Uncertainty Quantification and Reduction in Cardiac Electrophysiological Imaging

Cardiac electrophysiological (EP) imaging involves solving an inverse problem that infers cardiac electrical activity from body-surface electrocardiography data on a physical domain defined by the body torso. To avoid unreasonable solutions that may fit the data, this inference is often guided by data-independent prior assumptions about different properties of cardiac electrical sources as well as the physical domain. However, these prior assumptions may involve errors and uncertainties that could affect the inference accuracy. For example, common prior assumptions on the source properties, such as fixed spatial and/or temporal smoothness or sparseness assumptions, may not necessarily match the true source property at different conditions, leading to uncertainties in the inference. Furthermore, prior assumptions on the physical domain, such as the anatomy and tissue conductivity of different organs in the thorax model, represent an approximation of the physical domain, introducing errors to the inference. To determine the robustness of the EP imaging systems for future clinical practice, it is important to identify these errors/uncertainties and assess their impact on the solution. This dissertation focuses on the quantification and reduction of the impact of uncertainties caused by prior assumptions/models on cardiac source properties as well as anatomical modeling uncertainties on the EP imaging solution. To assess the effect of fixed prior assumptions/models about cardiac source properties on the solution of EP imaging, we propose a novel yet simple Lp-norm regularization method for volumetric cardiac EP imaging. This study reports the necessity of an adaptive prior model (rather than fixed model) for constraining the complex spatiotemporally changing properties of the cardiac sources. We then propose a multiple-model Bayesian approach to cardiac EP imaging that employs a continuous combination of prior models, each re-effecting a specific spatial property for volumetric sources. The 3D source estimation is then obtained as a weighted combination of solutions across all models. Including a continuous combination of prior models, our proposed method reduces the chance of mismatch between prior models and true source properties, which in turn enhances the robustness of the EP imaging solution. To quantify the impact of anatomical modeling uncertainties on the EP imaging solution, we propose a systematic statistical framework. Founded based on statistical shape modeling and unscented transform, our method quantifies anatomical modeling uncertainties and establish their relation to the EP imaging solution. Applied on anatomical models generated from different image resolutions and different segmentations, it reports the robustness of EP imaging solution to these anatomical shape-detail variations. We then propose a simplified anatomical model for the heart that only incorporates certain subject-specific anatomical parameters, while discarding local shape details. Exploiting less resources and processing for successful EP imaging, this simplified model provides a simple clinically-compatible anatomical modeling experience for EP imaging systems. Different components of our proposed methods are validated through a comprehensive set of synthetic and real-data experiments, including various typical pathological conditions and/or diagnostic procedures, such as myocardial infarction and pacing. Overall, the methods presented in this dissertation for the quantification and reduction of uncertainties in cardiac EP imaging enhance the robustness of EP imaging, helping to close the gap between EP imaging in research and its clinical application

-Norm Regularization in Volumetric Imaging of Cardiac Current Sources

Advances in computer vision have substantially improved our ability to analyze the structure and mechanics of the heart. In comparison, our ability to observe and analyze cardiac electrical activities is much limited. The progress to computationally reconstruct cardiac current sources from noninvasive voltage data sensed on the body surface has been hindered by the ill-posedness and the lack of a unique solution of the reconstruction problem. Common L2- and L1-norm regularizations tend to produce a solution that is either too diffused or too scattered to reflect the complex spatial structure of current source distribution in the heart. In this work, we propose a general regularization with Lp-norm () constraint to bridge the gap and balance between an overly smeared and overly focal solution in cardiac source reconstruction. In a set of phantom experiments, we demonstrate the superiority of the proposed Lp-norm method over its L1 and L2 counterparts in imaging cardiac current sources with increasing extents. Through computer-simulated and real-data experiments, we further demonstrate the feasibility of the proposed method in imaging the complex structure of excitation wavefront, as well as current sources distributed along the postinfarction scar border. This ability to preserve the spatial structure of source distribution is important for revealing the potential disruption to the normal heart excitation

Electrocardiographic Imaging Using a Spatio-Temporal Basis of Body Surface Potentials - Application to Atrial Ectopic Activity

Electrocardiographic imaging (ECGI) strongly relies on a priori assumptions and additional information to overcome ill-posedness. The major challenge of obtaining good reconstructions consists in finding ways to add information that effectively restricts the solution space without violating properties of the sought solution. In this work, we attempt to address this problem by constructing a spatio-temporal basis of body surface potentials (BSP) from simulations of many focal excitations. Measured BSPs are projected onto this basis and reconstructions are expressed as linear combinations of corresponding transmembrane voltage (TMV) basis vectors. The novel method was applied to simulations of 100 atrial ectopic foci with three different conduction velocities. Three signal-to-noise ratios (SNR) and bases of six different temporal lengths were considered. Reconstruction quality was evaluated using the spatial correlation coefficient of TMVs as well as estimated local activation times (LAT). The focus localization error was assessed by computing the geodesic distance between true and reconstructed foci. Compared with an optimally parameterized Tikhonov-Greensite method, the BSP basis reconstruction increased the mean TMV correlation by up to 22, 24, and 32% for an SNR of 40, 20, and 0 dB, respectively. Mean LAT correlation could be improved by up to 5, 7, and 19% for the three SNRs. For 0 dB, the average localization error could be halved from 15.8 to 7.9 mm. For the largest basis length, the localization error was always below 34 mm. In conclusion, the new method improved reconstructions of atrial ectopic activity especially for low SNRs. Localization of ectopic foci turned out to be more robust and more accurate. Preliminary experiments indicate that the basis generalizes to some extent from the training data and may even be applied for reconstruction of non-ectopic activity

Non-invasive identification of atrial fibrillation drivers

Atrial fibrillation (AF) is one of the most common cardiac arrhythmias. Nowadays the fibrillatory process is known to be provoked by the high-frequency reentrant activity of certain atrial regions that propagates the fibrillatory activity to the rest of the atrial tissue, and the electrical isolation of these key regions has demonstrated its effectiveness in terminating the fibrillatory process. The location of the dominant regions represents a major challenge in the diagnosis and treatment of this arrhythmia. With the aim to detect and locate the fibrillatory sources prior to surgical procedure, non-invasive methods have been developed such as body surface electrical mapping (BSPM) which allows to record with high spatial resolution the electrical activity on the torso surface or the electrocardiographic imaging (ECGI) which allows to non-invasively reconstruct the electrical activity in the atrial surface. Given the novelty of these systems, both technologies suffer from a lack of scientific knowledge about the physical and technical mechanisms that support their operation. Therefore, the aim of this thesis is to increase that knowledge, as well as studying the effectiveness of these technologies for the localization of dominant regions in patients with AF. First, it has been shown that BSPM systems are able to noninvasively identify atrial rotors by recognizing surface rotors after band-pass filtering. Furthermore, the position of such surface rotors is related to the atrial rotor location, allowing the distinction between left or right atrial rotors. Moreover, it has been found that the surface electrical maps in AF suffer a spatial smoothing effect by the torso conductor volume, so the surface electrical activity can be studied with a relatively small number of electrodes. Specifically, it has been seen that 12 uniformly distributed electrodes are sufficient for the correct identification of atrial dominant frequencies, while at least 32 leads are needed for non-invasive identification of atrial rotors. Secondly, the effect of narrowband filtering on the effectiveness of the location of reentrant patterns was studied. It has been found that this procedure allows isolating the reentrant electrical activity caused by the rotor, increasing the detection rate for both invasive and surface maps. However, the spatial smoothing caused by the regularization of the ECGI added to the temporal filtering causes a large increase in the spurious reentrant activity, making it difficult to detect real reentrant patterns. However, it has been found that maps provided by the ECGI without temporal filtering allow the correct detection of reentrant activity, so narrowband filtering should be applied for intracavitary or surface signal only. Finally, we studied the stability of the markers used to detect dominant regions in ECGI, such as frequency maps or the rotor presence. It has been found that in the presence of alterations in the conditions of the inverse problem, such as electrical or geometrical noise, these markers are significantly more stable than the ECGI signal morphology from which they are extracted. In addition, a new methodology for error reduction in the atrial spatial location based on the curvature of the curve L has been proposed. The results presented in this thesis showed that BSPM and ECGI systems allows to non-invasively locate the presence of high-frequency rotors, responsible for the maintenance of AF. This detection has been proven to be unambiguous and robust, and the physical and technical mechanisms that support this behavior have been studied. These results indicate that both non-invasive systems provide information of great clinical value in the treatment of AF, so their use can be helpful for selecting and planning atrial ablation procedures.La fibrilación auricular (FA) es una de las arritmias cardiacas más frecuentes. Hoy en día se sabe que el proceso fibrilatorio está provocado por la actividad reentrante a alta frecuencia de ciertas regiones auriculares que propagan la actividad fibrilatoria en el resto del tejido auricular, y se ha demostrado que el aislamiento eléctrico de estas regiones dominantes permite detener el proceso fibrilatorio. La localización de las regiones dominantes supone un gran reto en el diagnóstico y tratamiento de la FA. Con el objetivo de poder localizar las fuentes fibrilatorias con anterioridad al procedimiento quirúrgico, se han desarrollado métodos no invasivos como la cartografía eléctrica de superficie (CES) que registra con gran resolución espacial la actividad eléctrica en la superficie del torso o la electrocardiografía por imagen (ECGI) que permite reconstruir la actividad eléctrica en la superficie auricular. Dada la novedad de estos sistemas, existe una falta de conocimiento científico sobre los mecanismos físicos y técnicos que sustentan su funcionamiento. Por lo tanto, el objetivo de esta tesis es aumentar dicho conocimiento, así como estudiar la eficacia de ambas tecnologías para la localización de regiones dominantes en pacientes con FA. En primer lugar, ha visto que los sistemas CES permiten identificar rotores auriculares mediante el reconocimiento de rotores superficiales tras el filtrado en banda estrecha. Además, la posición de los rotores superficiales está relacionada con la localización de dichos rotores, permitiendo la distinción entre rotores de aurícula derecha o izquierda. Por otra parte, se ha visto que los mapas eléctricos superficiales durante FA sufren una gran suavizado espacial por el efecto del volumen conductor del torso, lo que permite que la actividad eléctrica superficial pueda ser estudiada con un número relativamente reducido de electrodos. Concretamente, se ha visto que 12 electrodos uniformemente distribuidos son suficientes para una correcta identificación de frecuencias dominantes, mientras que son necesarios al menos 32 para una correcta identificación de rotores auriculares. Por otra parte, también se ha estudiado el efecto del filtrado en banda estrecha sobre la eficacia de la localización de patrones reentrantes. Así, se ha visto que este procedimiento permite aislar la actividad eléctrica reentrante provocada por el rotor, aumentando la tasa de detección tanto para señal obtenida de manera invasiva como para los mapas superficiales. No obstante, este filtrado temporal sobre la señal de ECGI provoca un gran aumento de la actividad reentrante espúrea que dificulta la detección de patrones reentrantes reales. Sin embargo, los mapas ECGI sin filtrado temporal permiten la detección correcta de la actividad reentrante, por lo el filtrado debería ser aplicado únicamente para señal intracavitaria o superficial. Por último, se ha estudiado la estabilidad de los marcadores utilizados en ECGI para detectar regiones dominantes, como son los mapas de frecuencia o la presencia de rotores. Se ha visto que en presencia de alteraciones en las condiciones del problema inverso, como ruido eléctrico o geométrico, estos marcadores son significativamente más estables que la morfología de la propia señal ECGI. Además, se ha propuesto una nueva metodología para la reducción del error en la localización espacial de la aurícula basado en la curvatura de la curva L. Los resultados presentados en esta tesis revelan que los sistemas de CES y ECGI permiten localizar de manera no invasiva la presencia de rotores de alta frecuencia. Esta detección es univoca y robusta, y se han estudiado los mecanismos físicos y técnicos que sustentan dicho comportamiento. Estos resultados indican que ambos sistemas no invasivos proporcionan información de gran valor clínico en el tratamiento de la FA, por lo que su uso puede ser de gran ayuda para la selección y planificaciLa fibril·lació auricular (FA) és una de les arítmies cardíaques més freqüents. Hui en dia es sabut que el procés fibrilatori està provocat per l'activitat reentrant de certes regions auriculars que propaguen l'activitat fibril·latoria a la resta del teixit auricular, i s'ha demostrat que l'aïllament elèctric d'aquestes regions dominants permet aturar el procés fibrilatori. La localització de les regions dominants suposa un gran repte en el diagnòstic i tractament d'aquesta arítmia. Amb l'objectiu de poder localitzar fonts fibril·latories amb anterioritat al procediment quirúrgic s'han desenvolupat mètodes no invasius com la cartografia elèctrica de superfície (CES) que registra amb gran resolució espacial l'activitat elèctrica en la superfície del tors o l'electrocardiografia per imatge (ECGI) que permet obtenir de manera no invasiva l'activitat elèctrica en la superfície auricular. Donada la relativa novetat d'aquests sistemes, existeix una manca de coneixement científic sobre els mecanismes físics i tècnics que sustenten el seu funcionament. Per tant, l'objectiu d'aquesta tesi és augmentar aquest coneixement, així com estudiar l'eficàcia d'aquestes tecnologies per a la localització de regions dominants en pacients amb FA. En primer lloc, s'ha vist que els sistemes CES permeten identificar rotors auriculars mitjançant el reconeixement de rotors superficials després del filtrat en banda estreta. A més, la posició dels rotors superficials està relacionada amb la localització d'aquests rotors, permetent la distinció entre rotors de aurícula dreta o esquerra. També s'ha vist que els mapes elèctrics superficials durant FA pateixen un gran suavitzat espacial per l'efecte del volum conductor del tors, el que permet que l'activitat elèctrica superficial pugui ser estudiada amb un nombre relativament reduït d'elèctrodes. Concretament, s'ha vist que 12 elèctrodes uniformement distribuïts són suficients per a una correcta identificació de freqüències dominants auriculars, mentre que són necessaris almenys 32 per a una correcta identificació de rotors auriculars. D'altra banda, també s'ha estudiat l'efecte del filtrat en banda estreta sobre l'eficàcia de la localització de patrons reentrants. Així, s'ha vist que aquest procediment permet aïllar l'activitat elèctrica reentrant provocada pel rotor, augmentant la taxa de detecció tant pel senyal obtingut de manera invasiva com per als mapes superficials. No obstant això, aquest filtrat temporal sobre el senyal de ECGI provoca un gran augment de l'activitat reentrant espúria que dificulta la detecció de patrons reentrants reals. A més, els mapes proporcionats per la ECGI sense filtrat temporal permeten la detecció correcta de l'activitat reentrant, per la qual cosa el filtrat hauria de ser aplicat únicament per a senyal intracavitària o superficial. Per últim, s'ha estudiat l'estabilitat dels marcadors utilitzats en ECGI per a detectar regions auriculars dominants, com són els mapes de freqüència o la presència de rotors. S'ha vist que en presència d'alteracions en les condicions del problema invers, com soroll elèctric o geomètric, aquests marcadors són significativament més estables que la morfologia del mateix senyal ECGI. A més, s'ha proposat una nova metodologia per a la reducció de l'error en la localització espacial de l'aurícula basat en la curvatura de la corba L. Els resultats presentats en aquesta tesi revelen que els sistemes de CES i ECGI permeten localitzar de manera no invasiva la presència de rotors d'alta freqüència. Aquesta detecció és unívoca i robusta, i s'han estudiat els mecanismes físics i tècnics que sustenten aquest comportament. Aquests resultats indiquen que els dos sistemes no invasius proporcionen informació de gran valor clínic en el tractament de la FA, pel que el seu ús pot ser de gran ajuda per a la selecció i planificació de procediments d'ablació auricular.Rodrigo Bort, M. (2016). Non-invasive identification of atrial fibrillation drivers [Tesis doctoral]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/75346TESISPremios Extraordinarios de tesis doctorale

Novel Methods to Incorporate Physiological Prior Knowledge into the Inverse Problem of Electrocardiography - Application to Localization of Ventricular Excitation Origins

17 Millionen Todesfälle jedes Jahr werden auf kardiovaskuläre Erkankungen zurückgeführt. Plötzlicher Herztod tritt bei ca. 25% der Patienten mit kardiovaskulären Erkrankungen auf und kann mit ventrikulärer Tachykardie in Verbindung gebracht werden. Ein wichtiger Schritt für die Behandlung von ventrikulärer Tachykardie ist die Detektion sogenannter Exit-Points, d.h. des räumlichen Ursprungs der Erregung. Da dieser Prozess sehr zeitaufwändig ist und nur von fähigen Kardiologen durchgeführt werden kann, gibt es eine Notwendigkeit für assistierende Lokalisationsmöglichkeiten, idealerweise automatisch und nichtinvasiv. Elektrokardiographische Bildgebung versucht, diesen klinischen Anforderungen zu genügen, indem die elektrische Aktivität des Herzens aus Messungen der Potentiale auf der Körperoberfläche rekonstruiert wird. Die resultierenden Informationen können verwendet werden, um den Erregungsursprung zu detektieren. Aktuelle Methoden um das inverse Problem zu lösen weisen jedoch entweder eine geringe Genauigkeit oder Robustheit auf, was ihren klinischen Nutzen einschränkt. Diese Arbeit analysiert zunächst das Vorwärtsproblem im Zusammenhang mit zwei Quellmodellen: Transmembranspannungen und extrazelluläre Potentiale. Die mathematischen Eigenschaften der Relation zwischen den Quellen des Herzens und der Körperoberflächenpotentiale werden systematisch analysiert und der Einfluss auf das inverse Problem verdeutlicht. Dieses Wissen wird anschließend zur Lösung des inversen Problems genutzt. Hierzu werden drei neue Methoden eingeführt: eine verzögerungsbasierte Regularisierung, eine Methode basierend auf einer Regression von Körperoberflächenpotentialen und eine Deep-Learning-basierte Lokalisierungsmethode. Diese drei Methoden werden in einem simulierten und zwei klinischen Setups vier etablierten Methoden gegenübergestellt und bewertet. Auf dem simulierten Datensatz und auf einem der beiden klinischen Datensätze erzielte eine der neuen Methoden bessere Ergebnisse als die konventionellen Ansätze, während Tikhonov-Regularisierung auf dem verbleibenden klinischen Datensatz die besten Ergebnisse erzielte. Potentielle Ursachen für diese Ergebnisse werden diskutiert und mit Eigenschaften des Vorwärtsproblems in Verbindung gebracht

Electrocardiographic Imaging Using a Spatio-Temporal Basis of Body Surface Potentials—Application to Atrial Ectopic Activity

Electrocardiographic imaging (ECGI) strongly relies on a priori assumptions and additional information to overcome ill-posedness. The major challenge of obtaining good reconstructions consists in finding ways to add information that effectively restricts the solution space without violating properties of the sought solution. In this work, we attempt to address this problem by constructing a spatio-temporal basis of body surface potentials (BSP) from simulations of many focal excitations. Measured BSPs are projected onto this basis and reconstructions are expressed as linear combinations of corresponding transmembrane voltage (TMV) basis vectors. The novel method was applied to simulations of 100 atrial ectopic foci with three different conduction velocities. Three signal-to-noise ratios (SNR) and bases of six different temporal lengths were considered. Reconstruction quality was evaluated using the spatial correlation coefficient of TMVs as well as estimated local activation times (LAT). The focus localization error was assessed by computing the geodesic distance between true and reconstructed foci. Compared with an optimally parameterized Tikhonov-Greensite method, the BSP basis reconstruction increased the mean TMV correlation by up to 22, 24, and 32% for an SNR of 40, 20, and 0 dB, respectively. Mean LAT correlation could be improved by up to 5, 7, and 19% for the three SNRs. For 0 dB, the average localization error could be halved from 15.8 to 7.9 mm. For the largest basis length, the localization error was always below 34 mm. In conclusion, the new method improved reconstructions of atrial ectopic activity especially for low SNRs. Localization of ectopic foci turned out to be more robust and more accurate. Preliminary experiments indicate that the basis generalizes to some extent from the training data and may even be applied for reconstruction of non-ectopic activity

Doctor of Philosophy

dissertationInverse Electrocardiography (ECG) aims to noninvasively estimate the electrophysiological activity of the heart from the voltages measured at the body surface, with promising clinical applications in diagnosis and therapy. The main challenge of this emerging technique lies in its mathematical foundation: an inverse source problem governed by partial differential equations (PDEs) which is severely ill-conditioned. Essential to the success of inverse ECG are computational methods that reliably achieve accurate inverse solutions while harnessing the ever-growing complexity and realism of the bioelectric simulation. This dissertation focuses on the formulation, optimization, and solution of the inverse ECG problem based on finite element methods, consisting of two research thrusts. The first thrust explores the optimal finite element discretization specifically oriented towards the inverse ECG problem. In contrast, most existing discretization strategies are designed for forward problems and may become inappropriate for the corresponding inverse problems. Based on a Fourier analysis of how discretization relates to ill-conditioning, this work proposes refinement strategies that optimize approximation accuracy o f the inverse ECG problem while mitigating its ill-conditioning. To fulfill these strategies, two refinement techniques are developed: one uses hybrid-shaped finite elements whereas the other adapts high-order finite elements. The second research thrust involves a new methodology for inverse ECG solutions called PDE-constrained optimization, an optimization framework that flexibly allows convex objectives and various physically-based constraints. This work features three contributions: (1) fulfilling optimization in the continuous space, (2) formulating rigorous finite element solutions, and (3) fulfilling subsequent numerical optimization by a primal-dual interiorpoint method tailored to the given optimization problem's specific algebraic structure. The efficacy o f this new method is shown by its application to localization o f cardiac ischemic disease, in which the method, under realistic settings, achieves promising solutions to a previously intractable inverse ECG problem involving the bidomain heart model. In summary, this dissertation advances the computational research of inverse ECG, making it evolve toward an image-based, patient-specific modality for biomedical research

Personalized noninvasive imaging of volumetric cardiac electrophysiology

Three-dimensionally distributed electrical functioning is the trigger of mechanical contraction of the heart. Disturbance of this electrical flow is known to predispose to mechanical catastrophe but, due to its amenability to certain intervention techniques, a detailed understanding of subject-specific cardiac electrophysiological conditions is of great medical interest. In current clinical practice, body surface potential recording is the standard tool for diagnosing cardiac electrical dysfunctions. However, successful treatments normally require invasive catheter mapping for a more detailed observation of these dysfunctions. In this dissertation, we take a system approach to pursue personalized noninvasive imaging of volumetric cardiac electrophysiology. Under the guidance of existing scientific knowledge of the cardiac electrophysiological system, we extract the subject specific cardiac electrical information from noninvasive body surface potential mapping and tomographic imaging data of individual subjects. In this way, a priori knowledge of system physiology leads the physiologically meaningful interpretation of personal data; at the same time, subject-specific information contained in the data identifies parameters in individual systems that differ from prior knowledge. Based on this perspective, we develop a physiological model-constrained statistical framework for the quantitative reconstruction of the electrical dynamics and inherent electrophysiological property of each individual cardiac system. To accomplish this, we first develop a coupled meshfree-BE (boundary element) modeling approach to represent existing physiological knowledge of the cardiac electrophysiological system on personalized heart-torso structures. Through a state space system approach and sequential data assimilation techniques, we then develop statistical model-data coupling algorithms for quantitative reconstruction of volumetric transmembrane potential dynamics and tissue property of 3D myocardium from body surface potential recoding of individual subjects. We also introduce a data integration component to build personalized cardiac electrophysiology by fusing tomographic image and BSP sequence of the same subject. In addition, we develop a computational reduction strategy that improves the efficiency and stability of the framework. Phantom experiments and real-data human studies are performed for validating each of the framework’s major components. These experiments demonstrate the potential of our framework in providing quantitative understanding of volumetric cardiac electrophysiology for individual subjects and in identifying latent threats in individual’s heart. This may aid in personalized diagnose, treatment planning, and fundamentally, prevention of fatal cardiac arrhythmia

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

On Learning and Generalization to Solve Inverse Problem of Electrophysiological Imaging

In this dissertation, we are interested in solving a linear inverse problem: inverse electrophysiological (EP) imaging, where our objective is to computationally reconstruct personalized cardiac electrical signals based on body surface electrocardiogram (ECG) signals. EP imaging has shown promise in the diagnosis and treatment planning of cardiac dysfunctions such as atrial flutter, atrial fibrillation, ischemia, infarction and ventricular arrhythmia. Towards this goal, we frame it as a problem of learning a function from the domain of measurements to signals. Depending upon the assumptions, we present two classes of solutions: 1) Bayesian inference in a probabilistic graphical model, 2) Learning from samples using deep networks. In both of these approaches, we emphasize on learning the inverse function with good generalization ability, which becomes a main theme of the dissertation. In a Bayesian framework, we argue that this translates to appropriately integrating different sources of knowledge into a common probabilistic graphical model framework and using it for patient specific signal estimation through Bayesian inference. In learning from samples setting, this translates to designing a deep network with good generalization ability, where good generalization refers to the ability to reconstruct inverse EP signals in a distribution of interest (which could very well be outside the sample distribution used during training). By drawing ideas from different areas like functional analysis (e.g. Fenchel duality), variational inference (e.g. Variational Bayes) and deep generative modeling (e.g. variational autoencoder), we show how we can incorporate different prior knowledge in a principled manner in a probabilistic graphical model framework to obtain a good inverse solution with generalization ability. Similarly, to improve generalization of deep networks learning from samples, we use ideas from information theory (e.g. information bottleneck), learning theory (e.g. analytical learning theory), adversarial training, complexity theory and functional analysis (e.g. RKHS). We test our algorithms on synthetic data and real data of the patients who had undergone through catheter ablation in clinics and show that our approach yields significant improvement over existing methods. Towards the end of the dissertation, we investigate general questions on generalization and stabilization of adversarial training of deep networks and try to understand the role of smoothness and function space complexity in answering those questions. We conclude by identifying limitations of the proposed methods, areas of further improvement and open questions that are specific to inverse electrophysiological imaging as well as broader, encompassing theory of learning and generalization