Gaussian process manifold interpolation for probabilistic atrial activation maps and uncertain conduction velocity

In patients with atrial fibrillation, local activation time (LAT) maps are routinely used for characterizing patient pathophysiology. The gradient of LAT maps can be used to calculate conduction velocity (CV), which directly relates to material conductivity and may provide an important measure of atrial substrate properties. Including uncertainty in CV calculations would help with interpreting the reliability of these measurements. Here, we build upon a recent insight into reduced-rank Gaussian processes (GPs) to perform probabilistic interpolation of uncertain LAT directly on human atrial manifolds. Our Gaussian process manifold interpolation (GPMI) method accounts for the topology of the atrium, and allows for calculation of statistics for predicted CV. We demonstrate our method on two clinical cases, and perform validation against a simulated ground truth. CV uncertainty depends on data density, wave propagation direction and CV magnitude. GPMI is suitable for probabilistic interpolation of other uncertain quantities on non-Euclidean manifolds. This article is part of the theme issue ‘Uncertainty quantification in cardiac and cardiovascular modelling and simulation’

Abbott Lab Instrumentation Validation

Over the past 40 years, since the initial catheter ablation procedure was completed, cardiac mapping has become an essential part of electrophysiological procedures. Cardiac mapping is an electrophysiological study that allows physicians to analyze the electrical activity of the heart in order to diagnose and treat cardiovascular disease. Institutions like Cal Poly can utilize professional instrumentation systems with an appropriate wet lab to develop new devices and study various phenomena in an in-vitro physiological environment. Cardiac mapping systems used in tandem with catheter ablation procedures are essential to ensuring that the trend of deaths due to cardiovascular disease continues to decline. This project thesis will signify the importance of the development of a wet lab integrated with Abbott’s Ensite Precision Cardiac Mapping System for future product development and in-vitro studies

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

Personalized Multi-Scale Modeling of the Atria: Heterogeneities, Fiber Architecture, Hemodialysis and Ablation Therapy

This book targets three fields of computational multi-scale cardiac modeling. First, advanced models of the cellular atrial electrophysiology and fiber orientation are introduced. Second, novel methods to create patient-specific models of the atria are described. Third, applications of personalized models in basic research and clinical practice are presented. The results mark an important step towards the patient-specific model-based atrial fibrillation diagnosis, understanding and treatment

Quantifying atrial anatomy uncertainty from clinical data and its impact on electro-physiology simulation predictions

Patient-specific computational models of structure and function are increasingly being used to diagnose disease and predict how a patient will respond to therapy. Models of anatomy are often derived after segmentation of clinical images or from mapping systems which are affected by image artefacts, resolution and contrast. Quantifying the impact of uncertain anatomy on model predictions is important, as models are increasingly used in clinical practice where decisions need to be made regardless of image quality. We use a Bayesian probabilistic approach to estimate the anatomy and to quantify the uncertainty about the shape of the left atrium derived from Cardiac Magnetic Resonance images. We show that we can quantify uncertain shape, encode uncertainty about the left atrial shape due to imaging artefacts, and quantify the effect of uncertain shape on simulations of left atrial activation times

Statistical and Graph-Based Signal Processing: Fundamental Results and Application to Cardiac Electrophysiology

The goal of cardiac electrophysiology is to obtain information about the mechanism, function, and performance of the electrical activities of the heart, the identification of deviation from normal pattern and the design of treatments. Offering a better insight into cardiac arrhythmias comprehension and management, signal processing can help the physician to enhance the treatment strategies, in particular in case of atrial fibrillation (AF), a very common atrial arrhythmia which is associated to significant morbidities, such as increased risk of mortality, heart failure, and thromboembolic events. Catheter ablation of AF is a therapeutic technique which uses radiofrequency energy to destroy atrial tissue involved in the arrhythmia sustenance, typically aiming at the electrical disconnection of the of the pulmonary veins triggers. However, recurrence rate is still very high, showing that the very complex and heterogeneous nature of AF still represents a challenging problem. Leveraging the tools of non-stationary and statistical signal processing, the first part of our work has a twofold focus: firstly, we compare the performance of two different ablation technologies, based on contact force sensing or remote magnetic controlled, using signal-based criteria as surrogates for lesion assessment. Furthermore, we investigate the role of ablation parameters in lesion formation using the late-gadolinium enhanced magnetic resonance imaging. Secondly, we hypothesized that in human atria the frequency content of the bipolar signal is directly related to the local conduction velocity (CV), a key parameter characterizing the substrate abnormality and influencing atrial arrhythmias. Comparing the degree of spectral compression among signals recorded at different points of the endocardial surface in response to decreasing pacing rate, our experimental data demonstrate a significant correlation between CV and the corresponding spectral centroids. However, complex spatio-temporal propagation pattern characterizing AF spurred the need for new signals acquisition and processing methods. Multi-electrode catheters allow whole-chamber panoramic mapping of electrical activity but produce an amount of data which need to be preprocessed and analyzed to provide clinically relevant support to the physician. Graph signal processing has shown its potential on a variety of applications involving high-dimensional data on irregular domains and complex network. Nevertheless, though state-of-the-art graph-based methods have been successful for many tasks, so far they predominantly ignore the time-dimension of data. To address this shortcoming, in the second part of this dissertation, we put forth a Time-Vertex Signal Processing Framework, as a particular case of the multi-dimensional graph signal processing. Linking together the time-domain signal processing techniques with the tools of GSP, the Time-Vertex Signal Processing facilitates the analysis of graph structured data which also evolve in time. We motivate our framework leveraging the notion of partial differential equations on graphs. We introduce joint operators, such as time-vertex localization and we present a novel approach to significantly improve the accuracy of fast joint filtering. We also illustrate how to build time-vertex dictionaries, providing conditions for efficient invertibility and examples of constructions. The experimental results on a variety of datasets suggest that the proposed tools can bring significant benefits in various signal processing and learning tasks involving time-series on graphs. We close the gap between the two parts illustrating the application of graph and time-vertex signal processing to the challenging case of multi-channels intracardiac signals

Finite element simulations: computations and applications to aerodynamics and biomedicine.

171 p.Las ecuaciones en derivadas parciales describen muchos fenómenos de interés práctico y sus solucionessuelen necesitar correr simulaciones muy costosas en clústers de cálculo.En el ámbito de los flujos turbulentos, en particular, el coste de las simulaciones es demasiado grande sise utilizan métodos básicos, por eso es necesario modelizar el sistema.Esta tesis doctoral trata principalmente de dos temas en Cálculo Científico.Por un lado, estudiamos nuevos desarrollos en la modelización y simulación de flujos turbulentos;utilizamos un Método de Elementos Finitos adaptativo y un modelo de ¿número de Reynolds infinito¿para reducir el coste computacional de simulaciones que, sin estas modificaciones, serían demasiadocostosas.De esta manera conseguimos lograr simulaciones evolutivas de flujos turbulentos con número deReynolds muy grande, lo cual se considera uno de los mayores retos en aerodinámica.El otro pilar de esta tesis es una aplicación biomédica.Desarrollamos un modelo computacional de Ablación (Cardiaca) por Radiofrecuencia, una terapiacomún para tratar varias enfermedades, por ejemplo algunas arritmias.Nuestro modelo mejora los modelos existentes en varias maneras, y en particular en tratar de obteneruna aproximación fiel de la geometría del sistema, lo cual se descubre ser crítico para simularcorrectamente la física del fenómeno