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

Integrated Cardiac Electromechanics: Modeling and Personalization

Cardiac disease remains the leading cause of morbidity and mortality in the world. A variety of heart diagnosis techniques have been developed during the last century, and generally fall into two groups. The first group evaluates the electrical function of the heart using electrophysiological data such as electrocardiogram (ECG), while the second group aims to assess the mechanical function of the heart through medical imaging data. Nevertheless, the heart is an integrated electromechanical organ, where its cyclic pumping arises from the synergy of its electrical and mechanical function which requires first to be electrically excited in order to contract. At the same time, cardiac electrical function experiences feedback from mechanical contraction. This inter-dependent relationship determines that neither electrical function nor mechanical function alone can completely reflect the pathophysiological conditions of the heart. The aim of this thesis is working towards building an integrated framework for heart diagnosis through evaluation of electrical and mechanical functions simultaneously. The basic rational is to obtain quantitative interpretation of a subject-specific heart system by combining an electromechanical heart model and individual clinical measurements of the heart. To this end, we first develop a biologically-inspired mathematical model of the heart that provides a general, macroscopic description of cardiac electromechanics. The intrinsic electromechanical coupling arises from both excitation-induced contraction and deformation-induced mechano-electrical feedback. Then, as a first step towards a fully electromechanically integrated framework, we develop a model-based approach for investigating the effect of cardiac motion on noninvasive transmural imaging of cardiac electrophysiology. Specifically, we utilize the proposed heart model to obtain updated heart geometry through simulation, and further recover the electrical activities of the heart from body surface potential maps (BSPMs) by solving an optimization problem. Various simulations of the heart have been performed under healthy and abnormal conditions, which demonstrate the physiological plausibility of the proposed integrated electromechanical heart model. What\u27s more, this work presents the effect of cardiac motion to the solution of noninvasive estimation of cardiac electrophysiology and shows the importance of integrating cardiac electrical and mechanical functions for heart diagnosis. This thesis also paves the road for noninvasive evaluation of cardiac electromechanics

Bayesian Inference with Combined Dynamic and Sparsity Models: Application in 3D Electrophysiological Imaging

Data-driven inference is widely encountered in various scientific domains to convert the observed measurements into information that cannot be directly observed about a system. Despite the quickly-developing sensor and imaging technologies, in many domains, data collection remains an expensive endeavor due to financial and physical constraints. To overcome the limits in data and to reduce the demand on expensive data collection, it is important to incorporate prior information in order to place the data-driven inference in a domain-relevant context and to improve its accuracy. Two sources of assumptions have been used successfully in many inverse problem applications. One is the temporal dynamics of the system (dynamic structure). The other is the low-dimensional structure of a system (sparsity structure). In existing work, these two structures have often been explored separately, while in most high-dimensional dynamic system they are commonly co-existing and contain complementary information. In this work, our main focus is to build a robustness inference framework to combine dynamic and sparsity constraints. The driving application in this work is a biomedical inverse problem of electrophysiological (EP) imaging, which noninvasively and quantitatively reconstruct transmural action potentials from body-surface voltage data with the goal to improve cardiac disease prevention, diagnosis, and treatment. The general framework can be extended to a variety of applications that deal with the inference of high-dimensional dynamic systems

Uncertainty Quantification and Reduction in Cardiac Electrophysiological Imaging

Cardiac electrophysiological (EP) imaging involves solving an inverse problem that infers cardiac electrical activity from body-surface electrocardiography data on a physical domain defined by the body torso. To avoid unreasonable solutions that may fit the data, this inference is often guided by data-independent prior assumptions about different properties of cardiac electrical sources as well as the physical domain. However, these prior assumptions may involve errors and uncertainties that could affect the inference accuracy. For example, common prior assumptions on the source properties, such as fixed spatial and/or temporal smoothness or sparseness assumptions, may not necessarily match the true source property at different conditions, leading to uncertainties in the inference. Furthermore, prior assumptions on the physical domain, such as the anatomy and tissue conductivity of different organs in the thorax model, represent an approximation of the physical domain, introducing errors to the inference. To determine the robustness of the EP imaging systems for future clinical practice, it is important to identify these errors/uncertainties and assess their impact on the solution. This dissertation focuses on the quantification and reduction of the impact of uncertainties caused by prior assumptions/models on cardiac source properties as well as anatomical modeling uncertainties on the EP imaging solution. To assess the effect of fixed prior assumptions/models about cardiac source properties on the solution of EP imaging, we propose a novel yet simple Lp-norm regularization method for volumetric cardiac EP imaging. This study reports the necessity of an adaptive prior model (rather than fixed model) for constraining the complex spatiotemporally changing properties of the cardiac sources. We then propose a multiple-model Bayesian approach to cardiac EP imaging that employs a continuous combination of prior models, each re-effecting a specific spatial property for volumetric sources. The 3D source estimation is then obtained as a weighted combination of solutions across all models. Including a continuous combination of prior models, our proposed method reduces the chance of mismatch between prior models and true source properties, which in turn enhances the robustness of the EP imaging solution. To quantify the impact of anatomical modeling uncertainties on the EP imaging solution, we propose a systematic statistical framework. Founded based on statistical shape modeling and unscented transform, our method quantifies anatomical modeling uncertainties and establish their relation to the EP imaging solution. Applied on anatomical models generated from different image resolutions and different segmentations, it reports the robustness of EP imaging solution to these anatomical shape-detail variations. We then propose a simplified anatomical model for the heart that only incorporates certain subject-specific anatomical parameters, while discarding local shape details. Exploiting less resources and processing for successful EP imaging, this simplified model provides a simple clinically-compatible anatomical modeling experience for EP imaging systems. Different components of our proposed methods are validated through a comprehensive set of synthetic and real-data experiments, including various typical pathological conditions and/or diagnostic procedures, such as myocardial infarction and pacing. Overall, the methods presented in this dissertation for the quantification and reduction of uncertainties in cardiac EP imaging enhance the robustness of EP imaging, helping to close the gap between EP imaging in research and its clinical application

Noninvasive Multi-Modality Studies of Cardiac Electrophysiology, Mechanics, and Anatomical Substrate in Healthy Adults, Arrhythmogenic Cardiomyopathy, and Heart Failure

Heart disease is a leading cause of death and disability and is a major contributor to healthcare costs. Many forms of heart disease are caused by abnormalities in the electrical function of heart muscle cells or the cardiac conduction system. Electrocardiographic Imaging (ECGI) is a noninvasive modality for imaging cardiac electrophysiology. By combining recordings of the voltage distribution on the torso surface with anatomical images of the heart-torso geometry, ECGI reconstructs voltages on the epicardium. This thesis applies ECGI to novel studies of human heart function and disease and explores new combinations of ECGI with additional imaging modalities. ECGI was applied in combination with late gadolinium enhancement (LGE) scar imaging MRI in patients with arrhythmogenic right ventricular cardiomyopathy (ARVC). ARVC carries a high risk of sudden cardiac death, and the hallmark feature of ARVC is the progressive replacement of healthy myocardium with fibrous and fatty tissue. By combining ECGI and LGE in ARVC patients we found that there are signs of conduction abnormalities before structural abnormalities can be detected in ARVC patients. Electrical and structural abnormalities in ARVC patients co-localized. We also found that PVCs, potential triggers for arrhythmia, originated in regions of structural and electrical abnormalities. ECGI was applied in combination with speckle tracking echocardiography (STE) to longitudinally image heart failure patients undergoing cardiac resynchronization therapy (CRT). STE is an echocardiographic technique for measuring strain (contraction) in the heart. CRT is a highly effective treatment for heart failure, however, around 30% of patients do not respond to the treatment. ECGI was more effective for predicting response to CRT than the current standard ECG criteria or STE indices. The timing of peak contraction in STE did not accurately reflect the electrical activation sequence. CRT caused improvements in contraction that persisted even when pacing was disabled. CRT prolonged repolarization at the site of the LV pacing lead, which may increase the risk of arrhythmia in CRT patients. The above studies contribute novel observations of human disease physiology and demonstrate the clinical feasibility and effectiveness of ECGI for noninvasive assessment of ARVC and CRT

Design and clinical validation of novel imaging strategies for analysis of arrhythmogenic substrate

_CURRENT CHALLENGES IN ELECTROPHYSIOLOGY_ Technical advances in cardiovascular electrophysiology have resulted in an increasing number of catheter ablation procedures reaching 200 000 in Europe for the year 2013. These advanced interventions are often complex and time consuming and may cause significant radiation exposure. Furthermore, a substantial number of ablation procedures remain associated with poor (initial) outcomes and frequently require ≥1 redo procedures. Innovations in modalities for substrate imaging could facilitate our understanding of the arrhythmogenic substrate, improve the design of patient-specific ablation strategies and improve the results of ablation procedures. _NOVEL SUBSTRATE IMAGING MODALITIES_ __Cardiac magnetic resonance__ Cardiac magnetic resonance imaging (CMR) can be considered the most comprehensive and suitable modality for the complete electrophysiology and catheter ablation workup (including patient selection, procedural guidance, and [procedural] follow-up). Utilizing inversion recovery CMR, fibrotic myocardium can be visualized and quantified 10–15 min after intravenous administration of Gadolinium contrast. This imaging technique is known as late Gadolinium enhancement (LGE) imaging. Experimental models have shown excellent agreement between size and shape in LGE CMR and areas of myocardial infarction by histopathology. Recent studies have also demonstrated how scar size, shape and location from pre-procedural LGE can be useful in guiding ventricular tachycardia’s (VT) ablation or atrial fibrillation (AF) ablation. These procedures are often time-consuming due to the preceding electrophysiological mapping study required to identify slow conduction zones involved in re-entry circuits. Post-processed LGE images provide scar maps, which could be integrated with electroanatomic mapping systems to facilitate these procedures. __Inverse potential mapping__ Through the years, various noninvasive electrocardiographic imaging techniques have emerged that estimate epicardial potentials or myocardial activation times from potentials recorded on the thorax. Utilizing an inverse procedure, the potentials on the heart surface or activation times of the myocardium are estimated with the recorded body surface potentials as source data. Although this procedure only estimates the time course of unipolar epicardial electrograms, several studies have demonstrated that the epicardial potentials and electrograms provide substantial information about intramyocardial activity and have great potential to facilitate risk-stratification and generate personalized ablation strategies. __Objectives of this thesis__ 1. To evaluate the utility of cardiac magnetic resonance derived geometrical and tissue characteristic information for patient stratification and guidance of AF ablation. 2. To design and evaluate the performance of a finite element model based inverse potential mapping in predicting the arrhythmogenic focus in idiopathic ventricular tachycardia using invasive electro-anatomical activation mapping as a reference standard

Stereotactic body radioablation therapy as an immediate and early term antiarrhythmic palliative therapeutic choice in patients with refractory ventricular tachycardia

Background: Stereotactic body radioablation therapy (SBRT) has recently been introduced with the ability to provide ablative energy noninvasively to arrhythmogenic substrate while reducing damage to normal cardiac tissue nearby and minimizing patients’ procedural risk. There is still debate regarding whether SBRT has a predominant effect in the early or late period after the procedure. We sought to assess the time course of SBRT’s efficacy as well as the value of using a blanking period following a SBRT session. Methods: Eight patients (mean age 58 ± 14 years) underwent eight SBRT sessions for refractory ventricular tachycardia (VT). SBRT was given using a linear accelerator device with a total dose of 25 Gy to the targeted area. Results: During a median follow-up of 8 months, all patients demonstrated VT recurrences; however, implantable cardioverter-defibrillator (ICD) and anti-tachycardia pacing therapies were significantly reduced with SBRT (8.46 to 0.83/per month, p = 0.047; 18.50 to 3.29/per month, p = 0.036, respectively). While analyzing the temporal SBRT outcomes, the 2 weeks to 3 months period demonstrated the most favorable outcomes. After 6 months, one patient was ICD therapy-free and the remaining patients demonstrated VT episodes. Conclusions: Our findings showed that the SBRT was associated with a marked reduction in the burden of VT and ICD interventions especially during first 3 months. Although SBRT does not seem to succeed complete termination of VT in long-term period, our findings support the strategy that SBRT can be utilized for immediate antiarrhythmic palliation in critically ill patients with otherwise untreatable refractory VT and electrical storm

Non-invasive identification of atrial fibrillation drivers

Atrial fibrillation (AF) is one of the most common cardiac arrhythmias. Nowadays the fibrillatory process is known to be provoked by the high-frequency reentrant activity of certain atrial regions that propagates the fibrillatory activity to the rest of the atrial tissue, and the electrical isolation of these key regions has demonstrated its effectiveness in terminating the fibrillatory process. The location of the dominant regions represents a major challenge in the diagnosis and treatment of this arrhythmia. With the aim to detect and locate the fibrillatory sources prior to surgical procedure, non-invasive methods have been developed such as body surface electrical mapping (BSPM) which allows to record with high spatial resolution the electrical activity on the torso surface or the electrocardiographic imaging (ECGI) which allows to non-invasively reconstruct the electrical activity in the atrial surface. Given the novelty of these systems, both technologies suffer from a lack of scientific knowledge about the physical and technical mechanisms that support their operation. Therefore, the aim of this thesis is to increase that knowledge, as well as studying the effectiveness of these technologies for the localization of dominant regions in patients with AF. First, it has been shown that BSPM systems are able to noninvasively identify atrial rotors by recognizing surface rotors after band-pass filtering. Furthermore, the position of such surface rotors is related to the atrial rotor location, allowing the distinction between left or right atrial rotors. Moreover, it has been found that the surface electrical maps in AF suffer a spatial smoothing effect by the torso conductor volume, so the surface electrical activity can be studied with a relatively small number of electrodes. Specifically, it has been seen that 12 uniformly distributed electrodes are sufficient for the correct identification of atrial dominant frequencies, while at least 32 leads are needed for non-invasive identification of atrial rotors. Secondly, the effect of narrowband filtering on the effectiveness of the location of reentrant patterns was studied. It has been found that this procedure allows isolating the reentrant electrical activity caused by the rotor, increasing the detection rate for both invasive and surface maps. However, the spatial smoothing caused by the regularization of the ECGI added to the temporal filtering causes a large increase in the spurious reentrant activity, making it difficult to detect real reentrant patterns. However, it has been found that maps provided by the ECGI without temporal filtering allow the correct detection of reentrant activity, so narrowband filtering should be applied for intracavitary or surface signal only. Finally, we studied the stability of the markers used to detect dominant regions in ECGI, such as frequency maps or the rotor presence. It has been found that in the presence of alterations in the conditions of the inverse problem, such as electrical or geometrical noise, these markers are significantly more stable than the ECGI signal morphology from which they are extracted. In addition, a new methodology for error reduction in the atrial spatial location based on the curvature of the curve L has been proposed. The results presented in this thesis showed that BSPM and ECGI systems allows to non-invasively locate the presence of high-frequency rotors, responsible for the maintenance of AF. This detection has been proven to be unambiguous and robust, and the physical and technical mechanisms that support this behavior have been studied. These results indicate that both non-invasive systems provide information of great clinical value in the treatment of AF, so their use can be helpful for selecting and planning atrial ablation procedures.La fibrilación auricular (FA) es una de las arritmias cardiacas más frecuentes. Hoy en día se sabe que el proceso fibrilatorio está provocado por la actividad reentrante a alta frecuencia de ciertas regiones auriculares que propagan la actividad fibrilatoria en el resto del tejido auricular, y se ha demostrado que el aislamiento eléctrico de estas regiones dominantes permite detener el proceso fibrilatorio. La localización de las regiones dominantes supone un gran reto en el diagnóstico y tratamiento de la FA. Con el objetivo de poder localizar las fuentes fibrilatorias con anterioridad al procedimiento quirúrgico, se han desarrollado métodos no invasivos como la cartografía eléctrica de superficie (CES) que registra con gran resolución espacial la actividad eléctrica en la superficie del torso o la electrocardiografía por imagen (ECGI) que permite reconstruir la actividad eléctrica en la superficie auricular. Dada la novedad de estos sistemas, existe una falta de conocimiento científico sobre los mecanismos físicos y técnicos que sustentan su funcionamiento. Por lo tanto, el objetivo de esta tesis es aumentar dicho conocimiento, así como estudiar la eficacia de ambas tecnologías para la localización de regiones dominantes en pacientes con FA. En primer lugar, ha visto que los sistemas CES permiten identificar rotores auriculares mediante el reconocimiento de rotores superficiales tras el filtrado en banda estrecha. Además, la posición de los rotores superficiales está relacionada con la localización de dichos rotores, permitiendo la distinción entre rotores de aurícula derecha o izquierda. Por otra parte, se ha visto que los mapas eléctricos superficiales durante FA sufren una gran suavizado espacial por el efecto del volumen conductor del torso, lo que permite que la actividad eléctrica superficial pueda ser estudiada con un número relativamente reducido de electrodos. Concretamente, se ha visto que 12 electrodos uniformemente distribuidos son suficientes para una correcta identificación de frecuencias dominantes, mientras que son necesarios al menos 32 para una correcta identificación de rotores auriculares. Por otra parte, también se ha estudiado el efecto del filtrado en banda estrecha sobre la eficacia de la localización de patrones reentrantes. Así, se ha visto que este procedimiento permite aislar la actividad eléctrica reentrante provocada por el rotor, aumentando la tasa de detección tanto para señal obtenida de manera invasiva como para los mapas superficiales. No obstante, este filtrado temporal sobre la señal de ECGI provoca un gran aumento de la actividad reentrante espúrea que dificulta la detección de patrones reentrantes reales. Sin embargo, los mapas ECGI sin filtrado temporal permiten la detección correcta de la actividad reentrante, por lo el filtrado debería ser aplicado únicamente para señal intracavitaria o superficial. Por último, se ha estudiado la estabilidad de los marcadores utilizados en ECGI para detectar regiones dominantes, como son los mapas de frecuencia o la presencia de rotores. Se ha visto que en presencia de alteraciones en las condiciones del problema inverso, como ruido eléctrico o geométrico, estos marcadores son significativamente más estables que la morfología de la propia señal ECGI. Además, se ha propuesto una nueva metodología para la reducción del error en la localización espacial de la aurícula basado en la curvatura de la curva L. Los resultados presentados en esta tesis revelan que los sistemas de CES y ECGI permiten localizar de manera no invasiva la presencia de rotores de alta frecuencia. Esta detección es univoca y robusta, y se han estudiado los mecanismos físicos y técnicos que sustentan dicho comportamiento. Estos resultados indican que ambos sistemas no invasivos proporcionan información de gran valor clínico en el tratamiento de la FA, por lo que su uso puede ser de gran ayuda para la selección y planificaciLa fibril·lació auricular (FA) és una de les arítmies cardíaques més freqüents. Hui en dia es sabut que el procés fibrilatori està provocat per l'activitat reentrant de certes regions auriculars que propaguen l'activitat fibril·latoria a la resta del teixit auricular, i s'ha demostrat que l'aïllament elèctric d'aquestes regions dominants permet aturar el procés fibrilatori. La localització de les regions dominants suposa un gran repte en el diagnòstic i tractament d'aquesta arítmia. Amb l'objectiu de poder localitzar fonts fibril·latories amb anterioritat al procediment quirúrgic s'han desenvolupat mètodes no invasius com la cartografia elèctrica de superfície (CES) que registra amb gran resolució espacial l'activitat elèctrica en la superfície del tors o l'electrocardiografia per imatge (ECGI) que permet obtenir de manera no invasiva l'activitat elèctrica en la superfície auricular. Donada la relativa novetat d'aquests sistemes, existeix una manca de coneixement científic sobre els mecanismes físics i tècnics que sustenten el seu funcionament. Per tant, l'objectiu d'aquesta tesi és augmentar aquest coneixement, així com estudiar l'eficàcia d'aquestes tecnologies per a la localització de regions dominants en pacients amb FA. En primer lloc, s'ha vist que els sistemes CES permeten identificar rotors auriculars mitjançant el reconeixement de rotors superficials després del filtrat en banda estreta. A més, la posició dels rotors superficials està relacionada amb la localització d'aquests rotors, permetent la distinció entre rotors de aurícula dreta o esquerra. També s'ha vist que els mapes elèctrics superficials durant FA pateixen un gran suavitzat espacial per l'efecte del volum conductor del tors, el que permet que l'activitat elèctrica superficial pugui ser estudiada amb un nombre relativament reduït d'elèctrodes. Concretament, s'ha vist que 12 elèctrodes uniformement distribuïts són suficients per a una correcta identificació de freqüències dominants auriculars, mentre que són necessaris almenys 32 per a una correcta identificació de rotors auriculars. D'altra banda, també s'ha estudiat l'efecte del filtrat en banda estreta sobre l'eficàcia de la localització de patrons reentrants. Així, s'ha vist que aquest procediment permet aïllar l'activitat elèctrica reentrant provocada pel rotor, augmentant la taxa de detecció tant pel senyal obtingut de manera invasiva com per als mapes superficials. No obstant això, aquest filtrat temporal sobre el senyal de ECGI provoca un gran augment de l'activitat reentrant espúria que dificulta la detecció de patrons reentrants reals. A més, els mapes proporcionats per la ECGI sense filtrat temporal permeten la detecció correcta de l'activitat reentrant, per la qual cosa el filtrat hauria de ser aplicat únicament per a senyal intracavitària o superficial. Per últim, s'ha estudiat l'estabilitat dels marcadors utilitzats en ECGI per a detectar regions auriculars dominants, com són els mapes de freqüència o la presència de rotors. S'ha vist que en presència d'alteracions en les condicions del problema invers, com soroll elèctric o geomètric, aquests marcadors són significativament més estables que la morfologia del mateix senyal ECGI. A més, s'ha proposat una nova metodologia per a la reducció de l'error en la localització espacial de l'aurícula basat en la curvatura de la corba L. Els resultats presentats en aquesta tesi revelen que els sistemes de CES i ECGI permeten localitzar de manera no invasiva la presència de rotors d'alta freqüència. Aquesta detecció és unívoca i robusta, i s'han estudiat els mecanismes físics i tècnics que sustenten aquest comportament. Aquests resultats indiquen que els dos sistemes no invasius proporcionen informació de gran valor clínic en el tractament de la FA, pel que el seu ús pot ser de gran ajuda per a la selecció i planificació de procediments d'ablació auricular.Rodrigo Bort, M. (2016). Non-invasive identification of atrial fibrillation drivers [Tesis doctoral]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/75346TESISPremios Extraordinarios de tesis doctorale

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

Three-dimensional cardiac computational modelling: methods, features and applications

[EN] The combination of computational models and biophysical simulations can help to interpret an array of experimental data and contribute to the understanding, diagnosis and treatment of complex diseases such as cardiac arrhythmias. For this reason, three-dimensional (3D) cardiac computational modelling is currently a rising field of research. The advance of medical imaging technology over the last decades has allowed the evolution from generic to patient-specific 3D cardiac models that faithfully represent the anatomy and different cardiac features of a given alive subject. Here we analyse sixty representative 3D cardiac computational models developed and published during the last fifty years, describing their information sources, features, development methods and online availability. This paper also reviews the necessary components to build a 3D computational model of the heart aimed at biophysical simulation, paying especial attention to cardiac electrophysiology (EP), and the existing approaches to incorporate those components. We assess the challenges associated to the different steps of the building process, from the processing of raw clinical or biological data to the final application, including image segmentation, inclusion of substructures and meshing among others. We briefly outline the personalisation approaches that are currently available in 3D cardiac computational modelling. Finally, we present examples of several specific applications, mainly related to cardiac EP simulation and model-based image analysis, showing the potential usefulness of 3D cardiac computational modelling into clinical environments as a tool to aid in the prevention, diagnosis and treatment of cardiac diseases.This work was partially supported by the "VI Plan Nacional de Investigacion Cientifica, Desarrollo e Innovacion Tecnologica" from the Ministerio de Economia y Competitividad of Spain (TIN2012-37546-C03-01 and TIN2011-28067) and the European Commission (European Regional Development Funds - ERDF - FEDER) and by "eTorso project" (GVA/2013-001404) from the Generalitat Valenciana (Spain). ALP is financially supported by the program "Ayudas para contratos predoctorales para la formacion de doctores" from the Ministerio de Economia y Competitividad of Spain (BES-2013-064089).López Pérez, AD.; Sebastián Aguilar, R.; Ferrero De Loma-Osorio, JM. (2015). Three-dimensional cardiac computational modelling: methods, features and applications. BioMedical Engineering OnLine. 14(35):1-31. https://doi.org/10.1186/s12938-015-0033-5S1311435Koushanpour E, Collings W: Validation and dynamic applications of an ellipsoid model of the left ventricle. J Appl Physiol 1966, 21: 1655–61.Ghista D, Sandler H: An analytic elastic-viscoelastic model for the shape and the forces in the left ventricle. J Biomech 1969, 2: 35–47.Janz RF, Grimm AF: Finite-Element Model for the Mechanical Behavior of the Left Ventricle: prediction of deformation in the potassium-arrested rat heart. Circ Res 1972, 30: 244–52.Van den Broek JHJM, Van den Broek MHLM: Application of an ellipsoidal heart model in studying left ventricular contractions. J Biomech 1980, 13: 493–503.Colli Franzone P, Guerri L, Pennacchio M, Taccardi B: Spread of excitation in 3-D models of the anisotropic cardiac tissue. II. Effects of fiber architecture and ventricular geometry. Math Biosci 1998, 147: 131–71.Kerckhoffs RCP, Bovendeerd PHM, Kotte JCS, Prinzen FW, Smits K, Arts T: Homogeneity of cardiac contraction despite physiological asynchrony of depolarization: a model study. Ann Biomed Eng 2003, 31: 536–47.Sermesant M, Moireau P, Camara O, Sainte-Marie J, Andriantsimiavona R, Cimrman R, et al.: Cardiac function estimation from MRI using a heart model and data assimilation: advances and difficulties. Med Image Anal 2006, 10: 642–56.Okajima M, Fujino T, Kobayashi T, Yamada K: Computer simulation of the propagation process in excitation of the ventricles. Circ Res 1968, 23: 203–11.Horan LG, Hand RC, Johnson JC, Sridharan MR, Rankin TB, Flowers NC: A theoretical examination of ventricular repolarization and the secondary T wave. Circ Res 1978, 42: 750–7.Miller WT, Geselowitz DB: Simulation studies of the electrocardiogram. I. The normal heart. Circ Res 1978, 43: 301–15.Vetter FJ, McCulloch AD: Three-dimensional analysis of regional cardiac function: a model of rabbit ventricular anatomy. Prog Biophys Mol Biol 1998, 69: 157–83.Nielsen PMF, LeGrice IJ, Smaill BH, Hunter PJ: Mathematical model of geometry and fibrous structure of the heart. Am J Physiol Heart Circ Physiol 1991, 260: H1365–78.Stevens C, Remme E, LeGrice I, Hunter P: Ventricular mechanics in diastole: material parameter sensitivity. J Biomech 2003, 36: 737–48.Aoki M, Okamoto Y, Musha T, Harumi KI: Three-dimensional simulation of the ventricular depolarization and repolarization processes and body surface potentials: normal heart and bundle branch block. IEEE Trans Biomed Eng 1987, 34: 454–62.Thakor NV, Eisenman LN: Three-dimensional computer model of the heart: fibrillation induced by extrastimulation. Comput Biomed Res 1989, 22: 532–45.Freudenberg J, Schiemann T, Tiede U, Höhne KH: Simulation of cardiac excitation patterns in a three-dimensional anatomical heart atlas. Comput Biol Med 2000, 30: 191–205.Trunk P, Mocnik J, Trobec R, Gersak B: 3D heart model for computer simulations in cardiac surgery. Comput Biol Med 2007, 37: 1398–403.Siregar P, Sinteff JP, Julen N, Le Beux P: An interactive 3D anisotropic cellular automata model of the heart. Comput Biomed Res 1998, 31: 323–47.Harrild DM, Henriquez CS: A computer model of normal conduction in the human atria. Circ Res 2000, 87: e25–36.Bodin ON, Kuz’min AV: Synthesis of a realistic model of the surface of the heart. Biomed Eng (NY) 2006, 40: 280–3.Ruiz-Villa CA, Tobón C, Rodríguez JF, Ferrero JM, Hornero F, Saíz J: Influence of atrial dilatation in the generation of re-entries caused by ectopic activity in the left atrium. Comput Cardiol 2009, 36: 457–60.Blanc O, Virag N, Vesin JM, Kappenberger L: A computer model of human atria with reasonable computation load and realistic anatomical properties. IEEE Trans Biomed Eng 2001, 48: 1229–37.Zemlin CW, Herzel H, Ho SY, Panfilov AV: A realistic and efficient model of excitation propagation in the human atria. In Comput Simul Exp Assess Card Electrophysiol. Edited by: Virag N, Kappenberger L, Blanc O. Futura Publishing Company, Inc, Arkmonk, New York; 2001:29–34.Seemann G, Höper C, Sachse FB, Dössel O, Holden AV, Zhang H: Heterogeneous three-dimensional anatomical and electrophysiological model of human atria. Philos Trans R Soc A Math Phys Eng Sci 2006, 364: 1465–81.Zhao J, Butters TD, Zhang H, LeGrice IJ, Sands GB, Smaill BH: Image-based model of atrial anatomy and electrical activation: a computational platform for investigating atrial arrhythmia. IEEE Trans Med Imaging 2013, 32: 18–27.Creswell LL, Wyers SG, Pirolo JS, Perman WH, Vannier MW, Pasque MK: Mathematical modeling of the heart using magnetic resonance imaging. IEEE Trans Med Imaging 1992, 11: 581–9.Lorange M, Gulrajani RM: A computer heart model incorporating anisotropic propagation: I. Model construction and simulation of normal activation. J Electrocardiol 1993, 26: 245–61.Winslow RL, Scollan DF, Holmes A, Yung CK, Zhang J, Jafri MS: Electrophysiological modeling of cardiac ventricular function: from cell to organ. Annu Rev Biomed Eng 2000, 2: 119–55.Virag N, Jacquemet V, Henriquez CS, Zozor S, Blanc O, Vesin JM, et al.: Study of atrial arrhythmias in a computer model based on magnetic resonance images of human atria. Chaos 2002, 12: 754–63.Helm PA, Tseng HJ, Younes L, McVeigh ER, Winslow RL: Ex vivo 3D diffusion tensor imaging and quantification of cardiac laminar structure. Magn Reson Med 2005, 54: 850–9.Arevalo HJ, Helm PA, Trayanova NA: Development of a model of the infarcted canine heart that predicts arrhythmia generation from specific cardiac geometry and scar distribution. Comput Cardiol 2008, 35: 497–500.Plotkowiak M, Rodriguez B, Plank G, Schneider JE, Gavaghan D, Kohl P, et al.: High performance computer simulations of cardiac electrical function based on high resolution MRI datasets. In Int Conf Comput Sci 2008, LNCS 5101. Springer–Verlag, Berlin Heidelberg; 2008:571–80.Heidenreich EA, Ferrero JM, Doblaré M, Rodríguez JF: Adaptive macro finite elements for the numerical solution of monodomain equations in cardiac electrophysiology. Ann Biomed Eng 2010, 38: 2331–45.Gurev V, Lee T, Constantino J, Arevalo H, Trayanova NA: Models of cardiac electromechanics based on individual hearts imaging data: Image-based electromechanical models of the heart. Biomech Model Mechanobiol 2011, 10: 295–306.Deng D, Jiao P, Ye X, Xia L: An image-based model of the whole human heart with detailed anatomical structure and fiber orientation. Comput Math Methods Med 2012, 2012: 16.Aslanidi OV, Nikolaidou T, Zhao J, Smaill BH, Gilbert SH, Holden AV, et al.: Application of micro-computed tomography with iodine staining to cardiac imaging, segmentation, and computational model development. IEEE Trans Med Imaging 2013, 32: 8–17.Haddad R, Clarysse P, Orkisz M, Croisille P, Revel D, Magnin IE: A realistic anthropomorphic numerical model of the beating heart. In Funct Imaging Model Heart 2005, LNCS 3504. Springer–Verlag, Berlin Heidelberg; 2005:384–93.Appleton B, Wei Q, Liu N, Xia L, Crozier S, Liu F, et al.: An electrical heart model incorporating real geometry and motion. In 27th Annu Int Conf Eng Med Biol Soc (IEEE-EMBS 2005). IEEE, Shanghai, China; 2006:345–8.Niederer S, Rhode K, Razavi R, Smith N: The importance of model parameters and boundary conditions in whole organ models of cardiac contraction. In Funct Imaging Model Heart 2009, LNCS 5528. Springer–Verlag, Berlin Heidelberg; 2009:348–56.Yang G, Toumoulin C, Coatrieux JL, Shu H, Luo L, Boulmier D: A 3D static heart model from a MSCT data set. In 27th Annu Int Conf IEEE Eng Med Biol Soc (IEEE-EMBS 2005). IEEE, Shangai, China; 2006:5499–502.Romero D, Sebastian R, Bijnens BH, Zimmerman V, Boyle PM, Vigmond EJ, et al.: Effects of the purkinje system and cardiac geometry on biventricular pacing: a model study. Ann Biomed Eng 2010, 38: 1388–98.Lorenzo-Valdés M, Sanchez-Ortiz GI, Mohiaddin R, Rueckert D: Atlas-based segmentation and tracking of 3D cardiac MR images using non-rigid registration. In Med Image Comput Comput Assist Interv 2002, LNCS 2488. Springer–Verlag, Berlin Heidelberg; 2002:642–50.Ordas S, Oubel E, Sebastian R, Frangi AF: Computational anatomy atlas of the heart. In 5th Int Symp Image Signal Process Anal (ISPA 2007). IEEE, Istanbul, Turkey; 2007:338–42.Burton RAB, Plank G, Schneider JE, Grau V, Ahammer H, Keeling SL, et al.: Three-dimensional models of individual cardiac histoanatomy: tools and challenges. Ann N Y Acad Sci 2006, 1080: 301–19.Plank G, Burton RAB, Hales P, Bishop M, Mansoori T, Bernabeu MO, et al.: Generation of histo-anatomically representative models of the individual heart: tools and application. Philos Trans R Soc A Math Phys Eng Sci 2009, 367: 2257–92.Bishop MJ, Plank G, Burton RAB, Schneider JE, Gavaghan DJ, Grau V, et al.: Development of an anatomically detailed MRI-derived rabbit ventricular model and assessment of its impact on simulations of electrophysiological function. Am J Physiol - Heart Circ Physiol 2010, 298: H699–718.Ecabert O, Peters J, Schramm H, Lorenz C, von Berg J, Walker MJ, et al.: Automatic model-based segmentation of the heart in CT images. IEEE Trans Med Imaging 2008, 27: 1189–201.Ecabert O, Peters J, Walker MJ, Ivanc T, Lorenz C, von Berg J, et al.: Segmentation of the heart and great vessels in CT images using a model-based adaptation framework. Med Image Anal 2011, 15: 863–76.Schulte RF, Sands GB, Sachse FB, Dössel O, Pullan AJ: Creation of a human heart model and its customisation using ultrasound images. Biomed Tech Eng 2001, 46: 26–8.Wenk JF, Zhang Z, Cheng G, Malhotra D, Acevedo-Bolton G, Burger M, et al.: First finite element model of the left ventricle with mitral valve: insights into ischemic mitral regurgitation. Ann Thorac Surg 2010, 89: 1546–53.Frangi AF, Rueckert D, Schnabel JA, Niessen WJ: Automatic construction of multiple-object three-dimensional statistical shape models: application to cardiac modeling. IEEE Trans Med Imaging 2002, 21: 1151–66.Hoogendoorn C, Duchateau N, Sánchez-Quintana D, Whitmarsh T, Sukno FM, De Craene M, et al.: A high-resolution atlas and statistical model of the human heart from multislice CT. IEEE Trans Med Imaging 2013, 32: 28–44.Vadakkumpadan F, Rantner LJ, Tice B, Boyle P, Prassl AJ, Vigmond E, et al.: Image-based models of cardiac structure with applications in arrhythmia and defibrillation studies. J Electrocardiol 2009, 42: 157.Perperidis D, Mohiaddin R, Rueckert D: Construction of a 4D statistical atlas of the cardiac anatomy and its use in classification. In Med Image Comput Comput Interv 2005, LNCS 3750. Springer–Verlag, Berlin Heidelberg; 2005:402–10.Lötjönen J, Kivistö S, Koikkalainen J, Smutek D, Lauerma K: Statistical shape model of atria, ventricles and epicardium from short- and long-axis MR images. Med Image Anal 2004, 8: 371–86.Lorenz C, von Berg J: A comprehensive shape model of the heart. Med Image Anal 2006, 10: 657–70.Mansoori T, Plank G, Burton R, Schneider J, Khol P, Gavaghan D, et al.: An iterative method for registration of high-resolution cardiac histoanatomical and MRI images. In 4th IEEE Int Symp Biomed Imaging: From Nano to Macro (ISBI 2007). IEEE, Arlington, VA (USA); 2007:572–5.Gibb M, Burton RAB, Bollensdorff C, Afonso C, Mansoori T, Schotten U, et al.: Resolving the three-dimensional histology of the heart. In Comput Methods Syst Biol - Lect Notes Comput Sci 7605. Springer, Berlin Heidelberg; 2012:2–16.Burton RAB, Lee P, Casero R, Garny A, Siedlecka U, Schneider JE, et al.: Three-dimensional histology: tools and application to quantitative assessment of cell-type distribution in rabbit heart. Europace 2014,16(Suppl 4):iv86–95.Niederer SA, Shetty AK, Plank G, Bostock J, Razavi R, Smith NP, et al.: Biophysical modeling to simulate the response to multisite left ventricular stimulation using a quadripolar pacing lead. Pacing Clin Electrophysiol 2012, 35: 204–14.Weese J, Groth A, Nickisch H, Barschdorf H, Weber FM, Velut J, et al.: Generating anatomical models of the heart and the aorta from medical images for personalized physiological simulations. Med Biol Eng Comput 2013, 51: 1209–19.Gibb M, Bishop M, Burton R, Kohl P, Grau V, Plank G, et al.: The role of blood vessels in rabbit propagation dynamics and cardiac arrhythmias. In Funct Imaging Model Heart - FIMH 2009, LNCS 5528. Springer, Berlin Heidelberg; 2009:268–76.Prassl AJ, Kickinger F, Ahammer H, Grau V, Schneider JE, Hofer E, et al.: Automatically generated, anatomically accurate meshes for cardiac electrophysiology problems. IEEE Trans Biomed Eng 2009, 56: 1318–30.Dux-Santoy L, Sebastian R, Felix-Rodriguez J, Ferrero JM, Saiz J: Interaction of specialized cardiac conduction system with antiarrhythmic drugs: a simulation study. IEEE Trans Biomed Eng 2011, 58: 3475–8.Lamata P, Niederer S, Nordsletten D, Barber DC, Roy I, Hose DR, et al.: An accurate, fast and robust method to generate patient-specific cubic Hermite meshes. Med Image Anal 2011, 15: 801–13.Pathmanathan P, Cooper J, Fletcher A, Mirams G, Murray P, Osborne J, et al.: A computational study of discrete mechanical tissue models. Phys Biol 2009, 6: 036001.Niederer SA, Kerfoot E, Benson AP, Bernabeu MO, Bernus O, Bradley C, et al.: Verification of cardiac tissue electrophysiology simulators using an N-version benchmark. Philos Trans R Soc A Math Phys Eng Sci 2011, 369: 4331–51.Ten Tusscher KHWJ, Panfilov AV: Cell model for efficient simulation of wave propagation in human ventricular tissue under normal and pathological conditions. Phys Med Biol 2006, 51: 6141–56.LeGrice I, Smaill B, Chai L, Edgar S, Gavin J, Hunter P: Laminar structure of the heart: ventricular myocyte arrangement and connective tissue architecture in the dog. Am J Physiol Heart Circ Physiol 1995, 269: H571–82.Anderson RH, Smerup M, Sanchez-Quintana D, Loukas M, Lunkenheimer PP: The three-dimensional arrangement of the myocytes in the ventricular walls. Clin Anat 2009, 22: 64–76.Clerc L: Directional differences of impulse spread in trabecular muscle from mammalian heart. J Physiol 1976, 255: 335–46.Streeter DD Jr, Spotnitz HM, Patel DP, Ross J Jr, Sonnenblick EH: Fiber orientation in the canine left ventricle during diastole and systole. Circ Res 1969, 24: 339–47.Scollan D, Holmes A, Winslow R, Forder J: Histological validation of myocardial microstructure obtained from diffusion tensor magnetic resonance imaging. Am J Physiol Heart Circ Physiol 1998, 275: H2308–18.Hsu EW, Muzikant AL, Matulevicius SA, Penland RC, Henriquez CS: Magnetic resonance myocardial fiber-orientation mapping with direct histological correlation. Am J Physiol Heart Circ Physiol 1998, 274: H1627–34.Holmes AA, Scollan DF, Winslow RL: Direct histological validation of diffusion tensor MRI in formaldehyde-fixed myocardium. Magn Reson Med 2000, 44: 157–61.Sermesant M, Forest C, Pennec X, Delingette H, Ayache N: Deformable biomechanical models: application to 4D cardiac image analysis. Med Image Anal 2003, 7: 475–88.Peyrat JM, Sermesant M, Pennec X, Delingette H, Xu C, McVeigh ER, et al.: A computational framework for the statistical analysis of cardiac diffusion tensors: application to a small database of canine hearts. IEEE Trans Med Imaging 2007, 26: 1500–14.Toussaint N, Sermesant M, Stoeck CT, Kozerke S, Batchelor PG: In vivo human 3D cardiac fibre architecture: reconstruction using curvilinear interpolation of diffusion tensor images. Med Image Comput Comput Assist Interv 2010,13(Pt 1):418–25.Toussaint N, Stoeck CT, Schaeffter T, Kozerke S, Sermesant M, Batchelor PG: In vivo human cardiac fibre architecture estimation using shape-based diffusion tensor processing. Med Image Anal 2013, 17: 1243–55.Bishop MJ, Hales P, Plank G, Gavaghan DJ, Scheider J, Grau V: Comparison of rule-based and DTMRI-derived fibre architecture in a whole rat ventricular computational model. In Funct Imaging Model Heart 2009, LNCS 5528. Springer–Verlag, Berlin Heidelberg; 2009:87–96.Bayer JD, Blake RC, Plank G, Trayanova NA: A novel rule-based algorithm for assigning myocardial fiber orientation to computational heart models. Ann Biomed Eng 2012, 40: 2243–54.Dobrzynski H, Anderson RH, Atkinson A, Borbas Z, D’Souza A, Fraser JF, et al.: Structure, function and clinical relevance of the cardiac conduction system, including the atrioventricular ring and outflow tract tissues. Pharmacol Ther 2013, 139: 260–88.Tranum-Jensen J, Wilde AA, Vermeulen JT, Janse MJ: Morphology of electrophysiologically identified junctions between Purkinje fibers and ventricular muscle in rabbit and pig hearts. Circ Res 1991, 69: 429–37.Boyle PM, Deo M, Plank G, Vigmond EJ: Purkinje-mediated effects in the response of quiescent ventricles to defibrillation shocks. Ann Biomed Eng 2010, 38: 456–68.Behradfar E, Nygren A, Vigmond EJ: The role of Purkinje-myocardial coupling during ventricular arrhythmia: a modeling study. PLoS One 2014., 9: Article ID e88000DiFrancesco D, Noble D: A model of cardiac electrical activity incorporating ionic pumps and concentration changes. Philos Trans R Soc B Biol Sci 1985, 307: 353–98.Stewart P, Aslanidi OV, Noble D, Noble PJ, Boyett MR, Zhang H: Mathematical models of the electrical action potential of Purkinje fibre cells. Philos Trans R Soc A Math Phys Eng Sci 2009, 367: 2225–55.Li P, Rudy Y: A model of canine purkinje cell electrophysiology and Ca(2+) cycling: rate dependence, triggered activity, and comparison to ventricular myocytes. Circ Res 2011, 109: 71–9.Chinchapatnam P, Rhode KS, Ginks M, Mansi T, Peyrat JM, Lambiase P, et al.: Estimation of volumetric myocardial apparent conductivity from endocardial electro-anatomical mapping. In 31st Annu Int Conf IEEE Eng Med Biol Soc (EMBC 2009). IEEE, Minneapolis, MN (USA); 2009:2907–10.Durrer D, Van Dam RT, Freud GE, Janse MJ, Meijler FL, Arzbaecher RC: Total excitation of the isolated human heart. Circulation 1970, 41: 899–912.Pollard AE, Barr RC: Computer simulations of activation in an anatomically based model of the human ventricular conduction system. IEEE Trans Biomed Eng 1991, 38: 982–96.Abboud S, Berenfeld O, Sadeh D: Simulation of high-resolution QRS complex using a ventricular model with a fractal conduction system. Effects of ischemia on high-frequency QRS potentials. Circ Res 1991, 68: 1751–60.Sebastian R, Zimmerman V, Romero D, Sanchez-Quintana D, Frangi AF: Characterization and modeling of the peripheral cardiac conduction system. IEEE Trans Med Imaging 2013, 32: 45–55.Bordas R, Gillow K, Lou Q, Efimov IR, Gavaghan D, Kohl P, et al.: Rabbit-specific ventricular model of cardiac electrophysiological function including specialized conduction system. Prog Biophys Mol Biol 2011, 107: 90–100.Stephenson RS, Boyett MR, Hart G, Nikolaidou T, Cai X, Corno AF, et al.: Contrast enhanced micro-computed tomography resolves the 3-dimensional morphology of the cardiac conduction system in mammalian hearts. PLoS One 2012., 7: Article ID e35299Berenfeld O, Jalife J: Purkinje-Muscle reentry as a mechanism of polymorphic ventricular arrhythmias in a 3-dimensional model of the ventricles. Circ Res 1998, 82: 1063–77.Azzouzi A, Coudière Y, Turpault R, Zemzemi N: A mathematical model of the Purkinje-muscle junctions. Math Biosci Eng MBE 2011, 8: 915–30.Dux-Santoy L, Sebastian R, Rodriguez JF, Ferrero JM: Modeling the different sections of the cardiac conduction system to obtain realistic electrocardiograms. In 35th Annu Int Conf IEEE Eng Med Biol Soc (EMBC 2013). IEEE, Osaka, Japan; 2013:6846–9.Cardenes R, Sebastian R, Berruezo A, Camara O: Inverse