Branched Latent Neural Maps

We introduce Branched Latent Neural Maps (BLNMs) to learn finite dimensional input-output maps encoding complex physical processes. A BLNM is defined by a simple and compact feedforward partially-connected neural network that structurally disentangles inputs with different intrinsic roles, such as the time variable from model parameters of a differential equation, while transferring them into a generic field of interest. BLNMs leverage latent outputs to enhance the learned dynamics and break the curse of dimensionality by showing excellent generalization properties with small training datasets and short training times on a single processor. Indeed, their generalization error remains comparable regardless of the adopted discretization during the testing phase. Moreover, the partial connections significantly reduce the number of tunable parameters. We show the capabilities of BLNMs in a challenging test case involving electrophysiology simulations in a biventricular cardiac model of a pediatric patient with hypoplastic left heart syndrome. The model includes a 1D Purkinje network for fast conduction and a 3D heart-torso geometry. Specifically, we trained BLNMs on 150 in silico generated 12-lead electrocardiograms (ECGs) while spanning 7 model parameters, covering cell-scale and organ-level. Although the 12-lead ECGs manifest very fast dynamics with sharp gradients, after automatic hyperparameter tuning the optimal BLNM, trained in less than 3 hours on a single CPU, retains just 7 hidden layers and 19 neurons per layer. The resulting mean square error is on the order of $10^{-4}$ on a test dataset comprised of 50 electrophysiology simulations. In the online phase, the BLNM allows for 5000x faster real-time simulations of cardiac electrophysiology on a single core standard computer and can be used to solve inverse problems via global optimization in a few seconds of computational time

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

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

Bayesian Active Learning for Personalization and Uncertainty Quantification in Cardiac Electrophysiological Model

Cardiacvascular disease is the top death causing disease worldwide. In recent years, high-fidelity personalized models of the heart have shown an increasing capability to supplement clinical cardiology for improved patient-specific diagnosis, prediction, and treatment planning. In addition, they have shown promise to improve scientific understanding of a variety of disease mechanisms. However, model personalization by estimating the patient-specific tissue properties that are in the form of parameters of a physiological model is challenging. This is because tissue properties, in general, cannot be directly measured and they need to be estimated from measurements that are indirectly related to them through a physiological model. Moreover, these unknown tissue properties are heterogeneous and spatially varying throughout the heart volume presenting a difficulty of high-dimensional (HD) estimation from indirect and limited measurement data. The challenge in model personalization, therefore, summarizes to solving an ill-posed inverse problem where the unknown parameters are HD and the forward model is complex with a non-linear and computationally expensive physiological model. In this dissertation, we address the above challenge with following contributions. First, to address the concern of a complex forward model, we propose the surrogate modeling of the complex target function containing the forward model – an objective function in deterministic estimation or a posterior probability density function in probabilistic estimation – by actively selecting a set of training samples and a Bayesian update of the prior over the target function. The efficient and accurate surrogate of the expensive target function obtained in this manner is then utilized to accelerate either deterministic or probabilistic parameter estimation. Next, within the framework of Bayesian active learning we enable active surrogate learning over a HD parameter space with two novel approaches: 1) a multi-scale optimization that can adaptively allocate higher resolution to heterogeneous tissue regions and lower resolution to homogeneous tissue regions; and 2) a generative model from low-dimensional (LD) latent code to HD tissue properties. Both of these approaches are independently developed and tested within a parameter optimization framework. Furthermore, we devise a novel method that utilizes the surrogate pdf learned on an estimated LD parameter space to improve the proposal distribution of Metropolis Hastings for an accelerated sampling of the exact posterior pdf. We evaluate the presented methods on estimating local tissue excitability of a cardiac electrophysiological model in both synthetic data experiments and real data experiments. Results demonstrate that the presented methods are able to improve the accuracy and efficiency in patient-specific model parameter estimation in comparison to the existing approaches used for model personalization

Model for educational simulation of the neonatal electrocardiogram

Tese de mestrado. Engenharia Biomédica. Faculdade de Engenharia. Universidade do Porto. 200

Statistical atlases for electroanatomical mapping of cardiac arrhythmias

Electroanatomical mapping is a mandatory time-consuming planning step in cardiac catheter ablation. In practice, interventional cardiologists target specific endocardial areas for mapping based on personal experience, general electrophysiology principles, and preoperative anatomical scans. Effective fusion of all available information towards a useful mapping strategy has not been standardised and achieving the optimal map within time and space constraints is challenging. In this paper, a novel framework for computing optimal endocardial mapping locations in patients with congenital heart disease (CHD) is proposed. The method is based on a statistical electroanatomical model (SEAM) which is instantiated from preoperative anatomy in order to achieve an initial prediction of the electrical map. Simultaneously, the anatomical areas with the highest frequency of mapping among the similar cases in the dataset are detected and a classifier is trained to filter these points based on the electroanatomical data. The framework was tested in an iterative process of adding mapping points to the SEAM and computing the instantiation error, with retrospective clinical data of 66 CHD cases available

Mathematical modeling approaches for the diagnosis and treatment of reentrant atrial tachyarrhythmias

[EN] Atrial tachyarrhythmias present a high prevalence in the developed world, and several studies predict that in the coming decades it will be increased. Micro or macro-reentrant mechanisms of the electrical wavefronts that govern the mechanical behavior of the heart are one of the main responsibles for the maintenance of these arrhythmias. Atrial flutter is maintained by a macro-reentry around an anatomical or functional obstacle located in the atria. In the case of atrial fibrillation, the hypothesis which describes high frequency rotors as dominant sources of the fibrillation and responsible for the maintenance of the arrhythmia, has been gaining relevance in the last years. However, the therapies that target high frequency sources have a limited efficacy with current techniques. Radiofrequency ablation allows the destruction of parts of the cardiac tissue resulting in the interruption of the reentrant circuit in case of macro-reentries or the isolation of micro-reentrant circuits. The non-invasive location of reentrant circuits would increment the efficacy of these therapies and would shorten surgery interventions. In parallel, pharmacological therapies modify ionic expressions associated to the excitability and electrical refractoriness of the cardiac tissue with the objective of hindering the maintenance of reentrant behaviors. These therapies require a deep knowledge of the ionic mechanisms underlying the reentrant behavior and its properties in order to be effective. The research in these mechanisms allows the evaluation of new targets for the treatment and thus may improve the efficacy in atrial fibrillation termination. In this thesis, mathematical modeling is used to go forward in the minimization of the limitations associated to these treatments. Body surface potential mapping has been evaluated, both clinically and by means of mathematical simulations for the diagnosis and location of macro-reentrant circuits. The analysis of phase maps obtained from multiple lead electrocardiographic recordings distributed in the whole torso allowed the discrimination between different reentrant circuits. It is the reason why this technique is presented as a tool for the non-invasive location of macro and micro-reentrant circuits. A population of mathematical models designed in this thesis based on the action potentials recordings of atrial cardiomyocites from 149 patients, allowed the evaluation of the ionic mechanisms defining the properties of reentrant behaviors. This study has allowed us defining the blockade of ICaL as a target for the pharmacological treatment. The blockade of this current is associated with the increase of the movement in the core of the rotor which easies the collision of the rotor with other wavefronts or anatomical obstacles promoting the extinction of the reentry. The variability observed between patients modeled in our population has allowed showing and explaining the mechanisms promoting divergent results of a single treatment. This is why the introduction of populations of models will allow the prevention of side effects associated to inter-subject variability and to go forward in the development of individualized therapies. These works are built through a simulation platform of cardiac electrophysiology based in Graphic Processing Units (GPUs) and developed in this thesis. The platform allows the simulation of cellular models, tissues and organs with a realistic geometry and shows features comparable to that of the platforms used by the most relevant electrophysiology research groups at the moment.[ES] Las taquiarritmias auriculares tienen una alta prevalencia en el mundo desarrollado, además diversos estudios poblacionales indican que en las próximas décadas ésta se verá incrementada. Los mecanismos de micro o macro-reentrada de los frentes de onda eléctricos que rigen el comportamiento mecánico del corazón, se presentan como una de las principales causas del mantenimiento de estas arritmias. El flutter auricular es mantenido por un macro-reentrada alrededor de un obstáculo anatómico o funcional en las aurículas, mientras que en el caso de la fibrilación auricular la hipótesis que define a los rotores de alta frecuencia como elementos dominantes y responsables del mantenimiento de la arritmia se ha ido imponiendo al resto en los últimos años. Sin embargo, las terapias que tienen como objetivo finalizar o aislar estas reentradas tienen todavía una eficacia limitada. La ablación por radiofrecuencia permite eliminar zonas del tejido cardiaco resultando en la interrupción del circuito de reentrada en el caso de macro-reentradas o el aislamiento de comportamientos micro-reentrantes. La localización no invasiva de los circuitos reentrantes incrementaría la eficacia de estas terapias y reduciría la duración de las intervenciones quirúrgicas. Por otro lado, las terapias farmacológicas alteran las expresiones iónicas asociadas a la excitabilidad y la refractoriedad del tejido con el fin de dificultar el mantenimiento de comportamientos reentrantes. Este tipo de terapias exigen incrementar el conocimiento de los mecanismos subyacentes que explican el proceso de reentrada y sus propiedades, la investigación de estos mecanismos permite definir las dianas terapéuticas que mejoran la eficacia en la extinción de estos comportamientos. En esta tesis el modelado matemático se utiliza para dar un paso importante en la minimización de las limitaciones asociadas a estos tratamientos. La cartografía eléctrica de superficie ha sido testada, clínicamente y con simulaciones matemática,s como técnica de diagnóstico y localización de circuitos macro-reentrantes. El análisis de mapas de fase obtenidos a partir de los registros multicanal de derivaciones electrocardiográficas distribuidas en la superficie del torso permite diferenciar distintos circuitos de reentrada. Es por ello que esta técnica de registro y análisis se presenta como una herramienta para la localización no invasiva de circuitos macro y micro-reentrantes. Una población de modelos matemáticos, diseñada en esta tesis a partir de los registros de los potenciales de acción de 149 pacientes, ha permitido evaluar los mecanismos iónicos que definen las propiedades asociadas a los procesos de reentrada. Esto ha permitido apuntar al bloqueo de la corriente ICaL como diana terapéutica. Ésta se asocia al incremento del movimiento del núcleo que facilita el impacto del rotor con otros frentes de onda u obstáculos extinguiéndose así el comportamiento reentrante. La variabilidad entre pacientes reflejada en la población de modelos ha permitido además mostrar los mecanismos por los cuales un mismo tratamiento puede mostrar efectos divergentes, así el uso de poblaciones de modelos matemáticos permitirá prevenir efectos secundarios asociados a la variabilidad entre pacientes y profundizar en el desarrollo de terapias individualizadas. Estos trabajos se cimientan sobre una plataforma de simulación de electrofisiología cardiaca de basado en Unidades de Procesado Gráfico (GPUs) y desarrollada en esta tesis. La plataforma permite la simulación de modelos celulares cardiacos así como de tejidos u órganos con geometría realista, mostrando unas prestaciones comparables con las de las utilizadas por los grupos de investigación más potentes en el campo de la electrofisiología.[CA] Les taquiarítmies auriculars tenen una alta prevalença en el món desenvolupat, a més diversos estudis poblacionals indiquen que en les pròximes dècades aquesta es veurà incrementada. Els mecanismes de micro o macro-reentrada dels fronts d'ona elèctrics que regeixen el comportament mecànic del cor, es presenten com una de les principals causes del manteniment d'aquestes arítmies. El flutter auricular és mantingut per una macro-reentrada al voltant d'un obstacle anatòmic o funcional en les aurícules, mentre que en el cas de la fibril·lació auricular la hipòtesi que defineix als rotors d'alta freqüència com a elements dominants i responsables del manteniment de l'arítmia s'ha anat imposant a la resta en els últims anys. No obstant això, les teràpies que tenen com a objectiu finalitzar o aïllar aquestes reentrades tenen encara una eficàcia limitada. L'ablació per radiofreqüència permet eliminar zones del teixit cardíac resultant en la interrupció del circuit de reentrada en el cas de macro-reentrades o l'aïllament de comportaments micro-reentrants. La localització no invasiva dels circuits reentrants incrementaria l'eficàcia d'aquestes teràpies i reduiria la durada de les intervencions quirúrgiques. D'altra banda, les teràpies farmacològiques alteren les expressions iòniques associades a la excitabilitat i la refractaritat del teixit amb la finalitat de dificultar el manteniment de comportaments reentrants. Aquest tipus de teràpies exigeixen incrementar el coneixement dels mecanismes subjacents que expliquen el procés de reentrada i les seues propietats, la recerca d'aquests mecanismes permet definir les dianes terapèutiques que milloren l'eficàcia en l'extinció d'aquests comportaments. En aquesta tesi el modelatge matemàtic s'utilitza per a fer un pas important en la minimització de les limitacions associades a aquests tractaments. La cartografia elèctrica de superfície ha sigut testada, clínicament i amb simulacions matemàtiques com a tècnica de diagnòstic i localització de circuits macro-reentrants. L'anàlisi de mapes de fase obtinguts a partir dels registres multicanal de derivacions electrocardiogràfiques distribuïdes en la superfície del tors permet diferenciar diferents circuits de reentrada. És per açò que aquesta tècnica de registre i anàlisi es presenta com una eina per a la localització no invasiva de circuits macro i micro-reentrants. Una població de models matemàtics, dissenyada en aquesta tesi a partir dels registres dels potencials d'acció de 149 pacients, ha permès avaluar els mecanismes iònics que defineixen les propietats associades als processos de reentrada. Açò ha permès apuntar al bloqueig del corrent ICaL com a diana terapèutica. Aquesta s'associa a l'increment del moviment del nucli que facilita l'impacte del rotor amb altres fronts d'ona o obstacles extingint-se així el comportament reentrant. La variabilitat entre pacients reflectida en la població de models ha permès a més mostrar els mecanismes pels quals un mateix tractament pot mostrar efectes divergents, així l'ús de poblacions de models matemàtics permetrà prevenir efectes secundaris associats a la variabilitat entre pacients i aprofundir en el desenvolupament de teràpies individualitzades. Aquests treballs es fonamenten sobre una plataforma de simulació de electrofisiologia cardíaca basat en Unitats de Processament Gràfic (GPUs) i desenvolupada en aquesta tesi. La plataforma permet la simulació de models cel·lulars cardíacs així com de teixits o òrgans amb geometria realista, mostrant unes prestacions comparables amb les de les utilitzades per els grups de recerca més importants en aquesta área.Liberos Mascarell, A. (2016). Mathematical modeling approaches for the diagnosis and treatment of reentrant atrial tachyarrhythmias [Tesis doctoral no publicada]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/62166TESI

Traversed Graph Representation for Sparse Encoding of Macro-Reentrant Tachycardia

© Springer International Publishing Switzerland 2016.Macro-reentrant atrial and ventricular tachycardias originate from additional circuits in which the activation of the cardiac chambers follows a high-frequency rotating pattern. The macro-reentrant circuit can be interrupted by targeted radiofrequency energy delivery with a linear lesion transecting the pathway. The choice of the optimal ablation site is determined by the operator’s experience, thus limiting the procedure success, increasing its duration and also unnecessarily extending the ablated tissue area in the case of incorrect ablation target estimation. In this paper, an algorithm for automatic intraoperative detection of the tachycardia reentry path is proposed by modelling the propagation as a graph traverse problem. Moreover, the optimal ablation point where the path should be transected is computed. Finally, the proposed method is applied to sparse electroanatomical data to demonstrate its use when undersampled mapping occurs. Thirteen electroanatomical maps of right ventricle and right and left atrium tachycardias from patients treated for congenital heart disease were analysed retrospectively in this study, with prediction accuracy tested against the recorded ablation sites and arrhythmia termination points

Haemodynamic optimization of cardiac resynchronization therapy

Heart failure carries a very poor prognosis, unless treated with the appropriate pharmacological agents which, have been evaluated in large randomized clinical trials and have demonstrated improvements in morbidity and mortality of this cohort of patients. A significant proportion of these patients develop conduction abnormalities involving both the atrioventricular node and also the specialised conduction tissue (bundle of His and Purkinje fibers) of the ventricular myocardium which is most commonly evidenced by the presence of a wide QRS, typically left bundle branch block. The net effect of these conduction abnormalities is inefficient filling and contraction of the left ventricle. The presence of these conduction abnormalities is an additional strong marker of poor prognosis. Over the last 15 years pacing treatments have been developed aimed at mitigating the conduction disease. Large scale randomized multicentre trials have repeatedly demonstrated the effectiveness of cardiac pacing, officially recognized as cardiac resynchronization therapy (CRT). This mode of pacing therapy has undoubtedly had a positive impact on both the morbidity and mortality of these patients. Despite the large advancement in the management of heart failure patients by pacing therapies, a significant proportion of patients (30%) being offered CRT are classed as non-responders. Many explanations have been put forward for the lack of response. The presence of scar at the pacing site with failure to capture or delayed capture of myocardium, too much left ventricular scar therefore minimal contractile response, incorrect pacing site due to often limited anatomical options of lead placement and insufficient programming i.e optimization, of pacemaker settings such as the AV and VV delay are just some of the suggested areas perceived to be responsible for the lack of patients’ response to cardiac resynchronization therapy. The effect of optimization of pacemaker settings is a field that has been investigated extensively in the last decade. Disappointingly, current methods of assessing the effect of optimization of pacemaker settings on several haemodynamic parameters, such as cardiac output and blood pressure, are marred with very poor reproducibility, so measurement of any effect of optimization is close to being meaningless. Moreover, detailed understanding of the effects of CRT on coronary physiology and cardiac mechanoenergetics is equally, disappointingly, lacking. In this thesis, I investigated the acute effects of cardiac resynchronization therapy and AV optimization on coronary physiology and cardiac mechanoenergetics. This was accomplished using very detailed and demanding series of invasive catheterization studies. I used novel analytical mathematical techniques, such as wave intensity analysis, which have been developed locally and this provided a unique insight of the important physiological entities defining coronary physiology and cardiac mechanics. I explored in detail the application and reliability of photoplethysmography as a tool for non-invasive optimization of the AV delay. Photoplethysmography has the potential of miniaturization and therefore implantation alongside pacemaker devices. I compared current optimization techniques (Echocardiography and ECG) of VV delay against beat-to-beat blood pressure using the Finometer device and defined the criteria that a technique requires if such a technique can be used meaningfully for the optimization of pacemaker settings both in clinical practice and in clinical trials. Finally, I investigated the impact of atrial pacing and heart rate on the optimal AV delay and attempted to characterize the mechanisms underlying any changes of the optimal AV delay under these varying patient and pacing states. In this thesis I found that optimization of AV delay of cardiac resynchronization therapy not only improved cardiac contraction and external cardiac work, but also cardiac relaxation and coronary blood flow, when compared against LBBB. I found that most of the increase in coronary blood flow occurred during diastole and that the predominant drive for this was ventricular microcirculatory suction as evidenced by the increased intracoronary diastolic backward-travelling decompression wave. I showed that non-invasive haemodynamic optimization using the plethysmograph signal of an inexpensive pulse oximeter is as reliable as using the Finometer. Appropriate processing of the oximetric signal improved the reproducibility of the optimal AV delay. The advantage of this technology is that it might be miniaturized and implanted to provide automated optimization. In this thesis I found that other commonly used modalities of VV optimization such as echocardiography and ECG lack internal validity as opposed to non-invasive haemodynamic optimization using blood pressure. This finding will encourage avoidance of internally invalid modalities, which may cause more harm than good. In this thesis I found that the sensed and paced optimal AV delays have, on average, a bigger difference than the one assumed by the device manufacturers and clinicians. As a significant proportion of patients will be atrially paced, especially during exercise, optimization during this mode of pacing is equally crucial as it is during atrial sensing. Finally, I found that the optimal AV delay decreases with increasing heart rate, and the slope of this is within the range of existing pacemaker algorithms used for rate adaptation of AV delay, strengthening the argument for the rate adaptation to be programmed on.Imperial Users Onl

Personalization of Cardiac Electrophysiology Model using the Unscented Kalman Filtering

International audienceCardiac electrophysiology mapping techniques now allow to record denser intra-operative electrograms (ECG). The patient-specific information extracted from these clinical recordings is extremely valuable. A growing field of research focuses on the personalization of electro-physiology models using this patient-specific information. The modeling in silico of a patient electrophysiology is needed to better understand the mechanism of cardiac arrhythmia. In the scope of ischemic cardiomyopa-thy, the predictive power of patient-specific simulations may also provide a substantial guidance in defining the optimal location of the implantable defibrillator, since all possible configurations could be tested in silico. This article describes an innovative personalization approach based on an unscented Kalman filter. Following an iterative process, the apparent conductivity is efficiently estimated in specific regions. A sensitivity analysis is performed to assess the filter parameters. With three patient cases, we finally demonstrate the accuracy and efficiency of our algorithm