Mechanistic Inquiry into the Role of Tissue Remodeling in Fibrotic Lesions in Human Atrial Fibrillation

AbstractAtrial fibrillation (AF), the most common arrhythmia in humans, is initiated when triggered activity from the pulmonary veins propagates into atrial tissue and degrades into reentrant activity. Although experimental and clinical findings show a correlation between atrial fibrosis and AF, the causal relationship between the two remains elusive. This study used an array of 3D computational models with different representations of fibrosis based on a patient-specific atrial geometry with accurate fibrotic distribution to determine the mechanisms by which fibrosis underlies the degradation of a pulmonary vein ectopic beat into AF. Fibrotic lesions in models were represented with combinations of: gap junction remodeling; collagen deposition; and myofibroblast proliferation with electrotonic or paracrine effects on neighboring myocytes. The study found that the occurrence of gap junction remodeling and the subsequent conduction slowing in the fibrotic lesions was a necessary but not sufficient condition for AF development, whereas myofibroblast proliferation and the subsequent electrophysiological effect on neighboring myocytes within the fibrotic lesions was the sufficient condition necessary for reentry formation. Collagen did not alter the arrhythmogenic outcome resulting from the other fibrosis components. Reentrant circuits formed throughout the noncontiguous fibrotic lesions, without anchoring to a specific fibrotic lesion

Multiscale Modeling and Simulation of Human Heart Failure

Tesis por compendio[EN] Heart failure (HF) constitutes a major public health problem worldwide. Operationally it is defined as a clinical syndrome characterized by the marked and progressive inability of the ventricles to fill and generate adequate cardiac output to meet the demands of cellular metabolism that may have significant variability in its etiology and it is the final common pathway of various cardiac pathologies. Much attention has been paid to the understanding of the arrhythmogenic mechanisms induced by the structural, electrical, and metabolic remodeling of the failing heart. Due to the complexity of the electrophysiological changes that may occur during heart failure, the scientific literature is complex and sometimes equivocal. Nevertheless, a number of common features of failing hearts have been documented. At the cellular level, prolongation of the action potential (AP) involving ion channel remodeling and alterations in calcium handling have been established as the hallmark characteristics of myocytes isolated from failing hearts. At the tissue level, intercellular uncoupling and fibrosis are identified as major arrhythmogenic factors. In this Thesis a computational model for cellular heart failure was proposed using a modified version of Grandi et al. model for human ventricular action potential that incorporates the formulation of the late sodium current (INaL) in order to study the arrhythmogenic processes due to failing phenotype. Experimental data from several sources were used to validate the model. Due to extensive literature in the subject a sensitivity analysis was performed to assess the influence of main ionic currents and parameters upon most related biomarkers. In addition, multiscale simulations were carried out to characterize this pathology (transmural cardiac fibres and tissues). The proposed model for the human INaL and the electrophysiological remodeling of myocytes from failing hearts accurately reproduce experimental observations. An enhanced INaL appears to be an important contributor to the electrophysiological phenotype and to the dysregulation of calcium homeostasis of failing myocytes. Our strand simulation results illustrate how the presence of M cells and heterogeneous electrophysiological remodeling in the human failing ventricle modulate the dispersion of action potential duration (APD) and repolarization time (RT). Conduction velocity (CV) and the safety factor for conduction (SF) were also reduced by the progressive structural remodeling during heart failure. In our transmural ventricular tissue simulations, no reentry was observed in normal conditions or in the presence of HF ionic remodeling. However, defined amount of fibrosis and/or cellular uncoupling were sufficient to elicit reentrant activity. Under conditions where reentry was generated, HF electrophysiological remodeling did not alter the width of the vulnerable window (VW). However, intermediate fibrosis and cellular uncoupling significantly widened the VW. In conclusion, enhanced fibrosis in failing hearts, as well as reduced intercellular coupling, combine to increase electrophysiological gradients and reduce electrical propagation. In that sense, structural remodeling is a key factor in the genesis of vulnerability to reentry, mainly at intermediates levels of fibrosis and intercellular uncoupling.[ES] La insuficiencia cardíaca (IC) constituye un importante problema de salud pública en todo el mundo. Operacionalmente se define como un síndrome clínico caracterizado por la incapacidad marcada y progresiva de los ventrículos para llenar y generar gasto cardíaco adecuado para satisfacer las demandas del metabolismo celular, que puede tener una variabilidad significativa en su etiología y es la vía final común de varias patologías cardíacas. Se ha prestado mucha atención a la comprensión de los mecanismos arritmogénicos inducidos por la remodelación estructural, eléctrica, y metabólica del corazón afectado de IC. Debido a la complejidad de los cambios electrofisiológicos que pueden ocurrir durante la IC, la literatura científica es compleja y, a veces equívoca. Sin embargo, se han documentado una serie de características comunes en corazones afectados de IC. A nivel celular, se han establecido como las características distintivas de los miocitos aislados de corazones afectados de IC la prolongación del potencial de acción (PA), que implica la remodelación de los canales iónicos y las alteraciones en la dinámica del calcio. A nivel de los tejidos, el desacoplamiento intercelular y la fibrosis se identifican como los principales factores arritmogénicos. En esta tesis se propuso un modelo celular computacional para la insuficiencia cardíaca utilizando una versión modificada del modelo de potencial de acción ventricular humano de Grandi y colaboradores que incorpora la formulación de la corriente tardía de sodio (INaL) con el fin de estudiar los procesos arritmogénicas debido al fenotipo de la IC. Los datos experimentales de varias fuentes se utilizaron para validar el modelo. Debido a la extensa literatura en la temática se realizó un análisis de sensibilidad para evaluar la influencia de las principales corrientes iónicas y los parámetros sobre los biomarcadores relacionados. Además, se llevaron a cabo simulaciones multiescala para caracterizar esta patología (en fibras y tejidos transmurales). El modelo propuesto para la corriente tardía de sodio y la remodelación electrofisiológica de los miocitos de corazones afectados de IC reprodujeron con precisión las observaciones experimentales. Una INaL incrementada parece ser un importante contribuyente al fenotipo electrofisiológico y la desregulación de la homeostasis del calcio de los miocitos afectados de IC. Nuestros resultados de la simulaciones en fibra ilustran cómo la presencia de células M y el remodelado electrofisiológico heterogéneo en el ventrículo humano afectado de IC modulan la dispersión de la duración potencial de acción (DPA) y el tiempo de repolarización (TR). La velocidad de conducción (VC) y el factor de seguridad para la conducción (FS) también se redujeron en la remodelación estructural progresiva durante la insuficiencia cardíaca. En nuestras simulaciones transmurales de tejido ventricular, no se observó reentrada en condiciones normales o en presencia de la remodelación iónica de la IC. Sin embargo, determinadas cantidades de fibrosis y / o desacoplamiento celular eran suficientes para provocar la actividad reentrante. En condiciones donde se había generado la reentrada, el remodelado electrofisiológico de la IC no alteró la anchura de la ventana vulnerable (VV). Sin embargo, niveles intermedios de fibrosis y el desacoplamiento celular ampliaron significativamente la VV. En conclusión, niveles elevados de fibrosis en corazones afectados de IC, así como la reducción de acoplamiento intercelular, se combinan para aumentar los gradientes electrofisiológicos y reducir la propagación eléctrica. En ese sentido, la remodelación estructural es un factor clave en la génesis de la vulnerabilidad a las reentradas, principalmente en niveles intermedios de fibrosis y desacoplamiento intercelular. El remodelado electrofisiológico promueve la arritmogénesis y puede ser alterado dependi[CA] La insuficiència cardíaca (IC) constitueix un important problema de salut pública arreu del món. A efectes pràctics, es defineix com una síndrome clínica caracteritzada per la incapacitat marcada i progressiva dels ventricles per omplir i generar el cabal cardíac adequat, per tal de satisfer les demandes del metabolisme cel·lular, el qual pot tenir una variabilitat significativa en la seua etiologia i és la via final comuna de diverses patologies cardíaques. S'ha prestat molta atenció a la comprensió dels mecanismes aritmogènics induïts per la remodelació estructural, elèctrica, i metabòlica del cor afectat d'IC. A causa de la complexitat dels canvis electrofisiològics que poden ocórrer durant la IC, trobem que la literatura científica és complexa i, de vegades, equívoca. No obstant això, s'han documentat una sèrie de característiques comunes en cors afectats d'IC. A nivell cel·lular, com característiques distintives dels miòcits aïllats de cors afectats d'IC, s'han establert la prolongació del potencial d'acció (PA), que implica la remodelació dels canals iònics, i les alteracions en la dinàmica del calci. A nivell dels teixits, el desacoblament intercel·lular i la fibrosi s'identifiquen com els principals factors aritmogènics. Per tal d'estudiar els processos aritmogènics a causa del fenotip de la IC, es va proposar un model cel·lular computacional d'IC utilitzant una versió modificada del model de potencial d'acció ventricular humà de Grandi i els seus col·laboradors, el qual incorpora la formulació del corrent de sodi tardà (INaL). Amb l'objectiu de validar el model es van utilitzar dades experimentals de diverses fonts. A causa de l'extensa literatura en la temàtica, es va realitzar una anàlisi de sensibilitat per tal d'avaluar la influència de les principals corrents iòniques i els paràmetres sobre els biomarcadors relacionats. A més, es van dur a terme simulacions multiescala per a la caracterització d'aquesta patología (fibres i teixits transmurals). El model proposat per al corrent de sodi tardà i la remodelació electrofisiològica dels miòcits de cors afectats d'IC van reproduir amb precisió les observacions experimentals. Una INaL incrementada sembla contribuir de manera important al fenotip electrofisiològic i a la desregulació de l'homeòstasi del calci dels miòcits afectats d'IC. Els resultats de les nostres simulacions en fibra indiquen que la presència de cèl·lules M i el remodelat electrofisiològic heterogeni en el ventricle humà afectat d'IC modulen la dispersió de la durada del potencial d'acció (DPA) i el temps de repolarització (TR). La velocitat de conducció (VC) i el factor de seguretat per a la conducció (FS) també es van reduir en la remodelació estructural progressiva durant la IC. A les nostres simulacions transmurals de teixit ventricular, no s'observà cap reentrada ni en condicions normals ni en presència de la remodelació iònica de la IC. No obstant això, amb determinades quantitats de fibrosi i/o desacoblament cel·lular sí que es provocà l'activitat reentrant. I amb les condicions que produïren la reentrada, el remodelat electrofisiològic de la IC no va alterar l'amplada de la finestra vulnerable (FV). Tanmateix, nivells intermedis de fibrosi i el desacoblament cel·lular sí que ampliaren significativament la FV. En conclusió, nivells elevats de fibrosi en cors afectats d'IC, així com la reducció d'acoblament intercel·lular, es combinen per augmentar els gradients electrofisiològics i reduir la propagació elèctrica. Per tant, la remodelació estructural és un factor clau en la gènesi de la vulnerabilitat a les reentrades, principalment en nivells intermedis de fibrosi i desacoblament intercel·lular.Gómez García, JF. (2015). Multiscale Modeling and Simulation of Human Heart Failure [Tesis doctoral no publicada]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/52389TESISCompendi

Computational modelling of the human heart and multiscale simulation of its electrophysiological activity aimed at the treatment of cardiac arrhythmias related to ischaemia and Infarction

[ES] Las enfermedades cardiovasculares constituyen la principal causa de morbilidad y mortalidad a nivel mundial, causando en torno a 18 millones de muertes cada año. De entre ellas, la más común es la enfermedad isquémica cardíaca, habitualmente denominada como infarto de miocardio (IM). Tras superar un IM, un considerable número de pacientes desarrollan taquicardias ventriculares (TV) potencialmente mortales durante la fase crónica del IM, es decir, semanas, meses o incluso años después la fase aguda inicial. Este tipo concreto de TV normalmente se origina por una reentrada a través de canales de conducción (CC), filamentos de miocardio superviviente que atraviesan la cicatriz del infarto fibrosa y no conductora. Cuando los fármacos anti-arrítmicos resultan incapaces de evitar episodios recurrentes de TV, la ablación por radiofrecuencia (ARF), un procedimiento mínimamente invasivo realizado mediante cateterismo en el laboratorio de electrofisiología (EF), se usa habitualmente para interrumpir de manera permanente la propagación eléctrica a través de los CCs responsables de la TV. Sin embargo, además de ser invasivo, arriesgado y requerir mucho tiempo, en casos de TVs relacionadas con IM crónico, hasta un 50% de los pacientes continúa padeciendo episodios recurrentes de TV tras el procedimiento de ARF. Por tanto, existe la necesidad de desarrollar nuevas estrategias pre-procedimiento para mejorar la planificación de la ARF y, de ese modo, aumentar esta tasa de éxito relativamente baja. En primer lugar, realizamos una revisión exhaustiva de la literatura referente a los modelos cardiacos 3D existentes, con el fin de obtener un profundo conocimiento de sus principales características y los métodos usados en su construcción, con especial atención sobre los modelos orientados a simulación de EF cardíaca. Luego, usando datos clínicos de un paciente con historial de TV relacionada con infarto, diseñamos e implementamos una serie de estrategias y metodologías para (1) generar modelos computacionales 3D específicos de paciente de ventrículos infartados que puedan usarse para realizar simulaciones de EF cardíaca a nivel de órgano, incluyendo la cicatriz del infarto y la región circundante conocida como zona de borde (ZB); (2) construir modelos 3D de torso que permitan la obtención del ECG simulado; y (3) llevar a cabo estudios in-silico de EF personalizados y pre-procedimiento, tratando de replicar los verdaderos estudios de EF realizados en el laboratorio de EF antes de la ablación. La finalidad de estas metodologías es la de localizar los CCs en el modelo ventricular 3D para ayudar a definir los objetivos de ablación óptimos para el procedimiento de ARF. Por último, realizamos el estudio retrospectivo por simulación de un caso, en el que logramos inducir la TV reentrante relacionada con el infarto usando diferentes configuraciones de modelado para la ZB. Validamos nuestros resultados mediante la reproducción, con una precisión razonable, del ECG del paciente en TV, así como en ritmo sinusal a partir de los mapas de activación endocárdica obtenidos invasivamente mediante sistemas de mapeado electroanatómico en este último caso. Esto permitió encontrar la ubicación y analizar las características del CC responsable de la TV clínica. Cabe destacar que dicho estudio in-silico de EF podría haberse efectuado antes del procedimiento de ARF, puesto que nuestro planteamiento está completamente basado en datos clínicos no invasivos adquiridos antes de la intervención real. Estos resultados confirman la viabilidad de la realización de estudios in-silico de EF personalizados y pre-procedimiento de utilidad, así como el potencial del abordaje propuesto para llegar a ser en un futuro una herramienta de apoyo para la planificación de la ARF en casos de TVs reentrantes relacionadas con infarto. No obstante, la metodología propuesta requiere de notables mejoras y validación por medio de es[CA] Les malalties cardiovasculars constitueixen la principal causa de morbiditat i mortalitat a nivell mundial, causant entorn a 18 milions de morts cada any. De elles, la més comuna és la malaltia isquèmica cardíaca, habitualment denominada infart de miocardi (IM). Després de superar un IM, un considerable nombre de pacients desenvolupen taquicàrdies ventriculars (TV) potencialment mortals durant la fase crònica de l'IM, és a dir, setmanes, mesos i fins i tot anys després de la fase aguda inicial. Aquest tipus concret de TV normalment s'origina per una reentrada a través dels canals de conducció (CC), filaments de miocardi supervivent que travessen la cicatriu de l'infart fibrosa i no conductora. Quan els fàrmacs anti-arítmics resulten incapaços d'evitar episodis recurrents de TV, l'ablació per radiofreqüència (ARF), un procediment mínimament invasiu realitzat mitjançant cateterisme en el laboratori de electrofisiologia (EF), s'usa habitualment per a interrompre de manera permanent la propagació elèctrica a través dels CCs responsables de la TV. No obstant això, a més de ser invasiu, arriscat i requerir molt de temps, en casos de TVs relacionades amb IM crònic fins a un 50% dels pacients continua patint episodis recurrents de TV després del procediment d'ARF. Per tant, existeix la necessitat de desenvolupar noves estratègies pre-procediment per a millorar la planificació de l'ARF i, d'aquesta manera, augmentar la taxa d'èxit, que es relativament baixa. En primer lloc, realitzem una revisió exhaustiva de la literatura referent als models cardíacs 3D existents, amb la finalitat d'obtindre un profund coneixement de les seues principals característiques i els mètodes usats en la seua construcció, amb especial atenció sobre els models orientats a simulació de EF cardíaca. Posteriorment, usant dades clíniques d'un pacient amb historial de TV relacionada amb infart, dissenyem i implementem una sèrie d'estratègies i metodologies per a (1) generar models computacionals 3D específics de pacient de ventricles infartats capaços de realitzar simulacions de EF cardíaca a nivell d'òrgan, incloent la cicatriu de l'infart i la regió circumdant coneguda com a zona de vora (ZV); (2) construir models 3D de tors que permeten l'obtenció del ECG simulat; i (3) dur a terme estudis in-silico de EF personalitzats i pre-procediment, tractant de replicar els vertaders estudis de EF realitzats en el laboratori de EF abans de l'ablació. La finalitat d'aquestes metodologies és la de localitzar els CCs en el model ventricular 3D per a ajudar a definir els objectius d'ablació òptims per al procediment d'ARF. Finalment, a manera de prova de concepte, realitzem l'estudi retrospectiu per simulació d'un cas, en el qual aconseguim induir la TV reentrant relacionada amb l'infart usant diferents configuracions de modelatge per a la ZV. Validem els nostres resultats mitjançant la reproducció, amb una precisió raonable, del ECG del pacient en TV, així com en ritme sinusal a partir dels mapes d'activació endocardíac obtinguts invasivament mitjançant sistemes de mapatge electro-anatòmic en aquest últim cas. Això va permetre trobar la ubicació i analitzar les característiques del CC responsable de la TV clínica. Cal destacar que aquest estudi in-silico de EF podria haver-se efectuat abans del procediment d'ARF, ja que el nostre plantejament està completament basat en dades clíniques no invasius adquirits abans de la intervenció real. Aquests resultats confirmen la viabilitat de la realització d'estudis in-silico de EF personalitzats i pre-procediment d'utilitat, així com el potencial de l'abordatge proposat per a arribar a ser en un futur una eina de suport per a la planificació de l'ARF en casos de TVs reentrants relacionades amb infart. No obstant això, la metodologia proposada requereix de notables millores i validació per mitjà d'estudis de simulació amb grans cohorts de pacients.[EN] Cardiovascular diseases represent the main cause of morbidity and mortality worldwide, causing around 18 million deaths every year. Among these diseases, the most common one is the ischaemic heart disease, usually referred to as myocardial infarction (MI). After surviving to a MI, a considerable number of patients develop life-threatening ventricular tachycardias (VT) during the chronic stage of the MI, that is, weeks, months or even years after the initial acute phase. This particular type of VT is typically sustained by reentry through slow conducting channels (CC), which are filaments of surviving myocardium that cross the non-conducting fibrotic infarct scar. When anti-arrhythmic drugs are unable to prevent recurrent VT episodes, radiofrequency ablation (RFA), a minimally invasive procedure performed by catheterization in the electrophysiology (EP) laboratory, is commonly used to interrupt the electrical conduction through the CCs responsible for the VT permanently. However, besides being invasive, risky and time-consuming, in the cases of VTs related to chronic MI, up to 50% of patients continue suffering from recurrent VT episodes after the RFA procedure. Therefore, there exists a need to develop novel pre-procedural strategies to improve RFA planning and, thereby, increase this relatively low success rate. First, we conducted an exhaustive review of the literature associated with the existing 3D cardiac models in order to gain a deep knowledge about their main features and the methods used for their construction, with special focus on those models oriented to simulation of cardiac EP. Later, using a clinical dataset of a chronically infarcted patient with a history of infarct-related VT, we designed and implemented a number of strategies and methodologies to (1) build patient-specific 3D computational models of infarcted ventricles that can be used to perform simulations of cardiac EP at the organ level, including the infarct scar and the surrounding region known as border zone (BZ); (2) construct 3D torso models that enable to compute the simulated ECG; and (3) carry out pre-procedural personalized in-silico EP studies, trying to replicate the actual EP studies conducted in the EP laboratory prior to the ablation. The goal of these methodologies is to allow locating the CCs into the 3D ventricular model in order to help in defining the optimal ablation targets for the RFA procedure. Lastly, as a proof-of-concept, we performed a retrospective simulation case study, in which we were able to induce an infarct-related reentrant VT using different modelling configurations for the BZ. We validated our results by reproducing with a reasonable accuracy the patient's ECG during VT, as well as in sinus rhythm from the endocardial activation maps invasively recorded via electroanatomical mapping systems in this latter case. This allowed us to find the location and analyse the features of the CC responsible for the clinical VT. Importantly, such in-silico EP study might have been conducted prior to the RFA procedure, since our approach is completely based on non-invasive clinical data acquired before the real intervention. These results confirm the feasibility of performing useful pre-procedural personalized in-silico EP studies, as well as the potential of the proposed approach to become a helpful tool for RFA planning in cases of infarct-related reentrant VTs in the future. Nevertheless, the developed methodology requires further improvements and validation by means of simulation studies including large cohorts of patients.During the carrying out of this doctoral thesis, the author Alejandro Daniel López Pérez was financially supported by the Ministerio de Economía, Industria y Competitividad of Spain through the program Ayudas para contratos predoctorales para la formación de doctores, with the grant number BES-2013-064089.López Pérez, AD. (2019). Computational modelling of the human heart and multiscale simulation of its electrophysiological activity aimed at the treatment of cardiac arrhythmias related to ischaemia and Infarction [Tesis doctoral]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/124973TESI

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

Doctor of Philosophy

dissertationAtrial fibrillation (AF) is the leading cause of ischemic stroke and is the most commonly observed arrhythmia in clinical cardiology. Catheter ablation of AF, in which specific regions of cardiac anatomy associated with AF are intenionally injured to create scar tissue, has been honed over the last 15 years to become a relatively common and safe treatment option. However, the success of these anatomically driven ablation strategies, particularly in hearts that have been exposed to AF for extended periods, remains poor. AF induces changes in the electrical and structural properties of the cardiac tissue that further promotes the permanence of AF. In a process known as electroanatomical (EAM) mapping, clinicians record time signals known as electrograms (EGMs) from the heart and the locations of the recording sites to create geometric representations, or maps, of the electrophysiological properties of the heart. Analysis of the maps and the individual EGM morphologies can indicate regions of abnormal tissue, or substrates that facilitate arrhythmogenesis and AF perpetuation. Despite this progress, limitations in the control of devices currently used for EAM acquisition and reliance on suboptimal metrics of tissue viability appear to be hindering the potential of treatment guided by substrate mapping. In this research, we used computational models of cardiac excitation to evaluate param- eters of EAM that affect the performance of substrate mapping. These models, which have been validated with experimental and clinical studies, have yielded new insights into the limitations of current mapping systems, but more importantly, they guided us to develop new systems and metrics for robust substrate mapping. We report here on the progress in these simulation studies and on novel measurement approaches that have the potential to improve the robustness and precision of EAM in patients with arrhythmias. Appropriate detection of proarrhythmic substrates promises to improve ablation of AF beyond rudimentary destruction of anatomical targets to directed targeting of complicit tissues. Targeted treatment of AF sustaining tissues, based on the substrate mapping approaches described in this dissertation, has the potential to improve upon the efficacy of current AF treatment options

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

Stories from different worlds in the universe of complex systems: A journey through microstructural dynamics and emergent behaviours in the human heart and financial markets

A physical system is said to be complex if it exhibits unpredictable structures, patterns or regularities emerging from microstructural dynamics involving a large number of components. The study of complex systems, known as complexity science, is maturing into an independent and multidisciplinary area of research seeking to understand microscopic interactions and macroscopic emergence across a broad spectrum systems, such as the human brain and the economy, by combining specific modelling techniques, data analytics, statistics and computer simulations. In this dissertation we examine two different complex systems, the human heart and financial markets, and present various research projects addressing specific problems in these areas. Cardiac fibrillation is a diffuse pathology in which the periodic planar electrical conduction across the cardiac tissue is disrupted and replaced by fast and disorganised electrical waves. In spite of a century-long history of research, numerous debates and disputes on the mechanisms of cardiac fibrillation are still unresolved while the outcomes of clinical treatments remain far from satisfactory. In this dissertation we use cellular automata and mean-field models to qualitatively replicate the onset and maintenance of cardiac fibrillation from the interactions among neighboring cells and the underlying topology of the cardiac tissue. We use these models to study the transition from paroxysmal to persistent atrial fibrillation, the mechanisms through which the gap-junction enhancer drug Rotigaptide terminates cardiac fibrillation and how focal and circuital drivers of fibrillation may co-exist as projections of transmural electrical activities. Financial markets are hubs in which heterogeneous participants, such as humans and algorithms, adopt different strategic behaviors to exchange financial assets. In recent decades the widespread adoption of algorithmic trading, the electronification of financial transactions, the increased competition among trading venues and the use of sophisticated financial instruments drove the transformation of financial markets into a global and interconnected complex system. In this thesis we introduce agent-based and state-space models to describe specific microstructural dynamics in the stock and foreign exchange markets. We use these models to replicate the emergence of cross-currency correlations from the interactions between heterogeneous participants in the currency market and to disentangle the relationships between price fluctuations, market liquidity and demand/supply imbalances in the stock market.Open Acces

Alternans and Atrial Fibrillation: From Cellular Mechanisms to Arrhythmogenesis

Atrial fibrillation (AF) is the most common cardiac arrhythmia, but knowledge of the arrhythmogenic substrate is incomplete. Alternans, the beat-to-beat alternation in cardiac electrical signals, typically occurs at fast heart rates and can sometimes lead to arrhythmia. Atrial alternans has been observed at slow pacing rates in cardioverted AF patients, suggesting that alternans may play an important role in the arrhythmogenic substrate of AF. The mechanisms underlying alternans in patients at slow pacing rates, and the contribution of atrial alternans to arrhythmogenesis, are currently unknown. In order to address these gaps in understanding, a computational approach was used to elucidate the cellular mechanisms underlying alternans and to assess the effects of alternans on arrhythmogenesis in the atria. Simulations revealed that reduced ryanodine receptor (RyR2) inactivation, resulting in a steep sarcoplasmic reticulum (SR) Ca2+ release-load relationship, was responsible for alternans at slower pacing rates. The effect of these Ca2+-driven alternans (CDA) on arrhythmogenesis was explored using an anatomically realistic, 3D model of the human atria. It was found that CDA significantly increased the vulnerability of the atria to arrhythmia. Furthermore, CDA was found to promote arrhythmia maintenance through frequent wavebreak, which led to increased arrhythmia complexity and scroll wave persistence. Thus, these findings suggest that disrupted SR Ca2+ release in the atria is linked to arrhythmogenesis via the influence of alternans. This research provides a rationale for new mechanistic therapies for AF, suggesting that targeting RyR2s may be an effective antiarrhythmic strategy. Incorporation of these findings into future models may aid in the development of better treatment strategies for AF