Standard Quasi-Conformal Flattening of the Right and Left Atria

Abstract

Two-dimensional standard representations of 3D anatomical structures are a simple and intuitive way for analysing patient information across populations and image modalities. They also allow 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 (LA) and right atrium (RA) remains challenging due to their sub-structural complexity. Quasi-conformal flattening techniques, successfully applied to cardiac ventricles, require additional constraints in the case of the atria to correctly place the adjacent structures, i.e. the pulmonary veins, the vena cava (VC) or the appendages. Some registration-based methods exist to flatten the LA but they can be 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 both (left and right) atria is obtained quickly and without errors related to registration. In our approach the RA is mapped to a standard 2D map where the holes corresponding to superior and inferior VC are fixed within a disk. Similarly, the LA is divided into 5 regions which are then mapped to their analogous two-dimensional regions. We illustrate the application of the method to visualize atrial wall thickness measurements, and late gadolinium enhanced magnetic resonance data.