Electrocardiographic Inverse Solution Research Articles

Localization of Activation Origin on Patient-Specific Endocardial Surface by the Equivalent Double Layer (EDL) Source Model With Sparse Bayesian Learning.

Ablation treatment of ventricular arrhythmias can be facilitated by pre-procedure planning aided by electrocardiographic inverse solution, which can help to localize the origin of arrhythmia. Our aim was to improve localization accuracy of the inverse solution for activation originating on the left-ventricular endocardial surface, by using a sparse Bayesian learning (SBL). The inverse problem of electrocardiography was solved by reconstructing endocardial potentials from time integrals of body-surface electrocardiograms and from patient-specific geometry of the heart and torso for three patients with structurally normal ventricular myocardium, who underwent endocardial catheter mapping that included pace mapping. Complementary simulations using dipole sources in patient-specific geometry were also performed. The proposed method is using sparse property of the equivalent-double-layer (EDL) model of cardiac sources; it employs the SBL and makes use of the spatio-temporal features of the cardiac action potentials. The mean localization error of the proposed method for pooled pacing sites ( n=52) was significantly smaller ( p=0.0039) than that achieved for the same patients in the study of Erem etal. Simulation experiments localized the source dipoles ( n=48) from forward-simulated potentials with the error of 9.4 ± 4.5mm (mean ± SD). The results of our clinical and simulation experiments demonstrate that localization of left-ventricular endocardial activation by means of the Bayesian approach, based on sparse representation of sources by EDL, is feasible and accurate. The proposed approach to localizing endocardial sources may have important applications in pre-procedure assessment of arrhythmias and in guiding their ablation treatment.

Localization of Activation Origin on Patient-Specific Epicardial Surface by Empirical Bayesian Method

Ablation treatment of ventricular arrhythmias can be facilitated by pre-procedure planning aided by electrocardiographic inverse solution, which can help to localize the origin of arrhythmia. Our aim was to improve localization accuracy of the inverse solution by using a novel Bayesian approach. The inverse problem of electrocardiography was solved by reconstructing epicardial potentials from 120 body-surface electrocardiograms and from patient-specific geometry of the heart and torso for four patients suffering from scar-related ventricular tachycardia who underwent epicardial catheter mapping, which included pace-mapping. Simulations using dipole sources in patient-specific geometry were also performed. The proposed method, using dynamic spatio-temporal apriori constraints of the solution, was compared with classical Tikhonov methods based on fixed constraints. The mean localization error of the proposed method for all available pacing sites (n=78) was significantly smaller than that achieved by Tikhonov methods; specifically, the localization accuracy for pacing in the normal tissue (n=17) was [Formula: see text]mm (mean ± SD) versus [Formula: see text]mm reported in the previous study using the same clinical data and Tikhonov regularization. Simulation experiments further supported these clinical findings. The promising results of invivo and in silico experiments presented in this study provide a strong incentive to pursuing further investigation of data-driven Bayesian methods in solving the electrocardiographic inverse problem. The proposed approach to localizing origin of ventricular activation sequence may have important applications in pre-procedure assessment of arrhythmias and in guiding their ablation treatment.

Localization of ventricular activation origin using patient-specific geometry: Preliminary results.

Catheter ablation of ventricular tachycardia (VT) may include induction of VT and localization of VT-exit site. Our aim was to assess localization performance of a novel statistical pace-mapping method and compare it with performance of an electrocardiographic inverse solution. Seven patients undergoing ablation of VT (4 with epicardial, 3 with endocardial exit) aided by electroanatomic mapping underwent intraprocedural 120-lead body-surface potential mapping (BSPM). Two approaches to localization of activation origin were tested: (1) A statistical method, based on multiple linear regression (MLR), which required only the conventional 12-lead ECG for a sufficient number of pacing sites with known origin together with patient-specific geometry of the endocardial/epicardial surface obtained by electroanatomic mapping; and (2) a classical deterministic inverse solution for recovering heart-surface potentials, which required BSPM and patient-specific geometry of the heart and torso obtained via computed tomography (CT). For the MLR method, at least 10-15 pacing sites with known coordinates, together with their corresponding 12-lead ECGs, were required to derive reliable patient-specific regression equations, which then enabled accurate localization of ventricular activation with unknown origin. For 4 patients who underwent epicardial mapping, the median of localization error for the MLR was significantly lower than that for the inverse solution (10.6vs. 27.3mm, P=0.034); a similar result held for 3 patients who underwent endocardial mapping (7.7vs. 17.1mm, P=0.017). The pooled localization error for all epicardial and endocardial sites was also significantly smaller for the MLR compared with the inverse solution (P=0.005). The novel pace-mapping approach to localizing the origin of ventricular activation offers an easily implementable supplement and/or alternative to the preprocedure inverse solution; its simplicity makes it suitable for real-time applications during clinical catheter-ablation procedures.

Computational Aspects of Electrocardiological Inverse Solutions

The purpose of this work is to investigate the effect of certain numerical factors on the electrocardiographic inverse solution. Since usually the zero-order Tikhonov regularization is applied in order to solve the inverse problem, choosing the right regularization parameter is very important. The used linear equation system solver also plays an important role in the accuracy of the solution. Therefore these two factors were studied in a well defined model environment. Reference epicardial and body surface potential maps were generated in 1003 epicardial and 344 body surface points, respectively, by the Wei-Harumi model, for the QRS interval. The inverse problem has been solved with various regularization parameters and linear equation system solvers. The highest correlations (> 0.9) occurred in the first half of the QRS interval and the correlation fell below 0.6 at the end of the QRS. The result was highly dependent on the chosen regularization parameter and equation system solver, and it was significantly influenced also by the complexity of the epicardial potential distribution. The optimal solving configuration proved to be the application of the Cholesky factorization with the regularization parameter of 10−14.

Comparison of epicardial potential maps derived from the 12-lead electrocardiograms with scintigraphic images during controlled myocardial ischemia

Our aim was to cross-validate electrocardiographic (ECG) and scintigraphic imaging of acute myocardial ischemia. The former method was based on inverse calculation of heart-surface potentials from the body-surface ECGs, and the latter, on a single photon emission computed tomography (SPECT). A boundary-element torso model with 352 body-surface and 202 heart-surface nodes was used to perform the ECG inverse solution. Potentials at 352 body-surface nodes were calculated from those acquired at 12-lead ECG measurement sites using regression coefficients developed from a design set (n = 892) of body-surface potential mapping (BSPM) data. The test set (n = 18) consisted of BSPM data from patients who underwent a balloon-inflation angioplasty of either the left anterior descending coronary artery (LAD) (n = 7), left circumflex coronary artery (LCx) (n = 2), or the right coronary artery (RCA) (n = 9). Body-surface potential mapping distributions at J point for 352 nodes were estimated from the 12-lead ECG, and an agreement with those estimated from 120 leads was assessed by a correlation coefficient (CC) (in percent). These estimates yielded very similar BSPM distributions, with a CC of 91.0% ± 8.1% (mean ± SD) for the entire test set and 94.1% ± 1.4%, 96.7% ± 0.8%, and 87.4% ± 10.3% for LAD, LCx, and RCA subgroups, respectively. Corresponding heart-surface potential distributions obtained by inverse solution correlated with a lower CC of 69.3% ± 18.0% overall and 73.7% ± 10.8%, 84.7% ± 1.1%, and 62.6% ± 21.8%, respectively, for subgroups. Bull's-eye displays of heart-surface potentials calculated from estimated BSPM distributions had an area of positive potentials that qualitatively corresponded, in general, with the underperfused territory suggested by SPECT images. For the LAD and LCx groups, all 9 ECG-derived bull's-eye images indicated the expected territory; for the RCA group, 6 of 9 ECG-derived images were as expected; 2 of 3 misclassified cases had very small ECG changes in response to coronary-artery occlusion, and their SPECT images showed indiscernible patterns. In conclusion, our findings demonstrate that noninvasive ECG imaging based on just the 12-lead ECG might provide useful estimates of the regions of myocardial ischemia that agree with those provided by scintigraphic techniques.

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.

Quantitative assessment of myocardial ischemia by electrocardiographic and scintigraphic imaging

We calculated distributions of epicardial potentials from body-surface electrocardiograms (ECGs) recorded during controlled myocardial ischemia and compared them with scintigraphic estimates of ischemia’s extent/severity>. The study population consisted of patients suffering from single-vessel coronary artery disease, referred for elective percutaneous transluminal coronary angioplasty of either the left anterior descending ( n = 7), the right coronary ( n = 9), or the left circumflex ( n = 2) artery. After the target vessel had been dilated, a 1960s “study” inflation was performed with a non-perfusion-type balloon catheter; at its commencement, technetium-99m sestamibi was injected via a femoral-vein catheter, and ECGs were recorded throughout the inflation from 120 leads. Single photon emission computed tomographic imaging was performed one hour after the injection of radionuclide to obtain an “occlusion image”, and again one hour after a repeat injection 24 hours later to obtain a “control image”; the latter image was subtracted from the former, to derive a scintigraphic difference map (Δ map). The ECGs were signal-averaged over a 10-s window at preinflation and peak-inflation states, the preinflation averaged complexes were subtracted from the peak-inflation ones to produce body-surface Δ maps, and the corresponding Δ maps of epicardial potentials were calculated by applying the electrocardiographic inverse solution; this procedure is referred to as electrocardiographic imaging. The ECG-derived epicardial Δ maps related spatially to the scintigraphic Δ maps in all patients. The percent areas and surface integrals of positive values in ECG-derived Δ maps were found to be very good single-variable predictors of the extent ( r = 0.73; p = 0.0006) and severity ( r = 0.72; p = 0.0008) of the scintigraphically-estimated perfusion defect; a regression equation using two ECG-derived predictors further improved the agreement with scintigraphic estimates ( r = 0.81; p = 0.0004 for estimates of severity). These findings suggest that noninvasive electrocardiographic imaging might provide quantitative estimates of the extent/ severity of myocardial ischemia that agree closely with those provided by scintigraphic techniques.

Application of an electrocardiographic inverse solution to localize ischemia during coronary angioplasty.

Localization of Ischemia. This study demonstrates the utility of an electrocardiographic inverse solution, coupled with body surface potential mapping (BSPM), in localizing acute ischemia in patients undergoing percutaneous transluminal coronary angioplasty (PTCA). PTCA balloon inflations produce complete occlusion and acute transient ischemia, which can be detected electrocardiographically with BSPM. Comparisons between maps recorded both during and before the inflation of the PTCA balloon allow patient- and artery-specific characterizations of the resulting ischemia. Knowledge of the patient's coronary anatomy and the location of the occlusion site by coronary angiography permit an estimation based on cardiac hemodynamics of the region of myocardium most likely to suffer from PTCA-induced ischemia. Electrocardiographic inverse solutions provide a means of predicting cardiac potentials from body surface maps. In this study, we describe an inverse solution we have developed to localize the transient ischemia produced by PTCA. To validate the procedure, we compared the locations of predicted ischemia in seven patients with a qualitative estimate of the perfusion region based on fluoroscopic examination of each patient's coronary anatomy and PTCA balloon location. In each case, the region of ischemia predicted by the model included the perfusion zone determined fluoroscopically. These results suggest that electrical changes induced by acute ischemia can be localized with an electrocardiographic inverse solution.

Electrocardiographic inverse solution for ectopic origin of excitation in two-dimensional propagation model

Inverse calculations were examined that sought the origin of a cardiac ectopic excitation sequence. Cardiac anatomy and its geometric relationships to sites on the body surface were adapted from human cross-sectional images to form a two-dimensional model, which included ventricular muscle and a primitive conduction system. The surrounding volume conductor was modelled in a simplified way as unbounded, homogeneous and isotropic. In a series of tests, one ectopic origin was designated the 'true' origin. The ECG for this true origin was compared to ECGs for 197 ectopic 'trial' origins, and differences between the wave forms for true versus trial origins were determined. Core issues were the magnitudes of changes in ECG wave forms as a function of the site of origin, whether these changes were sufficient to imply uniqueness, and what spatial resolution might be expected, in the presence of realistic noise levels. For a noise level of 10 microV RMS, the origin of excitation was localised to a single region of the muscle using one wave form from the body surface, with a resolution of 10 mm. The resolution was not improved significantly with a second electrode on the body surface, but was substantially improved with an endocardial electrode.

Determination of the site of accessory pathway in WPW syndrome by an electrocardiographic inverse solution

Determination of the site of accessory pathway in WPW syndrome by an electrocardiographic inverse solution

Location of the accessory pathway in WPW syndrome by an electrocardiographic inverse solution

Location of the accessory pathway in WPW syndrome by an electrocardiographic inverse solution

Imaging and processing of meridian and acupoint phenomena

The phenomena of meridians and acupoints were investigated by measuring the electrical resistance of the skin over the body with an electro-dermometer. The measurements were then processed in different ways by computer and expressed as screen images to correlate the electrical resistance of the skin to the meridian and acupoint phenomena. The electrocardiographic inverse solution is one of the most promising methods for further understanding the electrophysiological abnormalities of the heart. The initial portion of the QRS in WPW syndrome would be characterized by a single activation front, since the delta wave corresponds to the localized ventricular activation propagated over the accessory atrioventricular pathway. In this study, the location of the dipole was estimated by using an equivalent dipole method for 10 patients with WPW syndrome, and was then compared with the site estimated from a standard electrocardiogram and body surface potential map. In spite of such limitations as the instability of the solution, electrode location error, and lack of an individual torso model, the results demonstrated that the single dipole approxi- mation was appropriate during the delta wave by both the infinite medium model and the plane boundary model, since the index of the nondipolarity was small.

Optimisation of the locations of multiple-dipole heart generators in a simple torso model

Electrocardiographic inverse solutions frequently assume multiple-dipole equivalent generators with locations fixed throught the QRS complex. This paper describes investigations which extend the solution to optimise the dipole locations at any instant of time. The combined results lead to a moving multiple-dipole inverse solution which is more accurate than the conventional solutions at each instant and also contains information related to the dynamic movement of the physiological generators. Tests so far have been limited to a 3-dipole solution in a highly simplified torso model. The generators in this study were dipoles displaced varying amounts from a standard central location; the inverse solution starts by using the standard location and then is led to an improved solution by a guided search. Moderate displacements, as compared to the size of the heart model, were shown to yield root mean square errors in the inverse-solution source strengths as high as 40% when the latter were found via a least-mean-square procedure. The method of steepest descent was utilised in the second step to improve the locations and strengths of the initially assumed equivalent-dipole generators and thus improve the accuracy of the inverse solution. The percentage root-mean-square source-strength errors were reduced from as high as 40% to under 10% in most cases. The initial position error of up to 10% for the source dipoles typically was reduced to less than 5% throught the use of the search routine. The ability of the solution dipoles to track the original locations was demonstrated.