Danila Potyagaylo

Binary optimization for source localization in the inverse problem of ECG.

Abstract The goal of ECG-imaging (ECGI) is to reconstruct heart electrical activity from body surface potential maps. The problem is ill-posed, which means that it is extremely sensitive to measurement and modeling errors. The most commonly used method to tackle this obstacle is Tikhonov regularization, which consists in converting the original problem into a well-posed one by adding a penalty term. The method, despite all its practical advantages, has however a serious drawback: The obtained solution is often over-smoothed, which can hinder precise clinical diagnosis and treatment planning. In this paper, we apply a binary optimization approach to the transmembrane voltage (TMV)-based problem. For this, we assume the TMV to take two possible values according to a heart abnormality under consideration. In this work, we investigate the localization of simulated ischemic areas and ectopic foci and one clinical infarction case. This affects only the choice of the binary values, while the core of the algorithms remains the same, making the approximation easily adjustable to the application needs. Two methods, a hybrid metaheuristic approach and the difference of convex functions (DC), algorithm were tested. For this purpose, we performed realistic heart simulations for a complex thorax model and applied the proposed techniques to the obtained ECG signals. Both methods enabled localization of the areas of interest, hence showing their potential for application in ECGI. For the metaheuristic algorithm, it was necessary to subdivide the heart into regions in order to obtain a stable solution unsusceptible to the errors, while the analytical DC scheme can be efficiently applied for higher dimensional problems. With the DC method, we also successfully reconstructed the activation pattern and origin of a simulated extrasystole. In addition, the DC algorithm enables iterative adjustment of binary values ensuring robust performance.

Influence of Modeling Errors on the Initial Estimate for Nonlinear Myocardial Activation Times Imaging Calculated With Fastest Route Algorithm

Noninvasive reconstruction of cardiac electrical activity has a great potential to support clinical decision making, planning, and treatment. Recently, significant progress has been made in the estimation of the cardiac activation from body surface potential maps (BSPMs) using boundary element method (BEM) with the equivalent double layer (EDL) as a source model. In this formulation, noninvasive assessment of activation times results in a nonlinear optimization problem with an initial estimate calculated with the fastest route algorithm (FRA). Each FRA-simulated activation sequence is converted into the ECG. The best initialization is determined by the sequence providing the highest correlation between predicted and measured potentials. We quantitatively assess the effects of the forward modeling errors on the FRA-based initialization. We present three simulation setups to investigate the effects of volume conductor model simplifications, neglecting the cardiac anisotropy and geometrical errors on the localization of ectopic beats starting on the ventricular surface. For the analysis, 12-lead ECG and 99 electrodes BSPM system were used. The areas in the heart exposing the largest localization errors were volume conductor model and electrode configuration specific with an average error <;10 mm. The results show the robustness of the FRA-based initialization with respect to the considered modeling errors.

Noninvasive localization of ectopic foci: a new optimization approach for simultaneous reconstruction of transmembrane voltages and epicardial potentials

The goal of ECG imaging is the reconstruction of cardiac electrical activities from the potentials measured on the thorax surface. The tool can gain prominent clinical value for diagnosis and pre-interventional planning. The problem is however ill-posed, i.e. it is highly sensitive to modelling and measurement errors. In order to overcome this obstacle a regularization technique must be applied. In this paper we propose a new optimization based method for simultaneous reconstruction of transmembrane voltages and epicardial potentials for localizing the origin of ventricular ectopic beats. Compared to second-order Tikhonov regularization, the new approach showed superior performance in marking activated regions and provided meaningful results where Tikhonov method failed.

Assessment of the equivalent dipole layer source model in the reconstruction of cardiac activation times on the basis of BSPMs produced by an anisotropic model of the heart

Promising results have been reported in noninvasive estimation of cardiac activation times (AT) using the equivalent dipole layer (EDL) source model in combination with the boundary element method (BEM). However, the assumption of equal anisotropy ratios in the heart that underlies the EDL model does not reflect reality. In the present study, we quantify the errors of the nonlinear AT imaging based on the EDL approximation. Nine different excitation patterns (sinus rhythm and eight ectopic beats) were simulated with the monodomain model. Based on the bidomain theory, the body surface potential maps (BSPMs) were calculated for a realistic finite element volume conductor with an anisotropic heart model. For the forward calculations, three cases of bidomain conductivity tensors in the heart were considered: isotropic, equal, and unequal anisotropy ratios in the intra- and extracellular spaces. In all inverse reconstructions, the EDL model with BEM was employed: AT were estimated by solving the nonlinear optimization problem with the initial guess provided by the fastest route algorithm. Expectedly, the case of unequal anisotropy ratios resulted in larger localization errors for almost all considered activation patterns. For the sinus rhythm, all sites of early activation were correctly estimated with an optimal regularization parameter being used. For the ectopic beats, all but one foci were correctly classified to have either endo- or epicardial origin with an average localization error of 20.4 mm for unequal anisotropy ratio. The obtained results confirm validation studies and suggest that cardiac anisotropy might be neglected in clinical applications of the considered EDL-based inverse procedure.

ECG imaging of ventricular tachycardia: evaluation against simultaneous non-contact mapping and CMR-derived grey zone

Abstract ECG imaging is an emerging technology for the reconstruction of cardiac electric activity from non-invasively measured body surface potential maps. In this case report, we present the first evaluation of transmurally imaged activation times against endocardially reconstructed isochrones for a case of sustained monomorphic ventricular tachycardia (VT). Computer models of the thorax and whole heart were produced from MR images. A recently published approach was applied to facilitate electrode localization in the catheter laboratory, which allows for the acquisition of body surface potential maps while performing non-contact mapping for the reconstruction of local activation times. ECG imaging was then realized using Tikhonov regularization with spatio-temporal smoothing as proposed by Huiskamp and Greensite and further with the spline-based approach by Erem et al. Activation times were computed from transmurally reconstructed transmembrane voltages. The results showed good qualitative agreement between the non-invasively and invasively reconstructed activation times. Also, low amplitudes in the imaged transmembrane voltages were found to correlate with volumes of scar and grey zone in delayed gadolinium enhancement cardiac MR. The study underlines the ability of ECG imaging to produce activation times of ventricular electric activity—and to represent effects of scar tissue in the imaged transmembrane voltages.

Magnetocardiography did not uncover electrically silent ischemia in an in-silico study case

Over the last decades, the information content derived from cardiac electric and magnetic field measurements has been debated. Our co-workers Wilhelms et al. investigated electrically silent acute ischemia in human ventricles caused by occlusion of a coronary artery. In the present work, we extend the previous study by calculating associated magnetic fields produced by early stage acute ischemia with varying transmural extent. Multiscale computational simulations were performed for calculations of body surface potential maps (BSPM) and magnetocardiograms (MCG) on a magnetometer sensor matrix situated above the anterior chest wall. Depending on the ischemia size, the ST-segments of the simulated electrocardiograms (ECG) experienced depression for subendocardial cases and elevation for transmural ischemia. One intermediate extent resulted in a zero ST-segment which makes it diagnostically indistinguishable from the healthy case. Magnetic field calculations for this electrically silent ischemia also revealed no difference compared to the control case. Otherwise, both ECG and MCG signals during ST-segments showed either depression or elevation from zero line. In this simulation study, MCG did not deliver additional information to uncover electrically silent ischemia. For a general conclusion, further in-silico investigations with different ischemia shapes, sizes and positions should be performed and clinical studies with recordings of both ECG and MCG signals have to be conducted.

Automatic camera-based identification and 3-D reconstruction of electrode positions in electrocardiographic imaging.

Abstract Electrocardiographic imaging (ECG imaging) is a method to depict electrophysiological processes in the heart. It is an emerging technology with the potential of making the therapy of cardiac arrhythmia less invasive, less expensive, and more precise. A major challenge for integrating the method into clinical workflow is the seamless and correct identification and localization of electrodes on the thorax and their assignment to recorded channels. This work proposes a camera-based system, which can localize all electrode positions at once and to an accuracy of approximately 1±1 mm. A system for automatic identification of individual electrodes is implemented that overcomes the need of manual annotation. For this purpose, a system of markers is suggested, which facilitates a precise localization to subpixel accuracy and robust identification using an error-correcting code. The accuracy of the presented system in identifying and localizing electrodes is validated in a phantom study. Its overall capability is demonstrated in a clinical scenario.

Use of a Tolerance Operator in Wavefront-Based ECG Imaging of Transmembrane Voltages

Techniques for the non-invasive imaging of transmembrane voltages (TMVs) throughout the myocardial wall would be of great value for the identification and management of cardiac diseases. Related diagnostic techniques could pave the road for breakthroughs in pre-interventional treatment planning.

ECGI in atrial fibrillation: A clinician's wish list

Have we a challenge of credibility in the invasive treatment of atrial fibrillation (AFIB)? The incidence of AFIB in the European Union (EU) is about 600,000 cases per year, while only 100,000 get an invasive treatment with a failure rate of close to 40%. Those that remain in AFIB need two times more hospitalizations and three times more re-hospitalizations. AFIB accounts for over 1% of the EU health care costs. Too many patients are not referred and the indication rates of cardiac ablation are inexplicably variable throughout the EU. A reflection is made on how electrocardiographic imaging (ECGI) can contribute to bringing the therapy to an advanced level by achieving a higher success rate, efficiently increasing access to ablation therapies, a better patient selection and therapy planning, personalization and follow up.

Modelling of patient-specific Purkinje activation based on measured ECGs

Abstract The Purkinje system is part of the fast-conducting ventricular excitation system. The anatomy of the Purkinje system varies from person to person and imposes a unique excitation pattern on the ventricular myocardium, which defines the morphology of the QRS complex of the ECG to a large degree. While it cannot be imaged in-vivo, it plays an important role for personalizing computer simulations of cardiac electrophysiology. Here, we present a new method to automatically model and customize the Purkinje system based on the measured electrocardiogram (ECG) of a patient. A graphbased algorithm was developed to generate Purkinje systems based on the parameters fibre density, minimal distance from the atrium, conduction velocity, and position and timing of excitation sources mimicking the bundle branches. Based on the resulting stimulation profile, the activation times of the ventricles were calculated using the fast marching approach. Predescribed action potentials and a finite element lead field matrix were employed to obtain surface ECG signals. The root mean square error (RMSE) between the simulated and measured QRS complexes of the ECGs was used as cost function to perform optimization of the Purkinje parameters. One complete evaluation from Purkinje tree generation to the simulated ECG could be computed in about 10 seconds on a standard desktop computer. The measured ECG of the patient used to build the anatomical model was matched via parallel simplex optimization with a remaining RMSE of 4.05 mV in about 16 hours. The approach presented here allows to tailor the structure of the Purkinje system through the measured ECG in a patient-specific way. The computationally efficient implementation facilitates global optimization.