Search

In this work, we present a PDE-aware deep learning model for the numerical solution to the inverse problem of electrocardiography. The model both leverages data availability and exploits the knowledge of a physically based mathematical model, expressed by means of partial differential equations (PDEs), to carry out the task at hand. The goal is to estimate the epicardial potential field from measurements of the electric potential at a discrete set of points on the body surface. The employment of deep learning techniques in this context is made difficult by the low amount of clinical data at disposal, as measuring cardiac potentials requires invasive procedures. Suitably exploiting the underlying physically based mathematical model allowed circumventing the data availability issue and led to the development of fast-training and low-complexity models. Physical awareness has been pursued by means of two elements: the projection of the epicardial potential onto a space-time reduced subspace, spanned by the numerical solutions of the governing PDEs, and the inclusion of a tensorial reduced basis solver of the forward problem in the network architecture. Numerical tests have been conducted only on synthetic data, obtained via a full order model approximation of the problem at hand, and two variants of the model have been addressed. Both proved to be accurate, up to an average ℓ 1-norm relative error on epicardial activation maps of 3.5%, and both could be trained in ≇ 15 min. Nevertheless, some improvements, mostly concerning data generation, are necessary in order to bridge the gap with clinical applications. [ABSTRACT FROM AUTHOR]

Introduction: Electrogram (EGM) fractionation is often associated with diseased atrial tissue; however, mechanisms for fractionation occurring above an established threshold of 0.5 mV have never been characterized. We sought to investigate during sinus rhythm (SR) the mechanisms underlying bipolar EGM fractionation with high‐density mapping in patients with atrial fibrillation (AF). Methods: Forty‐five patients undergoing AF ablation (73% paroxysmal, 27% persistent) were mapped at high density (18562 ± 2551 points) during SR (Rhythmia). Only bipolar EGMs with voltages above 0.5 mV were considered for analysis. When fractionation (> 40 ms and >4 deflections) was detected, we classified the mechanisms as slow conduction, wave‐front collision, or a pivot point. The relationship between EGM duration and amplitude, and tissue anisotropy and slow conduction, was then studied using a computational model. Results: Of the 45 left atria analyzed, 133 sites of EGM fragmentation were identified with voltages above 0.5 mV. The most frequent mechanism (64%) was slow conduction (velocity 0.45 m/s ± 0.2) with mean EGM voltage of 1.1 ± 0.5 mV and duration of 54.9 ± 9.4 ms. Wavefront collision was the second most frequent (19%), characterized by higher voltage (1.6 ± 0.9 mV) and shorter duration (51.3 ± 11.3 ms). Pivot points (9%) were associated with the highest degree of fractionation with 70.7 ± 6.6 ms and 1.8 ± 1 mV. In 10 sites (8%) fractionation was unexplained. The EGM duration was significantly different among the 3 mechanisms (p =.0351). Conclusion: In patients with a history of AF, EGM fractionation can occur at amplitudes > 0.5 mV when in SR in areas often considered not to be diseased tissue. The main mechanism of EGM fractionation is slow conduction, followed by wavefront collision and pivot sites. [ABSTRACT FROM AUTHOR]

We present a new, computationally efficient framework to perform forward uncertainty quantification (UQ) in cardiac electrophysiology. We consider the monodomain model to describe the electrical activity in the cardiac tissue, coupled with the Aliev‐Panfilov model to characterize the ionic activity through the cell membrane. We address a complete forward UQ pipeline, including both: (i) a variance‐based global sensitivity analysis for the selection of the most relevant input parameters, and (ii) a way to perform uncertainty propagation to investigate the impact of intra‐subject variability on outputs of interest depending on the cardiac potential. Both tasks exploit stochastic sampling techniques, thus implying overwhelming computational costs because of the huge amount of queries to the high‐fidelity, full‐order computational model obtained by approximating the coupled monodomain/Aliev‐Panfilov system through the finite element method. To mitigate this computational burden, we replace the full‐order model with computationally inexpensive projection‐based reduced‐order models (ROMs) aimed at reducing the state‐space dimensionality. Resulting approximation errors on the outputs of interest are finally taken into account through artificial neural network (ANN)‐based models, enhancing the accuracy of the whole UQ pipeline. Numerical results show that the proposed physics‐based ROMs outperform regression‐based emulators relying on ANNs built with the same amount of training data, in terms of both numerical accuracy and overall computational efficiency. [ABSTRACT FROM AUTHOR]

The increasing availability of extensive and accurate clinical data is rapidly shaping cardiovascular care by improving the understanding of physiological and pathological mechanisms of the cardiovascular system and opening new frontiers in designing therapies and interventions. In this direction, mathematical and numerical models provide a complementary relevant tool, able not only to reproduce patient‐specific clinical indicators but also to predict and explore unseen scenarios. With this goal, clinical data are processed and provided as inputs to the mathematical model, which quantitatively describes the physical processes that occur in the cardiac tissue. In this paper, the process of integration of clinical data and mathematical models is discussed. Some challenges and contributions in the field of cardiac electrophysiology are reported. [ABSTRACT FROM AUTHOR]

We introduce universal solution manifold network (USM-Net), a novel surrogate model, based on artificial neural networks (ANNs), which applies to differential problems whose solution depends on physical and geometrical parameters. We employ a mesh-less architecture, thus overcoming the limitations associated with image segmentation and mesh generation required by traditional discretization methods. Our method encodes geometrical variability through scalar landmarks, such as coordinates of points of interest. In biomedical applications, these landmarks can be inexpensively processed from clinical images. We present proof-of-concept results obtained with a data-driven loss function based on simulation data. Nonetheless, our framework is non-intrusive and modular, as we can modify the loss by considering additional constraints, thus leveraging available physical knowledge. Our approach also accommodates a universal coordinate system, which supports the USM-Net in learning the correspondence between points belonging to different geometries, boosting prediction accuracy on unobserved geometries. Finally, we present two numerical test cases in computational fluid dynamics involving variable Reynolds numbers as well as computational domains of variable shape. The results show that our method allows for inexpensive but accurate approximations of velocity and pressure, avoiding computationally expensive image segmentation, mesh generation, or re-training for every new instance of physical parameters and shape of the domain. [ABSTRACT FROM AUTHOR]