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

Contains fulltext : 191955.pdf (Publisher’s version ) (Open Access

Functional Mapping of Three-Dimensional Electrical Activation in Ventricles

University of Minnesota Ph.D. dissertation. 2010. Major: Biomedical Engineering. Advisor: Bin He. 1 computer file (PDF); 139 pages.Ventricular arrhythmias account for nearly 400,000 deaths per year in the United States alone. Electrical mapping of the ventricular activation could facilitate the diagnosis and treatment of arrhythmias, e.g. guiding catheter ablation. To date, both direct mapping and non-contact mapping techniques have been routinely used in electrophysiology labs for obtaining the electrical activity on the endocardial surface. Non-invasive functional mapping methods are also developed to estimate the electrical activity on the epicardium or on both epicardium and endocardium from the body surface measurements. Though successful, the results using above methods are all limited on the surface of the heart and thus cannot directly characterize the cardiac events originating within the myocardial wall. Our group's goal is to develop a functional mapping method to estimate the three-dimensional cardiac electrical activity from either non-invasive body surface potential maps or minimally-invasive intracavitary potential maps, by solving the so-called "inverse problem". Hence the information under the surface of the heart could be revealed to better characterize the cardiac activation. In the present thesis study, the previously developed three-dimensional cardiac electrical imaging (3DCEI) approach has been further investigated. Its function is expanded for not only estimating the global activation sequence but also reconstructing the potential at any myocardial site throughout the ventricle. New algorithms under the 3DCEI scheme are also explored for more powerful mapping capability. The performance of the enhanced 3DCEI approach is rigorously evaluated in both control and diseased swine models when the clinical settings are mimicked. The promising results validate the feasibility of estimating detailed three-dimensional cardiac activation by using the 3DCEI approach, and suggest that 3DCEI has great potential of guiding the clinical management of cardiac arrhythmias in a more efficient way

In silico validation of electrocardiographic imaging to reconstruct the endocardial and epicardial repolarization pattern using the equivalent dipole layer source model

The solution of the inverse problem of electrocardiology allows the reconstruction of the spatial distribution of the electrical activity of the heart from the body surface electrocardiogram (electrocardiographic imaging, ECGI). ECGI using the equivalent dipole layer (EDL) model has shown to be accurate for cardiac activation times. However, validation of this method to determine repolarization times is lacking. In the present study, we determined the accuracy of the EDL model in reconstructing cardiac repolarization times, and assessed the robustness of the method under less ideal conditions (addition of noise and errors in tissue conductivity). A monodomain model was used to determine the transmembrane potentials in three different excitationrepolarization patterns (sinus beat and ventricular ectopic beats) as the gold standard. These were used to calculate the body surface ECGs using a finite element model. The resulting body surface electrograms (ECGs) were used as input for the EDLbased inverse reconstruction of repolarization times. The reconstructed repolarization times correlated well (COR > 0.85) with the gold standard, with almost no decrease in correlation after adding errors in tissue conductivity of the model or noise to the body surface ECG. Therefore, ECGI using the EDL model allows adequate reconstruction of cardiac repolarization times

Non-invasive estimation of QLV from the standard 12-lead ECG in patients with left bundle branch block

Background: Cardiac resynchronization therapy (CRT) is a treatment for patients with heart failure and electrical dyssynchrony, i.e., left bundle branch block (LBBB) ECG pattern. CRT resynchronizes ventricular contraction with a right ventricle (RV) and a left ventricle (LV) pacemaker lead. Positioning the LV lead in the latest electrically activated region (measured from Q wave onset in the ECG to LV sensing by the left pacemaker electrode [QLV]) is associated with favorable outcome. However, optimal LV lead placement is limited by coronary venous anatomy and the inability to measure QLV non-invasively before implantation. We propose a novel non-invasive method for estimating QLV in sinus-rhythm from the standard 12-lead ECG. Methods: We obtained 12-lead ECG, LV electrograms and LV lead position in a standard LV 17-segment model from procedural recordings from 135 standard CRT recipients. QLV duration was measured post-operatively. Using a generic heart geometry and corresponding forward model for ECG computation, the electrical activation pattern of the heart was fitted to best match the 12-lead ECG in an iterative optimization procedure. This procedure initialized six activation sites associated with the His-Purkinje system. The initial timing of each site was based on the directions of the vectorcardiogram (VCG). Timing and position of the sites were then changed iteratively to improve the match between simulated and measured ECG. Noninvasive estimation of QLV was done by calculating the time difference between Q-onset on the computed ECG and the activation time corresponding to centroidal epicardial activation time of the segment where the LV electrode is positioned. The estimated QLV was compared to the measured QLV. Further, the distance between the actual LV position and the estimated LV position was computed from the generic ventricular model. Results: On average there was no difference between QLV measured from procedural recordings and non-invasive estimation of QLV ( [Formula: see text] ). Median distance between actual LV pacing site and the estimated pacing site was 18.6 mm (IQR 17.3 mm). Conclusion: Using the standard 12-lead ECG and a generic heart model it is possible to accurately estimate QLV. This method may potentially be used to support patient selection, optimize implant procedures, and to simulate optimal stimulation parameters prior to pacemaker implantation

Noninvasive mapping of repolarization:Validation in healthy and diseased hearts

The initiation and maintenance of (reentrant) arrhythmias is facilitated by local heterogeneities in cardiac activation and repolarization. Detection of these heterogeneities by cardiac mapping is important for guiding local therapy and for early risk stratification of patients, and is presently mostly performed by invasive techniques. A non-invasive method for localization of functional heterogeneities may help the treatment of patients with life threatening ventricular arrhythmias, may support risk stratification and may help to reduce mortality caused by these arrhythmias. This thesis investigates a non-invasive method to determine and localize functional repolarization heterogeneities based on potentials measured at the body surface. It demonstrates that parameters that highlight multiple repolarization moments in the standard 12-lead ECG, better characterize the underlying repolarization gradient than the single time point of latest global repolarization (QTtime). For further localization of possible heterogeneities, this thesis uses the equivalent dipole layer (EDL) method for the solution of the inverse problem of electrocardiography; the mathematical reconstruction of cardiac electrical activity from body surface electrograms and a geometric model of the torso. The accuracy was investigated in in-silico, ex-vivo, and in-vivo settings, showing good correlations with gold standard repolarization times, even in the presence of noise, abnormal repolarization or myocardial infarction. In addition, comparison of the EDL method with the more commonly used epicardial potential (EP) method shows that both methods provide accurate reconstruction of cardiac activation and repolarization patterns and beat origins, with the EDL method showing a better correlation for activation timings and beat origins than the EP method. Although the use of this technique for noninvasive mapping of repolarization is promising, we provide directions for future research to improve accuracy of inverse reconstruction

Three-dimensional Multiscale Modelling and Simulation of Atria and Torso Electrophysiology

A better understanding of the electrical activity of the heart under physiological and pathological conditions has always been key for clinicians and researchers. Over the last years, the information in the P-wave signals has been extensively analysed to un-cover the mechanisms underlying atrial arrhythmias by localizing ectopic foci or high-frequency rotors. However, the relationship between the activation of the different areas of the atria and the characteristics of the P-wave signals or body surface poten-tial maps are still far from being completely understood. Multiscale anatomical and functional models of the heart are a new technological framework that can enable the investigation of the heart as a complex system. This thesis is centred in the construction of a multiscale framework that allows the realistic simulation of atrial and torso electrophysiology and integrates all the anatom-ical and functional descriptions described in the literature. The construction of such model involves the development of heterogeneous cellular and tissue electrophysiolo-gy models fitted to empirical data. It also requires an accurate 3D representation of the atrial anatomy, including tissue fibre arrangement, and preferential conduction axes. This multiscale model aims to reproduce faithfully the activation of the atria under physiological and pathological conditions. We use the model for two main applica-tions. First, to study the relationship between atrial activation and surface signals in sinus rhythm. This study should reveal the best places for recording P-waves signals in the torso, and which are the regions of the atria that make the most significant contri-bution to the body surface potential maps and determine the main P-wave characteris-tics. Second, to spatially cluster and classify ectopic atrial foci into clearly differenti-ated atrial regions by using the body surface P-wave integral map (BSPiM) as a bi-omarker. We develop a machine-learning pipeline trained from simulations obtained from the atria-torso model aiming to validate whether ectopic foci with similar BSPiM naturally cluster into differentiated non-intersected atrial regions, and whether new BSPiM could be correctly classified with high accuracy.En la actualidad, una mejor compresión de la actividad eléctrica del corazón en condi-ciones fisiológicas y patológicas es clave para médicos e investigadores. A lo largo de los últimos años, la información derivada de la onda P se ha utilizado para intentar descubrir los mecanismos subyacentes a las arritmias auriculares mediante la localiza-ción de focos ectópicos y rotores de alta frecuencia. Sin embargo, la relación entre la activación de distintas regiones auriculares y las características tanto de las ondas P como de la distribución de potencial en la superficie del torso está lejos de entenderse completamente. Los modelos cardíacos funcionales y anatómicos son una nueva he-rramienta que puede facilitar la investigación relativa al corazón entendido como sis-tema complejo. La presente tesis se centra en la construcción de un modelo multiescala para la simula-ción realista de la electrofisiología cardíaca tanto a nivel auricular como de torso, integrando toda la información anatómica y funcional disponible en la literatura. La construcción de este modelo implica el desarrollo, en base a datos experimentales, de modelos electrofisiológicos heterogéneos tanto celulares como tisulares. Así mismo, es imprescindible una representación tridimensional precisa de la anatomía auricular, incluyendo la dirección de fibras y los haces de conducción preferentes. Este modelo multiescala busca reproducir fielmente la activación auricular en condiciones fisiológi-cas y patológicas. Su uso se ha centrado fundamentalmente en dos aplicaciones. En primer lugar, estudiar la relación entre la activación auricular en ritmo sinusal y las señales en la superficie del torso. Este estudio busca definir la mejor ubicación para el registro de las ondas P en el torso así como determinar aquellas regiones auriculares que contribuyen fundamentalmente a la formación y distribución de potenciales super-ficiales así como a las características de las ondas P. En segundo lugar, agrupar y cla-sificar espacialmente los focos ectópicos en regiones auriculares claramente diferen-ciables empleando como biomarcador los mapas superficiales de integral de la onda P (BSPiM). Se ha desarrollado para ello una metodología de aprendizaje automático en la que las simulaciones obtenidas con el modelo multiescala aurícula-torso sirven de entrenamiento, permitiendo validar si los focos ectópicos cuyos BSPiMs son similares se agrupan de forma natural en regiones auriculares no intersectadas y si BSPiMs nue-vos podrían ser clasificados prospectivamente con gran precisión.Avui en dia, una millor comprenssió de l'activitat elèctrica del cor en condicions fisio-lògiques i patològiques és clau per a metges i investigadors. Al llarg dels últims anys, la informació derivada de l'ona P s'ha utilitzat per intentar descobrir els mecanismes subjacents a les arítmies auriculars mitjançant la localització de focus ectòpics i rotors d'alta freqüència. No obstant això, la relació entre l'activació de diferents regions auri-culars i les característiques tant de les ones P com de la distribució de potencial en la superfície del tors està lluny d'entendre's completament. Els models cardíacs funcionals i anatòmics són una nova eina que pot facilitar la recerca relativa al cor entès com a sistema complex. La present tesi es centra en la construcció d'un model multiescala per a la simulació realista de la electrofisiologia cardíaca tant a nivell auricular com de tors, integrant tota la informació anatòmica i funcional disponible en la literatura. La construcció d'aquest model implica el desenvolupament, sobre la base de dades experimentals, de models electrofisiològics heterogenis, tant cel·lulars com tissulars. Així mateix, és imprescindible una representació tridimensional precisa de l'anatomia auricular, in-cloent la direcció de fibres i els feixos de conducció preferents. Aquest model multies-cala busca reproduir fidelment l'activació auricular en condicions fisiològiques i pa-tològiques. El seu ús s'ha centrat fonamentalment en dues aplicacions. En primer lloc, estudiar la relació entre l'activació auricular en ritme sinusal i els senyals en la superfí-cie del tors. A més a més, amb aquest estudi també es busca definir la millor ubicació per al registre de les ones P en el tors, així com, determinar aquelles regions auriculars que contribueixen fonamentalment a la formació i distribució de potencials superfi-cials a l'hora que es caracteritzen les ones P. En segon lloc, agrupar i classificar espa-cialment els focus ectòpics en regions auriculars clarament diferenciables emprant com a biomarcador els mapes superficials d'integral de l'ona P (BSPiM). És per això que s'ha desenvolupat una metodologia d'aprenentatge automàtic en la qual les simulacions obtingudes amb el model multiescala aurícula-tors serveixen d'entrenament, la qual cosa permet validar si els focus ectòpics, llurs BSPiMs són similars, s'agrupen de for-ma natural en regions auriculars no intersectades i si BSPiMs nous podrien ser classifi-cats de manera prospectiva amb precisió.Ferrer Albero, A. (2017). Three-dimensional Multiscale Modelling and Simulation of Atria and Torso Electrophysiology [Tesis doctoral no publicada]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/88402TESI

Theory, modelling and applications of electrocardiographic mapping

In this thesis, the genesis and applications of electromagnetic signals from the human heart are investigated through theory, modelling, signal processing and clinical studies. One objective of the thesis was to develop and test signal processing methods that would be applicable to multichannel electro- and magnetocardiographic data. A signal processing method based on a type of neural networks called the self-organizing maps is introduced for spatiotemporal analysis of the body surface potential maps produced by the beating heart. This method is capable of utilizing both the spatial morphology of the potential distributions on the body surface as well as their temporal development. A signal processing method aimed at providing a reliable electric baseline for more traditional isointegral analysis of the body surface potential mapping (BSPM) data is also introduced. Another objective of the thesis was to show the utility of electrocardiographic mapping in clinical use. This was demonstrated by applying electro- and magnetocardiographic mapping to evaluation of the propensity to life-threatening arrhythmias in postinfarction patients. Electrocardiographic mapping was found to perform equally well compared to more traditional SA-ECG, but electrocardiographic mapping may be more robust against individual variability in anatomy. A third objective of the thesis was to build a computer model of the human heart that is capable of simulating the normal ventricular activation. The propagation model is based on a bidomain formulation of the cardiac tissue applied to realistic geometry of the ventricles. An anatomically accurate model of the human conduction system that reproduces measured activation sequence of the human heart was developed in this thesis. The body surface potentials and the magnetic fields computed from the simulated activation corresponded to recordings from normal subjects. In summary, the thesis demonstrates the utility of electrocardiographic mapping in clinical use and introduces new signal processing methods that can be applied to this use. Finally, a computer model of the human heart binds together the physiology and anatomy of the human heart and body, classical electromagnetic theory, and computer science to explain the genesis and characteristics of the electromagnetic signals from the human heart.reviewe

Multiscale Modeling of the Ventricles: From Cellular Electrophysiology to Body Surface Electrocardiograms

This work is focused on different aspects within the loop of multiscale modeling: On the cellular level, effects of adrenergic regulation and the Long-QT syndrome have been investigated. On the organ level, a model for the excitation conduction system was developed and the role of electrophysiological heterogeneities was analyzed. On the torso level a dynamic model of a deforming heart was created and the effects of tissue conductivities on the solution of the forward problem were evaluated

Validation and Opportunities of Electrocardiographic Imaging: From Technical chievements to Clinical Applications

[EN] Electrocardiographic imaging (ECGI) reconstructs the electrical activity of the heart from a dense array of body-surface electrocardiograms and a patient-specific heart-torso geometry. Depending on how it is formulated, ECGI allows the reconstruction of the activation and recovery sequence of the heart, the origin of premature beats or tachycardia, the anchors/hotspots of re-entrant arrhythmias and other electrophysiological quantities of interest. Importantly, these quantities are directly and non-invasively reconstructed in a digitized model of the patient's three-dimensional heart, which has led to clinical interest in ECGI's ability to personalize diagnosis and guide therapy. Despite considerable development over the last decades, validation of ECGI is challenging. Firstly, results depend considerably on implementation choices, which are necessary to deal with ECGI's ill-posed character. Secondly, it is challenging to obtain (invasive) ground truth data of high quality. In this review, we discuss the current status of ECGI validation as well as the major challenges remaining for complete adoption of ECGI in clinical practice. Specifically, showing clinical benefit is essential for the adoption of ECGI. Such benefit may lie in patient outcome improvement, workflow improvement, or cost reduction. Future studies should focus on these aspects to achieve broad adoption of ECGI, but only after the technical challenges have been solved for that specific application/pathology. We propose 'best' practices for technical validation and highlight collaborative efforts recently organized in this field. Continued interaction between engineers, basic scientists, and physicians remains essential to find a hybrid between technical achievements, pathological mechanisms insights, and clinical benefit, to evolve this powerful technique toward a useful role in clinical practice.This study received financial support from the Hein Wellens Fonds, the Cardiovascular Research and Training Institute (CVRTI), the Nora Eccles Treadwell Foundation, the National Institute of General Medical Sciences of the National Institutes of Health (P41GM103545), the National Institutes of Health (NIH HL080093), the French government as part of the Investments of the Future program managed by the National Research Agency (ANR-10-IAHU-04), from the VEGA Grant Agency in Slovakia (2/0071/16), from the Slovak Research and Development Agency (APVV-14-0875), the Fondo Europeo de Desarrollo Regional (FEDER), the Instituto de Salud Carlos III (PI17/01106) and from Conselleria d'Educacio, Investigacio, Cultura i Esport de la Generalitat Valenciana (AICO/2018/267) and NIH grant (HL125998) and National Science Foundation (ACI-1350374).Cluitmans, M.; Brooks, D.; Macleod, RS.; Dossel, O.; Guillem Sánchez, MS.; Van Dam, P.; Svehlikova, J.... (2018). Validation and Opportunities of Electrocardiographic Imaging: From Technical chievements to Clinical Applications. Frontiers in Physiology. 9. https://doi.org/10.3389/fphys.2018.01305S9Andrews, C. M., Srinivasan, N. T., Rosmini, S., Bulluck, H., Orini, M., Jenkins, S., … Rudy, Y. (2017). Electrical and Structural Substrate of Arrhythmogenic Right Ventricular Cardiomyopathy Determined Using Noninvasive Electrocardiographic Imaging and Late Gadolinium Magnetic Resonance Imaging. Circulation: Arrhythmia and Electrophysiology, 10(7). doi:10.1161/circep.116.005105Aras, K., Good, W., Tate, J., Burton, B., Brooks, D., Coll-Font, J., … MacLeod, R. (2015). Experimental Data and Geometric Analysis Repository—EDGAR. Journal of Electrocardiology, 48(6), 975-981. doi:10.1016/j.jelectrocard.2015.08.008Austen, W., Edwards, J., Frye, R., Gensini, G., Gott, V., Griffith, L., … Roe, B. (1975). A reporting system on patients evaluated for coronary artery disease. Report of the Ad Hoc Committee for Grading of Coronary Artery Disease, Council on Cardiovascular Surgery, American Heart Association. Circulation, 51(4), 5-40. doi:10.1161/01.cir.51.4.5Bayley, R. H., & Berry, P. M. (1962). The electrical field produced by the eccentric current dipole in the nonhomogeneous conductor. American Heart Journal, 63(6), 808-820. doi:10.1016/0002-8703(62)90065-0Bear, L. R., Huntjens, P. R., Walton, R. D., Bernus, O., Coronel, R., & Dubois, R. (2018). Cardiac electrical dyssynchrony is accurately detected by noninvasive electrocardiographic imaging. Heart Rhythm, 15(7), 1058-1069. doi:10.1016/j.hrthm.2018.02.024Bear, L. R., LeGrice, I. J., Sands, G. B., Lever, N. A., Loiselle, D. S., Paterson, D. J., … Smaill, B. H. (2018). How Accurate Is Inverse Electrocardiographic Mapping? Circulation: Arrhythmia and Electrophysiology, 11(5). doi:10.1161/circep.117.006108Berger, T., Fischer, G., Pfeifer, B., Modre, R., Hanser, F., Trieb, T., … Hintringer, F. (2006). Single-Beat Noninvasive Imaging of Cardiac Electrophysiology of Ventricular Pre-Excitation. Journal of the American College of Cardiology, 48(10), 2045-2052. doi:10.1016/j.jacc.2006.08.019Berger, T., Pfeifer, B., Hanser, F. F., Hintringer, F., Fischer, G., Netzer, M., … Seger, M. (2011). Single-Beat Noninvasive Imaging of Ventricular Endocardial and Epicardial Activation in Patients Undergoing CRT. PLoS ONE, 6(1), e16255. doi:10.1371/journal.pone.0016255Dubois, R., Pashaei, A., Duchateau, J., & Vigmond, E. (2016). Evaluation of Combined Noninvasive Electrocardiographic Imaging and Phase Mapping approach for Atrial Fibrillation: A Simulation Study. 2016 Computing in Cardiology Conference (CinC). doi:10.22489/cinc.2016.037-540Duchateau, J., Potse, M., & Dubois, R. (2017). Spatially Coherent Activation Maps for Electrocardiographic Imaging. IEEE Transactions on Biomedical Engineering, 64(5), 1149-1156. doi:10.1109/tbme.2016.2593003Erem, B., Brooks, D. H., van Dam, P. M., Stinstra, J. G., & MacLeod, R. S. (2011). Spatiotemporal estimation of activation times of fractionated ECGs on complex heart surfaces. 2011 Annual International Conference of the IEEE Engineering in Medicine and Biology Society. doi:10.1109/iembs.2011.6091455Erem, B., van Dam, P. M., & Brooks, D. H. (2014). Identifying Model Inaccuracies and Solution Uncertainties in Noninvasive Activation-Based Imaging of Cardiac Excitation Using Convex Relaxation. IEEE Transactions on Medical Imaging, 33(4), 902-912. doi:10.1109/tmi.2014.2297952Erkapic, D., & Neumann, T. (2015). Ablation of Premature Ventricular Complexes Exclusively Guided by Three-Dimensional Noninvasive Mapping. Cardiac Electrophysiology Clinics, 7(1), 109-115. doi:10.1016/j.ccep.2014.11.010Everett, T. H., Lai-Chow Kok, Vaughn, R. H., Moorman, R., & Haines, D. E. (2001). Frequency domain algorithm for quantifying atrial fibrillation organization to increase defibrillation efficacy. IEEE Transactions on Biomedical Engineering, 48(9), 969-978. doi:10.1109/10.942586Faes, L., & Ravelli, F. (2007). A morphology-based approach to the evaluation of atrial fibrillation organization. IEEE Engineering in Medicine and Biology Magazine, 26(4), 59-67. doi:10.1109/memb.2007.384097Fitzpatrick, A. P., Gonzales, R. P., Lesh, M. D., odin, G. W., Lee, R. J., & Scheinman, M. M. (1994). New algorithm for the localization of accessory atrioventricular connections using a baseline electrocardiogram. Journal of the American College of Cardiology, 23(1), 107-116. doi:10.1016/0735-1097(94)90508-8Geselowitz, D. B. (1989). On the theory of the electrocardiogram. Proceedings of the IEEE, 77(6), 857-876. doi:10.1109/5.29327Geselowitz, D. B. (1992). Description of cardiac sources in anisotropic cardiac muscle. Journal of Electrocardiology, 25, 65-67. doi:10.1016/0022-0736(92)90063-6Ghanem, R. N., Jia, P., Ramanathan, C., Ryu, K., Markowitz, A., & Rudy, Y. (2005). Noninvasive Electrocardiographic Imaging (ECGI): Comparison to intraoperative mapping in patients. Heart Rhythm, 2(4), 339-354. doi:10.1016/j.hrthm.2004.12.022Ghosh, S., Rhee, E. K., Avari, J. N., Woodard, P. K., & Rudy, Y. (2008). Cardiac Memory in Patients With Wolff-Parkinson-White Syndrome. Circulation, 118(9), 907-915. doi:10.1161/circulationaha.108.781658Ghosh, S., Silva, J. N. A., Canham, R. M., Bowman, T. M., Zhang, J., Rhee, E. K., … Rudy, Y. (2011). Electrophysiologic substrate and intraventricular left ventricular dyssynchrony in nonischemic heart failure patients undergoing cardiac resynchronization therapy. Heart Rhythm, 8(5), 692-699. doi:10.1016/j.hrthm.2011.01.017Grace, A., Verma, A., & Willems, S. (2017). Dipole Density Mapping of Atrial Fibrillation. European Heart Journal, 38(1), 5-9. doi:10.1093/eurheartj/ehw585Dorset, D. L. (1996). Electron crystallography. Acta Crystallographica Section B Structural Science, 52(5), 753-769. doi:10.1107/s0108768196005599Haissaguerre, M., Hocini, M., Denis, A., Shah, A. J., Komatsu, Y., Yamashita, S., … Dubois, R. (2014). Driver Domains in Persistent Atrial Fibrillation. Circulation, 130(7), 530-538. doi:10.1161/circulationaha.113.005421HAISSAGUERRE, M., HOCINI, M., SHAH, A. J., DERVAL, N., SACHER, F., JAIS, P., & DUBOIS, R. (2013). Noninvasive Panoramic Mapping of Human Atrial Fibrillation Mechanisms: A Feasibility Report. Journal of Cardiovascular Electrophysiology, 24(6), 711-717. doi:10.1111/jce.12075Han, C., Pogwizd, S. M., Killingsworth, C. R., & He, B. (2011). Noninvasive imaging of three-dimensional cardiac activation sequence during pacing and ventricular tachycardia. Heart Rhythm, 8(8), 1266-1272. doi:10.1016/j.hrthm.2011.03.014Bin He, Guanglin Li, & Xin Zhang. (2003). Noninvasive imaging of cardiac transmembrane potentials within three-dimensional myocardium by means of a realistic geometry anisotropic heart model. IEEE Transactions on Biomedical Engineering, 50(10), 1190-1202. doi:10.1109/tbme.2003.817637Bin He, & Dongsheng Wu. (2001). Imaging and visualization of 3-D cardiac electric activity. IEEE Transactions on Information Technology in Biomedicine, 5(3), 181-186. doi:10.1109/4233.945288Horáček, B. M., Sapp, J. L., Penney, C. J., Warren, J. W., & Wang, J. J. (2011). Comparison of epicardial potential maps derived from the 12-lead electrocardiograms with scintigraphic images during controlled myocardial ischemia. Journal of Electrocardiology, 44(6), 707-712. doi:10.1016/j.jelectrocard.2011.08.009Horáček, B. M., Wang, L., Dawoud, F., Xu, J., & Sapp, J. L. (2015). Noninvasive electrocardiographic imaging of chronic myocardial infarct scar. Journal of Electrocardiology, 48(6), 952-958. doi:10.1016/j.jelectrocard.2015.08.035Jamil-Copley, S., Vergara, P., Carbucicchio, C., Linton, N., Koa-Wing, M., Luther, V., … Kanagaratnam, P. (2015). Application of Ripple Mapping to Visualize Slow Conduction Channels Within the Infarct-Related Left Ventricular Scar. Circulation: Arrhythmia and Electrophysiology, 8(1), 76-86. doi:10.1161/circep.114.001827Janssen, A. M., Potyagaylo, D., Dössel, O., & Oostendorp, T. F. (2017). 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. Medical & Biological Engineering & Computing, 56(6), 1013-1025. doi:10.1007/s11517-017-1715-xKnecht, S., Sohal, M., Deisenhofer, I., Albenque, J.-P., Arentz, T., Neumann, T., … Rostock, T. (2017). Multicentre evaluation of non-invasive biatrial mapping for persistent atrial fibrillation ablation: the AFACART study. EP Europace, 19(8), 1302-1309. doi:10.1093/europace/euw168Kuck, K.-H., Schaumann, A., Eckardt, L., Willems, S., Ventura, R., Delacrétaz, E., … Hansen, P. S. (2010). Catheter ablation of stable ventricular tachycardia before defibrillator implantation in patients with coronary heart disease (VTACH): a multicentre randomised controlled trial. The Lancet, 375(9708), 31-40. doi:10.1016/s0140-6736(09)61755-4Identification of Rotors during Human Atrial Fibrillation Using Contact Mapping and Phase Singularity Detection: Technical Considerations. (2017). IEEE Transactions on Biomedical Engineering, 64(2), 310-318. doi:10.1109/tbme.2016.2554660Leong, K. M. W., Ng, F. S., Yao, C., Roney, C., Taraborrelli, P., Linton, N. W. F., … Varnava, A. M. (2017). ST-Elevation Magnitude Correlates With Right Ventricular Outflow Tract Conduction Delay in Type I Brugada ECG. Circulation: Arrhythmia and Electrophysiology, 10(10). doi:10.1161/circep.117.005107Chenguang Liu, Eggen, M. D., Swingen, C. M., Iaizzo, P. A., & Bin He. (2012). Noninvasive Mapping of Transmural Potentials During Activation in Swine Hearts From Body Surface Electrocardiograms. IEEE Transactions on Medical Imaging, 31(9), 1777-1785. doi:10.1109/tmi.2012.2202914MacLeod, R. S., Ni, Q., Punske, B., Ershler, P. R., Yilmaz, B., & Taccardi, B. (2000). Effects of heart position on the body-surface electrocardiogram. Journal of Electrocardiology, 33, 229-237. doi:10.1054/jelc.2000.20357Metzner, A., Wissner, E., Tsyganov, A., Kalinin, V., Schlüter, M., Lemes, C., … Kuck, K.-H. (2017). Noninvasive phase mapping of persistent atrial fibrillation in humans: Comparison with invasive catheter mapping. Annals of Noninvasive Electrocardiology, 23(4), e12527. doi:10.1111/anec.12527Modre, R., Tilg, B., Fischer, G., Hanser, F., Messnarz, B., Seger, M., … Roithinger, F. X. (2003). Atrial Noninvasive Activation Mapping of Paced Rhythm Data. Journal of Cardiovascular Electrophysiology, 14(7), 712-719. doi:10.1046/j.1540-8167.2003.02558.xNarayan, S. M., Krummen, D. E., Shivkumar, K., Clopton, P., Rappel, W.-J., & Miller, J. M. (2012). Treatment of Atrial Fibrillation by the Ablation of Localized Sources. Journal of the American College of Cardiology, 60(7), 628-636. doi:10.1016/j.jacc.2012.05.022NG, J., KADISH, A. H., & GOLDBERGER, J. J. (2007). Technical Considerations for Dominant Frequency Analysis. Journal of Cardiovascular Electrophysiology, 18(7), 757-764. doi:10.1111/j.1540-8167.2007.00810.xOosterhoff, P., Meijborg, V. M. F., van Dam, P. M., van Dessel, P. F. H. M., Belterman, C. N. W., Streekstra, G. J., … Oostendorp, T. F. (2016). Experimental Validation of Noninvasive Epicardial and Endocardial Activation Imaging. Circulation: Arrhythmia and Electrophysiology, 9(8). doi:10.1161/circep.116.004104Oster, H. S., Taccardi, B., Lux, R. L., Ershler, P. R., & Rudy, Y. (1997). Noninvasive Electrocardiographic Imaging. Circulation, 96(3), 1012-1024. doi:10.1161/01.cir.96.3.1012Oster, H. S., Taccardi, B., Lux, R. L., Ershler, P. R., & Rudy, Y. (1998). Electrocardiographic Imaging. Circulation, 97(15), 1496-1507. doi:10.1161/01.cir.97.15.1496PEDRÓN-TORRECILLA, J., RODRIGO, M., CLIMENT, A. M., LIBEROS, A., PÉREZ-DAVID, E., BERMEJO, J., … GUILLEM, M. S. (2016). Noninvasive Estimation of Epicardial Dominant High-Frequency Regions During Atrial Fibrillation. Journal of Cardiovascular Electrophysiology, 27(4), 435-442. doi:10.1111/jce.12931Ploux, S., Lumens, J., Whinnett, Z., Montaudon, M., Strom, M., Ramanathan, C., … Bordachar, P. (2013). Noninvasive Electrocardiographic Mapping to Improve Patient Selection for Cardiac Resynchronization Therapy. Journal of the American College of Cardiology, 61(24), 2435-2443. doi:10.1016/j.jacc.2013.01.093Potyagaylo, D., Segel, M., Schulze, W. H. W., & Dössel, O. (2013). Noninvasive Localization of Ectopic Foci: A New Optimization Approach for Simultaneous Reconstruction of Transmembrane Voltages and Epicardial Potentials. Lecture Notes in Computer Science, 166-173. doi:10.1007/978-3-642-38899-6_20Punshchykova, O., Švehlíková, J., Tyšler, M., Grünes, R., Sedova, K., Osmančík, P., … Kneppo, P. (2016). Influence of Torso Model Complexity on the Noninvasive Localization of Ectopic Ventricular Activity. Measurement Science Review, 16(2), 96-102. doi:10.1515/msr-2016-0013RAMANATHAN, C., & RUDY, Y. (2001). Electrocardiographic Imaging: II. Effect of Torso Inhomogeneities on Noninvasive Reconstruction of Epicardial Potentials, Electrograms, and Isochrones. Journal of Cardiovascular Electrophysiology, 12(2), 241-252. doi:10.1046/j.1540-8167.2001.00241.xReddy, V. Y., Reynolds, M. R., Neuzil, P., Richardson, A. W., Taborsky, M., Jongnarangsin, K., … Josephson, M. E. (2007). Prophylactic Catheter Ablation for the Prevention of Defibrillator Therapy. New England Journal of Medicine, 357(26), 2657-2665. doi:10.1056/nejmoa065457Rodrigo, M., Climent, A. M., Liberos, A., Fernández-Avilés, F., Berenfeld, O., Atienza, F., & Guillem, M. S. (2017). Technical Considerations on Phase Mapping for Identification of Atrial Reentrant Activity in Direct- and Inverse-Computed Electrograms. Circulation: Arrhythmia and Electrophysiology, 10(9). doi:10.1161/circep.117.005008ROTEN, L., PEDERSEN, M., PASCALE, P., SHAH, A., ELIAUTOU, S., SCHERR, D., … HAÏSSAGUERRE, M. (2012). Noninvasive Electrocardiographic Mapping for Prediction of Tachycardia Mechanism and Origin of Atrial Tachycardia Following Bilateral Pulmonary Transplantation. Journal of Cardiovascular Electrophysiology, 23(5), 553-555. doi:10.1111/j.1540-8167.2011.02250.xRudy, Y. (2013). Noninvasive Electrocardiographic Imaging of Arrhythmogenic Substrates in Humans. Circulation Research, 112(5), 863-874. doi:10.1161/circresaha.112.279315Ghosh, S., Avari, J. N., Rhee, E. K., Woodard, P. K., & Rudy, Y. (2008). Noninvasive electrocardiographic imaging (ECGI) of epicardial activation before and after catheter ablation of the accessory pathway in a patient with Ebstein anomaly. Heart Rhythm, 5(6), 857-860. doi:10.1016/j.hrthm.2008.03.011Rudy, Y., Plonsey, R., & Liebman, J. (1979). The effects of variations in conductivity and geometrical parameters on the electrocardiogram, using an eccentric spheres model. Circulation Research, 44(1), 104-111. doi:10.1161/01.res.44.1.104SALINET, J. L., TUAN, J. H., SANDILANDS, A. J., STAFFORD, P. J., SCHLINDWEIN, F. S., & NG, G. A. (2013). Distinctive Patterns of Dominant Frequency Trajectory Behavior in Drug-Refractory Persistent Atrial Fibrillation: Preliminary Characterization of Spatiotemporal Instability. Journal of Cardiovascular Electrophysiology, 25(4), 371-379. doi:10.1111/jce.12331Dalu, Y. (1978). Relating the multipole moments of the heart to activated parts of the epicardium and endocardium. Annals of Biomedical Engineering, 6(4), 492-505. doi:10.1007/bf02584552Sánchez, C., Bueno-Orovio, A., Pueyo, E., & Rodríguez, B. (2017). Atrial Fibrillation Dynamics and Ionic Block Effects in Six Heterogeneous Human 3D Virtual Atria with Distinct Repolarization Dynamics. Frontiers in Bioengineering and Biotechnology, 5. doi:10.3389/fbioe.2017.00029Sanders, P., Berenfeld, O., Hocini, M., Jaïs, P., Vaidyanathan, R., Hsu, L.-F., … Haïssaguerre, M. (2005). Spectral Analysis Identifies Sites of High-Frequency Activity Maintaining Atrial Fibrillation in Humans. Circulation, 112(6), 789-797. doi:10.1161/circulationaha.104.517011Sapp, J. L., Bar-Tal, M., Howes, A. J., Toma, J. E., El-Damaty, A., Warren, J. W., … Horáček, B. M. (2017). Real-Time Localization of Ventricular Tachycardia Origin From the 12-Lead Electrocardiogram. JACC: Clinical Electrophysiology, 3(7), 687-699. doi:10.1016/j.jacep.2017.02.024Sapp, J. L., Dawoud, F., Clements, J. C., & Horáček, B. M. (2012). Inverse Solution Mapping of Epicardial Potentials. Circulation: Arrhythmia and Electrophysiology, 5(5), 1001-1009. doi:10.1161/circep.111.970160Sapp, J. L., Wells, G. A., Parkash, R., Stevenson, W. G., Blier, L., Sarrazin, J.-F., … Tang, A. S. L. (2016). Ventricular Tachycardia Ablation versus Escalation of Antiarrhythmic Drugs. New England Journal of Medicine, 375(2), 111-121. doi:10.1056/nejmoa1513614Schulze, W. H. W., Chen, Z., Relan, J., Potyagaylo, D., Krueger, M. W., Karim, R., … Dössel, O. (2016). ECG imaging of ventricular tachycardia: evaluation against simultaneous non-contact mapping and CMR-derived grey zone. Medical & Biological Engineering & Computing, 55(6), 979-990. doi:10.1007/s11517-016-1566-xShah, D. C., Jaïs, P., Haïssaguerre, M., Chouairi, S., Takahashi, A., Hocini, M., … Clémenty, J. (1997). Three-dimensional Mapping of the Common Atrial Flutter Circuit in the Right Atrium. Circulation, 96(11), 3904-3912. doi:10.1161/01.cir.96.11.3904Shome, S., & Macleod, R. (s. f.). Simultaneous High-Resolution Electrical Imaging of Endocardial, Epicardial and Torso-Tank Surfaces Under Varying Cardiac Metabolic Load and Coronary Flow. Lecture Notes in Computer Science, 320-329. doi:10.1007/978-3-540-72907-5_33SIMMS, H. D., & GESELOWITZ, D. B. (1995). Computation of Heart Surface Potentials Using the Surface Source Model. Journal of Cardiovascular Electrophysiology, 6(7), 522-531. doi:10.1111/j.1540-8167.1995.tb00425.xSvehlikova, J., Teplan, M., & Tysler, M. (2018). Geometrical constraint of sources in noninvasive localization of premature ventricular contractions. Journal of Electrocardiology, 51(3), 370-377. doi:10.1016/j.jelectrocard.2018.02.013Tsyganov, A., Wissner, E., Metzner, A., Mironovich, S., Chaykovskaya, M., Kalinin, V., … Kuck, K.-H. (2018). Mapping of ventricular arrhythmias using a novel noninvasive epicardial and endocardial electrophysiology system. Journal of Electrocardiology, 51(1), 92-98. doi:10.1016/j.jelectrocard.2017.07.018Umapathy, K., Nair, K., Masse, S., Krishnan, S., Rogers, J., Nash, M. P., & Nanthakumar, K. (2010). Phase Mapping of Cardiac Fibrillation. Circulation: Arrhythmia and Electrophysiology, 3(1), 105-114. doi:10.1161/circep.110.853804Van Dam, P. M., Oostendorp, T. F., Linnenbank, A. C., & van Oosterom, A. (2009). Non-Invasive Imaging of Cardiac Activation and Recovery. Annals of Biomedical Engineering, 37(9), 1739-1756. doi:10.1007/s10439-009-9747-5Van Oosterom, A. (2001). Genesis of the T wave as based on an equivalent surface source model. Journal of Electrocardiology, 34(4), 217-227. doi:10.1054/jelc.2001.28896Van Oosterom, A. (2002). Solidifying the solid angle. Journal of Electrocardiology, 35(4), 181-192. doi:10.1054/jelc.2002.37176Van Oosterom, A. (2004). ECGSIM: an interactive tool for stu