Inverse estimation of terminal connections in the cardiac conduction system

Modeling the cardiac conduction system is a challenging problem in the context of computational cardiac electrophysiology. Its ventricular section, the Purkinje system, is responsible for triggering tissue electrical activation at discrete terminal locations, which subsequently spreads throughout the ventricles. In this paper, we present an algorithm that is capable of estimating the location of the Purkinje system triggering points from a set of random measurements on tissue. We present the properties and the performance of the algorithm under controlled synthetic scenarios. Results show that the method is capable of locating most of the triggering points in scenarios with a fair ratio between terminals and measurements. When the ratio is low, the method can locate the terminals with major impact in the overall activation map. Mean absolute errors obtained indicate that solutions provided by the algorithm are useful to accurately simulate a complete patient ventricular activation map

Probabilistic learning of the Purkinje network from the electrocardiogram

The identification of the Purkinje conduction system in the heart is a challenging task, yet essential for a correct definition of cardiac digital twins for precision cardiology. Here, we propose a probabilistic approach for identifying the Purkinje network from non-invasive clinical data such as the standard electrocardiogram (ECG). We use cardiac imaging to build an anatomically accurate model of the ventricles; we algorithmically generate a rule-based Purkinje network tailored to the anatomy; we simulate physiological electrocardiograms with a fast model; we identify the geometrical and electrical parameters of the Purkinje-ECG model with Bayesian optimization and approximate Bayesian computation. The proposed approach is inherently probabilistic and generates a population of plausible Purkinje networks, all fitting the ECG within a given tolerance. In this way, we can estimate the uncertainty of the parameters, thus providing reliable predictions. We test our methodology in physiological and pathological scenarios, showing that we are able to accurately recover the ECG with our model. We propagate the uncertainty in the Purkinje network parameters in a simulation of conduction system pacing therapy. Our methodology is a step forward in creation of digital twins from non-invasive data in precision medicine. An open source implementation can be found at http://github.com/fsahli/purkinje-learningComment: 18 pages, 9 figure

Simulazioni paziente-specifiche e stampa3D a supporto della pianificazione chirurgica in ambito cardiovascolare

Con il termine pianificazione chirurgica si intendono tutte le procedure che precedono l’intervento chirurgico. Le implementazioni della pianificazione sono molteplici in funzione della necessità clinica. In primo luogo, è necessario comprendere qual è il quesito clinico di interesse e l’intervento più adatto. Una volta definito l’intervento, si decidono i parametri clinici che permettono di valutare il successo dello stesso. A queste valutazioni dobbiamo aggiungere le informazioni di cui il clinico necessita prima di effettuare l’operazione. In queste fasi, la capacità di comunicazione tra clinico e ingegnere al fine di ottenere il risultato atteso è fondamentale. Una volta noti questi aspetti è possibile realizzare una vera e propria procedura di surgical planning che può essere applicata in supporto al servizio sanitario in modo da eseguire interventi ed erogare terapie che siano il quanto più specifiche per il singolo paziente. Per il sistema sanitario minori tempi di operazione comportano minori costi ospedalieri, gli operatori coinvolti nell’intervento vedono ridotto il carico di lavoro, infine per il paziente vengono ridotti i rischi di infezione ed i tempi di anestesia. Nuovi sviluppi della pianificazione chirurgica consistono nella possibilità di realizzare simulazioni che permettano al clinico di analizzare il potenziale futuro del paziente e trarne conclusioni. La trattazione è suddivisa in una prima parte di descrizione degli aspetti comuni a tutti i processi di pianificazione chirurgica con una particolare attenzione all’ambio cardiovascolare, ed in una seconda parte dove sono analizzati due studi differenti che verificano l’efficacia dell’impianto di protesi valvolare. L’obbiettivo della trattazione è quello di offrire una panoramica sulle possibili applicazioni future in ambito clinico

Modeling cardiac muscle fibers in ventricular and atrial electrophysiology simulations

Since myocardial fibers drive the electric signal propagation throughout the myocardium, accurately modeling their arrangement is essential for simulating heart electrophysiology (EP). Rule-Based-Methods (RBMs) represent a commonly used strategy to include cardiac fibers in computational models. A particular class of such methods is known as Laplace-Dirichlet-Rule-Based-Methods (LDRBMs) since they rely on the solution of Laplace problems. In this work we provide a unified framework, based on LDRBMs, for generating full heart muscle fibers. First, we review existing ventricular LDRBMs providing a communal mathematical description and introducing also some modeling improvements with respect to the existing literature. We then carry out a systematic comparison of LDRBMs based on meaningful biomarkers produced by numerical EP simulations. Next we propose, for the first time, a LDRBM to be used for generating atrial fibers. The new method, tested both on idealized and realistic atrial models, can be applied to any arbitrary geometries. Finally, we present numerical results obtained in a realistic whole heart where fibers are included for all the four chambers using the discussed LDRBMs

Personalized Cardiac Computational Models: From Clinical Data to Simulation of Infarct-Related Ventricular Tachycardia

In the chronic stage of myocardial infarction, a significant number of patients develop life-threatening ventricular tachycardias (VT) due to the arrhythmogenic nature of the remodeled myocardium. Radiofrequency ablation (RFA) is a common procedure to isolate reentry pathways across the infarct scar that are responsible for VT. Unfortunately, this strategy show relatively low success rates; up to 50% of patients experience recurrent VT after the procedure. In the last decade, intensive research in the field of computational cardiac electrophysiology (EP) has demonstrated the ability of three-dimensional (3D) cardiac computational models to perform in-silico EP studies. However, the personalization and modeling of certain key components remain challenging, particularly in the case of the infarct border zone (BZ). In this study, we used a clinical dataset from a patient with a history of infarct-related VT to build an image-based 3D ventricular model aimed at computational simulation of cardiac EP, including detailed patient-specific cardiac anatomy and infarct scar geometry. We modeled the BZ in eight different ways by combining the presence or absence of electrical remodeling with four different levels of image-based patchy fibrosis (0, 10, 20, and 30%). A 3D torso model was also constructed to compute the ECG. Patient-specific sinus activation patterns were simulated and validated against the patient's ECG. Subsequently, the pacing protocol used to induce reentrant VTs in the EP laboratory was reproduced in-silico. The clinical VT was induced with different versions of the model and from different pacing points, thus identifying the slow conducting channel responsible for such VT. Finally, the real patient's ECG recorded during VT episodes was used to validate our simulation results and to assess different strategies to model the BZ. Our study showed that reduced conduction velocities and heterogeneity in action potential duration in the BZ are the main factors in promoting reentrant activity. Either electrical remodeling or fibrosis in a degree of at least 30% in the BZ were required to initiate VT. Moreover, this proof-of-concept study confirms the feasibility of developing 3D computational models for cardiac EP able to reproduce cardiac activation in sinus rhythm and during VT, using exclusively non-invasive clinical data

Patient-specific generation of the Purkinje network driven by clinical measurements of a normal propagation

The propagation of the electrical signal in the Purkinje network is the starting point for the activation of the ventricular muscular cells leading to the contraction of the ventricle. In the computational models, describing the electrical activity of the ventricle is therefore important to account for the Purkinje fibers. Until now, the inclusion of such fibers has been obtained either by using surrogates such as space-dependent conduction properties or by generating a network based on an a priori anatomical knowledge. The aim of this work was to propose a new method for the generation of the Purkinje network using clinical measures of the activation times on the endocardium related to a normal electrical propagation, allowing to generate a patient-specific network. The measures were acquired by means of the EnSite NavX system. This system allows to measure for each point of the ventricular endocardium the time at which the activation front, that spreads through the ventricle, has reached the subjacent muscle. We compared the accuracy of the proposed method with the one of other strategies proposed so far in the literature for three subjects with a normal electrical propagation. The results showed that with our method we were able to reduce the absolute errors, intended as the difference between the measured and the computed data, by a factor in the range 9-25 %, with respect to the best of the other strategies. This highlighted the reliability of the proposed method and the importance of including a patient-specific Purkinje network in computational models

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

Numerical approximation of cardiac electro-fluid-mechanical models:coupling strategies for large-scale simulation

The mathematical modeling of the heart involves several challenges, which are intrinsically related to the complexity of its function. A satisfactory cardiac model must be able to describe a wide range of different processes, such as the evolution of the transmembrane potential in the myocardium, the deformation caused by the muscles contraction, and the dynamics of the blood inside the heart chambers. In this work, we focus on the coupling of the electrophysiology, the active and the passive mechanics, and the fluid dynamics of the blood in the left ventricle (LV) of the human heart. The models describing the previously mentioned processes are called âsingle core modelsâ, and can be regarded as the building blocks of an âintegrated modelâ. In this thesis, we first review the isolated single core mathematical models for the description of the LV function, and discuss their space and time discretizations with particular emphasis on the coupling conditions. We consider both implicit and semi-implicit schemes for the time discretization. The fully discretized single core problems thus obtained are then combined to define integrated electromechanics and electrofluidmechanics problems. We then focus on the numerical coupling strategy for the electromechanics solver in the framework of the active strain formulation. First, we propose a monolithic strategy where the discretized core models are solved simultaneously; then, several novel segregated strategies, where the discretized core models are solved sequentially, are proposed and systematically compared with each other. The segregated strategies are obtained by exploiting a Godunov splitting scheme, which introduces a first order error on the solution. We show that, while the monolithic approach is more accurate and more stable for relatively large timesteps, segregated approaches allow to solve the integrated problem much more efficiently in terms of computational resources. Moreover, with segregated approaches, it is possible to use different timesteps for the different core models in a staggered fashion, thus further improving the computational efficiency of the schemes. The monolithic and the segregated strategies for the electromechanics are used to solve a benchmark problem with idealized geometry: the results are then compared in terms of accuracy and efficiency. We numerically confirm that the segregated strategies are accurate at least of order one. In light of the results obtained, we employ the proposed strategies to simulate the electromechanics of a subject-specific LV for a full heartbeat. We simulate both healthy and pathological scenarios: in the latter case, we account for an ischemic necrosis of the tissue and analyze several clinical indicators such as pressure-volume loops and the end systolic pressure-volume relationship. Finally, we use the proposed strategies to simulate the electrofluidmechanics of a realistic LV during the systolic phase of the heartbeat. When defining the integrated cardiac models, we establish a preprocess pipeline aimed at preparing geometries and data for both idealized and subject-specific simulations. The pipeline is succesfully used for the setting up of large scale simulations in a high performance computing framework, where the (strong and weak) scalability of the proposed coupling strategies is assessed