Physiological-Model-Constrained Noninvasive Reconstruction of Volumetric Myocardial Transmembrane Potentials

Systematic review of computational techniques, dataset utilization, and feature extraction in electrocardiographic imaging

This study aimed to analyze computational techniques in ECG imaging (ECGI) reconstruction, focusing on dataset identification, problem-solving, and feature extraction. We employed a PRISMA approach to review studies from Scopus and Web of Science, applying Cochrane principles to assess risk of bias. The selection was limited to English peer-reviewed papers published from 2010 to 2023, excluding studies that lacked computational technique descriptions. From 99 reviewed papers, trends show a preference for traditional methods like the boundary element and Tikhonov methods, alongside a rising use of advanced technologies including hybrid techniques and deep learning. These advancements have enhanced cardiac diagnosis and treatment precision. Our findings underscore the need for robust data utilization and innovative computational integration in ECGI, highlighting promising areas for future research and advances. This shift toward tailored cardiac care suggests significant progress in diagnostic and treatment methods.

Solving the Inverse Problem of Electrocardiography for Cardiac Digital Twins: A Survey

Cardiac digital twins (CDTs) are personalized virtual representations used to understand complex cardiac mechanisms. A critical component of CDT development is solving the ECG inverse problem, which enables the reconstruction of cardiac sources and the estimation of patient-specific electrophysiology (EP) parameters from surface ECG data. Despite challenges from complex cardiac anatomy, noisy ECG data, and the ill-posed nature of the inverse problem, recent advances in computational methods have greatly improved the accuracy and efficiency of ECG inverse inference, strengthening the fidelity of CDTs. This paper aims to provide a comprehensive review of the methods for solving ECG inverse problems, their validation strategies, their clinical applications, and their future perspectives. For the methodologies, we broadly classify state-of-the-art approaches into two categories: deterministic and probabilistic methods, including both conventional and deep learning-based techniques. Integrating physics laws with deep learning models holds promise, but challenges such as capturing dynamic electrophysiology accurately, accessing accurate domain knowledge, and quantifying prediction uncertainty persist. Integrating models into clinical workflows while ensuring interpretability and usability for healthcare professionals is essential. Overcoming these challenges will drive further research in CDTs.

Simulation Optimization of Spatiotemporal Dynamics in 3D Geometries

Many engineering and healthcare systems are featured with spatiotemporal dynamic processes. The optimal control of such systems often involves sequential decision making. However, traditional sequential decision-making methods are not applicable to optimize dynamic systems that involves complex 3D geometries. Simulation modeling offers an unprecedented opportunity to evaluate alternative decision options and search for the optimal plan. In this paper, we develop a novel simulation optimization framework for sequential optimization of 3D dynamic systems. We first propose to measure the similarity between functional simulation outputs using coherence to assess the effectiveness of decision actions. Second, we develop a novel Gaussian Process (GP) model by constructing a valid kernel based on Hausdorff distance to estimate the coherence for different decision paths. Finally, we devise a new Monte Carlo Tree Search (MCTS) algorithm, i.e., Normal-Gamma GP MCTS (NG-GP-MCTS), to sequentially optimize the spatiotemporal dynamics. We implement the NG-GP-MCTS algorithm to design an optimal ablation path for restoring normal sinus rhythm (NSR) from atrial fibrillation (AF). We evaluate the performance of NG-GP-MCTS with spatiotemporal cardiac simulation in a 3D atrial geometry. Computer experiments show that our algorithm is highly promising for designing effective sequential procedures to optimize spatiotemporal dynamics in complex geometries.

Understanding the Utility of Endocardial Electrocardiographic Imaging in Epi-Endocardial Mapping of 3D Reentrant Circuits

Background

Studies of VT mechanisms are largely based on a 2D portrait of reentrant circuits on one surface of the heart. This oversimplifies the 3D circuit that involves the depth of the myocardium. Simultaneous epicardial and endocardial (epi-endo) mapping was shown to facilitate a 3D delineation of VT circuits, which is however difficult via invasive mapping.

Objective

This study investigates the capability of noninvasive epicardial-endocardial electrocardiographic imaging (ECGI) to elucidate the 3D construct of VT circuits, emphasizing the differentiation of epicardial, endocardial, and intramural circuits and to determine the proximity of mid-wall exits to the epicardial or endocardial surfaces.

Methods

120-lead ECGs of VT in combination with subject-specific heart-torso geometry are used to compute unipolar electrograms (CEGM) on ventricular epicardium and endocardia. Activation isochrones are constructed, and the percentage of activation within VT cycle length is calculated on each surface. This classifies VT circuits into 2D (surface only), uniform transmural, nonuniform transmural, and mid-myocardial (focal on surfaces). Furthermore, the endocardial breakthrough time was accurately measured using Laplacian eigenmaps, and by correlating the delay time of the epi-endo breakthroughs, the relative distance of a mid-wall exit to the epicardium or the endocardium surfaces was identified.

Results

We analyzed 23 simulated and in-vivo VT circuits on post-infarction porcine hearts. In simulated circuits, ECGI classified 21% as 2D and 78% as 3D: 82.6% of these were correctly classified. The relative timing between epicardial and endocardial breakthroughs was correctly captured across all cases. In in-vivo circuits, ECGI classified 25% as 2D and 75% as 3D: in all cases, circuit exits and entrances were consistent with potential critical isthmus delineated from combined LGE-MRI and catheter mapping data.

Conclusions

ECGI epi-endo mapping has the potential for fast delineation of 3D VT circuits, which may augment detailed catheter mapping for VT ablation.

Multi-Source Data and Knowledge Fusion via Deep Learning for Dynamical Systems: Applications to Spatiotemporal Cardiac Modeling

Advanced sensing and imaging provide unprecedented opportunities to collect data from diverse sources for increasing information visibility in spatiotemporal dynamical systems. Furthermore, the fundamental physics of the dynamical system is commonly elucidated through a set of partial differential equations (PDEs), which plays a critical role in delineating the manner in which the sensing signals can be modeled. Reliable predictive modeling of such spatiotemporal dynamical systems calls upon the effective fusion of fundamental physics knowledge and multi-source sensing data. This paper proposes a multi-source data and knowledge fusion framework via deep learning for dynamical systems with applications to spatiotemporal cardiac modeling. This framework not only achieves effective data fusion through capturing the physics-based information flow between different domains, but also incorporates the geometric information of a 3D system through a graph Laplacian for robust spatiotemporal predictive modeling. We implement the proposed framework to model cardiac electrodynamics under both healthy and diseased heart conditions. Numerical experiments demonstrate the superior performance of our framework compared with traditional approaches that lack the capability for effective data fusion or geometric information incorporation.

Frequency-Enhanced Geometric-Constrained Reconstruction for Localizing Myocardial Infarction in 12-Lead Electrocardiograms

Determining the location of myocardial infarction is crucial for clinical management and therapeutic stratagem. However, existing diagnostic tools either sacrifice ease of use or are limited by their spatial resolution. Addressing this, we aim to refine myocardial infarction localization via surface potential reconstruction of the ventricles in 12-lead electrocardiograms (ECG). A notable obstacle is the ill-posed nature of such reconstructions. To overcome this, we introduce the frequency-enhanced geometric-constrained iterative network (FGIN). FGIN begins by mining the latent features from ECG data across both time and frequency domains. Subsequently, it increases the data dimensionality of ECG and captures intricate features using convolutional layers. Finally, FGIN incorporates ventricular geometry as a constraint on surface potential distribution. It allocates variable weights to distinct edges. Experimental validation of FGIN confirms its efficacy over synthetic and clinical datasets. On the synthetic dataset, FGIN outperforms seven existing reconstruction methods, attaining the highest Pearson Correlation Coefficient of 0.8624, the lowest Root Mean Square Error of 0.1548, and the highest Structural Similarity Index Measure of 0.7988. On the clinical public dataset (2007 PhysioNet/Computers in Cardiology Challenge), FGIN achieves better localization results than other approaches, according to the clinical standard 17-segment model, achieving an average Segment Overlap of 87.2%. Clinical trials on 50 patients demonstrate FGIN's effectiveness, showing an average accuracy of 91.6% and an average Segment Overlap of 88.2%.

Hybrid Neural State-Space Modeling for Supervised and Unsupervised Electrocardiographic Imaging

State-space modeling (SSM) provides a general framework for many image reconstruction tasks. Error in a priori physiological knowledge of the imaging physics, can bring incorrectness to solutions. Modern deep-learning approaches show great promise but lack interpretability and rely on large amounts of labeled data. In this paper, we present a novel hybrid SSM framework for electrocardiographic imaging (ECGI) to leverage the advantage of state-space formulations in data-driven learning. We first leverage the physics-based forward operator to supervise the learning. We then introduce neural modeling of the transition function and the associated Bayesian filtering strategy. We applied the hybrid SSM framework to reconstruct electrical activity on the heart surface from body-surface potentials. In unsupervised settings of both in-silico and in-vivo data without cardiac electrical activity as the ground truth to supervise the learning, we demonstrated improved ECGI performances of the hybrid SSM framework trained from a small number of ECG observations in comparison to the fixed SSM. We further demonstrated that, when in-silico simulation data becomes available, mixed supervised and unsupervised training of the hybrid SSM achieved a further 40.6% and 45.6% improvements, respectively, in comparison to traditional ECGI baselines and supervised data-driven ECGI baselines for localizing the origin of ventricular activations in real data.

Neural network aided extended Kalman filtering for inverse imaging of cardiac transmembrane potential

Objective.The aim of this study is to address the limitations in reconstructing the electrical activity of the heart from the body surface electrocardiogram, which is an ill-posed inverse problem. Current methods often assume values commonly used in the literature in the absence ofa prioriknowledge, leading to errors in the model. Furthermore, most methods ignore the dynamic activation process inherent in cardiomyocytes during the cardiac cycle.Approach.To overcome these limitations, we propose an extended Kalman filter (EKF)-based neural network approach to dynamically reconstruct cardiac transmembrane potential (TMP). Specifically, a recurrent neural network is used to establish the state estimation equation of the EKF, while a convolutional neural network is used as the measurement equation. The Jacobi matrix of the network undergoes a correction feedback process to obtain the Kalman gain.Main results.After repeated iterations, the final estimated state vector, i.e. the reconstructed image of the TMP, is obtained. The results from both the final simulation and real experiments demonstrate the robustness and accurate quantification of the model.Significance.This study presents a new approach to cardiac TMP reconstruction that offers higher accuracy and robustness compared to traditional methods. The use of neural networks and EKFs allows dynamic modelling that takes into account the activation processes inherent in cardiomyocytes and does not requirea prioriknowledge of inputs such as forward transition matrices.

Nonlocal based FISTA network for noninvasive cardiac transmembrane potential imaging

Objective. The primary aim of our study is to advance our understanding and diagnosis of cardiac diseases. We focus on the reconstruction of myocardial transmembrane potential (TMP) from body surface potential mapping.Approach. We introduce a novel methodology for the reconstruction of the dynamic distribution of TMP. This is achieved through the integration of convolutional neural networks with conventional optimization algorithms. Specifically, we utilize the subject-specific transfer matrix to describe the dynamic changes in TMP distribution and ECG observations at the body surface. To estimate the TMP distribution, we employ LNFISTA-Net, a learnable non-local regularized iterative shrinkage-thresholding network. The coupled estimation processes are iteratively repeated until convergence.Main results. Our experiments demonstrate the capabilities and benefits of this strategy. The results highlight the effectiveness of our approach in accurately estimating the TMP distribution, thereby providing a reliable method for the diagnosis of cardiac diseases.Significance. Our approach demonstrates promising results, highlighting its potential utility for a range of applications in the medical field. By providing a more accurate and dynamic reconstruction of TMP, our methodology could significantly improve the diagnosis and treatment of cardiac diseases, thereby contributing to advancements in healthcare.

Efficient Classification of ECG Images Using a Lightweight CNN with Attention Module and IoT

Cardiac disorders are a leading cause of global casualties, emphasizing the need for the initial diagnosis and prevention of cardiovascular diseases (CVDs). Electrocardiogram (ECG) procedures are highly recommended as they provide crucial cardiology information. Telemedicine offers an opportunity to provide low-cost tools and widespread availability for CVD management. In this research, we proposed an IoT-based monitoring and detection system for cardiac patients, employing a two-stage approach. In the initial stage, we used a routing protocol that combines routing by energy and link quality (REL) with dynamic source routing (DSR) to efficiently collect data on an IoT healthcare platform. The second stage involves the classification of ECG images using hybrid-based deep features. Our classification system utilizes the "ECG Images dataset of Cardiac Patients", comprising 12-lead ECG images with four distinct categories: abnormal heartbeat, myocardial infarction (MI), previous history of MI, and normal ECG. For feature extraction, we employed a lightweight CNN, which automatically extracts relevant ECG features. These features were further optimized through an attention module, which is the method's main focus. The model achieved a remarkable accuracy of 98.39%. Our findings suggest that this system can effectively aid in the identification of cardiac disorders. The proposed approach combines IoT, deep learning, and efficient routing protocols, showcasing its potential for improving CVD diagnosis and management.

Improving Generalization by Learning Geometry-Dependent and Physics-Based Reconstruction of Image Sequences

Deep neural networks have shown promise in image reconstruction tasks, although often on the premise of large amounts of training data. In this paper, we present a new approach to exploit the geometry and physics underlying electrocardiographic imaging (ECGI) to learn efficiently with a relatively small dataset. We first introduce a non-Euclidean encoding-decoding network that allows us to describe the unknown and measurement variables over their respective geometrical domains. We then explicitly model the geometry-dependent physics in between the two domains via a bipartite graph over their graphical embeddings. We applied the resulting network to reconstruct electrical activity on the heart surface from body-surface potentials. In a series of generalization tasks with increasing difficulty, we demonstrated the improved ability of the network to generalize across geometrical changes underlying the data using less than 10% of training data and fewer variations of training geometry in comparison to its Euclidean alternatives. In both simulation and real-data experiments, we further demonstrated its ability to be quickly fine-tuned to new geometry using a modest amount of data.

Learning to Disentangle Inter-Subject Anatomical Variations in Electrocardiographic Data

OBJECTIVE

This work investigates the possibility of disentangled representation learning of inter-subject anatomical variations within electrocardiographic (ECG) data.

METHODS

Since ground truth anatomical factors are generally not known in clinical ECG for assessing the disentangling ability of the models, the presented work first proposes the SimECG data set, a 12-lead ECG data set procedurally generated with a controlled set of anatomical generative factors. Second, to perform such disentanglement, the presented method evaluates and compares deep generative models with latent density modeled by nonparametric Indian Buffet Process to account for the complex generative process of ECG data.

RESULTS

In the simulated data, the experiments demonstrate, for the first time, concrete evidence of the possibility to disentangle key generative anatomical factors within ECG data in separation from task-relevant generative factors. We achieve a disentanglement score of 92.1% while disentangling five anatomical generative factors and the task-relevant generative factor. In both simulated and real-data experiments, this work further provides quantitative evidence for the benefit of disentanglement learning on the downstream clinical task of localizing the origin of ventricular activation. Overall, the presented method achieves an improvement of around 18.5%, and 11.3% for the simulated dataset, and around 7.2%, and 3.6% for the real dataset, over baseline CNN, and standard generative model, respectively.

CONCLUSION

These results demonstrate the importance as well as the feasibility of the disentangled representation learning of inter-subject anatomical variations within ECG data.

SIGNIFICANCE

This work suggests the important research direction to deal with the well-known challenge posed by the presence of significant inter-subject variations during an automated analysis of ECG data.

Fast Posterior Estimation of Cardiac Electrophysiological Model Parameters via Bayesian Active Learning

Probabilistic estimation of cardiac electrophysiological model parameters serves an important step toward model personalization and uncertain quantification. The expensive computation associated with these model simulations, however, makes direct Markov Chain Monte Carlo (MCMC) sampling of the posterior probability density function (pdf) of model parameters computationally intensive. Approximated posterior pdfs resulting from replacing the simulation model with a computationally efficient surrogate, on the other hand, have seen limited accuracy. In this study, we present a Bayesian active learning method to directly approximate the posterior pdf function of cardiac model parameters, in which we intelligently select training points to query the simulation model in order to learn the posterior pdf using a small number of samples. We integrate a generative model into Bayesian active learning to allow approximating posterior pdf of high-dimensional model parameters at the resolution of the cardiac mesh. We further introduce new acquisition functions to focus the selection of training points on better approximating the shape rather than the modes of the posterior pdf of interest. We evaluated the presented method in estimating tissue excitability in a 3D cardiac electrophysiological model in a range of synthetic and real-data experiments. We demonstrated its improved accuracy in approximating the posterior pdf compared to Bayesian active learning using regular acquisition functions, and substantially reduced computational cost in comparison to existing standard or accelerated MCMC sampling.

Noninvasive Cardiac Transmembrane Potential Imaging via Global Features Based FISTA Network

Noninvasive electrophysiological imaging plays an important role in the clinical diagnosis and treatment of heart diseases over recent years. Transmembrane potential (TMP) is one of the most important cardiac physiological signals, which can be used to diagnose heart disease such as premature beat and myocardial infarction. Considering the nonlocal self-similarity of TMP distribution and integrating traditional optimization strategy into deep learning, we proposed a novel global features based Fast Iterative Shrinkage/Thresholding network, named as GFISTA-Net. The proposed method has two main advantages over traditional methods, namely, the l1-norm regularization helps to avoid overfitting the model on high-dimensional but small-training data, and facilitates embedded the spatio-temporal correlation of TMP. Experiments demonstrate the power of our method.

An Inverse Eikonal Method for Identifying Ventricular Activation Sequences from Epicardial Activation Maps

A key mechanism controlling cardiac function is the electrical activation sequence of the heart's main pumping chambers termed the ventricles. As such, personalization of the ventricular activation sequences is of pivotal importance for the clinical utility of computational models of cardiac electrophysiology. However, a direct observation of the activation sequence throughout the ventricular volume is virtually impossible. In this study, we report on a novel method for identification of activation sequences from activation maps measured at the outer surface of the heart termed the epicardium. Conceptually, the method attempts to identify the key factors governing the ventricular activation sequence - the timing of earliest activation sites (EAS) and the velocity tensor field within the ventricular walls - from sparse and noisy activation maps sampled from the epicardial surface and fits an Eikonal model to the observations. Regularization methods are first investigated to overcome the severe ill-posedness of the inverse problem in a simplified 2D example. These methods are then employed in an anatomically accurate biventricular model with two realistic activation models of varying complexity - a simplified trifascicular model (3F) and a topologically realistic model of the His-Purkinje system (HPS). Using epicardial activation maps at full resolution, we first demonstrate that reconstructing the volumetric activation sequence is, in principle, feasible under the assumption of known location of EAS and later evaluate robustness of the method against noise and reduced spatial resolution of observations. Our results suggest that the FIMIN algorithm is able to robustly recover the full 3D activation sequence using epicardial activation maps at a spatial resolution achievable with current mapping systems and in the presence of noise. Comparing the accuracy achieved in the reconstructed activation maps with clinical data uncertainties suggests that the FIMIN method may be suitable for the patient- specific parameterization of activation models.

Sequential estimation of the generated curing heat of composite materials by data assimilation: A numerical study

The models and parameters related to the generated curing heat in the molding simulation of composite materials are dependent on the type of resin used and the experimental conditions. Therefore, in this study, we estimated the generated curing heat that changes with time by a data assimilation method, which combines the observation values with simulation values, so that the heat curing simulation of carbon fiber reinforced polymers (CFRPs) becomes closer to the experimental conditions. In the data assimilation method, the temperature distribution on the surface of the composite material was used as an observation value, and the generated curing heat was estimated using an ensemble Kalman filter. By optimizing the data assimilation parameters in advance using the response surface method and estimating the generated curing heat by numerical experiments, the generated curing heat could be estimated with an accuracy represented by the time mean error of less than 6%.

Embedding high-dimensional Bayesian optimization via generative modeling: Parameter personalization of cardiac electrophysiological models

The estimation of patient-specific tissue properties in the form of model parameters is important for personalized physiological models. Because tissue properties are spatially varying across the underlying geometrical model, it presents a significant challenge of high-dimensional (HD) optimization at the presence of limited measurement data. A common solution to reduce the dimension of the parameter space is to explicitly partition the geometrical mesh. In this paper, we present a novel concept that uses a generative variational auto-encoder (VAE) to embed HD Bayesian optimization into a low-dimensional (LD) latent space that represents the generative code of HD parameters. We further utilize VAE-encoded knowledge about the generative code to guide the exploration of the search space. The presented method is applied to estimating tissue excitability in a cardiac electrophysiological model in a range of synthetic and real-data experiments, through which we demonstrate its improved accuracy and substantially reduced computational cost in comparison to existing methods that rely on geometry-based reduction of the HD parameter space.

Multi-branch fusion network for Myocardial infarction screening from 12-lead ECG images

BACKGROUND AND OBJECTIVE

Myocardial infarction (MI) is a myocardial anoxic incapacitation caused by severe cardiovascular obstruction that can cause irreversible injury or even death. In medical field, the electrocardiogram (ECG) is a common and effective way to diagnose myocardial infarction, which often requires a wealth of medical knowledge. It is necessary to develop an approach that can detect the MI automatically.

METHODS

In this paper, we propose a multi-branch fusion framework for automatic MI screening from 12-lead ECG images, which consists of multi-branch network, feature fusion and classification network. First, we use text detection and position alignment to automatically separate twelve leads from ECG images. Then, those 12 leads are input into the multi-branch network constructed by a shallow neural network to get 12 feature maps. After concatenating those feature maps by depth fusion, classification is explored to judge the given ECG is MI or not.

RESULTS

Based on extensive experiments on an ECG image dataset, performances of different combinations of structures are analyzed. The proposed network is compared with other networks and also compared with physicians in the practical use. All the experiments verify that the proposed method is effective for MI screening based on ECG images, which achieves accuracy, sensitivity, specificity and F1-score of 94.73%, 96.41%, 95.94% and 93.79% respectively.

CONCLUSIONS

Rather than using the typical one-dimensional electrical ECG signal, this paper gives an effective model to screen MI by analyzing 12-lead ECG images. Extracting and analyzing these 12 leads from their corresponding ECG images is a good attempt in the application of MI screening.

Noninvasive Reconstruction of Transmural Transmembrane Potential With Simultaneous Estimation of Prior Model Error

To reconstruct electrical activity in the heart from body-surface electrocardiograms (ECGs) is an ill-posed inverse problem. Electrophysiological models have been found effective in regularizing these inverse problems by incorporating a priori knowledge about how the electrical potential in the heart propagates over time. However, these models suffer from model errors arising from, for example, parameters associated with tissue properties and the earliest sites of excitation. We present a Bayesian approach to simultaneously estimate transmembrane potential (TMP) signals and prior model errors, exploiting sparsity of the error in the gradient domain in the form of a novel sparse prior based on variational lower bound of the generalized Gaussian distribution. In synthetic and real-data experiments, we demonstrate the improvement of accuracy in TMP reconstruction brought by simultaneous model error estimation. We further provide theoretical and empirical justifications for the change of performances in the presented method at the presence of different model errors.

Inverse localization of earliest cardiac activation sites from activation maps based on the viscous Eikonal equation

In this study we propose a novel method for identifying the locations of earliest activation in the human left ventricle from activation maps measured at the epicardial surface. Electrical activation is modeled based on the viscous Eikonal equation. The sites of earliest activation are identified by solving a minimization problem. Arbitrary initial locations are assumed, which are then modified based on a shape derivative based perturbation field until a minimal mismatch between the computed and the given activation maps on the epicardial surface is achieved. The proposed method is tested in two numerical benchmarks, a generic 2D unit-square benchmark, and an anatomically accurate MRI-derived 3D human left ventricle benchmark to demonstrate potential utility in a clinical context. For unperturbed input data, our localization method is able to accurately reconstruct the earliest activation sites in both benchmarks with deviations of only a fraction of the used spatial discretization size. Further, with the quality of the input data reduced by spatial undersampling and addition of noise, we demonstrate that an accurate identification of the sites of earliest activation is still feasible.

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.

Learning Domain Shift in Simulated and Clinical Data: Localizing the Origin of Ventricular Activation From 12-Lead Electrocardiograms

Building a data-driven model to localize the origin of ventricular activation from 12-lead electrocardiograms (ECG) requires addressing the challenge of large anatomical and physiological variations across individuals. The alternative of a patient-specific model is, however, difficult to implement in clinical practice because the training data must be obtained through invasive procedures. In this paper, we present a novel approach that overcomes this problem of the scarcity of clinical data by transferring the knowledge from a large set of patient-specific simulation data while utilizing domain adaptation to address the discrepancy between the simulation and clinical data. The method that we have developed quantifies non-uniformly distributed simulation errors, which are then incorporated into the process of domain adaptation in the context of both classification and regression. This yields a quantitative model that, with the addition of 12-lead ECG data from each patient, provides progressively improved patient-specific localizations of the origin of ventricular activation. We evaluated the performance of the presented method in localizing 75 pacing sites on three in-vivo premature ventricular contraction (PVC) patients. We found that the presented model showed an improvement in localization accuracy relative to a model trained on clinical ECG data alone or a model trained on combined simulation and clinical data without considering domain shift. Furthermore, we demonstrated the ability of the presented model to improve the real-time prediction of the origin of ventricular activation with each added clinical ECG data, progressively guiding the clinician towards the target site.

Cardiac implantable electronic device infections: Observational data from a tertiary care center in Lebanon

With increasing rates of device implantation, there is an increased recognition of device infection. We conducted a retrospective observational study in a tertiary care center in Lebanon, with data collected from medical records of patients presenting with cardiac implantable electronic device (CIED) infection from 2000 to 2017 with the purpose of identifying etiologies, risk factors and other parameters, and comparing them to available data from the rest of the world. We identified a total of 22 CIED infections. The most common microbial etiologies, including involvement in polymicrobial infection, were coagulase-negative staphylococci (45.5%) and Staphylococcus aureus (22.7%). Rare cases of Brucella melitensis, Sphingomonas paucimobilis, and Kytococcus schroeteri device infection were seen. Heart failure was seen in 77.3% of patients, hypertension in 68.2%, and chronic kidney disease in 50%. Skin changes were the most common presenting symptoms (86.4%). Antibiotics were given to all patients and all had their devices removed, with 36.4% undergoing new device implantation. This is the first study of CIED infections in Lebanon and the Middle East. Local epidemiology and occupational exposure must be considered while contemplating the microbial etiology of infection. Close monitoring after device implantation is important in preventing device infection that carries high risk of morbidity and mortality.

Reduction of Artefacts in JPEG-XR Compressed Images

The JPEG-XR encoding process utilizes two types of transform operations: Photo Overlap Transform (POT) and Photo Core Transform (PCT). Using the Device Porting Kit (DPK) provided by Microsoft, we performed encoding and decoding processes on JPEG XR images. It was discovered that when the quantization parameter is >1-lossy compression conditions, the resulting image displays chequerboard block artefacts, border artefacts and corner artefacts. These artefacts are due to the nonlinearity of transforms used by JPEG-XR. Typically, it is not so visible; however, it can cause problems while copying and scanning applications, as it shows nonlinear transforms when the source and the target of the image have different configurations. Hence, it is important for document image processing pipelines to take such artefacts into account. Additionally, these artefacts are most problematic for high-quality settings and appear more visible at high compression ratios. In this paper, we analyse the cause of the above artefacts. It was found that the main problem lies in the step of POT and quantization. To solve this problem, the use of a "uniform matrix" is proposed. After POT (encoding) and before inverse POT (decoding), an extra step is added to multiply this uniform matrix. Results suggest that it is an easy and effective way to decrease chequerboard, border and corner artefacts, thereby improving the image quality of lossy encoding JPEG XR than the original DPK program with no increased calculation complexity or file size.

Impact of the Endocardium in a Parameter Optimization to Solve the Inverse Problem of Electrocardiography

Electrocardiographic imaging aims at reconstructing cardiac electrical events from electrical signals measured on the body surface. The most common approach relies on the inverse solution of the Laplace equation in the torso to reconstruct epicardial potential maps from body surface potential maps. Here we apply a method based on a parameter identification problem to reconstruct both activation and repolarization times. From an ansatz of action potential, based on the Mitchell-Schaeffer ionic model, we compute body surface potential signals. The inverse problem is reduced to the identification of the parameters of the Mitchell-Schaeffer model. We investigate whether solving the inverse problem with the endocardium improves the results or not. We solved the parameter identification problem on two different meshes: one with only the epicardium, and one with both the epicardium and the endocardium. We compared the results on both the heart (activation and repolarization times) and the torso. The comparison was done on validation data of sinus rhythm and ventricular pacing. We found similar results with both meshes in 6 cases out of 7: the presence of the endocardium slightly improved the activation times. This was the most visible on a sinus beat, leading to the conclusion that inclusion of the endocardium would be useful in situations where endo-epicardial gradients in activation or repolarization times play an important role.

Retrieving hidden atrial repolarization waves from standard surface ECGs

BACKGROUND

This study estimates atrial repolarization activities (Ta waves), which are typically hidden most of the time from body surface electrocardiography when diagnosing cardiovascular diseases. The morphology of Ta waves has been proven to be an important marker for the early sign of inferior injury, such as acute atrial infarction, or arrhythmia, such as atrial fibrillation. However, Ta waves are usually unseen except during conduction system malfunction, such as long QT interval or atrioventricular block. Therefore, justifying heart diseases based on atrial repolarization becomes impossible in sinus rhythm.

METHODS

We obtain TMPs in the atrial part of the myocardium which reflects the correct excitation sequence starting from the atrium to the end of the apex.

RESULTS

The resulting TMP shows the hidden atrial part of ECG waves.

CONCLUSIONS

This extraction makes many diseases, such as acute atrial infarction or arrhythmia, become easily diagnosed.

Validation and Opportunities of Electrocardiographic Imaging: From Technical Achievements to Clinical Applications

Electrocardiographic imaging (ECGI) reconstructs the electrical activity of the heart from a dense array of body-surface electrocardiograms and a patient-specific heart-torso geometry. Depending on how it is formulated, ECGI allows the reconstruction of the activation and recovery sequence of the heart, the origin of premature beats or tachycardia, the anchors/hotspots of re-entrant arrhythmias and other electrophysiological quantities of interest. Importantly, these quantities are directly and non-invasively reconstructed in a digitized model of the patient's three-dimensional heart, which has led to clinical interest in ECGI's ability to personalize diagnosis and guide therapy. Despite considerable development over the last decades, validation of ECGI is challenging. Firstly, results depend considerably on implementation choices, which are necessary to deal with ECGI's ill-posed character. Secondly, it is challenging to obtain (invasive) ground truth data of high quality. In this review, we discuss the current status of ECGI validation as well as the major challenges remaining for complete adoption of ECGI in clinical practice. Specifically, showing clinical benefit is essential for the adoption of ECGI. Such benefit may lie in patient outcome improvement, workflow improvement, or cost reduction. Future studies should focus on these aspects to achieve broad adoption of ECGI, but only after the technical challenges have been solved for that specific application/pathology. We propose 'best' practices for technical validation and highlight collaborative efforts recently organized in this field. Continued interaction between engineers, basic scientists, and physicians remains essential to find a hybrid between technical achievements, pathological mechanisms insights, and clinical benefit, to evolve this powerful technique toward a useful role in clinical practice.

Electrocardiographic Imaging Using a Spatio-Temporal Basis of Body Surface Potentials-Application to Atrial Ectopic Activity

Electrocardiographic imaging (ECGI) strongly relies on a priori assumptions and additional information to overcome ill-posedness. The major challenge of obtaining good reconstructions consists in finding ways to add information that effectively restricts the solution space without violating properties of the sought solution. In this work, we attempt to address this problem by constructing a spatio-temporal basis of body surface potentials (BSP) from simulations of many focal excitations. Measured BSPs are projected onto this basis and reconstructions are expressed as linear combinations of corresponding transmembrane voltage (TMV) basis vectors. The novel method was applied to simulations of 100 atrial ectopic foci with three different conduction velocities. Three signal-to-noise ratios (SNR) and bases of six different temporal lengths were considered. Reconstruction quality was evaluated using the spatial correlation coefficient of TMVs as well as estimated local activation times (LAT). The focus localization error was assessed by computing the geodesic distance between true and reconstructed foci. Compared with an optimally parameterized Tikhonov-Greensite method, the BSP basis reconstruction increased the mean TMV correlation by up to 22, 24, and 32% for an SNR of 40, 20, and 0 dB, respectively. Mean LAT correlation could be improved by up to 5, 7, and 19% for the three SNRs. For 0 dB, the average localization error could be halved from 15.8 to 7.9 mm. For the largest basis length, the localization error was always below 34 mm. In conclusion, the new method improved reconstructions of atrial ectopic activity especially for low SNRs. Localization of ectopic foci turned out to be more robust and more accurate. Preliminary experiments indicate that the basis generalizes to some extent from the training data and may even be applied for reconstruction of non-ectopic activity.

Characterizing the Location and Extent of Myocardial Infarctions With Inverse ECG Modeling and Spatiotemporal Regularization

Myocardial infarction (MI) is among the leading causes of death in the United States. It is imperative to identify and characterize MIs for timely delivery of life-saving medical interventions. Cardiac electrical activity propagates in space and evolves over time. Traditional works focus on the analysis of time-domain ECG (e.g., 12-lead ECG) on the body surface for the detection of MIs, but tend to overlook spatiotemporal dynamics in the heart. Body surface potential mappings (BSPMs) provide high-resolution distribution of electric potentials over the entire torso, and therefore provide richer information than 12-lead ECG. However, BSPM are available on the body surface. Clinicians are in need of a closer look of the electric potentials in the heart to investigate cardiac pathology and optimize treatment strategies. In this paper, we applied the method of spatiotemporal inverse ECG (ST-iECG) modeling to map electrical potentials from the body surface to the heart, and then characterize the location and extent of MIs by investigating the reconstructed heart-surface electrograms. First, we investigate the impact of mesh resolution on the inverse ECG modeling. Second, we solve the inverse ECG problem and reconstruct heart-surface electrograms using the ST-iECG model. Finally, we propose a wavelet-clustering method to investigate the pathological behaviors of heart-surface electrograms, and thereby characterize the extent and location of MIs. The proposed methodology is evaluated and validated with real data of MIs from human subjects. Experimental results show that negative QRS waves in heart-surface electrograms indicate potential regions of MI, and the proposed ST-iECG model yields superior characterization results of MIs on the heart surface over existing methods.

Activation recovery interval imaging of premature ventricular contraction

Dispersion of ventricular repolarization due to abnormal activation contributes to the susceptibility to cardiac arrhythmias. However, the global pattern of repolarization is difficult to assess clinically. Activation recovery interval (ARI) has been used to understand the properties of ventricular repolarization. In this study, we developed an ARI imaging technique to noninvasively reconstruct three-dimensional (3D) ARI maps in 10 premature ventricular contraction (PVC) patients and evaluated the results with the endocardial ARI maps recorded by a clinical navigation system (CARTO). From the analysis results of a total of 100 PVC beats in 10 patients, the average correlation coefficient is 0.86±0.05 and the average relative error is 0.06±0.03. The average localization error is 4.5±2.3 mm between the longest ARI sites in 3D ARI maps and those in CARTO endocardial ARI maps. The present results suggest that ARI imaging could serve as an alternative of evaluating global pattern of ventricular repolarization noninvasively and could assist in the future investigation of the relationship between global repolarization dispersion and the susceptibility to cardiac arrhythmias.

Quantifying the uncertainty in model parameters using Gaussian process-based Markov chain Monte Carlo in cardiac electrophysiology

Model personalization requires the estimation of patient-specific tissue properties in the form of model parameters from indirect and sparse measurement data. Moreover, a low-dimensional representation of the parameter space is needed, which often has a limited ability to reveal the underlying tissue heterogeneity. As a result, significant uncertainty can be associated with the estimated values of the model parameters which, if left unquantified, will lead to unknown variability in model outputs that will hinder their reliable clinical adoption. Probabilistic estimation of model parameters, however, remains an unresolved challenge. Direct Markov Chain Monte Carlo (MCMC) sampling of the posterior distribution function (pdf) of the parameters is infeasible because it involves repeated evaluations of the computationally expensive simulation model. To accelerate this inference, one popular approach is to construct a computationally efficient surrogate and sample from this approximation. However, by sampling from an approximation, efficiency is gained at the expense of sampling accuracy. In this paper, we address this issue by integrating surrogate modeling of the posterior pdf into accelerating the Metropolis-Hastings (MH) sampling of the exact posterior pdf. It is achieved by two main components: (1) construction of a Gaussian process (GP) surrogate of the exact posterior pdf by actively selecting training points that allow for a good global approximation accuracy with a focus on the regions of high posterior probability; and (2) use of the GP surrogate to improve the proposal distribution in MH sampling, in order to improve the acceptance rate. The presented framework is evaluated in its estimation of the local tissue excitability of a cardiac electrophysiological model in both synthetic data experiments and real data experiments. In addition, the obtained posterior distributions of model parameters are interpreted in relation to the factors contributing to parameter uncertainty, including different low-dimensional representations of the parameter space, parameter non-identifiability, and parameter correlations.

Estimation of state and material properties during heat-curing molding of composite materials using data assimilation: A numerical study

Accurate simulations of carbon fiber-reinforced plastic (CFRP) molding are vital for the development of high-quality products. However, such simulations are challenging and previous attempts to improve the accuracy of simulations by incorporating the data acquired from mold monitoring have not been completely successful. Therefore, in the present study, we developed a method to accurately predict various CFRP thermoset molding characteristics based on data assimilation, a process that combines theoretical and experimental values. The degree of cure as well as temperature and thermal conductivity distributions during the molding process were estimated using both temperature data and numerical simulations. An initial numerical experiment demonstrated that the internal mold state could be determined solely from the surface temperature values. A subsequent numerical experiment to validate this method showed that estimations based on surface temperatures were highly accurate in the case of degree of cure and internal temperature, although predictions of thermal conductivity were more difficult.

Spatially Adaptive Multi-Scale Optimization for Local Parameter Estimation in Cardiac Electrophysiology

To obtain a patient-specific cardiac electro-physiological (EP) model, it is important to estimate the 3-D distributed tissue properties of the myocardium. Ideally, the tissue property should be estimated at the resolution of the cardiac mesh. However, such high-dimensional estimation faces major challenges in identifiability and computation. Most existing works reduce this dimension by partitioning the cardiac mesh into a pre-defined set of segments. The resulting low-resolution solutions have a limited ability to represent the underlying heterogeneous tissue properties of varying sizes, locations, and distributions. In this paper, we present a novel framework that, going beyond a uniform low-resolution approach, is able to obtain a higher resolution estimation of tissue properties represented by spatially non-uniform resolution. This is achieved by two central elements: 1) a multi-scale coarse-to-fine optimization that facilitates higher resolution optimization using the lower resolution solution and 2) a spatially adaptive decision criterion that retains lower resolution in homogeneous tissue regions and allows higher resolution in heterogeneous tissue regions. The presented framework is evaluated in estimating the local tissue excitability properties of a cardiac EP model on both synthetic and real data experiments. Its performance is compared with optimization using pre-defined segments. Results demonstrate the feasibility of the presented framework to estimate local parameters and to reveal heterogeneous tissue properties at a higher resolution without using a high number of unknowns.

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.

Noninvasive Imaging of Human Atrial Activation during Atrial Flutter and Normal Rhythm from Body Surface Potential Maps

Background

Knowledge of atrial electrophysiological properties is crucial for clinical intervention of atrial arrhythmias and the investigation of the underlying mechanism. This study aims to evaluate the feasibility of a novel noninvasive cardiac electrical imaging technique in imaging bi-atrial activation sequences from body surface potential maps (BSPMs).

Methods

The study includes 7 subjects, with 3 atrial flutter patients, and 4 healthy subjects with normal atrial activations. The subject-specific heart-torso geometries were obtained from MRI/CT images. The equivalent current densities were reconstructed from 208-channel BSPMs by solving the inverse problem using individual heart-torso geometry models. The activation times were estimated from the time instant corresponding to the highest peak in the time course of the equivalent current densities. To evaluate the performance, a total of 32 cycles of atrial flutter were analyzed. The imaged activation maps obtained from single beats were compared with the average maps and the activation maps measured from CARTO, by using correlation coefficient (CC) and relative error (RE).

Results

The cardiac electrical imaging technique is capable of imaging both focal and reentrant activations. The imaged activation maps for normal atrial activations are consistent with findings from isolated human hearts. Activation maps for isthmus-dependent counterclockwise reentry were reconstructed on three patients with typical atrial flutter. The method was capable of imaging macro counterclockwise reentrant loop in the right atrium and showed inter-atria electrical conduction through coronary sinus. The imaged activation sequences obtained from single beats showed good correlation with both the average activation maps (CC = 0.91±0.03, RE = 0.29±0.05) and the clinical endocardial findings using CARTO (CC = 0.70±0.04, RE = 0.42±0.05).

Conclusions

The noninvasive cardiac electrical imaging technique is able to reconstruct complex atrial reentrant activations and focal activation patterns in good consistency with clinical electrophysiological mapping. It offers the potential to assist in radio-frequency ablation of atrial arrhythmia and help defining the underlying arrhythmic mechanism.

Noninvasive epicardial and endocardial electrocardiographic imaging of scar-related ventricular tachycardia

BACKGROUND

The majority of life-threatening ventricular tachycardias (VTs) are sustained by heterogeneous scar substrates with narrow strands of surviving tissue. An effective treatment for scar-related VT is to modify the underlying scar substrate by catheter ablation. If activation sequence and entrainment mapping can be performed during sustained VT, the exit and isthmus of the circuit can often be identified. However, with invasive catheter mapping, only monomorphic VT that is hemodynamically stable can be mapped in this manner. For the majority of patients with poorly tolerated VTs or multiple VTs, a close inspection of the re-entry circuit is not possible. A noninvasive approach to fast mapping of unstable VTs can potentially allow an improved identification of critical ablation sites.

METHODS

For patients who underwent catheter ablation of scar-related VT, CT scan was obtained prior to the ablation procedure and 120-lead body-surface electrocardiograms (ECGs) were acquired during induced VTs. These data were used for noninvasive ECG imaging to computationally reconstruct electrical potentials on the epicardium and on the endocardium of both ventricles. Activation time and phase maps of the VT circuit were extracted from the reconstructed electrograms. They were analyzed with respect to scar substrate obtained from catheter mapping, as well as VT exits confirmed through ablation sites that successfully terminated the VT.

RESULTS

The reconstructed re-entry circuits correctly revealed both epicardial and endocardial origins of activation, consistent with locations of exit sites confirmed from the ablation procedure. The temporal dynamics of the re-entry circuits, particularly the slowing of conduction as indicated by the crowding and zig-zag conducting of the activation isochrones, collocated well with scar substrate obtained by catheter voltage maps. Furthermore, the results indicated that some re-entry circuits involve both the epicardial and endocardial layers, and can only be properly interpreted by mapping both layers simultaneously.

CONCLUSIONS

This study investigated the potential of ECG-imaging for beat-to-beat mapping of unstable reentrant circuits. It shows that simultaneous epicardial and endocardial mapping may improve the delineation of the 3D spatial construct of a re-entry circuit and its exit. It also shows that the use of phase mapping can reveal regions of slow conduction that collocate well with suspected heterogeneous regions within and around the scar.

Spatially Coherent Activation Maps for Electrocardiographic Imaging

OBJECTIVE

Cardiac mapping is an important diagnostic step in cardiac electrophysiology. One of its purposes is to generate a map of the depolarization sequence. This map is constructed in clinical routine either by directly analyzing cardiac electrograms (EGMs) recorded invasively or an estimate of these EGMs obtained by a noninvasive technique. Activation maps based on noninvasively estimated EGMs often show artefactual jumps in activation times. To overcome this problem, we present a new method to construct the activation maps from reconstructed unipolar EGMs.

METHODS

On top of the standard estimation of local activation time from unipolar intrinsic deflections, we propose to mutually compare the EGMs in order to estimate the delays in activation for neighboring recording locations. We then describe a workflow to construct a spatially coherent activation map from local activation times and delay estimates in order to create more accurate maps. The method is optimized using simulated data and evaluated on clinical data from 12 different activation sequences.

RESULTS

We found that the standard methodology created lines of artificially strong activation time gradient. The proposed workflow enhanced these maps significantly.

CONCLUSION

Estimating delays between neighbors is an interesting option for activation map computation in electrocardiographic imaging.

Noninvasive Imaging of High-Frequency Drivers and Reconstruction of Global Dominant Frequency Maps in Patients With Paroxysmal and Persistent Atrial Fibrillation

OBJECTIVE

Highest dominant-frequency (DF) drivers maintaining atrial fibrillation (AF) activities are effective ablation targets for restoring sinus rhythms in patients. This study aims to investigate whether AF drivers with highest activation rate can be noninvasively localized by means of a frequency-based cardiac electrical imaging (CEI) technique, which may aid in the planning of ablation strategy and the investigation of the underlying mechanisms of AF.

METHOD

A total of seven out of 13 patients were recorded with spontaneous paroxysmal or persistent AF and analyzed. The biatrial DF maps were reconstructed by coupling 5-s BSPM with CT-determined patient geometry. The CEI results were compared with ablation sites and DFs found from BSPMs.

RESULTS

CEI imaged left-to-right maximal frequency gradient (7.42 ± 0.66 Hz versus 5.85 ± 1.2 Hz, LA versus RA, p < 0.05) in paroxysmal AF patients. Patients with persistent AF were imaged with a loss of the intrachamber frequency gradient and a dispersion of the fast sources in both chambers. CEI was able to capture the AF behaviors, which were characterized by short-term stability, dynamic transition, and spatial repetition of the highest DF sites. The imaged highest DF sites were consistent with ablation sites in patients studied.

CONCLUSIONS

The frequency-based CEI allows localization of AF drivers with highest DF and characterization of the spatiotemporal frequency behaviors, suggesting the possibility for individualizing treatment strategy and advancing understanding of the underlying AF mechanisms.

SIGNIFICANCE

The establishment of noninvasive imaging techniques localizing AF drivers would facilitate management of this significant cardiac arrhythmia.

Examining the Impact of Prior Models in Transmural Electrophysiological Imaging: A Hierarchical Multiple-Model Bayesian Approach

Noninvasive cardiac electrophysiological (EP) imaging aims to mathematically reconstruct the spatiotemporal dynamics of cardiac sources from body-surface electrocardiographic (ECG) data. This ill-posed problem is often regularized by a fixed constraining model. However, a fixed-model approach enforces the source distribution to follow a pre-assumed structure that does not always match the varying spatiotemporal distribution of actual sources. To understand the model-data relation and examine the impact of prior models, we present a multiple-model approach for volumetric cardiac EP imaging where multiple prior models are included and automatically picked by the available ECG data. Multiple models are incorporated as an Lp-norm prior for sources, where p is an unknown hyperparameter with a prior uniform distribution. To examine how different combinations of models may be favored by different measurement data, the posterior distribution of cardiac sources and hyperparameter p is calculated using a Markov Chain Monte Carlo (MCMC) technique. The importance of multiple-model prior was assessed in two sets of synthetic and real-data experiments, compared to fixed-model priors (using Laplace and Gaussian priors). The results showed that the posterior combination of models (the posterior distribution of p) as determined by the ECG data differed substantially when reconstructing sources with different sizes and structures. While the use of fixed models is best suited in situations where the prior assumption fits the actual source structures, the use of an automatically adaptive set of models may have the ability to better address model-data mismatch and to provide consistent performance in reconstructing sources with different properties.

Temporal Sparse Promoting Three Dimensional Imaging of Cardiac Activation

A new Cardiac Electrical Sparse Imaging (CESI) technique is proposed to image cardiac activation throughout the three-dimensional myocardium from body surface electrocardiogram (ECG) with the aid of individualized heart-torso geometry. The sparse property of cardiac electrical activity in the time domain is utilized in the temporal sparse promoting inverse solution, one formulated to achieve higher spatial-temporal resolution, stronger robustness and thus enhanced capability in imaging cardiac electrical activity. Computer simulations were carried out to evaluate the performance of this imaging method under various circumstances. A total of 12 single site pacing and 7 dual sites pacing simulations with artificial and the hospital recorded sensor noise were used to evaluate the accuracy and stability of the proposed method. Simulations with modeling error on heart-torso geometry and electrode-torso registration were also performed to evaluate the robustness of the technique. In addition to the computer simulations, the CESI algorithm was further evaluated using experimental data in an animal model where the noninvasively imaged activation sequences were compared with those measured with simultaneous intracardiac mapping. All of the CESI results were compared with conventional weighted minimum norm solutions. The present results show that CESI can image with better accuracy, stability and stronger robustness in both simulated and experimental circumstances. In sum, we have proposed a novel method for cardiac activation imaging, and our results suggest that the CESI has enhanced performance, and offers the potential to image the cardiac activation and to assist in the clinical management of ventricular arrhythmias.

An ideally parameterized unscented Kalman filter for the inverse problem of electrocardiography

ECG imaging as noninvasive method is aiming to reconstruct the distribution of the transmembrane voltage amplitudes (TMVs) from the body surface potential map (BSPM). Due to the ill-posedness, standard approaches like the Tikhonov regularization method cause blurring and artefacts in the solution. To suppress blurring and artefacts, this work investigated a model based approach, the unscented Kalman filter (UKF). The intention of this paper is to show the potential of an UKF approach by using an idealized parametrization.

Noninvasive electrocardiographic imaging of chronic myocardial infarct scar

BACKGROUND

Myocardial infarction (MI) scar constitutes a substrate for ventricular tachycardia (VT), and an accurate delineation of infarct scar may help to identify reentrant circuits and thus facilitate catheter ablation. One of the recent advancements in characterization of a VT substrate is its volumetric delineation within the ventricular wall by noninvasive electrocardiographic imaging. This paper compares, in four specific cases, epicardial and volumetric inverse solutions, using magnetic resonance imaging (MRI) with late gadolinium enhancement as a gold standard.

METHODS

For patients with chronic MI, who presented at Glasgow Western Infirmary, delayed-enhancement MRI and 120-lead body surface potential mapping (BSPM) data were acquired and 4 selected cases were later made available to a wider community as part of the 2007 PhysioNet/Computers in Cardiology Challenge. These data were used to perform patient-specific inverse solutions for epicardial electrograms and morphology-based criteria were applied to delineate infarct scar on the epicardial surface. Later, the Rochester group analyzed the same data by means of a novel inverse solution for reconstructing intramural transmembrane potentials, to delineate infarct scar in three dimensions. Comparison of the performance of three specific inverse-solution algorithms is presented here, using scores based on the 17-segment ventricular division scheme recommended by the American Heart Association.

RESULTS

The noninvasive methods delineating infarct scar as three-dimensional (3D) intramural distribution of transmembrane action potentials outperform estimates providing scar delineation on the epicardial surface in all scores used for comparison. In particular, the extent of infarct scar (its percentage mass relative to the total ventricular mass) is rendered more accurately by the 3D estimate. Moreover, the volumetric rendition of scar border provides better clues to potential targets for catheter ablation.

CONCLUSIONS

Electrocardiographic inverse solution providing transmural distribution of ventricular action potentials is a promising tool for noninvasively delineating the extent and location of chronic MI scar. Further validation on a larger data set with detailed gold-standard data is needed to confirm observations reported in this study.

Sensitivity of Noninvasive Cardiac Electrophysiological Imaging to Variations in Personalized Anatomical Modeling

OBJECTIVE

Noninvasive cardiac electrophysiological (EP) imaging techniques rely on anatomically-detailed heart-torso models derived from high-quality tomographic images of individual subjects. However, anatomical modeling involves variations that lead to unresolved uncertainties in the outcome of EP imaging, bringing questions to the robustness of these methods in clinical practice. In this study, we design a systematic statistical approach to assess the sensitivity of EP imaging methods to the variations in personalized anatomical modeling.

METHODS

We first quantify the variations in personalized anatomical models by a novel application of statistical shape modeling. Given the statistical distribution of the variation in personalized anatomical models, we then employ unscented transform to determine the sensitivity of EP imaging outputs to the variation in input personalized anatomical modeling.

RESULTS

We test the feasibility of our proposed approach using two of the existing EP imaging methods: epicardial-based electrocardiographic imaging and transmural electrophysiological imaging. Both phantom and real-data experiments show that variations in personalized anatomical models have negligible impact on the outcome of EP imaging.

CONCLUSION

This study verifies the robustness of EP imaging methods to the errors in personalized anatomical modeling and suggests the possibility to simplify the process of anatomical modeling in future clinical practice.

SIGNIFICANCE

This study proposes a systematic statistical approach to quantify anatomical modeling variations and assess their impact on EP imaging, which can be extended to find a balance between the quality of personalized anatomical models and the accuracy of EP imaging that may improve the clinical feasibility of EP imaging.

Noninvasive reconstruction of cardiac transmembrane potentials using a kernelized extreme learning method

Non-invasively reconstructing the cardiac transmembrane potentials (TMPs) from body surface potentials can act as a regression problem. The support vector regression (SVR) method is often used to solve the regression problem, however the computational complexity of the SVR training algorithm is usually intensive. In this paper, another learning algorithm, termed as extreme learning machine (ELM), is proposed to reconstruct the cardiac transmembrane potentials. Moreover, ELM can be extended to single-hidden layer feed forward neural networks with kernel matrix (kernelized ELM), which can achieve a good generalization performance at a fast learning speed. Based on the realistic heart-torso models, a normal and two abnormal ventricular activation cases are applied for training and testing the regression model. The experimental results show that the ELM method can perform a better regression ability than the single SVR method in terms of the TMPs reconstruction accuracy and reconstruction speed. Moreover, compared with the ELM method, the kernelized ELM method features a good approximation and generalization ability when reconstructing the TMPs.

Imaging cardiac activation sequence during ventricular tachycardia in a canine model of nonischemic heart failure

Noninvasive cardiac activation imaging of ventricular tachycardia (VT) is important in the clinical diagnosis and treatment of arrhythmias in heart failure (HF) patients. This study investigated the ability of the three-dimensional cardiac electrical imaging (3DCEI) technique for characterizing the activation patterns of spontaneously occurring and norepinephrine (NE)-induced VTs in a newly developed arrhythmogenic canine model of nonischemic HF. HF was induced by aortic insufficiency followed by aortic constriction in three canines. Up to 128 body-surface ECGs were measured simultaneously with bipolar recordings from up to 232 intramural sites in a closed-chest condition. Data analysis was performed on the spontaneously occurring VTs (n=4) and the NE-induced nonsustained VTs (n=8) in HF canines. Both spontaneously occurring and NE-induced nonsustained VTs initiated by a focal mechanism primarily from the subendocardium, but occasionally from the subepicardium of left ventricle. Most focal initiation sites were located at apex, right ventricular outflow tract, and left lateral wall. The NE-induced VTs were longer, more rapid, and had more focal sites than the spontaneously occurring VTs. Good correlation was obtained between imaged activation sequence and direct measurements (averaged correlation coefficient of ∼0.70 over 135 VT beats). The reconstructed initiation sites were ∼10 mm from measured initiation sites, suggesting good localization in such a large animal model with cardiac size similar to a human. Both spontaneously occurring and NE-induced nonsustained VTs had focal initiation in this canine model of nonischemic HF. 3DCEI is feasible to image the activation sequence and help define arrhythmia mechanism of nonischemic HF-associated VTs.

Using transmural regularization and dynamic modeling for noninvasive cardiac potential imaging of endocardial pacing with imprecise thoracic geometry

Cardiac electrical imaging from body surface potential measurements is increasingly being seen as a technology with the potential for use in the clinic, for example for pre-procedure planning or during-treatment guidance for ventricular arrhythmia ablation procedures. However several important impediments to widespread adoption of this technology remain to be effectively overcome. Here we address two of these impediments: the difficulty of reconstructing electric potentials on the inner (endocardial) as well as outer (epicardial) surfaces of the ventricles, and the need for full anatomical imaging of the subject's thorax to build an accurate subject-specific geometry. We introduce two new features in our reconstruction algorithm: a nonlinear low-order dynamic parameterization derived from the measured body surface signals, and a technique to jointly regularize both surfaces. With these methodological innovations in combination, it is possible to reconstruct endocardial activation from clinically acquired measurements with an imprecise thorax geometry. In particular we test the method using body surface potentials acquired from three subjects during clinical procedures where the subjects' hearts were paced on their endocardia using a catheter device. Our geometric models were constructed using a set of CT scans limited in axial extent to the immediate region near the heart. The catheter system provides a reference location to which we compare our results. We compare our estimates of pacing site localization, in terms of both accuracy and stability, to those reported in a recent clinical publication , where a full set of CT scans were available and only epicardial potentials were reconstructed.

Hierarchical multiple-model Bayesian approach to transmural electrophysiological imaging

Noninvasive electrophysiological (EP) imaging of the heart aims to mathematically reconstruct the spatiotemporal dynamics of cardiac current sources from body-surface electrocardiographic (ECG) data. This ill-posed problem is often regularized by a fixed constraining model. However, this approach enforces the source distribution to follow a preassumed spatial structure that does not always match the varying spatiotemporal distribution of current sources. We propose a hierarchical Bayesian approach to transmural EP imaging that employs a continuous combination of multiple models, each reflecting a specific spatial property for current sources. Multiple models are incorporated as an Lp-norm prior for current sources, where p is an unknown hyperparameter with a prior probabilistic distribution. The current source estimation is obtained as an optimally weighted combination of solutions across all models, the weight being determined from the posterior distribution of p inferred from ECG data. The accuracy of our approach is assessed in a set of synthetic and real-data experiments on human heart-torso models. While the use of fixed models (L1- and L2-norm) only properly recovers sources with specific structures, our method delivers consistent performance in reconstructing sources with various extents and structures.