Fast quasi-conformal regional flattening of the left atrium

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). Quasi-conformal 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 registration-based 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.