Spatial Characterization and Estimation of Intracardiac Propagation Patterns During Atrial Fibrillation

This doctoral thesis is in the field of biomedical signal processing with focus on methods for the analysis of atrial fibrillation (AF). Paper I of the present thesis addresses the challenge of extracting spatial properties of AF from body surface signals. Different parameters are extracted to estimate the preferred direction of atrial activation and the complexity of the atrial activation pattern. In addition, the relation of the spatial properties to AF organization, which is quantified by AF frequency, is evaluated. While no significant correlation between the preferred direction of atrial activation and AF frequency could be observed, the complexity of the atrial activation pattern was found to increase with AF frequency. The remaining three papers deal with the analysis of the propagation of the electrical activity in the atria during AF based on intracardiac signals. In Paper II, a time-domain method to quantify propagation patterns along a linear catheter based on the detected atrial activation times is developed. Taking aspects on intra-atrial signal organization into account, the detected activation times are combined into wavefronts, and parameters related to the consistency of the wavefronts over time and the activation order along the catheter are extracted. Furthermore, the potential relationship of the extracted parameters to established measures from body surface signals is investigated. While the degree of wavefront consistency was not reflected by the applied body surface measures, AF frequency could distinguish between recordings with different degrees of intra-atrial signal organization. This supports the role of AF frequency as an organization measure of AF. In Paper III, a novel method to analyze intracardiac propagation patterns based on causality analysis in the frequency domain is introduced. In particular, the approach is based on the partial directed coherence (PDC), which evaluates directional coupling between multiple signals in the frequency domain. The potential of the method is illustrated with simulation scenarios based on a detailed ionic model of the human atrial cell as well as with real data recordings, selected to present typical propagation mechanisms and recording situations in atrial tachyarrhythmias. For simulated data, the PDC is correctly reflecting the direction of coupling and thus the propagation between all recording sites. For real data, clear propagation patterns are identified which agree with previous clinical observations. Thus, the results illustrate the ability of the novel approach to identify propagation patterns from intracardiac signals during AF which can provide important information about the underlying AF mechanisms, potentially improving the planning and outcome of ablation. However, spurious couplings over long distances can be observed when analyzing real data comprised by a large number of simultaneously recorded signals, which gives room for further improvement of the method. The derivation of the PDC is entirely based on the fit of a multivariate autoregressive (MVAR) model, commonly estimated by the least-squares (LS) method. In Paper IV, the adaptive group least absolute selection and shrinkage operator (LASSO) is introduced in order to avoid overfitting of the MVAR model and to incorporate prior information such as sparsity of the solution. The sparsity can be motivated by the observation that direct couplings over longer distances are likely to be zero during AF; an information which has been further incorporated by proposing distance-adaptive group LASSO. In simulations, adaptive and distance-adaptive group LASSO are found to be superior to LS estimation in terms of both detection and estimation accuracy. In addition, the results of both simulations and real data analysis indicate that further improvements can be achieved when the distance between the recording sites is known or can be estimated. This further promotes the PDC as a method for analysis of AF propagation patterns, which may contribute to a better understanding of AF mechanisms as well as improved AF treatment

Numerical simulation of electrocardiograms for full cardiac cycles in healthy and pathological conditions

This work is dedicated to the simulation of full cycles of the electrical activity of the heart and the corresponding body surface potential. The model is based on a realistic torso and heart anatomy, including ventricles and atria. One of the specificities of our approach is to model the atria as a surface, which is the kind of data typically provided by medical imaging for thin volumes. The bidomain equations are considered in their usual formulation in the ventricles, and in a surface formulation on the atria. Two ionic models are used: the Courtemanche-Ramirez-Nattel model on the atria, and the "Minimal model for human Ventricular action potentials" (MV) by Bueno-Orovio, Cherry and Fenton in the ventricles. The heart is weakly coupled to the torso by a Robin boundary condition based on a resistor- capacitor transmission condition. Various ECGs are simulated in healthy and pathological conditions (left and right bundle branch blocks, Bachmann's bundle block, Wolff-Parkinson-White syndrome). To assess the numerical ECGs, we use several qualitative and quantitative criteria found in the medical literature. Our simulator can also be used to generate the signals measured by a vest of electrodes. This capability is illustrated at the end of the article

Rotor detection in atrial fibrillation

Atrial fibrillation (AF) is one of the most common arrhythmias in the clinical practice. Catheter ablation method was developed more than 20 years ago as an approach to terminate this rhythm disorder. Since its outbreak, this technique obtained international acceptance among the clinicians, and technological advances in this field increased its safety while reducing the procedure duration. However, there is no perfect AF treatment procedure described yet, since the understanding of the driving and sustaining AF mechanisms remains poor, with pulmonary vein isolation being the most common ablation strategy. Several theories try to explain the initiating and maintenance mechanisms of the AF, ranging from multiple wavelets propagating at random in the atria to ectopic focus fired from the pulmonary veins. Alternatively, spatiotemporal stable sources (rotors) have been proposed as the maintenance mechanism of AF. The most representative characteristic of a rotor is the re-entry spiral-like propagation pattern that the electrical wavefront exhibits as it propagates. The assessment of its presence and posterior ablation of the sites where rotors anchor might improve the success of AF ablation. Technical solutions emerged focusing on the rotor assessment problem. They base their methods on the reconstruction of the atrial activity using multi-electrode catheters and phase maps, in which they detect singularity points, the sites where rotors spin. The ablation of these sites showed promising results, but the difficulty to reproduce the results by other authors increased the controversy on this technique. In this Thesis we address the rotor detection problem in the time domain as opposed to current methods based on the phase domain of the signals. We develop a new method to identify local activation times (LATs) in unipolar electrograms (EGMs) recorded with multi-electrode catheters. We propose a new filtering scheme to enhance the activation component of the EGM while considerably reducing the presence of noise in the signal. This signal processing method reects the real activity of the tissue in contact with the electrode. It opposes the Hilbert transform (HT) used to extract the phase component of the signal, that do not correlate well with the temporal activations. With the EGM LATs we perform a spatial interpolation translating the electrode positions of the catheter into a regular 2D grid. This way we generate isochronal maps revealing the electrical wavefronts in the atrium. What is more, this step guarantees compatibility with multi-electrode catheters, not restricting the method to specific models. With the isochronal maps, we develop a new rotor detection algorithm based on the optical flow of the wavefront dynamics, and a rotation pattern match. Additionally, we develop a new method based on Granger's causality to estimate the directionality of the wavefronts, that provides an additional indicator for rotational patterns. We validate the methods using in silico and real AF signals. We implement these methods into a system that can assess the presence of rotational activation sites in the atrium. Our system is able to operate in realtime with multi-electrode catheters of different topologies in contact with the atrial wall. We integrate signal acquisition and processing in our system, allowing direct acquisition of the signals without requiring signal exportation from a recording device, which delays the clinical procedure. We address the computational time handicap by designing parallelizable signal processing steps. We employ multi-core processors and GPU based code to distribute the computations and minimize the processing times, achieving near real-time results. The results presented in this Thesis provide a new technical solution to detect the presence of rotational activity (rotors) in AF patients in real-time. Although the presence of rotational activity is itself controversial, we individually validate each of the steps of the procedure and obtain evidence of the presence of rotational activity in AF patients. The system has been also found useful to characterize the atrial sites where rotational activity was found in terms of spatial and voltage distribution. The results of this Thesis provide a new alternative to existing methods based on phase analysis and open a new research line in the detection of the mechanisms sustaining AF.La fibrilación auricular (FA) es una de las arritmias más comunes en la práctica clínica. Para tratar de terminar esta fibrilación en pacientes se desarrollo el método de ablación con catéter hace ya más de 20 años. Desde su puesta en marchar esta técnica ha ido ganando aceptación internacional por parte de la comunidad médica, y los avances tecnológicos desarrollados en esta línea han aumentado la seguridad y disminuido la duración del procedimiento. Sin embargo todavía no existe un tratamiento perfecto para tratar la FA, debido en parte a que el conocimiento de los mecanismos que inician y sostienen la fibrilación son limitados. Como método de ablación el aislamiento de las venas pulmonares prevalece como el más empleado en la práctica, pero se hace necesario el desarrollo de nuevos métodos para hacer frente al problema de la FA. Distintas teorías tratan de explicar los mecanismos de inicio y mantenimiento de la FA, desde unas basadas en la propagación de múltiples frentes de onda aleatorios en las aurículas, hasta las que basan su hipótesis en focos ectópicos disparados principalmente desde las venas pulmonares, entre otras teorías. Recientemente, una de estas teorías basada en fuentes espacio-temporalmente estables (rotores) se propuso como mecanismo de mantenimiento de la FA. La característica más representativa de un rotor es su patrón de reentrada en forma de espiral que realiza el frente de onda eléctrico en el tejido auricular. La evaluación de la presencia de rotores y la posterior de los sitios en los que se encuentren puede mejorar el éxito de la ablación en pacientes con FA. En vista de esta tendencia por la búsqueda de rotores se desarrollaron soluciones técnicas para la evaluación de zonas que alberguen actividad rotacional. Sus técnicas se basan en la reconstrucción de la actividad auricular empleando catéteres multi-electrodo y detectando puntos de singularidad en mapas de phase, esto es la posición en la aurícula en la que el rotor gira. La ablación de estos puntos mostró resultados prometedores, pero la dificultad por replicar los resultados por parte de otros autores incremento la controversia con respecto a esta técnica. En esta Tesis abordamos el problema de la detección de rotores en el dominio del tiempo, oponiéndonos a las técnicas actuales basadas en el dominio de la fase de las señales. Para ello hemos desarrollado un nuevo para identificar tiempos de activación local en electrogramas unipolares registrados con catéteres multi-electrodo. Para ello proponemos un nuevo método de filtrado para realzar la activación del electrograma reduciendo considerablemente la presencia de ruido en la señal. Con este procesado de la señal extraemos y reflejamos la actividad real del tejido en contacto con el electrodo. Al mismo tiempo nos oponemos a la transformada de Hilbert empleada para calcular la componente de fase de la señal, que es sabido no tiene una buena correlación con las activaciones temporales. Con los electrogramas y los tiempos de activación locales aplicamos una interpolación espacial logrando trasladar la posición de los electrodos en el catéter a una rejilla regular en 2D. Mediante este paso generamos mapas isócronos que reconstruyen los frentes de onda eléctricos que se propagan en la aurícula. Además, la interpolación nos permite garantizar una compatibilidad con otros catéteres multi-electrodos, no restringiendo el uso de nuestro método a modelos específicos. Con los mapas isócronos hemos desarrollado un nuevo algoritmo de detección de rotores basado en el flujo óptico de la dinámica del frente de onda que hacemos coincidir con un patrón de rotación. Adicionalmente hemos desarrollado un nuevo método basad en la causalidad propuesta por Granger para estimar la dirección de los frentes de propagación, que sirve como indicador adicional para encontrar patrones de activación rotacional. Hemos validado todos y cada uno de los métodos empleando señales in silico así como señales reales de pacientes con FA. En la parte de aplicación, hemos implementado los métodos en un sistema que evalúa la presencia de actividad rotacional en la aurícula. Nuestro sistema opera en tiempo real siendo compatible con catéteres multi-electrodo de diferentes topologías asegurando contacto con la pared auricular. Para evitar sobreextender el procedimiento clínico, hemos integrado las partes de adquisición y procesado de señal conjuntamente, lo que nos permite un registro de las señales directo sin viii necesidad de requerir un exportado adicional desde un sistema de registro. Para hacer frente al objetivo de presentar los resultados en tiempo real hemos diseñado todos los pasos de procesado de señal para que sean paralelizables. Para ello empleamos procesadores multinúcleo y código para ejecutar en tarjetas gráficas (GPUs) para distribuir las computaciones y minimizar el tiempo de procesado, logrando resultados en quasi tiempo real. Hemos empleado el sistema de detección de rotores para estudiar la distribución espacial y de voltaje de los sitios que muestran actividad rotacional en la aurícula. Aunque la presencia de actividad rotacional es en sí misma controvertida, hemos validad individualmente todos y cada uno de los pasos descritos obteniendo evidencia de la presencia de actividad rotacional en pacientes con FA.Programa Oficial de Doctorado en Multimedia y ComunicacionesPresidente: Pablo Laguna Lasaosa.- Secretario: Pablo Martínez Olmos.- Vocal: Batiste Andreu Martínez Climen

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

三次元心臓モデルと不均一振動モデルによる心臓活動電位のコンピュータシミュレーション

Tohoku University西條芳文論

Non-Invasive Electrocardiographic Imaging of Ventricular Activities: Data-Driven and Model-Based Approaches

Die vorliegende Arbeit beleuchtet ausgewählte Aspekte der Vorwärtsmodellierung, so zum Beispiel die Simulation von Elektro- und Magnetokardiogrammen im Falle einer elektrisch stillen Ischämie sowie die Anpassung der elektrischen Potentiale unter Variation der Leitfähigkeiten. Besonderer Fokus liegt auf der Entwicklung neuer Regularisierungsalgorithmen sowie der Anwendung und Bewertung aktuell verwendeter Methoden in realistischen in silico bzw. klinischen Studien

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

Efficient Numerical Methods for Heart Simulation

The heart is one the most important organs in the human body and many other live creatures. The electrical activity in the heart controls the heart function, and many heart diseases are linked to the abnormalities in the electrical activity in the heart. Mathematical equations and computer simulation can be used to model the electrical activity in the heart. The heart models are challenging to solve because of the complexity of the models and the huge size of the problems. Several cell models have been proposed to model the electrical activity in a single heart cell. These models must be coupled with a heart model to model the electrical activity in the entire heart. The bidomain model is a popular model to simulate the propagation of electricity in myocardial tissue. It is a continuum-based model consisting of non-linear ordinary differential equations (ODEs) describing the electrical activity at the cellular scale and a system of partial differential equations (PDEs) describing propagation of electricity at the tissue scale. Because of this multi-scale, ODE/PDE structure of the model, splitting methods that treat the ODEs and PDEs in separate steps are natural candidates as numerical methods. First, we need to solve the problem at the cellular scale using ODE solvers. One of the most popular methods to solve the ODEs is known as the Rush-Larsen (RL) method. Its popularity stems from its improved stability over integrators such as the forward Euler (FE) method along with its easy implementation. The RL method partitions the ODEs into two sets: one for the gating variables, which are treated by an exponential integrator, and another for the remaining equations, which are treated by the FE method. The success of the RL method can be understood in terms of its relatively good stability when treating the gating variables. However, this feature would not be expected to be of benefit on cell models for which the stiffness is not captured by the gating equations. We demonstrate that this is indeed the case on a number of stiff cell models. We further propose a new partitioned method based on the combination of a first-order generalization of the RL method with the FE method. This new method leads to simulations of stiff cell models that are often one or two orders of magnitude faster than the original RL method. After solving the ODEs, we need to use bidomain solvers to solve the bidomain model. Two well-known, first-order time-integration methods for solving the bidomain model are the semi-implicit method and the Godunov operator-splitting method. Both methods decouple the numerical procedure at the cellular scale from that at the tissue scale but in slightly different ways. The methods are analyzed in terms of their accuracy, and their relative performance is compared on one-, two-, and three-dimensional test cases. As suggested by the analysis, the test cases show that the Godunov method is significantly faster than the semi-implicit method for the same level of accuracy, specifically, between 5 and 15 times in the cases presented. Second-order bidomain solvers can generally be expected to be more effective than first-order bidomain solvers under normal accuracy requirements. However, the simplest and the most commonly applied second-order method for the PDE step, the Crank-Nicolson (CN) method, may generate unphysical oscillations. We investigate the performance of a two-stage, L-stable singly diagonally implicit Runge-Kutta method for solving the PDEs of the bidomain model and present a stability analysis. Numerical experiments show that the enhanced stability property of this method leads to more physically realistic numerical simulations compared to both the CN and Backward Euler (BE) methods