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

3D model električne aktivnosti srca

The aim of this study is to develop a new, computationally-efficient, anatomically-realistic 3D bidomain cardiac electrical activity model using widely available software and standard low-cost hardware. The model incorporates whole-heart embedded in a human torso, spontaneous activation of sinoatrial node and specialized conduction system with heterogeneous action potential morphologies. The model is capable of generating realistic body surface electrocardiograms (ECGs) and is proposed as a useful tool for investigating some major issues in heart pathophysiology and in stimulation; such as simulating and optimizing synchronized electrical cardioversion, defibrillation and pacing stimulation.Cilj studije je razviti računalno efikasan, anatomski realističan 3D model električne aktivnosti cijelog ljudskog srca na široko dostupnoj računalnoj opremi. Model uključuje cijelo srce okruženo plućima i postavljeno unutar ljudskog torza, sa spontanom aktivacijom sinus-atrijskog čvora i specijaliziranim vodljivim putevima s heterogenim morfologijama akcijskih potencijala. Model omogućuje simuliranje elektrokardiograma (EKG) realističnog oblika te ga je moguće koristiti za istraživanje srčanih patofiziologija, simuliranje i optimizaciju sinkronizirane električne kardioverzije, defibrilacije ili simulacije različitih srčanih stimulacija

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

3D finite element electrical model of larval zebrafish ECG signals

Assessment of heart function in zebrafish larvae using electrocardiography (ECG) is a potentially useful tool in developing cardiac treatments and the assessment of drug therapies. In order to better understand how a measured ECG waveform is related to the structure of the heart, its position within the larva and the position of the electrodes, a 3D model of a 3 days post fertilisation (dpf) larval zebrafish was developed to simulate cardiac electrical activity and investigate the voltage distribution throughout the body. The geometry consisted of two main components; the zebrafish body was modelled as a homogeneous volume, while the heart was split into five distinct regions (sinoatrial region, atrial wall, atrioventricular band, ventricular wall and heart chambers). Similarly, the electrical model consisted of two parts with the body described by Laplace’s equation and the heart using a bidomain ionic model based upon the Fitzhugh-Nagumo equations. Each region of the heart was differentiated by action potential (AP) parameters and activation wave conduction velocities, which were fitted and scaled based on previously published experimental results. ECG measurements in vivo at different electrode recording positions were then compared to the model results. The model was able to simulate action potentials, wave propagation and all the major features (P wave, R wave, T wave) of the ECG, as well as polarity of the peaks observed at each position. This model was based upon our current understanding of the structure of the normal zebrafish larval heart. Further development would enable us to incorporate features associated with the diseased heart and hence assist in the interpretation of larval zebrafish ECGs in these conditions

Mapping of the electrical activity of human atria. Multiscale modelling and simulations

La fibrilación auricular es una de las arritmias cardíacas más comunes observadas en la práctica clínica. Por lo tanto, es de vital importancia desarrollar nuevas tecnologías destinadas a diagnosticar y acabar con este tipo de arritmia, para mejorar la calidad de vida de los pacientes y reducir los costes de los sistemas nacionales de salud. En los últimos años ha aumentado el uso de las nuevas técnicas de mapeo auricular, basadas en sistemas multi-electrodo para mapear la actividad eléctrica en humanos. Dichas técnicas permiten localizar y ablacionar los impulsores de la fibrilación auricular, como son las fuentes focales o los rotores. Sin embargo, todavía existe incertidumbre sobre su precisión y los procedimientos experimentales para su análisis están limitados debido a su carácter invasivo. Por lo tanto, las simulaciones computacionales son una herramienta muy útil para superar estas limitaciones, al permitir reproducir con fidelidad las observaciones experimentales, dividir el problema bajo estudio en sub-estudios más simples, y realizar investigaciones preliminares imposibles de llevar a cabo en el práctica clínica. Esta tesis doctoral se centra en el análisis de la precisión de los sistemas de mapeo multi-electrodo a través de modelos y simulaciones computacionales. Para ello, desarrollamos modelos realistas multi-escala con el objetivo de simular actividad eléctrica auricular reentrante, en primer lugar en una lámina de tejido auricular, y en segundo lugar en las aurículas completas. Posteriormente, analizamos los efectos de las configuraciones geométricas multi-electrodo en la precisión de la localización de los rotores, mediante el uso de agrupaciones multi-electrodo con distancias inter-electrodo equidistantes, así como a través de catéteres de tipo basket con distancias inter-electrodo no equidistantes. Después de calcular los electrogramas unipolares intracavitarios, realizamos mapas de fase, detecciones de singularidad de fase para rastrear los rotores, y mapas de frecuencia dominantes. Finalmente, descubrimos que la precisión de los sistemas de mapeo multi-electrodo depende de su posición dentro de la cavidad auricular, de la distancia entre los electrodos y el tejido, de la distancia inter-electrodo, y de la contribución de las fuentes de campo lejano. Además, como consecuencia de estos factores que pueden afectar a la precisión de los sistemas de mapeo multi-electrodo, observamos la aparición de rotores falsos que podrían contribuir al fracaso de los procesos de ablación de la fibrilación auricular.Atrial fibrillation is one of the most common cardiac arrhythmias seen in clinical practice. Therefore, it is of vital importance to develop new technologies aimed at diagnosing and terminating this kind of arrhythmia, to improve the quality of life of patients and to reduce costs to national health systems. In the last years, new atrial mapping techniques based on multi-electrode systems are increasingly being used to map the atrial electrical activity in humans and localise and target atrial fibrillation drivers in the form of focal sources or rotors. However, significant concerns remain about their accuracy and experimental approaches to analyse them are limited due to their invasive character. Therefore, computer simulations are a helpful tool to overcome these limitations since they can reproduce with fidelity experimental observations, permit to split the problem to treat into more simple substudies, and allow the possibility of performing preliminary investigations impossible to carry out in the clinical practice. This PhD thesis is focused on the analysis for accuracy of the multielectrode mapping systems through computational models and simulations. For this purpose, we developed realistic multiscale models in order to simulate atrial electrical reentrant activity, first in a sheet of atrial tissue and, then, in the whole atria. Then, we analysed the effects of the multi-electrode geometrical configurations on the accuracy of localizing rotors, by using multi-electrode arrays with equidistant inter-electrode distances, as well as multi-electrode basket catheters with non-equidistant inter-electrode distances. After computing the intracavitary unipolar electrograms, we performed phase maps, phase singularity detections to track rotors, and dominant frequency maps. We finally found out that the accuracy of multi-electrode mapping systems depends on their position inside the atrial cavity, the electrode-to-tissue distance, the inter-electrode distance, and the contribution of far field sources. Furthermore, as a consequence of these factors, false rotors might appear and could contribute to failure of atrial fibrillation ablation procedures.La fibril·lació auricular és una de les arítmies cardíaques més comuns observades en la pràctica clínica. Per tant, és de vital importància desenvolupar noves tecnologies destinades a diagnosticar i acabar amb aquest tipus d'arítmia, per tal de millorar la qualitat de vida dels pacients i reduir els costos dels sistemes nacionals de salut. En els últims anys, ha augmentat l'ús de les noves tècniques de mapeig auricular, basades en sistemes multielèctrode per a mapejar l'activitat elèctrica auricular en humans. Aquestes tècniques permeten localitzar i ablacionar els impulsors de la fibril·lació auricular, com són les fonts focals o els rotors. No obstant això, encara hi ha incertesa sobre la seua precisió i els procediments experimentals per al seu anàlisi estan limitats a causa del seu caràcter invasiu. Per tant, les simulacions computacionals són una eina molt útil per a superar aquestes limitacions, en permetre reproduir amb fidelitat les observacions experimentals, dividir el problema sota estudi en subestudis més simples, i realitzar investigacions preliminars impossibles de dur a terme en el pràctica clínica. Aquesta tesi doctoral es centra en l'anàlisi de la precisió del sistemes de mapeig multielèctrode mitjançant els models i les simulacions computacionals. Per a això, desenvolupàrem models realistes multiescala per tal de simular activitat elèctrica auricular reentrant, en primer lloc en una làmina de teixit auricular, i en segon lloc a les aurícules completes. Posteriorment, analitzàrem els efectes de les configuracions geomètriques multielèctrode en la precisió de la localització dels rotors, mitjançant l'ús d'agrupacions multielèctrode amb distàncies interelèctrode equidistants, així com catèters de tipus basket amb distàncies interelèctrode no equidistants. Després de calcular els electrogrames unipolars intracavitaris, vam realitzar mapes de fase, deteccions de singularitat de fase per a rastrejar els rotors, i mapes de freqüència dominants. Finalment, vam descobrir que la precisió dels sistemes de mapeig multielèctrode depèn de la seua posició dins de la cavitat auricular, de la distància entre els elèctrodes i el teixit, de la distància interelèctrode, i de la contribució de les fonts de camp llunyà. A més, com a conseqüència d'aquests factors, es va observar l'aparició de rotors falsos que podrien contribuir al fracàs de l'ablació de la fibril·lació auricular.Martínez Mateu, L. (2018). Mapping of the electrical activity of human atria. Multiscale modelling and simulations [Tesis doctoral no publicada]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/104604TESI

Multiscale Cohort Modeling of Atrial Electrophysiology : Risk Stratification for Atrial Fibrillation through Machine Learning on Electrocardiograms

Patienten mit Vorhofflimmern sind einem fünffach erhöhten Risiko für einen ischämischen Schlaganfall ausgesetzt. Eine frühzeitige Erkennung und Diagnose der Arrhythmie würde ein rechtzeitiges Eingreifen ermöglichen, um möglicherweise auftretende Begleiterkrankungen zu verhindern. Eine Vergrößerung des linken Vorhofs sowie fibrotisches Vorhofgewebe sind Risikomarker für Vorhofflimmern, da sie die notwendigen Voraussetzungen für die Aufrechterhaltung der chaotischen elektrischen Depolarisation im Vorhof erfüllen. Mithilfe von Techniken des maschinellen Lernens könnten Fibrose und eine Vergrößerung des linken Vorhofs basierend auf P Wellen des 12-Kanal Elektrokardiogramms im Sinusrhythmus automatisiert identifiziert werden. Dies könnte die Basis für eine nicht-invasive Risikostrat- ifizierung neu auftretender Vorhofflimmerepisoden bilden, um anfällige Patienten für ein präventives Screening auszuwählen. Zu diesem Zweck wurde untersucht, ob simulierte Vorhof-Elektrokardiogrammdaten, die dem klinischen Trainingssatz eines maschinellen Lernmodells hinzugefügt wurden, zu einer verbesserten Klassifizierung der oben genannten Krankheiten bei klinischen Daten beitra- gen könnten. Zwei virtuelle Kohorten, die durch anatomische und funktionelle Variabilität gekennzeichnet sind, wurden generiert und dienten als Grundlage für die Simulation großer P Wellen-Datensätze mit genau bestimmbaren Annotationen der zugrunde liegenden Patholo- gie. Auf diese Weise erfüllen die simulierten Daten die notwendigen Voraussetzungen für die Entwicklung eines Algorithmus für maschinelles Lernen, was sie von klinischen Daten unterscheidet, die normalerweise nicht in großer Zahl und in gleichmäßig verteilten Klassen vorliegen und deren Annotationen möglicherweise durch unzureichende Expertenannotierung beeinträchtigt sind. Für die Schätzung des Volumenanteils von linksatrialem fibrotischen Gewebe wurde ein merkmalsbasiertes neuronales Netz entwickelt. Im Vergleich zum Training des Modells mit nur klinischen Daten, führte das Training mit einem hybriden Datensatz zu einer Reduzierung des Fehlers von durchschnittlich 17,5 % fibrotischem Volumen auf 16,5 %, ausgewertet auf einem rein klinischen Testsatz. Ein Long Short-Term Memory Netzwerk, das für die Unterscheidung zwischen gesunden und P Wellen von vergrößerten linken Vorhöfen entwickelt wurde, lieferte eine Genauigkeit von 0,95 wenn es auf einem hybriden Datensatz trainiert wurde, von 0,91 wenn es nur auf klinischen Daten trainiert wurde, die alle mit 100 % Sicherheit annotiert wurden, und von 0,83 wenn es auf einem klinischen Datensatz trainiert wurde, der alle Signale unabhängig von der Sicherheit der Expertenannotation enthielt. In Anbetracht der Ergebnisse dieser Arbeit können Elektrokardiogrammdaten, die aus elektrophysiologischer Modellierung und Simulationen an virtuellen Patientenkohorten resul- tieren und relevante Variabilitätsaspekte abdecken, die mit realen Beobachtungen übereinstim- men, eine wertvolle Datenquelle zur Verbesserung der automatisierten Risikostratifizierung von Vorhofflimmern sein. Auf diese Weise kann den Nachteilen klinischer Datensätze für die Entwicklung von Modellen des maschinellen Lernens entgegengewirkt werden. Dies trägt letztendlich zu einer frühzeitigen Erkennung der Arrhythmie bei, was eine rechtzeitige Auswahl geeigneter Behandlungsstrategien ermöglicht und somit das Schlaganfallrisiko der betroffenen Patienten verringert

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

A study of early afterdepolarizations in a model for human ventricular tissue

Sudden cardiac death is often caused by cardiac arrhythmias. Recently, special attention has been given to a certain arrhythmogenic condition, the long-QT syndrome, which occurs as a result of genetic mutations or drug toxicity. The underlying mechanisms of arrhythmias, caused by the long-QT syndrome, are not fully understood. However, arrhythmias are often connected to special excitations of cardiac cells, called early afterdepolarizations (EADs), which are depolarizations during the repolarizing phase of the action potential. So far, EADs have been studied mainly in isolated cardiac cells. However, the question on how EADs at the single-cell level can result in fibrillation at the tissue level, especially in human cell models, has not been widely studied yet. In this paper, we study wave patterns that result from single-cell EAD dynamics in a mathematical model for human ventricular cardiac tissue. We induce EADs by modeling experimental conditions which have been shown to evoke EADs at a single-cell level: by an increase of L-type Ca currents and a decrease of the delayed rectifier potassium currents. We show that, at the tissue level and depending on these parameters, three types of abnormal wave patterns emerge. We classify them into two types of spiral fibrillation and one type of oscillatory dynamics. Moreover, we find that the emergent wave patterns can be driven by calcium or sodium currents and we find phase waves in the oscillatory excitation regime. From our simulations we predict that arrhythmias caused by EADs can occur during normal wave propagation and do not require tissue heterogeneities. Experimental verification of our results is possible for experiments at the cell-culture level, where EADs can be induced by an increase of the L-type calcium conductance and by the application of I blockers, and the properties of the emergent patterns can be studied by optical mapping of the voltage and calcium

Nonlinear physics of electrical wave propagation in the heart: a review

The beating of the heart is a synchronized contraction of muscle cells (myocytes) that are triggered by a periodic sequence of electrical waves (action potentials) originating in the sino-atrial node and propagating over the atria and the ventricles. Cardiac arrhythmias like atrial and ventricular fibrillation (AF,VF) or ventricular tachycardia (VT) are caused by disruptions and instabilities of these electrical excitations, that lead to the emergence of rotating waves (VT) and turbulent wave patterns (AF,VF). Numerous simulation and experimental studies during the last 20 years have addressed these topics. In this review we focus on the nonlinear dynamics of wave propagation in the heart with an emphasis on the theory of pulses, spirals and scroll waves and their instabilities in excitable media and their application to cardiac modeling. After an introduction into electrophysiological models for action potential propagation, the modeling and analysis of spatiotemporal alternans, spiral and scroll meandering, spiral breakup and scroll wave instabilities like negative line tension and sproing are reviewed in depth and discussed with emphasis on their impact in cardiac arrhythmias.Peer ReviewedPreprin

Reduced-order modeling for cardiac electrophysiology. Application to parameter identification

A reduced-order model based on Proper Orthogonal Decomposition (POD) is proposed for the bidomain equations of cardiac electrophysiology. Its accuracy is assessed through electrocardiograms in various configurations, including myocardium infarctions and long-time simulations. We show in particular that a restitution curve can efficiently be approximated by this approach. The reduced-order model is then used in an inverse problem solved by an evolutionary algorithm. Some attempts are presented to identify ionic parameters and infarction locations from synthetic ECGs.Comment: No. RR-7811 (2011