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

Identification of weakly coupled multiphysics problems. Application to the inverse problem of electrocardiography

This work addresses the inverse problem of electrocardiography from a new perspective, by combining electrical and mechanical measurements. Our strategy relies on the defini-tion of a model of the electromechanical contraction which is registered on ECG data but also on measured mechanical displacements of the heart tissue typically extracted from medical images. In this respect, we establish in this work the convergence of a sequential estimator which combines for such coupled problems various state of the art sequential data assimilation methods in a unified consistent and efficient framework. Indeed we ag-gregate a Luenberger observer for the mechanical state and a Reduced Order Unscented Kalman Filter applied on the parameters to be identified and a POD projection of the electrical state. Then using synthetic data we show the benefits of our approach for the estimation of the electrical state of the ventricles along the heart beat compared with more classical strategies which only consider an electrophysiological model with ECG measurements. Our numerical results actually show that the mechanical measurements improve the identifiability of the electrical problem allowing to reconstruct the electrical state of the coupled system more precisely. Therefore, this work is intended to be a first proof of concept, with theoretical justifications and numerical investigations, of the ad-vantage of using available multi-modal observations for the estimation and identification of an electromechanical model of the heart

Solving the inverse problem of electrocardiography in a realistic environment

Heart disease is a leading cause of death worldwide. Straightforward information about the cardiac electrophysiology can help to improve the quality of diagnosis of heart diseases. The inverse problem of electrocardiography and the intracardiac catheter measurement are two ways to get access to the electrophysiology in the heart. In this thesis six research topics related to these two techniques are included

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

Contributions To The Methodology Of Electrocardiographic Imaging (ECGI) And Application Of ECGI To Study Mechanisms Of Atrial Arrhythmia, Post Myocardial Infarction Electrophysiological Substrate, And Ventricular Tachycardia In Patients

ABSTRACT OF THE DISSERTATION Contributions to the Methodology of Electrocardiographic Imaging: ECGI) and Application of ECGI to Study Mechanisms of Atrial Arrhythmia, Post Myocardial Infarction Electrophysiological Substrate, and Ventricular Tachycardia in Patients by Yong Wang Doctor of Philosophy in Biomedical Engineering Washington University in St. Louis, 2009 Professor Yoram Rudy, Chair Electrocardiographic Imaging: ECGI) is a noninvasive imaging modality for cardiac electrophysiology and arrhythmia. ECGI reconstructs epicardial potentials, electrograms and isochrones from body-surface electrocardiograms combined with heart-torso geometry from computed tomography: CT). The application of a new meshless method, the Method of Fundamental Solutions: MFS) is introduced to ECGI with the following major advantages: 1. Elimination of meshing and manual mesh optimization processes, thereby enhancing automation and speeding the ECGI procedure. 2. Elimination of mesh-induced artifacts. 3. Simpler implementation. These properties of MFS enhance the practical application of ECGI as a clinical diagnostic tool. The current ECGI mode of operation is offline with generation of epicardial potential maps delayed to data acquisition. A real time ECGI procedure is proposed, by which the epicardial potentials can be reconstructed while the body surface potential data are acquired: \u3c 1msec/frame) during a clinical procedure. This development enables real-time monitoring, diagnosis, and interactive guidance of intervention for arrhythmia therapy. ECGI is applied to map noninvasively the electrophysiological substrate in eight post-MI patients during sinus rhythm: SR). Contrast-enhanced MRI: ceMRI) is conducted to determine anatomical scar. ECGI imaged regions of electrical scar corresponded closely in location, extent, and morphology to the anatomical scars. In three patients, late diastolic potentials are imaged in the scar epicardial border zone during SR. Scar-related ventricular tachycardia: VT) in two patients are imaged, showing the VT activation sequence in relation to the abnormal electrophysiological substrate. ECGI imaging the substrate in a beat-by-beat fashion could potentially help in noninvasive risk stratification for post-MI arrhythmias and facilitate substrate-based catheter ablation of these arrhythmias. ECGI is applied to eleven consecutive patients referred for VT catheter ablation procedure. ECGI is performed either before: 8 patients) or during: 3 patients) the ablation procedure. Blinded ECGI and invasive electrophysiology: EP) study results are compared. Over a wide range of VT types and locations, ECGI results are consistent with EP data regarding localization of the arrhythmia origin: including myocardial depth) and mechanism: focal, reentrant, fascicular). ECGI also provides mechanistic electrophysiological insights, relating arrhythmia patterns to the myocardial substrate. The study shows ECGI has unique potential clinical advantages, especially for hemodynamically intolerant VT or VT that is difficult to induce. Because it provides local cardiac information, ECGI may aid in better understanding of mechanisms of ventricular arrhythmia. Further prospective trials of ECGI with clinical endpoints are warranted. Many mechanisms for the initiation and perpetuation of atrial fibrillation: AF) have been demonstrated over the last several decades. The tools to study these mechanisms in humans have limitations, the most common being invasiveness of a mapping procedure. In this paper, we present simultaneous noninvasive biatrial epicardial activation sequences of AF in humans, obtained using the Electrocardiographic Imaging: ECGI) system, and analyzed in terms of mechanisms and complexity of activation patterns. We performed ECGI in 36 patients with a diagnosis of AF. To determine ECGI atrial accuracy, atrial pacing from different sites was performed in six patients: 37 pacing events), and ECGI was compared to registered CARTO images. Then, ECGI was performed on all 36 patients during AF and ECGI epicardial maps were analyzed for mechanisms and complexity. ECGI noninvasively imaged the low-amplitude signals of AF in a wide range of patients: 97% procedural success). The spatial accuracy in determining initiation sites as simulated by atrial pacing was ~ 6mm. ECGI imaged many activation patterns of AF, most commonly multiple wavelets: 92%), with pulmonary vein: 69%) and non-pulmonary vein: 62%) trigger sites. Rotor activity was seen rarely: 15%). AF complexity increased with longer clinical history of AF, though the degree of complexity of nonparoxysmal AF varied and overlapped. ECGI offers a way to identify unique epicardial activation patterns of AF in a patient-specific manner. The results are consistent with contemporary animal models of AF mechanisms and highlight the coexistence of a variety of mechanisms among patients

Electrophysiology

The outstanding evolution of recording techniques paved the way for better understanding of electrophysiological phenomena within the human organs, including the cardiovascular, ophthalmologic and neural systems. In the field of cardiac electrophysiology, the development of more and more sophisticated recording and mapping techniques made it possible to elucidate the mechanism of various cardiac arrhythmias. This has even led to the evolution of techniques to ablate and cure most complex cardiac arrhythmias. Nevertheless, there is still a long way ahead and this book can be considered a valuable addition to the current knowledge in subjects related to bioelectricity from plants to the human heart

Bioelectrical Signal Processing in Cardiology: inverse solution mapping on epicardial and endocardial potentials

Inverse electrocardiography is aimed at reconstructing the heart electrical activity and its corresponding spread throughout the heart from non-invasive body surface measurements obtained through the Electrocardiogram (ECG) technique. This field has showed increasing promise during the last decades due to its main application: predict possible cardiac diseases such that medical interventions are avoided and costs which were meant to these clinical operations are also reduced. Still, properly detection of these cardiac diseases is directly correlated with the performance of the inverse-solving regularization methods. This Final Project counts with the collaboration of the Department of Medicine and the Department of Mathematics and Statistics of the Dalhousie University, Canada, which provided us with subject-specific BSPM measurements and data extracted from CT-scans of catheter interventions. Hence, our principals goals would be the analysis, review, comparison and cross-validation of the computed results on the multiple variants of the automated inverse-solving algorithms. Accordingly, a final conclusion of the influence which every regularization method has on the inverse solutions would be conducted by means of specialized simulation programs and numerical error measures.La Electrocardiografía Inversa consiste en la reconstrucción de la actividad eléctrica del corazón y su correspondiente propagación en el corazón a partir de medidas no invasivas tomadas en la superficie corporal y obtenidas a través de la técnica llamada el Electrocardiograma (ECG). Este campo ha mostrado una creciente promesa durante las últimas décadas debido a su aplicación principal: predecir posibles enfermedades cardíacas y así evitar intervenciones quirúrgicas y reducir los costes que estaban destinados a éstas. Sin embargo, la correcta detección de estas enfermedades cardíacas está directamente relacionada con el funcionamiento de los métodos de regularización que solucionan el problema inverso. Este Proyecto Final cuenta con la colaboración del Departamento de Medicina y el Departamento de Matemáticas y Estadística de la Universidad de Dalhousie, Canadá, que nos ha proporcionado medidas de BSPM de un sujeto específico y datos extraídos de escáneres CT de intervenciones con catéter. Por lo tanto, nuestros objetivos fundamentales serán el análisis, la revisión, la comparación y la validación cruzada de los resultados en base a las múltiples variantes de los algoritmos automatizados para resolver el problema inverso. Consecuentemente, se llevará a cabo una conclusión final de la influencia que cada uno de los métodos de regularización tiene sobre las soluciones inversas mediante programas especializados en simulación y medidas de error numéricas.La Electrocardiografía Inversa consisteix en la reconstrucció de l'activitat elèctrica del cor i la seva corresponent propagació al llarg del cor a partir de mesuraments no invasius presos en la superfície del cos i obtinguts a través de la tècnica anomenada l’Electrocardiograma (ECG). Aquest camp ha mostrat una creixent promesa durant les últimes dècades gràcies a la seva aplicació principal: predir possibles malalties cardíaques i així evitar intervencions cirúrgiques i reduïr els costos que estaven destinats a aquestes. No obstant això, la correcta detecció d'aquestes malalties cardíaques està directament relacionada amb el funcionament dels mètodes de regularització que solucionen el problema invers. Aquest Projecte Final compta amb la col·laboració del Departament de Medicina i el Departament de Matemàtiques i Estadística de la Universitat de Dalhousie, Canadà, la qual ens ha proporcionat mesuraments de BSPM d’un subjecte específic i dades extretes de escàners CT de intervencions amb catèter. Així doncs, els nostres objectius fonamentals seran l'anàlisi, la revisió, la comparació i la validació creuada dels resultats en base a les múltiples variants dels algoritmes automatitzats per resoldre el problema invers. Conseqüentment, es durà a terme una conclusió final de la influència que cada un dels mètodes de regularització té sobre les solucions inverses per mitjà de programes especialitzats en simulació i mesures d'error numèriques

ECG Imaging of Ventricular Activity in Clinical Applications

ECG imaging was performed in humans to reconstruct ventricular activation patterns and localize their excitation origins. The precision of the non-invasive reconstructions was evaluated against invasive measurements and found to be in line with the state-of-the-art literature. Statistics were produced for various excitation origins and reveal the beat-to-beat robustness of the imaging method

Feasibility of improving risk stratification in the inherited cardiac conditions

Fatal ventricular arrhythmias can occur in patients with Hypertrophic Cardiomyopathy, Brugada Syndrome and rarely in patients with normal cardiac investigations. Despite very different pathogeneses, we hypothesised that a common electrophysiological substrate precipitates these arrhythmias and could be used as a marker for risk stratification. In Chapter 3 of this thesis, we found that fewer than half the cardiac arrest survivors with Brugada Syndrome would have been offered prophylactic defibrillators based on current risk scoring, highlighting the need for better risk stratification. Our group previously used a commercially available 252-electrode vest which constructs ventricular electrograms onto a CT image of the heart to show exercise related differences in high-risk patients. In Chapter 4, we applied this method to Brugada patients, but could not reproduce prior results. Further investigation revealed periodic changes in activation patterns after exercise that could explain this discrepancy. An alternative matrix approach was developed to overcome this problem. Exercise induced conduction heterogeneity differentiated Brugada patients from unaffected controls, but not those surviving cardiac arrest. However, if considered alongside spontaneous type 1 ECG and syncope, inducible conduction heterogeneity markedly improved identification of Brugada cardiac arrest survivors. In Chapter 5 the method was shown to differentiate idiopathic ventricular fibrillation patients from those fully recovered from acute ischaemic cardiac arrest, implying a permanent electrophysiological abnormality. In Chapter 8, we showed prolonged mean local activation times and activation-recovery intervals in hypertrophic cardiomyopathy cardiac arrest survivors compared to those without previous ventricular arrhythmia. These metrics were combined into both logistic regression and support vector machine models to strongly differentiate the groups. We concluded that electrophysiological changes could identify cardiac arrest survivors in various cardiac conditions, but a single factor common pathway was not established. Prospective studies are required to determine if using these parameters could enhance current risk stratification for sudden death.Open Acces