Deep Learning Framework for Real-Time Estimation of in-silico Thrombotic Risk Indices in the Left Atrial Appendage

Figures

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  Figure 1. Pipeline to generate the ground truth ECAP maps for the two datasets. LA, left atrium; LAA, left atrial appendage; PV, pulmonary veins; CFD, computational fluid dynamics; ECAP, endothelial cell activation potential.

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  Figure 2. (A) Scheme of the principal component analysis model (PCA). Once each shape was parameterized, the ECAP values were predicted through a simple multilayer perceptron formed by fully connected layers (FCN). Numbers below each layer represent the number of nodes in each of them. (B) The LAA morphology is flattened to a new 2D UV space in which the new axes are represented by the geodesic apical-ostium distance and the angle formed with respect to the centroid of each isoline, using the closest point to the circumflex artery as reference. ECAP, endothelial cell activation potential.

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  Figure 3. Each left atrial appendage (LAA) went through UV mapping, more colloquially known as flattening, and represented as a 2D image either as Bull's eye plot or a polar coordinate-based Cartesian grid representation. The U-Net architecture based on the work by Thuerey et al. (2020), received the spatial coordinates of the vertices sampled during the flattening process as the input features and then performed regression to predict their corresponding ECAP maps.

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  Figure 4. General overview of the geometric deep learning network architecture. The input vertex features consisted of the point-wise curvature and normal vectors. The spatial relations between the nodes were stored as edge attributes through Cartesian pseudo-coordinates. Twelve consecutive SplineConv layers (Fey et al., 2018) were employed in the local feature module, while a 1,024 feature vector was obtained after max pooling, representing the global features of each mesh. Numbers adjacent to each layer indicate the number of output features.

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  Figure 5. From left to right: ground-truth endothelial cell activation potential (ECAP) from fluid simulations; principal component analysis model (PCA-FCN) prediction; Cartesian grid and Bull's eye plot prediction; geometric deep learning prediction (Geometric). The mean absolute error (MAE) is also provided alongside. Higher ECAP values (in red) are linked to a higher risk of thrombus formation.

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  Figure 6. All results are shown on terms of the mean absolute error (MAE). (A) Results from the “Sequential Synthetic” experiment in which only the synthetic data was employed for training. (B) Results from the “Sequential Real” experiment which only trained and tested on the real cases. (C) Results from the “Sequential Real + Synthetic” test, in which all the synthetic geometries were employed as the training baseline and subsequently, batches of real data were sequentially added on top.

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  Figure 7. Predicted endothelial cell activation potential (ECAP) maps in a batch of left atrial appendages (LAA) from dataset 2 (i.e., patient-specific LA) alongside the ground-truth (GT) from fluid simulations. Higher ECAP values (in red) are linked to a higher risk of thrombus formation.