Fast Quasi-Conformal Regional Flattening of the Left Atrium

Abstract

Two-dimensional representation of 3D anatomical structures is a simple and intuitive way for analysing patient information across populations and image modalities. It also allows convenient visualizations that can be included in clinical reports for a fast overview of the whole structure. While cardiac ventricles, especially the left ventricle, have an established standard representation (e.g. bull's eye plot), the 2D depiction of the left atrium (LA) is challenging due to its sub-structural complexity including the pulmonary veins (PV) and the left atrial appendage (LAA). Quasiconformal flattening techniques, successfully applied to cardiac ventricles, require additional constraints in the case of the LA to place the PV and LAA in the same geometrical 2D location for different cases. Some registrationbased methods have been proposed but 3D (or 2D) surface registration is time-consuming and prone to errors if the geometries are very different. We propose a novel atrial flattening methodology where a quasi-conformal 2D map of the LA is obtained quickly and without errors related to registration. In our approach, the LA is divided into 5 regions which are then mapped to their analogue two-dimensional regions. A dataset of 67 human left atria from magnetic resonance images (MRI) was studied to derive a population-based 2D LA template representing the averaged relative locations of the PVs and LAA. The clinical application of the proposed methodology is illustrated on different use cases including the integration of MRI and electroanatomical data.

Sensitivity Analysis of In Silico Fluid Simulations to Predict Thrombus Formation after Left Atrial Appendage Occlusion

“…Post-processing and visualisation of the simulation results were performed using Par-aView 5.4.1 (https://www.paraview.org/). Finally, a quasiconformal (i.e., angle-preserving) flattening [42] was applied to obtain a 2D disk-like representation of the LA (mapping the MV contour to the external boundary of the 2D disk) for visualisation and interstudy comparison purposes.…”

“…It includes velocity and pressure profiles as well as ECAP maps (i.e., high values of ECAP indicating more thrombogenic risk since they reflect low velocities and more complex flows). For a simplified visualisation of in silico haemodynamic indices and easier comparison among the different cases, a flattening algorithm [42] was applied to the LA 3D meshes so that a 2D common representation of the LA was obtained. The white holes in the 2D maps correspond to the pulmonary veins.…”

A Cartesian Grid Representation of Left Atrial Appendages for a Deep Learning Estimation of Thrombogenic Risk Predictors

“…A method that could be attempted to bridge this problem would consist on obtaining a big enough dataset of real LAs. Correspondences among them could be set up by means of the fast flattening method proposed by Núñez-Garcia et al [23].…”

“…Thereby, a practical way of obtaining a Euclidean representation of the data is required, so that it can be fed to the mentioned algorithm. One such approach would consist on performing a flattening of the LAA geometry, which is a parametrization technique that consists on mapping 3D data into the 2D plane [22,23]. After it, 3D structures can be seen entirely in a single image, thus making them easier to understand.…”

Scar-Related Ventricular Arrhythmia Prediction from Imaging Using Explainable Deep Learning

“…LV Flattening To transform the TM from 3D to 2D, we used the LV quasiconformal flattening algorithm 5 based on the left atrial flattening proposed by [12]. In their LV extension, the authors proposed the manual selection of three landmarks: one at the centre of the apex and two points at the base.…”