Identification of Parameters describing Phenomenological Cardiac Action Potential Models using Sigma-Point Methods

Phenomenological action potential (AP) models allow reproducing characteristic features of cardiomyocytes’ electrical activity without fully describing the underlying biophysics, thus being very useful for whole-heart electrophysiological simulations. Methods to identify the parameter values of phenomenological models commonly attempt to reproduce specific AP properties rather than the whole AP waveform. In this work we propose the use of a sequential estimation approach based on sigma-point filters to adjust such parameters. The proposed methodology has been tested in estimating the parameters of the phenomenological Bueno-Cherry-Fenton model to replicate the APs generated with in silico models as well as experimentally measured APs. With the new method the whole AP waveforms can be reproduced more accurately than with previous parameter fitting methods and the AP duration restitution curves are in better agreement with available experimental data

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

Theroetical Analysis of Autonomic Nervous System Effects on Cardiac Elestrophysiology and its Relationship with Arrhythmic Risk

Las enfermedades cardiovasculares representan la principal causa de mortalidad y morbilidad en las sociedades industrializadas. Un porcentaje significativo de las muertes asociadas a estas enfermedades está relacionado con el desarrollo de arritmias cardíacas, siendo éstas definidas como anomalías en el funcionamiento eléctrico del corazón.Tres son los elementos principales que están involucrados en el desarrollo de las arritmias: un sustrato arritmogénico, un desencadenante y factores de modulación. El Sistema Nervioso Autónomo (SNA) es el más relevante de estos factores moduladores.El SNA está compuesto por dos ramas, simpática y parasimpática, que encierta medida actúan de forma antagónica entre sí. La posibilidad de revelar cómo el sistema nervioso simpático modula la actividad ventricular y participa en el desarrollo de arritmias, tal y como se ha observado experimentalmente, podría ser crucial para avanzar en el diseño de nuevas terapias clínicas dirigidas a prevenir o tratar estas anomalías rítmicas.Esta tesis investiga y analiza la variabilidad espacio-temporal de la repolarización ventricular humana, su modulación por el sistema nervioso simpático, los mecanismos que subyacen a incrementos notables en dicha variabilidad y la relación que existe con la generación de arritmias ventriculares. Para ello, se proponen metodología que combinan el procesado de señales ventriculares y el modelado in silico de miocitos ventriculares humanos. Los modelos in silico desarrollados incluyen descripciones teóricas acopladas de la electrofisiología, la dinámica del calcio, el estiramiento mecánico y la señalización -adrenérgica. Para tener en cuenta la variabilidad temporal(latido a latido) de la repolarización, se añade estocasticidad en las ecuaciones que definen la apertura y cierre de los canales iónicos de las principales corrientes activas durante la fase de repolarización del potencial de acción (AP), es decir, durante el retorno de la célula al estado de reposo después de una excitación. Por otro lado, para tener en cuenta la variabilidad espacial (célula a célula) de la repolarización, se construye y calibra una población de modelos representativos de diferentes características celulares utilizando para ellos datos experimentales disponibles. La investigación teórica y computacional de este estudio, combinada con el procesado de señales ventriculares tanto clínicas como experimentales, sienta las bases para futuros estudios que tengan como objetivo mejorar los métodos de estratificación del riesgo arrítmico y guiar la búsqueda de terapias antiarrítmicas más eficaces.En el Capítulo 2, se construye una población de modelos computacionales estocásticos representativos de células ventriculares humanas, los cuales se calibran experimentalmente.Estos modelos combinan la electrofisiología, la mecánica y la señalización-adrenérgica y se utizan para caracterizar de modo teórico la variabilidadespacio-temporal. La calibración de los modelos se basa en rangos experimentales de una serie de marcadores derivados del AP que describen su duración, amplitud y morfología.Mediante el uso de esta población de modelos estocásticos de AP se reproducenlas interacciones descritas experimentalmente entre un tipo particular de variabilidad temporal, asociada con las oscilaciones de baja frecuencia (LF) de la duración del AP (APD), y la variabilidad global latido a latido de la repolarización (BVR) en respuesta a un incremento de la actividad simpática. Además en este capítulo, se han estudiado los mecanismos iónicos que esán detrás de los incrementos simultáneos de ambos fenómenos y se ha demostrado que dichos mecanismos están asociados con la disminución de las corrientes rectificadora de entrada y rectificadora retardada rápida de K+ y a su vez de la corriente de Ca2+ tipo-L. Finalmente, se ha probado que niveles elevados de oscilaciones de baja frecuencia del APD y de BVR en ventrículos enfermosconducen a inestabilidades eléctricas y al desarrollo de eventos arritmogénicos.En el Capítulo 3, se investiga el retardo necesario para la manifestación de las oscilaciones LF del APD, como una forma particular de variabilidad de repolarización, en los miocitos ventriculares en respuesta a la provocación simpática. Mediante el uso de una población calibrada experimentalmente de modelos de AP ventriculares humanos, como en el Capítulo 2, se ha demostrado que esta latencia oscilatoria está asociada con la cinética lenta de fosforilación de la corriente rectificadora retardada lenta de K+ (IKs) en respuesta a la estimulación -adrenérgica. La estimulación previa de los receptores reduce sustancialmente el tiempo requerido para el desarrollo de oscilaciones de LF. Además, se ha demostrado que lapsos de tiempo cortos están íntimamente relacionados con mayores magnitudes oscilatorias del APD, medidas en elCapítulo 3, particularmente en células susceptibles de desarrollar eventos arritmogénicos en respuesta a la estimulación simpática.La calibración experimental de la población de modelos utilizados en los Capítulos 2 y 3 no garantiza que cada modelo de la población construida represente las medidas de un cardiomiocito ventricular humano individual. Es por esta razón que en el Capítulo 4 se desarrolla una metodología novedosa para construir poblaciones computacionales de modelos celulares ventriculares humanos que recapitulen más fielmente las evidencias experimentales disponibles. La metodología propuesta se basa en la formulación de representaciones estado-espacio no lineales y en el uso del filtro de Kalman (UKF) para la estimación de los parámetros y las variables de estado de un modelo AP estocástico subyacente para cada señal de potencial dada como entrada.Las pruebas realizadas sobre series de potencial sintéticas y experimentales demuestran que esta metodología permite establecer una correspondencia entre las trazas AP de entrada y los conjuntos de parámetros del modelo (conductancias de corriente iónicas) y las variables de estado (variables relacionadas con la apertura/cierre de los canales iónicos y concentraciones iónicas intracelulares). A su vez, se ha demostrado que la metodología propuesta es robusta y adecuada para la investigación de la variabilidad espacio-temporal en la repolarización ventricular humana.En el Capítulo 5 se proponen varias mejoras a la metodología desarrollada en elCapítulo 4 para estimar con mayor precisión los parámetros y las variables de estado de los modelos estocásticos de células ventriculares humanas a partir de señales individuales de AP dadas como entradas, y a su vez para reducir el tiempo de convergencia a fin de proporcionar una estimación más rápida. Las mejoras se han basado en el uso combinado del método UKF, presentado en el Capítulo 4, junto con el método Double Greedy Dimension Reduction (DGDR) con generación automática de biomarcadores.Además de estimar las conductancias de las corrientes iónicas en condiciones basales, el enfoque presentado en este capítulo también proporciona el conjunto de niveles de fosforilación inducidos por la estimulación -adrenérgica, contribuyendo así al análisis de patrones de repolarización espacio-temporal con y sin modulación autonómica.En conclusión, esta tesis presenta novedosas metodologías enfocadas hacia lacaracterización de la variabilidad espacio-temporal de la repolarización ventricular humana, el análisis de sus mecanismos subyacentes y la determinaci´ón de la relación entre aumentos en la variabilidad y el mayor riesgo de sufrir arritmias ventriculares y muerte súbita cardíaca. Se desarrollan conjuntos de modelos computacionales estocásticos celulares humanos con representación de la electrofisiología ventricular, la mecánica y la señalización -adrenérgica para analizar la variabilidad global de larepolarización, latido a latido y célula a célula, así como de un tipo particular de variabilidad en forma de oscilaciones de baja frecuencia. Para reproducir fielmente los patrones de variabilidad medidos experimentalmente de manera individual, se proponen metodologías para construir poblaciones de modelos AP ventriculares humanos donde los parámetros y las variables de estado de cada modelo se estiman a partir de una serie de potencial de entrada dada. Estos modelos personalizados abren la puerta a una investigación más robusta de las causas y consecuencias de la variabilidad espacio-temporal de la repolarización ventricular humanCardiovascular diseases represent the main cause of mortality and morbidity in industrialized societies. A significant percentage of deaths associated with these diseases is related to the generation of cardiac arrhythmias, defined as abnormalities in the electrical functioning of the heart. Three major elements are involved in the development of arrhythmias, which include an arrhythmogenic substrate, a trigger and modulating factors. The Autonomic Nervous System (ANS) is the most relevant of these modulators. The ANS is composed of two branches, sympathetic and parasympathetic, which to a certain extent act antagonistically to each other. The possibility of revealing how the sympathetic nervous system modulates the activity of the ventricles (lower heart chambers) and participates in the development of arrhythmias, as reported experimentally, could be crucial to advance in the design of new clinical therapies aimed at preventing or treating these rhythm abnormalities. This thesis investigates spatio-temporal variability of human ventricular repolarization, its modulation by the sympathetic nervous system, the mechanisms behind highly elevated variability and the relationship to the generation of ventricular arrhythmias. To that end, methodologies combining signal processing of ventricular signals and in silico modeling of human ventricular myocytes are proposed. The developed in silico models include coupled theoretical descriptions of electrophysiology, calcium dynamics, mechanical stretch and -adrenergic signaling. To account for temporal (beat-to-beat) repolarization variability, stochasticity is added into the equations defining the gating of the ion channels of the main currents active during action potential (AP) repolarization, i.e. during the return of the cell to the resting state after an excitation. To account for spatial (cell-to-cell) repolarization variability, a population of models representative of different cellular characteristics are constructed and calibrated based on available experimental data. The theoretical computational research of this study, combined with the processing of clinical and experimental ventricular signals, lays the ground for future studies aiming at improving arrhythmic risk stratification methods and at guiding the search for more efficient anti-arrhythmic therapies. In Chapter 2, a population of experimentally-calibrated stochastic human ventricular computational cell models coupling electrophysiology, mechanics and -adrenergic signaling are built to investigate spatio-temporal variability. Model calibration is based on experimental ranges of a number of AP-derived markers describing AP duration, amplitude and shape. By using the proposed population of stochastic AP models, the experimentally reported interactions between a particular type of temporal variability associated with low-frequency (LF) oscillations of AP duration (APD) and overall beat-to-beat variability of repolarization (BVR) in response to enhanced sympathetic activity are reproduced. Ionic mechanisms behind correlated increments in both phenomena are investigated and found to be related to downregulation of the inward and rapid delayed rectifier K+ currents and the L-type Ca2+ current. Concomitantly elevated levels of LF oscillations of APD and BVR in diseased ventricles are shown to lead to electrical instabilities and arrhythmogenic events. In Chapter 3, the time delay for manifestation of LF oscillations of APD, as a particular form of repolarization variability, is investigated in ventricular myocytes in response to sympathetic provocation. By using an experimentally-calibrated population of human ventricular AP models, as in Chapter 2, this oscillatory latency is demonstrated to be associated with the slow phosphorylation kinetics of the slow delayed rectifier K+ current IKs in response to -adrenergic stimulation. Prior stimulation of -adrenoceptors substantially reduces the time required for the development of LF oscillations. In addition, short time lapses are shown to be related to large APD oscillatory magnitudes, as measured in Chapter 2, particularly in cells susceptible to develop arrhythmogenic events in response to sympathetic stimulation. The experimental calibration of the population of models used in Chapter 2 and Chapter 3, despite ensuring that simulated population measurements lie within experimental limits, does not guarantee that each model in the constructed population represents the experimental measurements of an individual human ventricular cardiomyocyte. It is for that reason that in Chapter 4 a novel methodology is developed to construct computational populations of human ventricular cell models that more faithfully recapitulate individual available experimental evidences. The proposed methodology is based on the formulation of nonlinear state-space representations and the use of the Unscented Kalman Filter (UKF) to estimate parameters and state variables of an underlying stochastic AP model given any input voltage trace. Tests performed over synthetic and experimental voltage traces demonstrate that this methodology successfully renders a one-to-one match between input AP traces and sets of model parameters (ionic current conductances) and state variables (ionic gating variables and intracellular concentrations). The proposed methodology is shown to be robust for investigation of spatio-temporal variability in human ventricular repolarization. Chapter 5 improves the methodology developed in Chapter 4 to more accurately estimate parameters and state variables of stochastic human ventricular cell models from individual input voltage traces and to reduce the converge time so as to provide faster estimation. The improvements are based on the combined use of the UKF method of Chapter 4 together with Double Greedy Dimension Reduction (DGDR) method with automatic generation of biomarkers. Additionally, on top of estimating ionic current conductances at baseline conditions, the approach presented in this chapter also provides a set of -adrenergic-induced phosphorylation levels, thus contributing to the analysis of spatio-temporal repolarization patterns with and without autonomic modulation. In conclusion, this thesis presents novel methodologies for characterization of spatio-temporal variability of human ventricular repolarization, for dissection of its underlying mechanisms and for ascertainment of the relationship between elevated variability and increased risk for ventricular arrhythmias and sudden cardiac death. Sets of stochastic human computational cell models with representation of ventricular electrophysiology, mechanics and -adrenergic signaling are developed and used to analyze overall beat-to-beat and cell-to-cell repolarization variability as well as a particular type of variability in the form of LF oscillations. To faithfully reproduce experimentally measured variability patterns in a one-to-one manner, methodologies are proposed to construct populations of human ventricular AP models where the parameters and state variables of a model are estimated from a given input voltage trace. These personalized models open the door to more robust investigation of the causes and consequences of spatio-temporal variability of human ventricular repolarization.<br /

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

Modelling and Estimation of Spatiotemporal Cardiac Electrical Dynamics

The heart is a complex biological system in which electrical activation signals initiate at the pacemaker cells, propagate through the heart tissue to both trigger and synchronise the mechanical contractions. Abnormalities in the cardiac electrical signals lead to dangerous cardiac arrhythmias. Therefore, understanding the functionalities of the cardiac electrical activity is essential for the development of novel techniques to facilitate advanced diagnosis and treatment for arrhythmia. By combining experimental or clinical electrophysiology data with mathematical models, system theoretic approaches can be used to provide quantitative insights into the normal and pathological mechanisms of the cardiac electrical activity. This thesis proposes model-based estimation methods to reconstruct and quantify the underlying spatiotemporal cardiac electrical dynamics from the cardiac electrogram measurements. Firstly, a statistical model-based estimation framework is proposed to reconstruct the tissue dynamics from the cardiac electrogram measurements. The reconstruction of the tissue dynamics is based on an integrated model of cardiac electrical activity, which incorporates the cardiac action potential dynamics at the cell-level, tissue-level and extracellular-level. The dynamics of the cardiac tissue is described using the monodomain tissue model, which is coupled with the continuous version of modified Mitchell-Schaeffer model. The resulting model equations are of infinite-dimensional form, which is converted into a finite-dimensional state-space representation via a model reduction method. In order to estimate the hidden state variables of the tissue dynamics from the cardiac electrogram measurements, a combined detection-estimation framework using a single filter unscented-transform based smoothing algorithm is proposed. The detection step in the proposed method enables the inclusion of localised stimulus events into the model-based estimation framework. The performance of the proposed algorithms are demonstrated using the modelled cardiac activation patterns of normal and reentrant conditions, in both one-dimensional and two-dimensional tissue field. The findings from this proposed study illustrate that the hidden state variables of the tissue model can be estimated from the electrogram measurements, simultaneously by detecting the stimulus events. Therefore, this method shows that the complex spatiotemporal cardiac activity can be reconstructed from the coarse electrograms using the state estimation methods. Secondly, a complex network modelling approach is proposed to quantify the spatiotemporal organisation of electrical activation during human ventricular fibrillation. The proposed network modelling approach includes three different methods based on correlation analysis, graph theoretical measures and hierarchical clustering. Using the proposed approach, the level of spatiotemporal organisation is quantified during three episodes of VF in ten patients, recorded using multi-electrode epicardial recordings with 30 s coronary perfusion, 150 s global myocardial ischaemia and 30 s reflow. The findings show a steady decline in spatiotemporal organisation from the onset of VF with coronary perfusion. Following this, a transient increases in spatiotemporal organisation is observed during global myocardial ischaemia. However, the decline in spatiotemporal organisation continued during reflow. The results are consistent across all patients, and are consistent with the numbers of phase singularities. The findings show that the complex spatiotemporal patterns can be studied using complex network analysis

Planification de l’ablation radiofréquence des arythmies cardiaques en combinant modélisation et apprentissage automatique

Cardiac arrhythmias are heart rhythm disruptions which can lead to sudden cardiac death. They require a deeper understanding for appropriate treatment planning. In this thesis, we integrate personalized structural and functional data into a 3D tetrahedral mesh of the biventricular myocardium. Next, the Mitchell-Schaeffer (MS) simplified biophysical model is used to study the spatial heterogeneity of electrophysiological (EP) tissue properties and their role in arrhythmogenesis. Radiofrequency ablation (RFA) with the elimination of local abnormal ventricular activities (LAVA) has recently arisen as a potentially curative treatment for ventricular tachycardia but the EP studies required to locate LAVA are lengthy and invasive. LAVA are commonly found within the heterogeneous scar, which can be imaged non-invasively with 3D delayed enhanced magnetic resonance imaging (DE-MRI). We evaluate the use of advanced image features in a random forest machine learning framework to identify areas of LAVA-inducing tissue. Furthermore, we detail the dataset’s inherent error sources and their formal integration in the training process. Finally, we construct MRI-based structural patient-specific heart models and couple them with the MS model. We model a recording catheter using a dipole approach and generate distinct normal and LAVA-like electrograms at locations where they have been found in clinics. This enriches our predictions of the locations of LAVA-inducing tissue obtained through image-based learning. Confidence maps can be generated and analyzed prior to RFA to guide the intervention. These contributions have led to promising results and proofs of concepts.Les arythmies sont des perturbations du rythme cardiaque qui peuvent entrainer la mort subite et requièrent une meilleure compréhension pour planifier leur traitement. Dans cette thèse, nous intégrons des données structurelles et fonctionnelles à un maillage 3D tétraédrique biventriculaire. Le modèle biophysique simplifié de Mitchell-Schaeffer (MS) est utilisé pour étudier l’hétérogénéité des propriétés électrophysiologiques (EP) du tissu et leur rôle sur l’arythmogénèse. L’ablation par radiofréquence (ARF) en éliminant les activités ventriculaires anormales locales (LAVA) est un traitement potentiellement curatif pour la tachycardie ventriculaire, mais les études EP requises pour localiser les LAVA sont longues et invasives. Les LAVA se trouvent autour de cicatrices hétérogènes qui peuvent être imagées de façon non-invasive par IRM à rehaussement tardif. Nous utilisons des caractéristiques d’image dans un contexte d’apprentissage automatique avec des forêts aléatoires pour identifier des aires de tissu qui induisent des LAVA. Nous détaillons les sources d’erreur inhérentes aux données et leur intégration dans le processus d’apprentissage. Finalement, nous couplons le modèle MS avec des géométries du coeur spécifiques aux patients et nous modélisons le cathéter avec une approche par un dipôle pour générer des électrogrammes normaux et des LAVA aux endroits où ils ont été localisés en clinique. Cela améliore la prédiction de localisation du tissu induisant des LAVA obtenue par apprentissage sur l’image. Des cartes de confiance sont générées et peuvent être utilisées avant une ARF pour guider l’intervention. Les contributions de cette thèse ont conduit à des résultats et des preuves de concepts prometteurs

Loss of neuronal network resilience precedes seizures and determines the ictogenic nature of interictal synaptic perturbations

The mechanisms of seizure emergence, and the role of brief interictal epileptiform discharges (IEDs) in seizure generation are two of the most important unresolved issues in modern epilepsy research. Our study shows that the transition to seizure is not a sudden phenomenon,but a slow process characterized by the progressive loss of neuronal network resilience. From a dynamical perspective, the slow transition is governed by the principles of critical slowing, a robust natural phenomenon observable in systems characterized by transitions between dynamical regimes. In epilepsy, this process is modulated by the synchronous synaptic input from IEDs. IEDs are external perturbations that produce phasic changes in the slow transition process and exert opposing effects on the dynamics of a seizure-generating network, causing either anti-seizure or pro-seizure effects. We show that the multifaceted nature of IEDs is defined by the dynamical state of the network at the moment of the discharge occurrence