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 timeconsuming 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.

InverseVis: Revealing the Hidden with Curved Sphere Tracing

“…Eulzer et al [EEL*19] and Karim et al [KMJ*14] focused on the mitral valve and left atrium, respectively, using methods like those described by Lichtenberg et al [LER*20] for flattening complex structures. Ma et al [MKH*12], Nuñez‐Garcia et al [NGBD*19], Paun et al [PBI*17], and Roney et al [RPM*19] presented various techniques for mapping the ventricles and atria. These include quasi‐conformal mapping, and methods using Laplace's equation‥ Nevertheless, in contrast to our method, these aforementioned techniques fall short in providing spatial context surrounding the focal object.…”

Vessel Maps: A Survey of Map‐Like Visualizations of the Cardiovascular System

“…A color map is used to encode data recorded with MRI on the map. Similarly, Nuñez‐Garcia et al [NGBD * 19] studied the left and right atrium and provided a solution to parameterize these structures in a quasi‐conformal manner. To achieve this, boundary conditions must be satisfied.…”

“…Approaches that rely on mesh parameterizations Create one‐to‐one maps of surface meshes embedded in 3D. Mesh parameterizations are used for mapping different vascular structures comprising: specific structures like aneurysm surfaces [GSK * 12, MVB * 17, MVPL18, MGB * 19, MVG * 21], stenosis predilection sites [AS03, AS04, CUS * 17, CES * 08, CLC13, CUSF13, CCC16, CCLC17, CCR20, ZSC21], or heart valves and cavities [EEL * 19, KMJ * 14, LER * 20, MKH * 12, NGBD * 19, PBI * 17, RPM * 19, WTGZ * 17] but also arbitrary vessel tree walls [ERM * 21, ZHT * 02a, ZHT02b, ZHT03, ZHT05]. For techniques based on surface projections , the properties are projected onto a parametric structure like a cylinder, disk, or sphere [BSR * 14,KHB * 06,NGB * 09,OKG * 06,SCK * 16,TBB * 07].…”

Volumetric parcellation of the right ventricle for regional geometric and functional assessment

“…To avoid explicit registration, some authors have proposed parametrisation methods to create anatomical maps of organs ((Nuñez-Garcia et al, 2019;Vera et al, 2013;Paun et al, 2017;Hurdal and Stephenson, 2009)) by finding smooth bijective maps from each surface/volume to a common domain, a subset of R 2 or R 3 respectively. The parametrisations of individual anatomies can subsequently be used to obtain a point-to-point correspondence.…”