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

Doctor of Philosophy

dissertationComputational simulation has become an indispensable tool in the study of both basic mechanisms and pathophysiology of all forms of cardiac electrical activity. Because the heart is comprised of approximately 4 billion electrically active cells, it is not possible to geometrically model or computationally simulate each individual cell. As a result computational models of the heart are, of necessity, abstractions that approximate electrical behavior at the cell, tissue, and whole body level. The goal of this PhD dissertation was to evaluate several aspects of these abstractions by exploring a set of modeling approaches in the field of cardiac electrophysiology and to develop means to evaluate both the amplitude of these errors from a purely technical perspective as well as the impacts of those errors in terms of physiological parameters. The first project used subject specific models and experiments with acute myocardial ischemia to show that one common simplification used to model myocardial ischemia-the simplest form of the border zone between healthy and ischemic tissue-was not supported by the experimental results. We propose a alternative approximation of the border zone that better simulates the experimental results. The second study examined the impact of simplifications in geometric models on simulations of cardiac electrophysiology. Such models consist of a connected mesh of polygonal elements and must often capture complex external and internal boundaries. A conforming mesh contains elements that follow closely the shapes of boundaries; nonconforming meshes fit the boundaries only approximately and are easier to construct but their impact on simulation accuracy has, to our knowledge, remained unknown. We evaluated the impact of this simplification on a set of three different forms of bioelectric field simulations. The third project evaluated the impact of an additional geometric modeling error; positional uncertainty of the heart in simulations of the ECG. We applied a relatively novel and highly efficient statistical approach, the generalized Polynomial Chaos-Stochastic Collocation method (gPC-SC), to a boundary element formulation of the electrocardiographic forward problem to carry out the necessary comprehensive sensitivity analysis. We found variations large enough to mask or to mimic signs of ischemia in the ECG

Data-driven modelling of biological multi-scale processes

Biological processes involve a variety of spatial and temporal scales. A holistic understanding of many biological processes therefore requires multi-scale models which capture the relevant properties on all these scales. In this manuscript we review mathematical modelling approaches used to describe the individual spatial scales and how they are integrated into holistic models. We discuss the relation between spatial and temporal scales and the implication of that on multi-scale modelling. Based upon this overview over state-of-the-art modelling approaches, we formulate key challenges in mathematical and computational modelling of biological multi-scale and multi-physics processes. In particular, we considered the availability of analysis tools for multi-scale models and model-based multi-scale data integration. We provide a compact review of methods for model-based data integration and model-based hypothesis testing. Furthermore, novel approaches and recent trends are discussed, including computation time reduction using reduced order and surrogate models, which contribute to the solution of inference problems. We conclude the manuscript by providing a few ideas for the development of tailored multi-scale inference methods.Comment: This manuscript will appear in the Journal of Coupled Systems and Multiscale Dynamics (American Scientific Publishers

A Multiscale in Silico Study to Characterize the Atrial Electrical Activity of Patients With Atrial Fibrillation. A Translational Study to Guide Ablation Therapy

[ES] La fibrilación auricular es la arritmia cardíaca más común. Durante la fibrilación auricular, el sustrato auricular sufre una serie de cambios o remodelados a nivel eléctrico y estructural. La remodelación eléctrica se caracteriza por la alteración de una serie de canales iónicos, lo que cambia la morfología del potential de transmembrana conocido como potencial de acción. La remodelación estructural es un proceso complejo que involucra la interacción de varios procesos de señalización, interacción celular y cambios en la matriz extracelular. Durante la remodelación estructural, los fibroblastos que abundan en el tejido cardíaco, comienzan a diferenciarse en miofibroblastos que son los encargados de mantener la estructura de la matriz extracelular depositando colágeno. Además, la señalización paracrina de los miofibroblastos afecta a los canales iónicos de los miocitos circundantes. Se utilizaron modelos computacionales muy detallados a diferentes escalas para estudiar la remodelación estructural inducida a nivel celular y tisular. Se realizó una adaptación de un modelo de fibroblastos humanos a nivel celular para reproducir la electrofisiología de los miofibroblastos durante la fibrilación auricular. Además, se evaluó la exploración de la interacción del calcio en la electrofisiología de los miofibroblastos ajustando el canal de calcio a los datos experimentales. A nivel tisular, se estudió la infiltración de miofibroblastos para cuantificar el aumento de vulnerabilidad a una arritmia cardíaca. Los miofibroblastos cambian la dinámica de la reentrada. Una baja densidad de miofibroblastos permite la propagación a través del área fibrótica y crea puntos de salida de actividad focal y roturas de ondas dentro de esta área. Además, las composiciones de fibrosis juegan un papel clave en la alteración del patrón de propagación. La alteración del patrón de propagación afecta a los electrogramas recogidos en la superficie del tejido. La morfología del electrograma se alteró dependiendo de la disposición y composición del tejido fibrótico. Se combinaron modelos detallados de tejido cardíaco con modelos realistas de los catéteres de mapeo disponibles comercialmente para comprender las señales registradas clínicamente. Se generó un modelo de ruido a partir de señales clínicas para reproducir los artefactos de señal en el modelo. Se utilizaron electrogramas de modelos de dos dominios altamente detallados para entrenar un algoritmo de aprendizaje automático para caracterizar el sustrato fibrótico auricular. Las características que cuantifican la complejidad de las señales fueron extraídas para identificar la densidad fibrótica y la transmuralidad fibrótica. Posteriormente, se generaron mapas de fibrosis utilizando el registro del paciente como prueba de concepto. El mapa de fibrosis proporciona información sobre el sustrato fibrótico sin utilizar un valor único de corte de 0,5 milivoltios. Además, utilizando la medición del flujo de información como la entropía de transferencia combinada con gráficos dirigidos, en este estudio, se siguió la dirección de propagación del frente de onda. La transferencia de entropía con gráficos dirigidos proporciona información crucial durante la electrofisiología para comprender la dinámica de propagación de ondas durante la fibrilación auricular. En conclusión, esta tesis presenta un estudio in silico multiescala que proporciona información sobre los mediadores celulares responsables de la remodelación de la matriz extracelular y su electrofisiología. Además, proporciona una configuración realista para crear datos in silico que pueden ser usados para aplicaciones clínicas y servir de soporte al tratamiento de ablación.[CA] La fibril·lació auricular és l'arrítmia cardíaca més freqüent, en la qual el substrat auricular patix una sèrie de remodelacions elèctriques i estructurals. La remodelació de tipus elèctric es caracteritza per l'alteració d'un conjunt de canals iònics que modifica la morfologia del voltatge transmembrana, conegut com a potencial d'acció. La remodelació estructural és un fenomen complex que implica la relació entre diversos processos de senyalització, interaccions cel·lulars i canvis en la matriu extracel·lular. Durant la remodelació estructural, els abundants fibroblasts presents en el teixit cardíac comencen a diferenciar-se en miofibroblasts, els quals s'encarreguen de mantenir l'estructura de la matriu extracel·lular dipositant-hi col·lagen. A més, la senyalització paracrina dels miofibroblasts amb els miòcits circumdants també afectarà els canals iònics. Es van utilitzar models computacionals molt detallats a diferents escales per estudiar la remodelació estructural induïda a nivell tissular i cel·lular. Es va fer una adaptació a nivell cel·lular d'un model de fibroblasts humans per reproduir-hi l'electrofisiologia dels miofibroblasts durant la fibril·lació auricular. A més, l'exploració de la interacció del calci amb l'electrofisiologia dels miofibroblasts va ser avaluada mitjançant l'adequació del canal de calci a les dades experimentals. A nivell tissular es va estudiar la infiltració de miofibroblasts per tal de quantificar l'augment de vulnerabilitat que això conferia per patir una arrítmia cardíaca. Els miofibroblasts canvien la dinàmica de la reentrada, i presentar-ne una baixa densitat permet la propagació a través de la zona fibròtica, tot creant punts de sortida d'activitat focal i trencaments d'ones dins d'aquesta àrea. A més, les composicions de fibrosi tenen un paper clau en l'alteració del patró de propagació, afectant els electrogrames recollits en la superfície del teixit. La morfologia dels electrogrames es va veure alterada en funció de la disposició i la composició del teixit fibròtic. Per comprendre els senyals clínicament registrats es van combinar models detallats de teixits cardíacs amb models realistes dels catèters de cartografia disponibles comercialment. Es va generar un model de soroll a partir de senyals clínics per reproduir-hi els artefactes de senyal. Es van utilitzar electrogrames de models de bidominis molt detallats per entrenar un algoritme d'aprenentatge automàtic destinat a caracteritzar el substrat fibròtic auricular. Les característiques que quantifiquen la complexitat dels senyals van ser extretes per identificar la densitat i transmuralitat fibròtica. Posteriorment, es van generar mapes de fibrosi mitjançant la gravació del pacient com a prova de concepte. El mapa de fibrosi proporciona informació sobre el substrat fibròtic sense utilitzar un sol valor de tensió de tall de 0,5 mV. A més, utilitzant la mesura del flux d'informació com l'entropia de transferència combinada amb gràfics dirigits, en aquest estudi es va fer un seguiment de la direcció de propagació de l'ona. L'entropia de transferència amb gràfics dirigits proporciona informació crucial durant l'electrofisiologia per entendre la dinàmica de propagació d'ones durant la fibril·lació auricular. En conclusió, aquesta tesi presenta un estudi multi-escala in silico que proporciona informació sobre els mediadors cel·lulars responsables de la remodelació de la matriu extracel·lular i la seva electrofisiologia. A més, proporciona una configuració realista per crear dades in silico que es poden traduir a aplicacions clíniques que puguen donar suport al tractament de l'ablació.[EN] Atrial fibrillation is the most common cardiac arrhythmia. During atrial fibrillation, the atrial substrate undergoes a series of electrical and structural remodeling. The electrical remodeling is characterized by the alteration of specific ionic channels, which changes the morphology of the transmembrane voltage known as action potential. Structural remodeling is a complex process involving the interaction of several signalling pathways, cellular interaction, and changes in the extracellular matrix. During structural remodeling, fibroblasts, abundant in the cardiac tissue, start to differentiate into myofibroblasts, which are responsible for maintaining the extracellular matrix structure by depositing collagen. Additionally, myofibroblasts paracrine signalling with surrounding myocytes will also affect ionic channels. Highly detailed computational models at different scales were used to study the effect of structural remodeling induced at the cellular and tissue levels.At the cellular level, a human fibroblast model was adapted to reproduce the myofibroblast electrophsyiology during atrial fibrillation. Additionally, the calcium handling in myofibroblast electrophysiology was assessed by fitting calcium ion channel to experimental data. At the tissue level, myofibroblasts infiltration was studied to quantify the increase of vulnerability to cardiac arrhythmia. Myofibroblasts alter the dynamics of reentry. A low density of myofibroblasts allows the propagation through the fibrotic area and creates focal activity exit points and wave breaks inside this area. Moreover, fibrosis composition plays a key role in the alteration of the propagation pattern. The alteration of the propagation pattern affects the electrograms computed at the surface of the tissue. Electrogram morphology was altered depending on the arrangement and composition of the fibrotic tissue. Detailed cardiac tissue models were combined with realistic models of the commercially available mapping catheters to understand the clinically recorded signals. A noise model from clinical signals was generated to reproduce the signal artifacts in the model. Electrograms from highly detailed bidomain models were used to train a machine learning algorithm to characterize the atrial fibrotic substrate. Features that quantify the complexity of the signals were extracted to identify fibrotic density and fibrotic transmurality. Subsequently, fibrosis maps were generated using patient recordings as a proof of concept. Fibrosis map provides information about the fibrotic substrate without using a single cut-off voltage value of 0.5 mV. Furthermore, in this study, using information theory measurements such as transfer entropy combined with directed graphs, the wave propagation direction was tracked. Transfer entropy with directed graphs provides crucial information during electrophysiology to understand wave propagation dynamics during atrial fibrillation. In conclusion, this thesis presents a multiscale in silico study atrial fibrillation mechanisms providing insight into the cellular mediators responsible for the extracellular matrix remodeling and its electrophysiology. Additionally, it provides a realistic setup to create in silico data that can be translated to clinical applications that could support ablation treatment.Sánchez Arciniegas, JP. (2021). A Multiscale in Silico Study to Characterize the Atrial Electrical Activity of Patients With Atrial Fibrillation. A Translational Study to Guide Ablation Therapy [Tesis doctoral]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/171456TESI

A Multiscale In Silico Study to Characterize the Atrial Electrical Activity of Patients With Atrial Fibrillation : A Translational Study to Guide Ablation Therapy

The atrial substrate undergoes electrical and structural remodeling during atrial fibrillation. Detailed multiscale models were used to study the effect of structural remodeling induced at the cellular and tissue levels. Simulated electrograms were used to train a machine-learning algorithm to characterize the substrate. Also, wave propagation direction was tracked from unannotated electrograms. In conclusion, in silico experiments provide insight into electrograms\u27 information of the substrate

Simulating the Effect of Global Cardiac Ischaemia on the Dynamics of Ventricular Arrhythmias in the Human Heart

Cardiac arrhythmias are significant causes of death in the world, and ventricular fibrillation is a very dangerous type of cardiac arrhythmia. Global myocardial ischemia is a consequence of ventricular fibrillation (VF) and has been shown to change the dynamic behaviour of activation waves on the heart. The aim of this thesis is to use computational models to study the behaviour of re-entry in the human ventricles when the heart becomes globally ischaemic. The effects of two ischaemic components (hyperkalaemia and hypoxia) on spiral wave re-entry behaviour in two dimensional (2D) ventricular tissue using two ventricular action potential (AP) models were simulated (Ten Tusscher et al. 2006 (TP06) and O’Hara et al. 2011 (ORd)). A three dimensional (3D) model of the human ventricles is used to examine the influence of each ischaemic component on the stability of ventricular fibrillation. Firstly, the main ventricular AP models relevant to this thesis are reviewed. Then, the current-voltage properties of four different IK(ATP) formulations are examined to assess which formulation was more appropriate to simulate hypoxia/ischaemia. Secondly, how the formulation of IK(ATP) influences cell excitability and AP duration (APD) in models of human ventricular myocytes is studied. Finally, mechanisms underlying ventricular arrhythmia generation under the conditions of ischaemia are investigated