Inverse Electrocardiographic Source Localization of Ischemia: An Optimization Framework and Finite Element Solution

UncertainSCI: Uncertainty quantification for computational models in biomedicine and bioengineering

BACKGROUND

Computational biomedical simulations frequently contain parameters that model physical features, material coefficients, and physiological effects, whose values are typically assumed known a priori. Understanding the effect of variability in those assumed values is currently a topic of great interest. A general-purpose software tool that quantifies how variation in these parameters affects model outputs is not broadly available in biomedicine. For this reason, we developed the 'UncertainSCI' uncertainty quantification software suite to facilitate analysis of uncertainty due to parametric variability.

METHODS

We developed and distributed a new open-source Python-based software tool, UncertainSCI, which employs advanced parameter sampling techniques to build polynomial chaos (PC) emulators that can be used to predict model outputs for general parameter values. Uncertainty of model outputs is studied by modeling parameters as random variables, and model output statistics and sensitivities are then easily computed from the emulator. Our approaches utilize modern, near-optimal techniques for sampling and PC construction based on weighted Fekete points constructed by subsampling from a suitably randomized candidate set.

RESULTS

Concentrating on two test cases-modeling bioelectric potentials in the heart and electric stimulation in the brain-we illustrate the use of UncertainSCI to estimate variability, statistics, and sensitivities associated with multiple parameters in these models.

CONCLUSION

UncertainSCI is a powerful yet lightweight tool enabling sophisticated probing of parametric variability and uncertainty in biomedical simulations. Its non-intrusive pipeline allows users to leverage existing software libraries and suites to accurately ascertain parametric uncertainty in a variety of applications.

Quantifying and Visualizing Uncertainty for Source Localization in Electrocardiographic Imaging

Electrocardiographic imaging (ECGI) presents a clinical opportunity to noninvasively understand the sources of arrhythmias for individual patients. To help increase the effectiveness of ECGI, we provide new ways to visualize associated measurement and modeling errors. In this paper, we study source localization uncertainty in two steps: First, we perform Monte Carlo simulations of a simple inverse ECGI source localization model with error sampling to understand the variations in ECGI solutions. Second, we present multiple visualization techniques, including confidence maps, level-sets, and topology-based visualizations, to better understand uncertainty in source localization. Our approach offers a new way to study uncertainty in the ECGI pipeline.

Uncertainty Quantification in Simulations of Myocardial Ischemia

Computational models of myocardial ischemia are parameterized using assumptions of tissue properties and physiological values such as conductivity ratios in cardiac tissue and conductivity changes between healthy and ischemic tissues. Understanding the effect of uncertainty in these parameter selections would provide useful insight into the performance and variability of the modeling outputs. Recently developed uncertainty quantification tools allow for the application of polynomial chaos expansion uncertainty quantification to such bioelectric models in order to parsimoniously examine model response to input uncertainty. We applied uncertainty quantification to examine reconstructed extracellular potentials from the cardiac passive bidomain based on variation in the conductivity values for the ischemic tissue. We investigated the model response in both a synthetic dataset with simulated ischemic regions and a dataset with ischemic regions derived from experimental recordings. We found that extracellular longitudinal and intracellular longitudinal conductivities predominately affected simulation output, with the highest standard deviations in regions of extracellular potential elevations. We found that transverse conductivity had almost no effect on model output.

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.

A Novel MRI-Based Finite Element Modeling Method for Calculation of Myocardial Ischemia Effect in Patients With Functional Mitral Regurgitation

BACKGROUND

Functional Mitral Regurgitation (FMR) associated with coronary artery disease affects nearly 3 million patients in the United States. Both myocardial infarction (MI) and ischemia contribute to FMR development but uncertainty as to which patients will respond to revascularization (REVASC) of ischemia alone prevents rational decision making about FMR therapy. The aim of this study was to create patient-specific cardiac MRI (CMR) informed finite element (FE) models of the left ventricle (LV), calculate regional LV systolic contractility and then use optimized systolic material properties to simulate the effect of revascularization (virtual REVASC).

METHODS

We describe a novel FE method able to predict the effect of myocardial ischemia on regional LV function. CMR was obtained in five patients with multi-vessel coronary disease and FMR before and 3 months after percutaneous REVASC and a single healthy volunteer. Patient-specific FE models were created and divided into 17 sectors where the systolic contractility parameter, T m a x of each sector was a function of regional stress perfusion (SP-CMR) and myocardial infarction (LGE-CMR) scores. Sector-specific circumferential and longitudinal end-systolic strain and LV volume from CSPAMM were used in a formal optimization to determine the sector based myocardial contractility, T m a x and ischemia effect, α. Virtual REVASC was simulated by setting α to zero.

RESULTS

The FE optimization successfully converged with good agreement between calculated and experimental end-systolic strain and LV volumes. Specifically, the optimized T max for the healthy myocardium for five patients and the volunteer was 495.1, 336.8, 173.5, 227.9, 401.4, and 218.9 kPa. The optimized α was found to be 1.0, 0.44, and 0.08 for Patients 1, 2, and 3, and 0 for Patients 4 and 5. The calculated average of radial strain for Patients 1, 2, and 3 at baseline and after virtual REVASC was 0.23 and 0.25, respectively.

CONCLUSION

We developed a novel computational method able to predict the effect of myocardial ischemia in patients with FMR. This method can be used to predict the effect of ischemia on the regional myocardium and promises to facilitate better understanding of FMR response to REVASC.

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.

A NOVEL METHOD TO ISCHEMIC HEART DISEASE DETECTION BASED ON NON-INVASIVE ECG IMAGING

Electrocardiogram (ECG) signals containing very important information about the cardiac are one of the most common tools for physicians in the diagnosis of various types of cardiac diseases. Low accuracy in positioning, limitation of time accuracy, the similarity of signals between some diseases and normal signals and probability of missing some aspect of data are the defect aspects of this method. Importance of cardiac signals and defects of current methods in diagnosis show the need of substituting a new method to show the activity of cardiac. One of the most dangerous defections is ischemia, which corrects and on time diagnose could avoid the latter effect of it. Each of common methods for diagnosis of this illness has their own advantages and disadvantages. In this paper, we consider describing a non-invasive method for ischemic episode detection based on mapping of ECG signals. With this method, we can present the signals with virtual colors and facilitate the diagnosis of ischemic disease. So, a new method of 12-lead cardiac presentation is described that in fact present the 12-lead signals in two images. The result of this paper will present the indicators of sensitivity, specificity and accuracy in the context of disease diagnosis. This paper proposed a novel ECG imaging algorithm for classifying the normal and ischemic signals and 95.35% specificity, 96.79% sensitivity and 95.76% accuracy were achieved which are very much promising compared to the other methods and doctor’s accuracy.

ECG Imaging to Detect the Site of Ventricular Ischemia Using Torso Electrodes: A Computational Study

Electrocardiography provides some information useful for ischemic diagnosis. However, more recently there has been substantial growth in the area of ECG imaging, which by solving the inverse problem of electrocardiography aims to produce high-resolution mapping of the electrical and magnetic dynamics of the heart. Most inverse studies use the full resolution of the body surface potential (BSP) to reconstruct the epicardial potentials, however using a limited number of torso electrodes to interpolate the BSP is more clinically relevant and has an important effect on the reconstruction which must be quantified. A circular ischemic lesion on the right ventricle lateral wall 27 mm in radius is reconstructed using three Tikhonov methods along with 6 different electrode configurations ranging from 32 leads to 1,024 leads. The 2nd order Tikhonov solution performed the most accurately (~80% lesion identified) followed by the 1st (~50% lesion identified) and then the 0 order Tikhonov solution performed the worst with a maximum of ~30% lesion identified regardless of how many leads were used. With an increasing number of leads the solution produces less error, and the error becomes more localised around the lesion for all three regularisation methods. In noisy conditions, the relative performance gap of the 1st and 2nd order Tikhonov solutions was reduced, and determining an accurate regularisation parameter became relatively more difficult. Lesions located on the left ventricle walls were also able to be identified but comparatively to the right ventricle lateral wall performed marginally worse with lesions located on the interventricular septum being able to be indicated by the reconstructions but not successfully identified against the error. The quality of reconstruction was found to decrease as the lesion radius decreased, with a lesion radius of <20 mm becoming difficult to correctly identify against the error even when using >512 torso electrodes.

Design of an Interactive Simulation Environment for Arrays of Cardiac Cells

The electrical activity of cardiac cells is complex and their collective action difficult to visualize. Understanding what is happening, overall and cell by cell, requires detailed simulation. Here the design of such a simulation is defined by a list of required tasks. An example of the performance of such a simulation is presented, and its time to completion is measured.

Accuracy of electrocardiographic imaging using the method of fundamental solutions

Solving the inverse problem of electrocardiology via the Method of Fundamental Solutions has been proposed previously. The advantage of this approach is that it is a meshless method, so it is far easier to implement numerically than many other approaches. However, determining the heart surface potential distribution is still an ill-posed problem and thus requires some form of Tikhonov regularisation to obtain the required distributions. In this study, several methods for determining an "optimal" regularisation parameter are compared in the context of solving the inverse problem of electrocardiology via the Method of Fundamental Solutions. It is found that the Robust Generalised Cross-Validation method most often yields epicardial potential distributions with the least relative error when compared to the input distribution. The study also compares the inverse solutions obtained with the Method of Fundamental Solutions with those obtained in a previous study using the boundary element method. It is found that choosing the best solution methodology and regularisation parameter determination method depends on the particular scenario being considered.

A Common-Ground Review of the Potential for Machine Learning Approaches in Electrocardiographic Imaging Based on Probabilistic Graphical Models

Machine learning (ML) methods have seen an explosion in their development and application. They are increasingly being used in many different fields with considerable success. However, although the interest is growing, their impact in the field of electrocardiographic imaging (ECGI) remains limited. One of the main reasons that ML has yet to become more prevalent in ECGI is that the published literature is scattered and there is no common ground description and comparison of these methods in an ML framework. Here we address this limitation with a review of ECGI methods from the perspective of ML. We will use probabilistic modeling to provide a common ground framework to compare different methods and well known approaches. Finally, we will discuss which approaches have been used to do inference on these models and which alternatives could be utilized as the methods in ML become more mature.

Image-based modeling of acute myocardial ischemia using experimentally derived ischemic zone source representations

BACKGROUND

Computational models of myocardial ischemia often use oversimplified ischemic source representations to simulate epicardial potentials. The purpose of this study was to explore the influence of biophysically justified, subject-specific ischemic zone representations on epicardial potentials.

METHODS

We developed and implemented an image-based simulation pipeline, using intramural recordings from a canine experimental model to define subject-specific ischemic regions within the heart. Static epicardial potential distributions, reflective of ST segment deviations, were simulated and validated against measured epicardial recordings.

RESULTS

Simulated epicardial potential distributions showed strong statistical correlation and visual agreement with measured epicardial potentials. Additionally, we identified and described in what way border zone parameters influence epicardial potential distributions during the ST segment.

CONCLUSION

From image-based simulations of myocardial ischemia, we generated subject-specific ischemic sources that accurately replicated epicardial potential distributions. Such models are essential in understanding the underlying mechanisms of the bioelectric fields that arise during ischemia and are the basis for more sophisticated simulations of body surface ECGs.

Three-Dimensional Noninvasive Imaging of Ventricular Arrhythmias in Patients With Premature Ventricular Contractions

OBJECTIVE

Noninvasive imaging of cardiac electrical activity promises to provide important information regarding the underlying arrhythmic substrates for successful ablation intervention and further understanding of the mechanism of such lethal disease. The aim of this study is to evaluate the performance of a novel 3-D cardiac activation imaging technique to noninvasively localize and image origins of focal ventricular arrhythmias in patients undergoing radio frequency ablation.

METHODS

Preprocedural ECG gated contrast enhanced cardiac CT images and body surface potential maps were collected from 13 patients within a week prior to the ablation. The electrical activation images were estimated over the 3-D myocardium using a cardiac electric sparse imaging technique, and compared with CARTO activation maps and the ablation sites in the same patients.

RESULTS

Noninvasively-imaged activation sequences were consistent with the CARTO mapping results with an average correlation coefficient of 0.79, average relative error of 0.19, and average relative resolution error of 0.017. The imaged initiation sites of premature ventricular contractions (PVCs) were, on average, within 8 mm of the last successful ablation site and within 3 mm of the nearest ablation site.

CONCLUSION

The present results demonstrate the excellent performance of the 3-D cardiac activation imaging technique in imaging the activation sequence associated with PVC, and localizing the initial sites of focal ventricular arrhythmias in patients. These promising results suggest that the 3-D cardiac activation imaging technique may become a useful tool for aiding clinical diagnosis and management of ventricular arrhythmias.

Scalable and Accurate ECG Simulation for Reaction-Diffusion Models of the Human Heart

Realistic electrocardiogram (ECG) simulation with numerical models is important for research linking cellular and molecular physiology to clinically observable signals, and crucial for patient tailoring of numerical heart models. However, ECG simulation with a realistic torso model is computationally much harder than simulation of cardiac activity itself, so that many studies with sophisticated heart models have resorted to crude approximations of the ECG. This paper shows how the classical concept of electrocardiographic lead fields can be used for an ECG simulation method that matches the realism of modern heart models. The accuracy and resource requirements were compared to those of a full-torso solution for the potential and scaling was tested up to 14,336 cores with a heart model consisting of 11 million nodes. Reference ECGs were computed on a 3.3 billion-node heart-torso mesh at 0.2 mm resolution. The results show that the lead-field method is more efficient than a full-torso solution when the number of simulated samples is larger than the number of computed ECG leads. While the initial computation of the lead fields remains a hard and poorly scalable problem, the ECG computation itself scales almost perfectly and, even for several hundreds of ECG leads, takes much less time than the underlying simulation of cardiac activity.

Absence of Rapid Propagation through the Purkinje Network as a Potential Cause of Line Block in the Human Heart with Left Bundle Branch Block

Background: Cardiac resynchronization therapy is an effective device therapy for heart failure patients with conduction block. However, a problem with this invasive technique is the nearly 30% of non-responders. A number of studies have reported a functional line of block of cardiac excitation propagation in responders. However, this can only be detected using non-contact endocardial mapping. Further, although the line of block is considered a sign of responders to therapy, the mechanism remains unclear.

Methods: Herein, we created two patient-specific heart models with conduction block and simulated the propagation of excitation based on a cellmodel of electrophysiology. In one model with a relatively narrow QRS width (176 ms), we modeled the Purkinje network using a thin endocardial layer with rapid conduction. To reproduce a wider QRS complex (200 ms) in the second model, we eliminated the Purkinje network, and we simulated the endocardial mapping by solving the inverse problem according to the actual mapping system.

Results: We successfully observed the line of block using non-contact mapping in the model without the rapid propagation of excitation through the Purkinje network, although the excitation in the wall propagated smoothly. This model of slow conduction also reproduced the characteristic properties of the line of block, including dense isochronal lines and fractionated local electrocardiograms. Further, simulation of ventricular pacing from the lateral wall shifted the location of the line of block. By contrast, in the model with the Purkinje network, propagation of excitation in the endocardial map faithfully followed the actual propagation in the wall, without showing the line of block. Finally, switching the mode of propagation between the two models completely reversed these findings.

Conclusions: Our simulation data suggest that the absence of rapid propagation of excitation through the Purkinje network is the major cause of the functional line of block recorded by non-contact endocardial mapping. The line of block can be used to identify responders as these patients loose rapid propagation through the Purkinje network.

New Insights Into the Use of the 12-Lead Electrocardiogram for Diagnosing Acute Myocardial Infarction in the Emergency Department

The 12-lead electrocardiogram (ECG) remains the most immediately accessible and widely used initial diagnostic tool for guiding management in patients with suspected myocardial infarction (MI). Although the development of high-sensitivity cardiac troponin assays has improved the rule-in and rule-out and risk stratification of acute MI without ST elevation, the immediate management of the subset of acute MI with acute coronary occlusion depends on integrating clinical presentation and ECG findings. Careful interpretation of the ECG might yield subtle features suggestive of ischemia that might facilitate more rapid triage of patients with subtle acute coronary occlusion or, conversely, in identification of ST-elevation MI mimics (pseudo ST-elevation MI patterns). Our goal in this review article is to consider recent advances in the use of the ECG to diagnose coronary occlusion MIs, including the application of rules that allow MI to be diagnosed on the basis of atypical ECG manifestations. Such rules include the modified Sgarbossa criteria allowing identification of acute MI in left bundle branch block or ventricular pacing, the 3- and 4-variable formula to differentiate normal ST elevation (formerly called early repolarization) from subtle ECG signs of left anterior descending coronary artery occlusion, the differentiation of ST elevation of left ventricular aneurysm from that of acute anterior MI, and the use of lead aVL in the recognition of inferior MI. Improved use of the ECG is essential to improving the diagnosis and appropriate early management of acute coronary occlusion MIs, which will lead to improved outcomes for patients who present with acute coronary syndrome.

Regularization Techniques for ECG Imaging during Atrial Fibrillation: A Computational Study

The inverse problem of electrocardiography is usually analyzed during stationary rhythms. However, the performance of the regularization methods under fibrillatory conditions has not been fully studied. In this work, we assessed different regularization techniques during atrial fibrillation (AF) for estimating four target parameters, namely, epicardial potentials, dominant frequency (DF), phase maps, and singularity point (SP) location. We use a realistic mathematical model of atria and torso anatomy with three different electrical activity patterns (i.e., sinus rhythm, simple AF, and complex AF). Body surface potentials (BSP) were simulated using Boundary Element Method and corrupted with white Gaussian noise of different powers. Noisy BSPs were used to obtain the epicardial potentials on the atrial surface, using 14 different regularization techniques. DF, phase maps, and SP location were computed from estimated epicardial potentials. Inverse solutions were evaluated using a set of performance metrics adapted to each clinical target. For the case of SP location, an assessment methodology based on the spatial mass function of the SP location, and four spatial error metrics was proposed. The role of the regularization parameter for Tikhonov-based methods, and the effect of noise level and imperfections in the knowledge of the transfer matrix were also addressed. Results showed that the Bayes maximum-a-posteriori method clearly outperforms the rest of the techniques but requires a priori information about the epicardial potentials. Among the purely non-invasive techniques, Tikhonov-based methods performed as well as more complex techniques in realistic fibrillatory conditions, with a slight gain between 0.02 and 0.2 in terms of the correlation coefficient. Also, the use of a constant regularization parameter may be advisable since the performance was similar to that obtained with a variable parameter (indeed there was no difference for the zero-order Tikhonov method in complex fibrillatory conditions). Regarding the different targets, DF and SP location estimation were more robust with respect to pattern complexity and noise, and most algorithms provided a reasonable estimation of these parameters, even when the epicardial potentials estimation was inaccurate. Finally, the proposed evaluation procedure and metrics represent a suitable framework for techniques benchmarking and provide useful insights for the clinical practice.

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.

Numerical simulation of electrocardiograms for full cardiac cycles in healthy and pathological conditions

This work is dedicated to the simulation of full cycles of the electrical activity of the heart and the corresponding body surface potential. The model is based on a realistic torso and heart anatomy, including ventricles and atria. One of the specificities of our approach is to model the atria as a surface, which is the kind of data typically provided by medical imaging for thin volumes. The bidomain equations are considered in their usual formulation in the ventricles, and in a surface formulation on the atria. Two ionic models are used: the Courtemanche-Ramirez-Nattel model on the atria and the 'minimal model for human ventricular action potentials' by Bueno-Orovio, Cherry, and Fenton in the ventricles. The heart is weakly coupled to the torso by a Robin boundary condition based on a resistor-capacitor transmission condition. Various electrocardiograms (ECGs) are simulated in healthy and pathological conditions (left and right bundle branch blocks, Bachmann's bundle block, and Wolff-Parkinson-White syndrome). To assess the numerical ECGs, we use several qualitative and quantitative criteria found in the medical literature. Our simulator can also be used to generate the signals measured by a vest of electrodes. This capability is illustrated at the end of the article. Copyright © 2015 John Wiley & Sons, Ltd.

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.

Application of robust Generalised Cross-Validation to the inverse problem of electrocardiology

Robust Generalised Cross-Validation was proposed recently as a method for determining near optimal regularisation parameters in inverse problems. It was introduced to overcome a problem with the regular Generalised Cross-Validation method in which the function that is minimised to obtain the regularisation parameter often has a broad, flat minimum, resulting in a poor estimate for the parameter. The robust method defines a new function to be minimised which has a narrower minimum, but at the expense of introducing a new parameter called the robustness parameter. In this study, the Robust Generalised Cross-Validation method is applied to the inverse problem of electrocardiology. It is demonstrated that, for realistic situations, the robustness parameter can be set to zero. With this choice of robustness parameter, it is shown that the robust method is able to obtain estimates of the regularisation parameter in the inverse problem of electrocardiology that are comparable to, or better than, many of the standard methods that are applied to this inverse problem.

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.

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

Electrical activity at the level of the heart muscle can be noninvasively reconstructed from body-surface electrocardiograms (ECGs) and patient-specific torso-heart geometry. This modality, coined electrocardiographic imaging, could fill the gap between the noninvasive (low-resolution) 12-lead ECG and invasive (high-resolution) electrophysiology studies. Much progress has been made to establish electrocardiographic imaging, and clinical studies appear with increasing frequency. However, many assumptions and model choices are involved in its execution, and only limited validation has been performed. In this article, we will discuss the technical details, clinical applications and current limitations of commonly used methods in electrocardiographic imaging. It is important for clinicians to realise the influence of certain assumptions and model choices for correct and careful interpretation of the results. This, in combination with more extensive validation, will allow for exploitation of the full potential of noninvasive electrocardiographic imaging as a powerful clinical tool to expedite diagnosis, guide therapy and improve risk stratification.

Variational Bayesian electrophysiological imaging of myocardial infarction

The presence, size, and distribution of ischemic tissue bear significant prognostic and therapeutic implication for ventricular arrhythmias. While many approaches to 3D infarct detection have been developed via electrophysiological (EP) imaging from noninvasive electrocardiographic data, this ill-posed inverse problem remains challenging especially for septal infarcts that are hidden from body-surface data. We propose a variational Bayesian framework for EP imaging of 3D infarct using a total-variation prior. The posterior distribution of intramural action potential and all regularization parameters are estimated from body-surface data by minimizing the Kullback-Leibler divergence. Because of the uncertainty introduced in prior models, we hypothesize that the solution uncertainty plays as important a role as the point estimate in interpreting the reconstruction. This is verified in a set of phantom and real-data experiments, where regions of low confidence help to eliminate false-positives and to accurately identify infarcts of various locations (including septum) and distributions. Owing to the ability of total-variation prior in extracting the boundary between smooth regions, the presented method also has the potential to outline infarct border that is the most critical region responsible for ventricular arrhvthmias.

Computational generation of the Purkinje network driven by clinical measurements: the case of pathological propagations

To properly describe the electrical activity of the left ventricle, it is necessary to model the Purkinje fibers, responsible for the fast and coordinate ventricular activation, and their interaction with the muscular propagation. The aim of this work is to propose a methodology for the generation of a patient-specific Purkinje network driven by clinical measurements of the activation times related to pathological propagations. In this case, one needs to consider a strongly coupled problem between the network and the muscle, where the feedback from the latter to the former cannot be neglected as in a normal propagation. We apply the proposed strategy to data acquired on three subjects, one of them suffering from muscular conduction problems owing to a scar and the other two with a muscular pre-excitation syndrome (Wolff-Parkinson-White). To assess the accuracy of the proposed method, we compare the results obtained by using the patient-specific Purkinje network generated by our strategy with the ones obtained by using a non-patient-specific network. The results show that the mean absolute errors in the activation time is reduced for all the cases, highlighting the importance of including a patient-specific Purkinje network in computational models.

Noninvasive imaging of 3-dimensional myocardial infarction from the inverse solution of equivalent current density in pathological hearts

We propose a new approach to noninvasively image the 3-D myocardial infarction (MI) substrates based on equivalent current density (ECD) distribution that is estimated from the body surface potential maps (BSPMs) during S-T segment. The MI substrates were identified using a predefined threshold of ECD. Computer simulations were performed to assess the performance with respect to: 1) MI locations; 2) MI sizes; 3) measurement noise; 4) numbers of BSPM electrodes; and 5) volume conductor modeling errors. A total of 114 sites of transmural infarctions, 91 sites of epicardial infarctions, and 36 sites of endocardial infarctions were simulated. The simulation results show that: 1) Under 205 electrodes and 10-μV noise, the averaged accuracies of imaging transmural MI are 83.4% for sensitivity, 82.2% for specificity, 65.0% for Dice's coefficient, and 6.5 mm for distances between the centers of gravity (DCG). 2) For epicardial infarction, the averaged imaging accuracies are 81.6% for sensitivity, 75.8% for specificity, 45.3% for Dice's coefficient, and 7.5 mm for DCG; while for endocardial infarction, the imaging accuracies are 80.0% for sensitivity, 77.0% for specificity, 39.2% for Dice's coefficient, and 10.4 mm for DCG. 3) A reasonably good imaging performance was obtained under higher noise levels, fewer BSPM electrodes, and mild volume conductor modeling errors. The present results suggest that this method has the potential to aid in the clinical identification of the MI substrates.

New Additions to the Toolkit for Forward/Inverse Problems in Electrocardiography within the SCIRun Problem Solving Environment

Cardiac electrical imaging often requires the examination of different forward and inverse problem formulations based on mathematical and numerical approximations of the underlying source and the intervening volume conductor that can generate the associated voltages on the surface of the body. If the goal is to recover the source on the heart from body surface potentials, the solution strategy must include numerical techniques that can incorporate appropriate constraints and recover useful solutions, even though the problem is badly posed. Creating complete software solutions to such problems is a daunting undertaking. In order to make such tools more accessible to a broad array of researchers, the Center for Integrative Biomedical Computing (CIBC) has made an ECG forward/inverse toolkit available within the open source SCIRun system. Here we report on three new methods added to the inverse suite of the toolkit. These new algorithms, namely a Total Variation method, a non-decreasing TMP inverse and a spline-based inverse, consist of two inverse methods that take advantage of the temporal structure of the heart potentials and one that leverages the spatial characteristics of the transmembrane potentials. These three methods further expand the possibilities of researchers in cardiology to explore and compare solutions to their particular imaging problem.

Computing volume potentials for noninvasive imaging of cardiac excitation

BACKGROUND

In noninvasive imaging of cardiac excitation, the use of body surface potentials (BSP) rather than body volume potentials (BVP) has been favored due to enhanced computational efficiency and reduced modeling effort. Nowadays, increased computational power and the availability of open source software enable the calculation of BVP for clinical purposes. In order to illustrate the possible advantages of this approach, the explanatory power of BVP is investigated using a rectangular tank filled with an electrolytic conductor and a patient specific three dimensional model.

METHODS

MRI images of the tank and of a patient were obtained in three orthogonal directions using a turbo spin echo MRI sequence. MRI images were segmented in three dimensional using custom written software. Gmsh software was used for mesh generation. BVP were computed using a transfer matrix and FEniCS software.

RESULTS

The solution for 240,000 nodes, corresponding to a resolution of 5 mm throughout the thorax volume, was computed in 3 minutes. The tank experiment revealed that an increased electrode surface renders the position of the 4 V equipotential plane insensitive to mesh cell size and reduces simulated deviations. In the patient-specific model, the impact of assigning a different conductivity to lung tissue on the distribution of volume potentials could be visualized.

CONCLUSION

Generation of high quality volume meshes and computation of BVP with a resolution of 5 mm is feasible using generally available software and hardware. Estimation of BVP may lead to an improved understanding of the genesis of BSP and sources of local inaccuracies.

Comparison of minimum-norm estimation and beamforming in electrocardiography with acute ischemia

In the electrocardiographic (ECG) inverse problem, the electrical activity of the heart is estimated from measured electrocardiogram. A model of thorax conductivities and a model of the cardiac generator is required for the ECG inverse problem. Limitations and errors in methods, models, and data will lead to errors in the estimates. However, in experimental applications, the use of limited or erroneous models is often inevitable due to necessary model simplifications and the difficulty of obtaining accurate 3D anatomical imaging data. In this work, we focus on two methods for solving the inverse problem of ECG in the case of acute ischemia: minimum-norm (MN) estimation and linearly constrained minimum-variance beamforming. We study how these methods perform with different sizes of ischemia and with erroneous conductivity models. The results indicate that the beamformer can localize small ischemia given an accurate model, but it cannot be used for estimating the size of ischemia. The MN estimator is tolerant to geometry errors and excels in estimating the size of ischemia, although the beamformer performs better with accurate model and small ischemia.