Role of myocardial properties and pacing lead location on ECG in personalized paced heart models

Personalised cardiac models were built from the computed tomography imaging data for two patients with implanted cardiac resynchronisation therapy devices. The cardiac models comprised a biventricular model of myocardial electrophysiology coupled with a model of the torso to simulate the body surface potential map. The models were verified against electrocardiogams (ECG) recorded in the patients from 240 leads on the body surface under left ventricular pacing. The simulated ECG demonstrated a significant sensitivity to the myocardial anisotropy and location of the pacing electrode tip in the models. An apicobasal cellular heterogeneity was shown to be less significant for the ECG pattern at the paced-ventricle activation than that showed earlier by Keller and co-authors (2012) for the normal activation sequence. © 2017 IEEE Computer Society. All rights reserved.This study was supported by the RAS Presidium Programme I.33Π, and Government of the Russian Federation (agreement 02.A03.21.0006). We used the computational clusters of Ural Federal University and ”URAN” of Institute of Mathematics and Mechanics (Ekaterinburg)

ECG Simulation and Integration of Kalman Filter in Cardio Pediatric Cases

This article will show an overview of the model and simulations of general cardio pediatrics cases. To avoid simulated interference, Kalman and lowpass filter blocks are placed. In pediatric cases normal ECG (Electrocardiogram) curve is a bit different in relation to the middle-age persons. In cardio pediatric is represented especially the ECG curve with higher beats/min. Depending on the age of the child\u27s heart rate is variable. Therefore, identifying irregularities of the heart rate in children should be implemented a particular type of filter to eliminate rough measurement error on measurement signals. The model is obtained computationally shown in the examples of simulation in LabView and Java application programming interfaces. The model realization of the ECG signal is based on a few methods. Therefore, it selected only one method to display a simulated ECG signal. Installation of additional software filters allows us for realistic expectations after hardware integration. The real practical case is provided by a developed system with compiled firmware in the microcontroller. Firmware defines the behavior of the ECG signal after the integration of Kalman and the lowpass filter. Some cardio pediatric cases are processed with the method which can be applied Kalman or lowpass filter

A staggered-in-time and non-conforming-in-space numerical framework for realistic cardiac electrophysiology outputs

Computer-based simulations of non-invasive cardiac electrical outputs, such as electrocardiograms and body surface potential maps, usually entail severe computational costs due to the need of capturing fine-scale processes and to the complexity of the heart-torso morphology. In this work, we model cardiac electrical outputs by employing a coupled model consisting of a reaction-diffusion model - either the bidomain model or the most efficient pseudo-bidomain model - on the heart, and an elliptic model in the torso. We then solve the coupled problem with a segregated and staggered in-time numerical scheme, that allows for independent and infrequent solution in the torso region. To further reduce the computational load, main novelty of this work is in introduction of an interpolation method at the interface between the heart and torso domains, enabling the use of non-conforming meshes, and the numerical framework application to realistic cardiac and torso geometries. The reliability and efficiency of the proposed scheme is tested against the corresponding state-of-the-art bidomain-torso model. Furthermore, we explore the impact of torso spatial discretization and geometrical non-conformity on the model solution and the corresponding clinical outputs. The investigation of the interface interpolation method provides insights into the influence of torso spatial discretization and of the geometrical non-conformity on the simulation results and their clinical relevance.Comment: 26 pages,11 figures, 3 table

A Domain Decomposition Approch in the Electrocardiography Inverse Problem

International audienceThe mostly used mathematical formulation of the inverse problem in electrocardiography is based on a least method using a transfer matrix that maps the electrical potential on the heart to the body surface potential (BSP). This mathematical model is ill based and a lot of works have been concentrating on the regularization term without thinking of reformulating the problem itself. We propose in this study to solve the inverse problem based on a domain decomposition technique on a fictitious mirror-like boundary conditions. We conduct BSP simulations to produce synthetic data and use it to evaluate the accuracy of the inverse problem solution

C.E.P.S. : an efficient tool for cardiac electrophysiology simulations

International audienceNumerical models become a new and important tool to understand the mechanisms of cardiac arrythmias, delivering more and more accurate in-silico experiments. Beyond the development of mathematical models or numerical algorithms, a software tool must be developed to support this research. C.E.P.S. (Cardiac ElectroPhysiology Simulator) is a software tool under development by Inria Carmen team. Its purpose is to provide researchers from the modelling group, and collaborators, with a common environment to develop efficiently new models and numerical methods for cardiac electrophysiology. CEPS is designed to run on massively parallel architectures, and to make use of state-of-the-art and well known computing libraries to achieve realistic and complex heart simulations. Our short-term goals include solving monodomain and bidomain equations on 3D domain representing major structures of the heart (ventricles, atria and Purkinje fibers). CEPS supports the coupling surface/volume elements, surface/cable elements and volume/cable elements in order to include the complete structure of the heart. It is also designed to simulate electrocardiograms following heart/torso coupling. We also aim to automatically incorporate ionic models from CellML or JSIM databases. The structure of the code allows to easily include new PDE/ODE systems, to account for progresses in modelling, but also elements or numerical methods of arbitrary order of accuracy, for research on more efficient numerical solvers.Les modèles numériques sont un outil nouveau et important pour la compréhension des mécanismes des arythmies cardiaques, fournissant des expériences in-silico de plus en plus précises. Au-delà du développement de modèles mathématiques et d'algorithmes numériques, un logiciel doit être développé pour soutenir cette recherche. C.E.P.S. (Cardiac ElectroPhysiology Simulator ) est un outil logiciel en cours de développement par l'équipe-projet Inria Carmen. Son but est de fournir aux chercheurs du groupe de modélisation et ses collaborateurs avec un environnement commun pour développer de nouveaux modèles et méthodes numériques efficaces pour l'électrophysiologie cardiaque. CEPS est conçu pour fonctionner sur les architectures massivement parallèles, et utilise des bibliothèques de calcul bien connues pour réaliser des simulations cardiaques réalistes et complexes. Nos objectifs à court terme comprennent la résolution des équations monodomaine et bidomaine sur le domaine 3D représentant les grandes structures du cœur (ventricules , oreillettes et réseau de conduction cardique). CEPS prend en charge les éléments de couplage surface / volume, surface / câble et volume / câble afin d'y inclure la structure complète du cœur. CEPS est également conçu pour simuler les électrocardiogrammes suivants le couplage coeur / torse . Nous visons également à incorporer automatiquement des modèles ioniques des bases de données de CellML ou JSIM. La structure du code permet d'inclure facilement de nouvelles EDP / systèmes d'EDO

Solving the Inverse Problem of Electrocardiography on the Endocardium Using a Single Layer Source

The inverse problem of electrocardiography consists in reconstructing cardiac electrical activity from given body surface electrocardiographic measurements. Despite tremendous progress in the field over the last decades, the solution of this problem in terms of electrical potentials on both epi- and the endocardial heart surfaces with acceptable accuracy remains challenging. This paper presents a novel numerical approach aimed at improving the solution quality on the endocardium. Our method exploits the solution representation in the form of electrical single layer densities on the myocardial surface. We demonstrate that this representation brings twofold benefits: first, the inverse problem can be solved for the physiologically meaningful single layer densities. Secondly, a conventional transfer matrix for electrical potentials can be split into two parts, one of which turned out to posess regularizing properties leading to improved endocardial reconstructions. The method was tested in-silico for ventricular pacings utilizing realistic CT-based heart and torso geometries. The proposed approach provided more accurate solution on the ventricular endocardium compared to the conventional potential-based solutions with Tikhonov regularization of the 0th, 1st, and 2nd orders. Furthermore, we show a uniform spatio-temporal behavior of the single layer densities over the heart surface, which could be conveniently employed in the regularization procedure

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

Integrated Heart - Coupling multiscale and multiphysics models for the simulation of the cardiac function

Mathematical modelling of the human heart and its function can expand our understanding of various cardiac diseases, which remain the most common cause of death in the developed world. Like other physiological systems, the heart can be understood as a complex multiscale system involving interacting phenomena at the molecular, cellular, tissue, and organ levels. This article addresses the numerical modelling of many aspects of heart function, including the interaction of the cardiac electrophysiology system with contractile muscle tissue, the sub-cellular activation-contraction mechanisms, as well as the hemodynamics inside the heart chambers. Resolution of each of these sub-systems requires separate mathematical analysis and specially developed numerical algorithms, which we review in detail. By using specific sub-systems as examples, we also look at systemic stability, and explain for example how physiological concepts such as microscopic force generation in cardiac muscle cells, translate to coupled systems of differential equations, and how their stability properties influence the choice of numerical coupling algorithms. Several numerical examples illustrate three fundamental challenges of developing multiphysics and multiscale numerical models for simulating heart function, namely: (i) the correct upscaling from single-cell models to the entire cardiac muscle, (ii) the proper coupling of electrophysiology and tissue mechanics to simulate electromechanical feedback, and (iii) the stable simulation of ventricular hemodynamics during rapid valve opening and closure