile). ECGI mapped VT sites of origin onto the correct AHA segment with higher accuracy than a validated 12-lead ECG algorithm (83.3% versus 38.9%; P=0.015).

CONCLUSIONS

This simultaneous assessment demonstrates that CardioInsight localizes VT circuits with sufficient accuracy to provide a region of interest for targeting mapping for ablation. Resolution is not sufficient to guide discrete radiofrequency lesion delivery via catheter ablation without concomitant use of an electroanatomical mapping system but may be sufficient for segmental ablation with radiotherapy.

ML and MAP estimation of parameters for the Kalman filter and smoother applied to electrocardiographic imaging

In electrocardiographic imaging (ECGI), one solves the inverse problem of electrocardiography (ECG) to reconstruct equivalent cardiac sources based on the body surface potential measurements and a mathematical model of the torso. Due to attenuation and spatial smoothing within the torso, this inverse problem is ill-posed. Among many regularization approaches used in the ECG literature to overcome this ill-posedness, statistical techniques have received great attention because of their flexibility to represent the data, and ability to provide performance evaluation tools for quantification of uncertainties and errors in the model. However, despite their potential to accurately reconstruct the equivalent cardiac sources, one major challenge in these methods is how to best utilize the prior information available in terms of training data. In this paper, we address the question of how to define the prior probability distributions (pdf) of the sources and the error terms so that we can obtain more accurate and robust inverse solutions. We employ two methods, maximum likelihood (ML) and maximum a posteriori (MAP), for estimating the model parameters such as the prior pdfs, error pdfs, and the state-transition matrix, based on the same training data. These model parameters are then used for the state-space representation and estimation of the epicardial potentials, which constitute the equivalent cardiac sources in this study. The performances of ML- and MAP-based model parameter estimation methods are evaluated qualitatively and quantitatively at various noise levels and geometric disturbances using two different simulated datasets. Bayesian MAP estimation, which is also a well-known statistical inversion technique, and Tikhonov regularization, which can be formulated as a special and simplified version of Bayesian MAP estimation, have been included here for comparison with the Kalman filtering method. Our results show that the state-space approach outperforms Bayesian MAP estimation in all cases; ML yields accurate results when the test and training beats come from the same physiological model, but MAP is superior to ML, especially if the test and training beats are from different physiological models. Graphical Abstract ML and MAP estimation of parameters for the Kalman filter and smoother applied to electrocardiographic imaging.

Reduction of Effects of Noise on the Inverse Problem of Electrocardiography with Bayesian Estimation

To overcome the ill-posed nature of the inverse problem of electrocardiography (ECG) and stabilize the solutions, regularization is used. Despite several studies on noise, effect of prefiltering of ECG signals on the regularized inverse solutions has not been explored. We used Bayesian estimation for solving the inverse ECG problem with and without applying various prefiltering methods, and evaluated our results using experimental data that came from a Langendorff-perfused pig heart suspended in a human-shaped torso-tank. Epicardial electrograms were recorded during RV pacing using a 108-electrode array, simultaneously with ECGs from 128 electrodes embedded in the tank surface. Leave-one-beat-out protocol was used to obtain the prior probability density function (pdf) of electro-grams and noise statistics. Noise pdf was assumed to be zero mean-Gaussian, with covariance assumptions: a) independent and identically distributed (noi-iid), b) correlated (noi-corr). Reconstructed electrograms and activation times were compared to those directly recorded by the sock for 3 beats selected from the recording. Noi-corr is superior to noi-iid when the training set is a good match to data, but for applications requiring activation time derivation, careful selection of preprocessing methods, in particular to adequately remove high-frequency noise, and an appropriate noise model is needed.

Considering New Regularization Parameter-Choice Techniques for the Tikhonov Method to Improve the Accuracy of Electrocardiographic Imaging

The electrocardiographic imaging (ECGI) inverse problem highly relies on adding constraints, a process called regularization, as the problem is ill-posed. When there are no prior information provided about the unknown epicardial potentials, the Tikhonov regularization method seems to be the most commonly used technique. In the Tikhonov approach the weight of the constraints is determined by the regularization parameter. However, the regularization parameter is problem and data dependent, meaning that different numerical models or different clinical data may require different regularization parameters. Then, we need to have as many regularization parameter-choice methods as techniques to validate them. In this work, we addressed this issue by showing that the Discrete Picard Condition (DPC) can guide a good regularization parameter choice for the two-norm Tikhonov method. We also studied the feasibility of two techniques: The U-curve method (not yet used in the cardiac field) and a novel automatic method, called ADPC due its basis on the DPC. Both techniques were tested with simulated and experimental data when using the method of fundamental solutions as a numerical model. Their efficacy was compared with the efficacy of two widely used techniques in the literature, the L-curve and the CRESO methods. These solutions showed the feasibility of the new techniques in the cardiac setting, an improvement of the morphology of the reconstructed epicardial potentials, and in most of the cases of their amplitude.

His Resynchronization Versus Biventricular Pacing in Patients With Heart Failure and Left Bundle Branch Block

BACKGROUND

His bundle pacing is a new method for delivering cardiac resynchronization therapy (CRT).

OBJECTIVES

The authors performed a head-to-head, high-precision, acute crossover comparison between His bundle pacing and conventional biventricular CRT, measuring effects on ventricular activation and acute hemodynamic function.

METHODS

Patients with heart failure and left bundle branch block referred for conventional biventricular CRT were recruited. Using noninvasive epicardial electrocardiographic imaging, the authors identified patients in whom His bundle pacing shortened left ventricular activation time. In these patients, the authors compared the hemodynamic effects of His bundle pacing against biventricular pacing using a high-multiple repeated alternation protocol to minimize the effect of noise, as well as comparing effects on ventricular activation.

RESULTS

In 18 of 23 patients, left ventricular activation time was significantly shortened by His bundle pacing. Seventeen patients had a complete electromechanical dataset. In them, His bundle pacing was more effective at delivering ventricular resynchronization than biventricular pacing: greater reduction in QRS duration (-18.6 ms; 95% confidence interval [CI]: -31.6 to -5.7 ms; p = 0.007), left ventricular activation time (-26 ms; 95% CI: -41 to -21 ms; p = 0.002), and left ventricular dyssynchrony index (-11.2 ms; 95% CI: -16.8 to -5.6 ms; p < 0.001). His bundle pacing also produced a greater acute hemodynamic response (4.6 mm Hg; 95% CI: 0.2 to 9.1 mm Hg; p = 0.04). The incremental activation time reduction with His bundle pacing over biventricular pacing correlated with the incremental hemodynamic improvement with His bundle pacing over biventricular pacing (R = 0.70; p = 0.04).

CONCLUSIONS

His resynchronization delivers better ventricular resynchronization, and greater improvement in hemodynamic parameters, than biventricular pacing.

Evaluation of multivariate adaptive non-parametric reduced-order model for solving the inverse electrocardiography problem: a simulation study

In the inverse electrocardiography (ECG) problem, the goal is to reconstruct the heart's electrical activity from multichannel body surface potentials and a mathematical model of the torso. Over the years, researchers have employed various approaches to solve this ill-posed problem including regularization, optimization, and statistical estimation. It is still a topic of interest especially for researchers and clinicians whose goal is to adopt this technique in clinical applications. Among the wide range of mathematical tools available in the fields of operational research, inverse problems, optimization, and parameter estimation, spline-based techniques have been applied to inverse problems in several areas. If proper spline bases are chosen, the complexity of the problem can be significantly reduced while increasing estimation accuracy. However, there are few studies within the context of the inverse ECG problem that take advantage of this property of the spline-based approaches. In this paper, we evaluate the performance of Multivariate Adaptive Regression Splines (MARS)-based method for the solution of the inverse ECG problem using two different collections of simulated data. The results show that the MARS-based method improves the inverse ECG solutions and is "robust" to modeling errors, especially in terms of localizing the arrhythmia sources. Graphical Abstract Multivariate adaptive non-parametric model for inverse ECG problem.

Life-long tailoring of diagnosis and management of patients with idiopathic ventricular fibrillation-future perspectives in research

The diagnosis and management of idiopathic ventricular fibrillation is challenging, as it requires extensive diagnostic testing and offers few curative options due to unknown underlying disease. The resulting population is a heterogeneous group of patients with a largely unknown natural history. Structural patient characterisation, follow-up and innovations in diagnostic testing can improve our understanding of the disease mechanisms of idiopathic ventricular fibrillation, detect underlying disease during follow-up and aid in therapeutic management. Recently, initiatives have been launched in the Netherlands to investigate the role of high-resolution non-invasive electrocardiographic imaging and genetic and familial screening in idiopathic ventricular fibrillation.

Wavelet-promoted sparsity for non-invasive reconstruction of electrical activity of the heart

We investigated a novel sparsity-based regularization method in the wavelet domain of the inverse problem of electrocardiography that aims at preserving the spatiotemporal characteristics of heart-surface potentials. In three normal, anesthetized dogs, electrodes were implanted around the epicardium and body-surface electrodes were attached to the torso. Potential recordings were obtained simultaneously on the body surface and on the epicardium. A CT scan was used to digitize a homogeneous geometry which consisted of the body-surface electrodes and the epicardial surface. A novel multitask elastic-net-based method was introduced to regularize the ill-posed inverse problem. The method simultaneously pursues a sparse wavelet representation in time-frequency and exploits correlations in space. Performance was assessed in terms of quality of reconstructed epicardial potentials, estimated activation and recovery time, and estimated locations of pacing, and compared with performance of Tikhonov zeroth-order regularization. Results in the wavelet domain obtained higher sparsity than those in the time domain. Epicardial potentials were non-invasively reconstructed with higher accuracy than with Tikhonov zeroth-order regularization (p < 0.05), and recovery times were improved (p < 0.05). No significant improvement was found in terms of activation times and localization of origin of pacing. Next to improved estimation of recovery isochrones, which is important when assessing substrate for cardiac arrhythmias, this novel technique opens potentially powerful opportunities for clinical application, by allowing to choose wavelet bases that are optimized for specific clinical questions. Graphical Abstract The inverse problem of electrocardiography is to reconstruct heart-surface potentials from recorded bodysurface electrocardiograms (ECGs) and a torso-heart geometry. However, it is ill-posed and solving it requires additional constraints for regularization. We introduce a regularization method that simultaneously pursues a sparse wavelet representation in time-frequency and exploits correlations in space. Our approach reconstructs epicardial (heart-surface) potentials with higher accuracy than common methods. It also improves the reconstruction of recovery isochrones, which is important when assessing substrate for cardiac arrhythmias. This novel technique opens potentially powerful opportunities for clinical application, by allowing to choose wavelet bases that are optimized for specific clinical questions.

Geometrical constraint of sources in noninvasive localization of premature ventricular contractions

The inverse problem of electrocardiography for localization of a premature ventricular contraction (PVC) origin was solved and compared for three types of the equivalent cardiac electrical generator: transmembrane voltages, epicardial potentials, and dipoles. Instead of regularization methods usually used for the ill-posed inverse problems an assumption of a single point source representative of the heart generator was applied to the solution as a geometrical constraint. Body surface potential maps were simulated from eight modeled origins of the PVC in the heart model. Then the maps were corrupted by additional Gaussian noise with the signal-to-noise ratio (SNR) from 20 to 10dB and used as the input of the inverse solution. The inverse solution was computed from the first 30ms of the ventricular depolarization. It was assumed that during this period only a small part of the heart volume is activated thus it can be represented by a single point electrical source. Generally, the localization error was more dependent on the PVC origin position than on the type of the used heart generator. The most stable localization error between the inversely found results and the true PVC origin was not larger than 20mm for PVC origins located in the left ventricular wall and on the right ventricular anterior side. For such cases, the localization was robust to the noise up to SNR of 10dB for all studied types of the cardiac generator. For SNR 10dB the results became unstable mainly for the PVC origins in the septum and posterior right ventricle for the dipolar heart generator and for epicardial potentials defined on the pericardium when the range of the localization error increased up to 50mm. When the results for different electrical heart generators were considered altogether, the mean radius of the cloud of results did not exceed 20mm and the localization error of the cloud center was smaller than that obtained for a particular type of the cardiac generator. Combination of results from different models of a single point cardiac electrical generator can provide better information for the preliminary noninvasive localization of PVC than the use of one type of the generator.

Inverse estimation of cardiac activation times via gradient-based optimization

Computational modeling may provide a quantitative framework for integrating multiscale data to gain insight into mechanisms of heart disease, identify and test pharmacological and electrical therapy and interventions, and support clinical decisions. Patient-specific computational cardiac models can help guide such procedures, and cardiac inverse modeling is a promising alternative to adequately personalize these models. Indeed, full cardiac inverse modeling is currently becoming computationally feasible; however, fundamental work to assess the feasibility of emerging techniques is still needed. In this study, we use a partial differential equation-constrained optimal control approach to numerically investigate the identifiability of an initial activation sequence from synthetic (partial) observations of the extracellular potential using the bidomain approximation and 2D representations of cardiac tissue. Our results demonstrate that activation times and duration of several stimuli can be recovered even with high levels of noise, that it is sufficient to sample the observations at the electrocardiogram-relevant sampling frequency of 1 kHz, and that spatial resolutions that are coarser than the standard in electrophysiological simulations can be used. The optimization of activation times is still effective when synthetic data are generated with a different cell membrane kinetics model than optimized for. The findings thus indicate that the presented approach has potential for finding activation sequences from clinical data modalities, as an extension to existing cardiac imaging approaches.

Physiology-based regularization of the electrocardiographic inverse problem

The inverse problem of electrocardiography aims at noninvasively reconstructing electrical activity of the heart from recorded body-surface electrocardiograms. A crucial step is regularization, which deals with ill-posedness of the problem by imposing constraints on the possible solutions. We developed a regularization method that includes electrophysiological input. Body-surface potentials are recorded and a computed tomography scan is performed to obtain the torso–heart geometry. Propagating waveforms originating from several positions at the heart are simulated and used to generate a set of basis vectors representing spatial distributions of potentials on the heart surface. The real heart-surface potentials are then reconstructed from the recorded body-surface potentials by finding a sparse representation in terms of this basis. This method, which we named ‘physiology-based regularization’ (PBR), was compared to traditional Tikhonov regularization and validated using in vivo recordings in dogs. PBR recovered details of heart-surface electrograms that were lost with traditional regularization, attained higher correlation coefficients and led to improved estimation of recovery times. The best results were obtained by including approximate knowledge about the beat origin in the PBR basis.

New approaches to predicting the risk of sudden death

In this review article, we will explore some of the contemporary methods for predicting sudden cardiac death (SCD). These include experimental methods yet to be adopted in the clinical setting, and methods that have been extrapolated from observational data in those with a history of SCD. We will discuss how these relate to the different aetiologies and disease processes. We will also explore how these may be used in the clinical setting to decide on management.