Epicardial Potentials Research Articles

The Inverse Problem Utilizing the Boundary Element Method for a Nonstandard Female Torso

This paper proposes a new method of rapidly deriving the transfer matrix for the boundary element method (BEM) forward problem from a tailored female torso geometry in the clinical setting. The method allows rapid calculation of epicardial potentials (EP) from body surface potentials (BSP). The use of EPs in previous studies has been shown to improve the successful detection of the life-threatening cardiac condition--acute myocardial infarction. The MRI scanning of a cardiac patient in the clinical setting is not practical and other methods are required to accurately deduce torso geometries for calculation of the transfer matrix. The new method allows the noninvasive calculation of tailored torso geometries from a standard female torso and five measurements taken from the body surface of a patient. This scaling of the torso has been successfully validated by carrying out EP calculations on 40 scaled torsos and ten female subjects. It utilizes the BEM in the calculation of the transfer matrix as the BEM depends only upon the topology of the surfaces of the torso and the heart, the former can now be accurately deduced, leaving only the latter geometry as an unknown.

Finite-Element-Based Discretization and Regularization Strategies for 3-D Inverse Electrocardiography

We consider the inverse electrocardiographic problem of computing epicardial potentials from a body-surface potential map. We study how to improve numerical approximation of the inverse problem when the finite-element method is used. Being ill-posed, the inverse problem requires different discretization strategies from its corresponding forward problem. We propose refinement guidelines that specifically address the ill-posedness of the problem. The resulting guidelines necessitate the use of hybrid finite elements composed of tetrahedra and prism elements. Also, in order to maintain consistent numerical quality when the inverse problem is discretized into different scales, we propose a new family of regularizers using the variational principle underlying finite-element methods. These variational-formed regularizers serve as an alternative to the traditional Tikhonov regularizers, but preserves the L(2) norm and thereby achieves consistent regularization in multiscale simulations. The variational formulation also enables a simple construction of the discrete gradient operator over irregular meshes, which is difficult to define in traditional discretization schemes. We validated our hybrid element technique and the variational regularizers by simulations on a realistic 3-D torso/heart model with empirical heart data. Results show that discretization based on our proposed strategies mitigates the ill-conditioning and improves the inverse solution, and that the variational formulation may benefit a broader range of potential-based bioelectric problems.

P053 Reconstruction and Propagation of the Epicardial Potentials in a Dynamic Heart Model

P053 Reconstruction and Propagation of the Epicardial Potentials in a Dynamic Heart Model

On epicardial potential reconstruction using regularization schemes with the L1-norm data term

The electrocardiographic (ECG) inverse problem is ill-posed and usually solved by regularization schemes. These regularization methods, such as the Tikhonov method, are often based on the L2-norm data and constraint terms. However, L2-norm-based methods inherently provide smoothed inverse solutions that are sensitive to measurement errors, and also lack the capability of localizing and distinguishing multiple proximal cardiac electrical sources. This paper presents alternative regularization schemes employing the L1-norm data term for the reconstruction of epicardial potentials (EPs) from measured body surface potentials (BSPs). During numerical implementation, the iteratively reweighted norm algorithm was applied to solve the L1-norm-related schemes, and measurement noises were considered in the BSP data. The proposed L1-norm data term-based regularization schemes (with L1 and L2 penalty terms of the normal derivative constraint (labelled as L1TV and L1L2)) were compared with the L2-norm data terms (Tikhonov with zero-order and normal derivative constraints, labelled as ZOT and FOT, and the total variation method labelled as L2TV). The studies demonstrated that, with averaged measurement noise, the inverse solutions provided by the L1L2 and FOT algorithms have less relative error values. However, when larger noise occurred in some electrodes (for example, signal lost during measurement), the L1TV and L1L2 methods can obtain more accurate EPs in a robust manner. Therefore the L1-norm data term-based solutions are generally less perturbed by measurement noises, suggesting that the new regularization scheme is promising for providing practical ECG inverse solutions.

Late potential at the high ventricular septal level in a patient with Brugada: possible mechanisms and clinical implications

The Brugada syndrome (BS) accounts for approximately 20% of cases of sudden cardiac death in patients with structurally normal hearts. The electrophysiologic basis for ST-segment elevation in the precordial electrocardiogram (ECG) leads that characterize the Brugada phenotype and its strong linkage to ventricular tachycardia (VT)/ventricular fibrillation is still a subject of controversy. Electrocardiographic manifestations of the syndrome have been attributed to one of two basic mechanisms: (1) conduction delay in the right ventricular (RV) epicardial-free wall in the region of the outflow tract or (2) premature repolarization of the RV epicardial action potential secondary to loss of the action potential dome. Signal-averaged ECG recordings have demonstrated late potentials that extend beyond the QRS complex in patients with the BS, especially in the anterior wall of the RV outflow tract. The basis for these epicardial late potentials remains a subject of interest among basic and clinical electrophysiologists. Endocardial late potentials in BS are even less well understood. We present a case of a patient with Brugada syndrome with a distinct endocardial late potential in the high ventricular septum coinciding with the ST-segment elevation. We discuss the possible mechanisms for this intracardiac finding and its clinical significance. We also review the effect of isoproterenol infusion on both the late potential and the surface ECG.

The Application of Support Vector Regression Method for Solving the Inverse ECG Problem

The problem of noninvasive computing the epicardial surface potentials from torso surface potentials constitutes one form of the inverse problem of ECG, which can be acted as a regression problem with multi-input and multi-output. In this study, the SVR method is invoked to predict the inverse solutions, which compared with the common regularization methods. To build an effective SVR model, the hyper-parameters of SVR are set carefully by using the grid search optimization method. The experiment results shows that SVR method is an effective way for solving the inverse ECG problem, which can reconstruct more accurate epicardial surface potentials distribution than the common regularization method, such as Tikhonv method and LSQR method.

The transfer matrix for epicardial potential in a piece-wise homogeneous thorax model: the boundary element formulation

In epicardial potential imaging, the epicardial potential is reconstructed computationally from the measured body surface potential. The transfer function that relates the heart and body surface potentials is commonly constructed with some point-collocation-weighted boundary element technique, assuming an electrically homogeneous volume conductor. This assumption causes modeling errors. In this study, the system of surface integral equations that describes the relationship between the heart and body surface potentials is thoroughly derived in a piece-wise homogeneous volume conductor. The equations are discretized with the method of weighted residuals, enabling the use of Galerkin weighting in the numerical solution of the equations. The construction of the transfer matrix is described in detail for constant and linear collocation and Galerkin methods, and the resulting forward transfer matrices are validated via simple numerical simulations. The linear Galerkin method is found to generate the smallest errors. The presented method increases the accuracy of the forward-computed body surface potential and thus prepares the way for more accurate inverse reconstructions of epicardial potential.

The application of subspace preconditioned LSQR algorithm for solving the electrocardiography inverse problem

Regularization is an effective method for the solution of ill-posed ECG inverse problems, such as computing epicardial potentials from body surface potentials. The aim of this work was to explore more robust regularization-based solutions through the application of subspace preconditioned LSQR (SP-LSQR) to the study of model-based ECG inverse problems. Here, we presented three different subspace splitting methods, i.e., SVD, wavelet transform and cosine transform schemes, to the design of the preconditioners for ill-posed problems, and to evaluate the performance of algorithms using a realistic heart-torso model simulation protocol. The results demonstrated that when compared with the LSQR, LSQR-Tik and Tik-LSQR method, the SP-LSQR produced higher efficiency and reconstructed more accurate epcicardial potential distributions. Amongst the three applied subspace splitting schemes, the SVD-based preconditioner yielded the best convergence rate and outperformed the other two in seeking the inverse solutions. Moreover, when optimized by the genetic algorithms (GA), the performances of SP-LSQR method were enhanced. The results from this investigation suggested that the SP-LSQR was a useful regularization technique for cardiac inverse problems.

Diagnosis of acute right ventricular infarction

In acute inferior myocardial infarction (MI) due to right coronary artery occlusion, associated right ventricular infarction (RVMI) is best diagnosed by ST-segment elevation in an additional lead-precordial V4R. 1 Many studies and reviews have confirmed the value of lead V4R in recognizing RVMI and in prompting the clinical recognition of important hemodynamic consequences—systemic venous hypertension, clear lungs, and systemic hypoperfusion with low blood pressure. Appropriate therapy with intravenous fluid and inotropic agents is indicated. A variety of electrocardiogram (ECG) lead and display systems have been proposed as effective in capturing STsegment elevations not apparent in the standard 12-lead format. These include calculated epicardial potentials from 80-site body surface maps using a thoracic volume conductor model; a 24-lead system in which each of the standard 12 leads is inverted, producing an additional 12 leads for analysis, and various methods for predicting ECGs at nonrecorded sites from measured ECGs. An entire recent issue of Journal of Electrocardiology (volume 41 no. 3 May/ June 2008) was devoted to the lead system problem. None of the proposed techniques is widely accepted as yet or available in a standard commercial application. The addition of posterior (V7-V9) and right ventricular (V4R to V6R) leads in all suspected acute MI cases increased the sensitivity of diagnosis by 8.4%. In our method to rapidly identify acute RVMI, only a single additional lead (V4R) is recorded and that only if the word “inferior” has appeared in the computer diagnostic statement. Thus, no time is lost before a necessary V4R is

Arrhythmogenicity of Low‐Flow Reperfusion Following Acute Local Ischemia in Excised Rat Hearts

Clinical studies show that impaired myocardial reperfusion following thrombolytic therapy for coronary occlusions increases the incidence of ventricular arrhythmias; however the mechanisms are poorly understood. We studied arrhythmias during controlled low‐flow reperfusion (LFRP) in excised Langendorff‐perfused hearts (n=6). The left anterior coronary artery (LAD) was cannulated. An HPLC pump delivered perfusate to the LAD at a rate of 2 mL/min, followed by 20 min of local ischemia (0 mL/min) and then 20 min of LFRP (0.2 mL/min). The electrical response at each flow rate was monitored using an ECG and fluorescence imaging of epicardial potentials. We found that the highest heart rates and lowest heart rate variability occurred during LFRP (p<0.05). LFRP also resulted in the highest incidence of VF (p<0.05). During ischemia heart rate variability was highest and the incidence of VF was much lower than during LFRP (p<0.05). Fluorescence images revealed periodic ectopic beats during ischemia and numerous ectopic beats during LFRP. During LFRP, frequent episodes of monomorphic VT were driven by a single rotor and VF was driven by multiple transient rotors. In summary, LFRP fuels the continuous generation of ectopic beats that precede VT/VF. These findings match with our previous in‐vitro studies where we hypothesized that microreperfusion of ischemic border zones could result in ectopic beats and arrhythmias.

Application of L1-Norm Regularization to Epicardial Potential Solution of the Inverse Electrocardiography Problem

The electrocardiographic inverse problem of computing epicardial potentials from multi-electrode body-surface ECG measurements, is an ill-posed problem. Tikhonov regularization is commonly employed, which imposes penalty on the L2-norm of the potentials (zero-order) or their derivatives. Previous work has indicated superior results using L2-norm of the normal derivative of the solution (a first order regularization). However, L2-norm penalty function can cause considerable smoothing of the solution. Here, we use the L1-norm of the normal derivative of the potential as a penalty function. L1-norm solutions were compared to zero-order and first-order L2-norm Tikhonov solutions and to measured 'gold standards' in previous experiments with isolated canine hearts. Solutions with L1-norm penalty function (average relative error [RE] = 0.36) were more accurate than L2-norm (average RE = 0.62). In addition, the L1-norm method localized epicardial pacing sites with better accuracy (3.8 +/- 1.5 mm) compared to L2-norm (9.2 +/- 2.6 mm) during pacing in five pediatric patients with congenital heart disease. In a pediatric patient with Wolff-Parkinson-White syndrome, the L1-norm method also detected and localized two distinct areas of early activation around the mitral valve annulus, indicating the presence of two left-sided pathways which were not distinguished using L2 regularization.

Arrhythmogenic Brugada syndrome substrate: a proof of principle

The Brugada syndrome is an inherited, arrhythmogenic entity affecting predominantly young men without structural heart disease.1 It is associated with a specific ECG pattern of coved-type ST-segment elevation in right precordial leads ( Figure 1 ). Patients are at increased risk for sudden cardiac death often triggered by vagal influence and many times occurring at rest. After its description as a distinct entity in 1992, a first genetic link was identified in 1998.2 The Brugada syndrome has a complex electrophysiological substrate, and several aspects are important for understanding its pathology. Many lines of evidence suggest a central role of I to in the genesis of the Brugada syndrome. First, the balance of de- and repolarizing forces during the cardiac action potential is disturbed, leading to a loss of dome in epicardial action potentials and to increased dispersion of refractoriness. Reduced depolarizing (sodium current, I Na, or calcium current, I Ca) or increased repolarizing ion currents (transient outward … *Corresponding author. Tel: +49 69 6301 83661, fax: +49 69 6301 4037. E-mail address: j.ehrlich{at}em.uni-frankfurt.de

Using inverse electrocardiography to image myocardial infarction—reflecting on the 2007 PhysioNet/Computers in Cardiology Challenge

The goal of the 2007 PhysioNet/Computers in Cardiology Challenge was to try to establish how well it is possible to characterize the location and extent of old myocardial infarcts using electrocardiographic evidence supplemented by anatomical imaging information. A brief overview of the challenge and how different challengers approached the competition is provided, followed by detailed response of the first author to integrate electrophysiologic and anatomical data. The first author used the provided 120-electrode body-surface potential mapping data and magnetic resonance imaging heart and torso images to calculate epicardial potentials on customized ventricular geometries. A method was developed to define the location and extent of scar tissue based on the morphology of computed epicardial electrograms. Negative Q-wave deflection followed by R-wave on the left ventricular surface seemed to correspond with the location of the scar as determined by the gadolinium-enhanced magnetic resonance imaging gold standard in the supplied data sets. The method shows promising results as a noninvasive imaging tool to quantitatively characterize chronic infarcts and warrants further investigation on a larger patient data set.

Effect of Cardiac Motion on Solution of the Electrocardiography Inverse Problem

Previous studies of the ECG inverse problem often assumed that the heart was static during the cardiac cycle; consequently, a time-dependent geometrical error was thought to be unavoidably introduced. In this paper, cardiac motion is included in solutions to the electrocardiographic inverse problem. Cardiac dynamics are simulated based on a previously developed biventricular model that coupled the electrical and mechanical properties of the heart, and simulated the ventricular wall motion and deformation. In the forward computation, the heart surface source model method is employed to calculate the epicardial potentials from the action potentials, and then, the simulated epicardial potentials are used to calculate body surface potentials. With the inclusion of cardiac motion, the calculated body surface potentials are more reasonable than those in the case of static assumption. In the epicardial potential-based inverse studies, the Tikhonov regularization method is used to handle ill-posedness of the ECG inverse problem. The simulation results demonstrate that the solutions obtained from both the static ECG inverse problem and the dynamic ECG inverse problem approaches are approximately the same during the QRS complex period, due to the minimal deformation of the heart in this period. However, with the most obvious deformation occurring during the ST-T segment, the static assumption of heart always generates something akin to geometry noise in the ECG inverse problem causing the inverse solutions to have large errors. This study suggests that the inclusion of cardiac motion in solving the ECG inverse problem can lead to more accurate and acceptable inverse solutions.

Boundary Element Computations in the Forward and Inverse Problems of Electrocardiography: Comparison of Collocation and Galerkin Weightings

In electrocardiographic imaging, epicardial potentials are reconstructed computationally from electrocardiographic measurements. The reconstruction is typically done with the help of the boundary element method (BEM), using the point collocation weighting and constant or linear basis functions. In this paper, we evaluated the performance of constant and linear point collocation and Galerkin BEMs in the epicardial potential problem. The integral equations and discretizations were formulated in terms of the single- and double-layer operators. All inner element integrals were calculated analytically. The computational methods were validated against analytical solutions in a simplified geometry. On the basis of the validation, no method was optimal in all testing scenarios. In the forward computation of the epicardial potential, the linear Galerkin (LG) method produced the smallest errors. The LG method also produced the smallest discretization error on the epicardial surface. In the inverse computation of epicardial potential, the electrode-specific transfer matrix performed better than the full transfer matrix. The Tikhonov 2 regularization outperformed the Tikhonov 0. In the optimal modeling conditions, the best BEM technique depended on electrode positions and chosen error measure. When large modeling errors such as omission of the lungs were present, the choice of the basis and weighting functions was not significant.

Two hybrid regularization frameworks for solving the electrocardiography inverse problem

In this paper, two hybrid regularization frameworks, LSQR-Tik and Tik-LSQR, which integrate the properties of the direct regularization method (Tikhonov) and the iterative regularization method (LSQR), have been proposed and investigated for solving ECG inverse problems. The LSQR-Tik method is based on the Lanczos process, which yields a sequence of small bidiagonal systems to approximate the original ill-posed problem and then the Tikhonov regularization method is applied to stabilize the projected problem. The Tik-LSQR method is formulated as an iterative LSQR inverse, augmented with a Tikhonov-like prior information term. The performances of these two hybrid methods are evaluated using a realistic heart-torso model simulation protocol, in which the heart surface source method is employed to calculate the simulated epicardial potentials (EPs) from the action potentials (APs), and then the acquired EPs are used to calculate simulated body surface potentials (BSPs). The results show that the regularized solutions obtained by the LSQR-Tik method are approximate to those of the Tikhonov method, the computational cost of the LSQR-Tik method, however, is much less than that of the Tikhonov method. Moreover, the Tik-LSQR scheme can reconstruct the epcicardial potential distribution more accurately, specifically for the BSPs with large noisy cases. This investigation suggests that hybrid regularization methods may be more effective than separate regularization approaches for ECG inverse problems.

Truncated Total Least Squares: A New Regularization Method for the Solution of ECG Inverse Problems

The reconstruction of epicardial potentials (EPs) from body surface potentials (BSPs) can be characterized as an ill-posed inverse problem which generally requires a regularized numerical solution. Two kinds of errors/noise: geometric errors and measurement errors exist in the ECG inverse problem and make the solution of such problem more difficulty. In particular, geometric errors will directly affect the calculation of transfer matrix A in the linear system equation AX = B. In this paper, we have applied the truncated total least squares (TTLS) method to reconstruct EPs from BSPs. This method accounts for the noise/errors on both sides of the system equation and treats geometric errors in a new fashion. The algorithm is tested using a realistically shaped heart-lung-torso model with inhomogeneous conductivities. The h-adaptive boundary element method [h-BEM, a BEM mesh adaptation scheme which starts from preset meshes and then refines (adds/removes) grid with fixed order of interpolation function and prescribed numerical accuracy] is used for the forward modeling and the TTLS is applied for inverse solutions and its performance is also compared with conventional regularization approaches such as Tikhonov and truncated single value decomposition (TSVD) with zeroth-, first-, and second-order. The simulation results demonstrate that TTLS can obtain similar results in the situation of measurement noise only but performs better than Tikhonov and TSVD methods where geometric errors are involved, and that the zeroth-order regularization is the optimal choice for the ECG inverse problem. This investigation suggests that TTLS is able to robustly reconstruct EPs from BSPs and is a promising alternative method for the solution of ECG inverse problems.

Noninvasive Electrocardiographic Imaging (ECGI) of a univentricular heart with Wolff-Parkinson-White syndrome

Electrocardiographic imaging (ECGI) is a noninvasive functional imaging modality which reconstructs epicardial potentials, electrograms, and activation and recovery maps from body-surface ECG potentials. For this purpose, up to 256 ECGs are recorded by a 256-channel body surface potential mapping (BSPM) system and the heart-torso geometry is obtained using thoracic computed tomography (CT)1,2. This technique was developed and validated extensively in normal and abnormal canine hearts3–11. More recently, ECGI was validated in humans by comparison with direct intra-operative epicardial mapping in patients undergoing open-heart surgery12. To date, ECGI has been applied in adult human subjects for the following purposes: 1. To study cardiac electrophysiology of the normal adult human heart2. 2. To image electrophysiologic responses to pacing in heart failure patients undergoing cardiac resynchronization therapy13 (pacing sites were localized with an accuracy better than 10 mm)14. 3. To guide catheter ablation of focal ventricular and atrial tachycardias15,16. 4. To image typical atrial flutter prior to catheter ablation1 and atypical atrial flutter prior to a surgical Cox-Maze procedure17. Here we describe for the first time, a case where ECGI was applied to a pediatric patient with a congenital structural heart defect. The patient had a univentricular heart and Wolff-Parkinson-White syndrome, and ECGI was used to localize the accessory pathway and help guide catheter ablation. To date, there have been no reported cases of ECGI in the pediatric population.

Noninvasive electrocardiographic imaging of arrhythmogenesis: insights from modeling and human studies

Background Sudden cardiac death remains the leading cause of death, claiming more than 1000 lives per day in the United States alone. Noninvasive means to diagnose rhythm disorders of the heart have relied heavily on the 12-lead electrocardiogram and, to a lesser extent, on higher-resolution body-surface mapping. These lack sensitivity and specificity due to the smoothing effect of the torso volume conductor. In contrast, noninvasive electrocardiographic imaging (ECGI) reconstructs potentials, electrograms, and activation sequences directly on the heart surface from body-surface electrocardiograms and has been applied in animal as well as clinical studies. This presentation summarizes the application of ECGI for imaging epicardial arrhythmogenic substrates and associated properties, in particular, dispersion of myocardial repolarization, fractionated electrograms, and heterogeneous multipolar potential distributions. Methods Electrocardiographic imaging was evaluated in a canine model of temperature-induced dispersion of myocardial repolarization through localized warming and cooling and in 3 patients with preserved left ventricular ejection fraction (≥50%) undergoing open heart surgery. Noninvasively reconstructed epicardial potentials, electrograms (and derived measures), as well as activation sequences were compared with their measured counterparts. Results Epicardial measures of dispersion of repolarization (activation recovery intervals [ARIs] and QRST integrals) accurately reflected the underlying repolarization properties: prolonged ARIs and increased QRST (warming), shortened ARIs and decreased QRST (cooling), and gradients of adjacent prolonged and shortened ARIs (increased and decreased QRST) during simultaneous warming and cooling. In open-heart surgery patients, ECGI reflected the underlying arrhythmogenic substrate by noninvasively reconstructing fractionated electrograms (cross-correlation with measured electrograms = 0.72 ± 0.25), regions of heterogeneous multipolar potential distributions, and areas of slow conduction. Conclusion These studies demonstrate that ECGI can capture and localize noninvasively important electrophysiologic properties of the heart. Its clinical significance lies in mapping arrhythmogenic substrates, evaluation and guidance of therapy, and risk stratification.

Noninvasive electrocardiographic imaging (ECGI) of scar-related atypical atrial flutter

We report the first application of ECGI in a patient with atypical atrial flutter that developed after catheter ablation for PV isolation. ECGI detected and mapped regions of low voltages that coincided with scar tissue around the pulmonary veins from the previous catheter ablation procedures, as verified during a COX-MAZE surgical procedure. The flutter reentry circuit was constrained by the scar and mainly confined to the LA. The mitral isthmus between the coronary sinus and the PVs participated in the reentry circuit. ECGI also imaged a region of low potentials on the let atrial appendage (LAA), which is uncommon. Typically, the LAA is a region of high voltage, as measured by endocardial mapping. During the COX-MAZE procedure it was observed that the LAA is extensively scarred (due to the underlying disease, not prior ablation), consistent with the ECGI reconstruction of low voltages in this region. The case reported in this manuscript was unique from the ECGI perspective, because prior to the COX-MAZE procedure the diagnosis was atrial fibrillation. ECGI constructed a monomorphic stable reentrant activation pattern that was repeated for many beats, indicating anatomical rather than functional reentry. Both ECGI reconstruction of low potentials and direct observation during surgery consistently identified an extensive scar around which the ECGI reconstructed isochrones formed the reentry circuit; the scar provided the anatomical substrate that stabilized the reentry. The repeatability of the reentry pattern over many beats demonstrates the consistency of ECGI methodology. It should be recognized that ECGI generates the entire activation map during a single beat and is therefore well suited to detect beat-to-beat changes during an arrhythmia. In contrast, catheter mapping (e.g. CARTO) is conducted point-by-point in a roving-prove fashion and requires data from many beats to construct an activation map. As such, it cannot provide data for comparison to ECGI in most cases. Following the COX-MAZE procedure, the patient returned to normal sinus rhythm.