< Back to Article

The geometric evolution of aortic dissections: Predicting surgical success using fluctuations in integrated Gaussian curvature

Fig 3

Multi-Scale Surface Curvature Calculations.

By mapping the aortic surface to the unit sphere (Gauss map) [45], we have an independent measure of shape. The per-vertex shape operator is calculated using the Rusinkiewicz algorithm [46]. To minimize noise, the aorta is divided into multiple partitions with area A_j. The local integrated Gaussian curvature K_j is calculated as the product of each partition area and mean Gaussian curvature, . K_j is equivalent to the signed partition area mapped out by the normals projected onto the unit sphere. We define aortic shape by studying the statistics of the distributions of K_j. 〈K〉 and δK are the first and second distribution moments that define aortic shape geometry, respectively.

doi: https://doi.org/10.1371/journal.pcbi.1011815.g003