Body Surface Potential Recordings Research Articles

A two-step inverse solution for a single dipole cardiac source.

Introduction: The inverse problem of electrocardiography noninvasively localizes the origin of undesired cardiac activity, such as a premature ventricular contraction (PVC), from potential recordings from multiple torso electrodes. However, the optimal number and placement of electrodes for an accurate solution of the inverse problem remain undetermined. This study presents a two-step inverse solution for a single dipole cardiac source, which investigates the significance of the torso electrodes on a patient-specific level. Furthermore, the impact of the significant electrodes on the accuracy of the inverse solution is studied. Methods: Body surface potential recordings from 128 electrodes of 13 patients with PVCs and their corresponding homogeneous and inhomogeneous torso models were used. The inverse problem using a single dipole was solved in two steps: First, using information from all electrodes, and second, using a subset of electrodes sorted in descending order according to their significance estimated by a greedy algorithm. The significance of electrodes was computed for three criteria derived from the singular values of the transfer matrix that correspond to the inversely estimated origin of the PVC computed in the first step. The localization error (LE) was computed as the Euclidean distance between the ground truth and the inversely estimated origin of the PVC. The LE obtained using the 32 and 64 most significant electrodes was compared to the LE obtained when all 128 electrodes were used for the inverse solution. Results: The average LE calculated for both torso models and using all 128 electrodes was 28.8 ± 11.9mm. For the three tested criteria, the average LEs were 32.6 ± 19.9mm, 29.6 ± 14.7mm, and 28.8 ± 14.5mm when 32 electrodes were used. When 64 electrodes were used, the average LEs were 30.1 ± 16.8mm, 29.4 ± 12.0mm, and 29.5 ± 12.6mm. Conclusion: The study found inter-patient variability in the significance of torso electrodes and demonstrated that an accurate localization by the inverse solution with a single dipole could be achieved using a carefully selected reduced number of electrodes.

Bariatric surgery reduces ventricular repolarisation gradients in obese patients - results from an electrocardiographic imaging study

Abstract Funding Acknowledgements Type of funding sources: Public Institution(s). Main funding source(s): National Institute for Health Research (NIHR) British Heart Foundation Background Obesity confers higher risks of atrial arrhythmias and is associated with abnormal ventricular repolarisation. Despite this, the proarrhythmic substrate in obesity and its reversibility with weight loss has not been studied in-depth. Purpose To characterise the proarrhythmic substrate in obese patients, and its reversibility with bariatric surgery, using electrocardiographic imaging (ECGi). Methods ECGi was performed in 8 obese patients before (PreOb) and after (PostOb) bariatric surgery (mean age 39+/-11years, 7 female), and in 8 age- and sex-matched non-obese controls (NOb) (40+/-11 years). ECGi recordings were made at rest, on exercise, and during recovery from exercise. For ECGi analysis, >2000 atrial and ventricular epicardial electrograms were calculated from body surface potential recordings from 256 sites and information from cardiac magnetic resonance imaging, by solving the inverse problem. Local atrial and ventricular epicardial activation times (AT) were calculated as the steepest downslope of their respective activation complexes, and local ventricular repolarisation times (RT) as the steepest upslope of the T-wave. Atrial activation gradients (ATG) and ventricular repolarisation gradients (RTG) were calculated as the maximum difference within 10mm radius divided by the corresponding Euclidean distance. Results BMI was greater in PreOb vs NOb (46.6+/-4.8 vs 23.8+/-2.6kg/m2, p<0.0001) and decreased with surgery (PostOb 35.3+/-4.2kg/m2, p<0.0001). Total atrial AT was prolonged in PreOb vs NOb (68+/-12 vs 45+/-10ms, p=0.016) and did not change post-surgery (PreOb vs PostOb: 68+/-12 vs 67+/-16ms, p=0.81). Atrial ATG were also greater in PreOb vs NOb: max 254+/-111 vs 106+/-58ms, p=0.035; mean 24+/-6 vs 12+/-6ms, p=0.0087) and did not change with weight loss (PreOb vs PostOb: max 254+/-111 vs 222+/-69ms/mm, p=0.61; mean 24+/-6 vs 21+/-7ms/mm, p=0.52). Ventricular RTG were greater in PreOb vs NOb (max: 287+/-73 vs 131+/-89ms/mm, p=0.012; mean: 33+/-10 vs 17+/-9ms/mm, p=0.0052). Ventricular RTG decreased with weight loss (PreOb vs PostOb: max 287+/-73 vs 151+/-54ms/mm, p=0.0070; mean: 33+/-10 vs 21+/-8ms/mm, p=0.018), and were similar between PostOb and NOb (max, p=0.81; mean p=0.58). Ventricular AT and RT were non-different in NOb, PreOb and PostOb. Conclusion Obesity is associated with pro-arrhythmic electrophysiological remodelling, including steeper ventricular repolarisation gradients and slower atrial activation. At 6 months post-bariatric surgery, there was a reduction in ventricular repolarisation gradients though atrial conduction abnormalities persisted. These findings provide a mechanistic insight into obesity-related arrhythmic risks and its potential reversibility with weight loss surgery.

Electrocardiographic Imaging for Atrial Fibrillation: A Perspective From Computer Models and Animal Experiments to Clinical Value.

Electrocardiographic imaging (ECGI) is a technique to reconstruct non-invasively the electrical activity on the heart surface from body-surface potential recordings and geometric information of the torso and the heart. ECGI has shown scientific and clinical value when used to characterize and treat both atrial and ventricular arrhythmias. Regarding atrial fibrillation (AF), the characterization of the electrical propagation and the underlying substrate favoring AF is inherently more challenging than for ventricular arrhythmias, due to the progressive and heterogeneous nature of the disease and its manifestation, the small volume and wall thickness of the atria, and the relatively large role of microstructural abnormalities in AF. At the same time, ECGI has the advantage over other mapping technologies of allowing a global characterization of atrial electrical activity at every atrial beat and non-invasively. However, since ECGI is time-consuming and costly and the use of electrical mapping to guide AF ablation is still not fully established, the clinical value of ECGI for AF is still under assessment. Nonetheless, AF is known to be the manifestation of a complex interaction between electrical and structural abnormalities and therefore, true electro-anatomical-structural imaging may elucidate important key factors of AF development, progression, and treatment. Therefore, it is paramount to identify which clinical questions could be successfully addressed by ECGI when it comes to AF characterization and treatment, and which questions may be beyond its technical limitations. In this manuscript we review the questions that researchers have tried to address on the use of ECGI for AF characterization and treatment guidance (for example, localization of AF triggers and sustaining mechanisms), and we discuss the technological requirements and validation. We address experimental and clinical results, limitations, and future challenges for fruitful application of ECGI for AF understanding and management. We pay attention to existing techniques and clinical application, to computer models and (animal or human) experiments, to challenges of methodological and clinical validation. The overall objective of the study is to provide a consensus on valuable directions that ECGI research may take to provide future improvements in AF characterization and treatment guidance.

A Method for Normal Direction Judge Applied in Electrocardiographic Problem

Boundary Element Method (BEM) is widely used in electrocardiographic (ECG) problem. Formulations of these problems based on mathematical and numerical approximations of the known source in heart and the volume conductor that can transfer voltages on the surface of the body. To analyze the electric potentials on body surface or epicardial surface, a set of discrete equations derived from a boundary integral equations need to be solved. Solving these equations means to get the potential distribution eventually. In the process of solving, transfer matrix of discrete equations has received considerable attention, how to get an appropriate transfer matrix is an important issue. This paper found that the direction of normal vector could affect the results when calculating the transfer matrix and presents a method analogous to Mesh Current Method to deal with this direction problem. Several simulations have been carried out to verify the accurate results with the correct direction of normal vector using new method within a torso model given simultaneous epicardial and body surface potential recordings.

Inverse electrocardiographic source localization of ischemia: An optimization framework and finite element solution

With the goal of non-invasively localizing cardiac ischemic disease using body-surface potential recordings, we attempted to reconstruct the transmembrane potential (TMP) throughout the myocardium with the bidomain heart model. The task is an inverse source problem governed by partial differential equations (PDE). Our main contribution is solving the inverse problem within a PDE-constrained optimization framework that enables various physically-based constraints in both equality and inequality forms. We formulated the optimality conditions rigorously in the continuum before deriving finite element discretization, thereby making the optimization independent of discretization choice. Such a formulation was derived for the L2-norm Tikhonov regularization and the total variation minimization. The subsequent numerical optimization was fulfilled by a primal–dual interior-point method tailored to our problem’s specific structure. Our simulations used realistic, fiber-included heart models consisting of up to 18,000 nodes, much finer than any inverse models previously reported. With synthetic ischemia data we localized ischemic regions with roughly a 10% false-negative rate or a 20% false-positive rate under conditions up to 5% input noise. With ischemia data measured from animal experiments, we reconstructed TMPs with roughly 0.9 correlation with the ground truth. While precisely estimating the TMP in general cases remains an open problem, our study shows the feasibility of reconstructing TMP during the ST interval as a means of ischemia localization.

Evaluation of lead selection methods for optimal reconstruction of body surface potentials

In this study, several methods for optimal lead selection from multilead electrocardiographic recordings are analyzed. Two different lead selection methods have been implemented. For their evaluation, a linear transformation that reconstructs nonselected leads from selected leads is computed according to the least squares optimization, and the performance is evaluated in terms of the mean square error of the derived potentials and correlation. The algorithms were tested on a database of 72 body surface potential recordings: 18 controls, 18 bundle-branch block, 18 myocardial infarction, and 18 ventricular hypertrophy. Each data set was divided into a study and test subsets. Two experiments were carried out: (1) The lead selection, transformation matrix, and performance evaluation is carried out over the test data set (ideal case), and (2) the lead selection and transformation matrix is carried out over the study data set, but the performance is evaluated over the test data set (real case). Our results show important reconstruction errors with either lead selection methods, and only increasing the number of leads reduces the error in reconstruction. However, if a reduced number of leads are to be selected outside the standard 12-lead electrocardiogram, the method proposed by Lux has been shown to be the best option.

Accuracy of Quadratic Versus Linear Interpolation in Noninvasive Electrocardiographic Imaging (ECGI)

Electrocardiographic Imaging (ECGI) is a cardiac functional imaging modality, noninvasively reconstructing epicardial potentials, electrograms and isochrones (activation maps) from multi-channel body surface potential recordings. The procedure involves solving Laplace's equation in the source-free volume conductor between torso and epicardial surfaces, using Boundary Element Method (BEM). Previously, linear interpolation (LI) on three-noded triangular surface elements was used in the BEM formulation. Here, we use quadratic interpolation (QI) for potentials over six-noded linear triangles. The performance of LI and QI in ECGI is evaluated through direct comparison with measured data from an isolated canine heart suspended in a human-torso-shaped electrolyte tank. QI enhances the accuracy and resolution of ECGI reconstructions for two different inverse methods, Tikhonov regularization and Generalized Minimal Residual (GMRes) method, with the QI-GMRes combination providing the highest accuracy and resolution. QI reduces the average relative error (RE) between reconstructed and measured epicardial potentials by 25%. It preserves the amplitude (average RE reduced by 48%) and morphology of electrograms better (average correlation coefficient for QI approximately 0.97, LI approximately 0.92). We also applied QI to ECGI reconstructions in human subjects during cardiac pacing, where QI locates ventricular pacing sites with higher accuracy (< or = 10 mm) than LI (< or = 18 mm).