Computational generation of the Purkinje network driven by clinical measurements: The case of pathological propagations

Elena Faggiano, Fabio Nobile, Alfio Quarteroni, Christian Vergara
2014
Article

Résumé

To properly describe the electrical activity of the left ventricle, it is necessary to model the Purkinje fibers, responsible for the fast and coordinate ventricular activation, and their interaction with the muscular propagation. The aim of this work is to propose a methodology for the generation of a patient-specific Purkinje network driven by clinical measurements of the activation times related to pathological propagations. In this case, one needs to consider a strongly coupled problem between the network and the muscle, where the feedback from the latter to the former cannot be neglected as in a normal propagation. We apply the proposed strategy to data acquired on three subjects, one of them suffering from muscular conduction problems owing to a scar and the other two with a muscular pre-excitation syndrome (Wolff–Parkinson–White). To assess the accuracy of the proposed method, we compare the results obtained by using the patient-specific Purkinje network generated by our strategy with the ones obtained by using a non-patient-specific network. The results show that the mean absolute errors in the activation time is reduced for all the cases, highlighting the importance of including a patient-specific Purkinje network in computational models. Copyright © 2014 John Wiley & Sons, Ltd.

Official source

https://infoscience.epfl.ch/record/202221?ln=fr

À propos de ce résultat

Cette page est générée automatiquement et peut contenir des informations qui ne sont pas correctes, complètes, à jour ou pertinentes par rapport à votre recherche. Il en va de même pour toutes les autres pages de ce site. Veillez à vérifier les informations auprès des sources officielles de l'EPFL.

Concepts associés

Chargement

Publications associées

Chargement

, , ,

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.

Springer Verlag2014

Chargement

In this thesis, we propose new algorithms to solve inverse problems in the context of biomedical images. Due to ill-posedness, solving these problems require some prior knowledge of the statistics of the underlying images. The traditional algorithms, in the field, assume prior knowledge related to smoothness or sparsity of these images. Recently, they have been outperformed by the second generation algorithms which harness the power of neural networks to learn required statistics from training data. Even more recently, last generation deep-learning-based methods have emerged which require neither training nor training data. This thesis devises algorithms which progress through these generations. It extends these generations to novel formulations and applications while bringing more robustness. In parallel, it also progresses in terms of complexity, from proposing algorithms for problems with 1D data and an exact known forward model to the ones with 4D data and an unknown parametric forward model. We introduce five main contributions. The last three of them propose deep-learning-based latest-generation algorithms that require no prior training. 1) We develop algorithms to solve the continuous-domain formulation of inverse problems with both classical Tikhonov and total-variation regularizations. We formalize the problems, characterize the solution set, and devise numerical approaches to find the solutions. 2) We propose an algorithm that improves upon end-to-end neural-network-based second generation algorithms. In our method, a neural network is first trained as a projector on a training set, and is then plugged in as a projector inside the projected gradient descent (PGD). Since the problem is nonconvex, we relax the PGD to ensure convergence to a local minimum under some constraints. This method outperforms all the previous generation algorithms for Computed Tomography (CT). 3) We develop a novel time-dependent deep-image-prior algorithm for modalities that involve a temporal sequence of images. We parameterize them as the output of an untrained neural network fed with a sequence of latent variables. To impose temporal directionality, the latent variables are assumed to lie on a 1D manifold. The network is then tuned to minimize the data fidelity. We obtain state-of-the-art results in dynamic magnetic resonance imaging (MRI) and even recover intra-frame images. 4) We propose a novel reconstruction paradigm for cryo-electron-microscopy (CryoEM) called CryoGAN. Motivated by generative adversarial networks (GANs), we reconstruct a biomolecule's 3D structure such that its CryoEM measurements resemble the acquired data in a distributional sense. The algorithm is pose-or-likelihood-estimation-free, needs no ab initio, and is proven to have a theoretical guarantee of recovery of the true structure. 5) We extend CryoGAN to reconstruct continuously varying conformations of a structure from heterogeneous data. We parameterize the conformations as the output of a neural network fed with latent variables on a low-dimensional manifold. The method is shown to recover continuous protein conformations and their energy landscape.

EPFL2020

Chargement

On Vacuous and Non-Vacuous Generalization Bounds for Deep Neural Networks.

Konstantinos Pitas

Deep neural networks have been empirically successful in a variety of tasks, however their theoretical understanding is still poor. In particular, modern deep neural networks have many more parameters than training data. Thus, in principle they should overfit the training samples and exhibit poor generalization to the complete data distribution. Counter intuitively however, they manage to achieve both high training accuracy and high testing accuracy. One can prove generalization using a validation set, however this can be difficult when training samples are limited and at the same time we do not obtain any information about why deep neural networks generalize well. Another approach is to estimate the complexity of the deep neural network. The hypothesis is that if a network with high training accuracy has high complexity it will have memorized the data, while if it has low complexity it will have learned generalizable patterns. In the first part of this thesis we explore Spectral Complexity, a measure of complexity that depends on combinations of norms of the weight matrices of the deep neural network. For a dataset that is difficult to classify, with no underlying model and/or no recurring pattern, for example one where the labels have been chosen randomly, spectral complexity has a large value, reflecting that the network needs to memorize the labels, and will not generalize well. Putting back the real labels, the spectral complexity becomes lower reflecting that some structure is present and the network has learned patterns that might generalize to unseen data. Spectral complexity results in vacuous estimates of the generalization error (the difference between the training and testing accuracy), and we show that it can lead to counterintuitive results when comparing the generalization error of different architectures. In the second part of the thesis we explore non-vacuous estimates of the generalization error. In Chapter 2 we analyze the case of PAC-Bayes where a posterior distribution over the weights of a deep neural network is learned using stochastic variational inference, and the generalization error is the KL divergence between this posterior and a prior distribution. We find that a common approximation where the posterior is constrained to be Gaussian with diagonal covariance, known as the mean-field approximation, limits significantly any gains in bound tightness. We find that, if we choose the prior mean to be the random network initialization, the generalization error estimate tightens significantly. In Chapter 3 we explore an existing approach to learning the prior mean, in PAC-Bayes, from the training set. Specifically, we explore differential privacy, which ensures that the training samples contribute only a limited amount of information to the prior, making it distribution and not training set dependent. In this way the prior should generalize well to unseen data (as it hasn't memorized individual samples) and at the same time any posterior distribution that is close to it in terms of the KL divergence will also exhibit good generalization.

EPFL2020

Chargement

On Vacuous and Non-Vacuous Generalization Bounds for Deep Neural Networks.

Konstantinos Pitas

EPFL2020