The geometric evolution of aortic dissections: Predicting surgical success using fluctuations in integrated Gaussian curvature
Fig 4
Number of Surface Partitions Imposed by the Inner Scale ℓ.
Data for 302 aortas, including non-pathologic (black circles), pathologic with failed TEVAR (light gray circles), and pathologic with successful TEVAR (dark gray circles) aortas are plotted. The linear scaling can be used to define Aj ∼ ℓ2, which sets the number of partitions k used in the Gauss map calculations. The various linear fits are taken for different definitions of size: maximum aortic diameter (2Rm, red dashed line), mean radius (〈R〉, black solid line), median radius (, black dotted line), and mean inverse linearized aortic Casorati curvature (〈C1/2〉−1, black dashed line) are equivalent. Dimensionally scaled, aortic area (
, red dotted line) and volume (V1/3, red solid line) are also linear when plotted against ℓ = 2Rm. In this case, the fits are normalized by the pre-factors obtained from their fitting to the maximum dimeter (Fig 5). The normalized data is shown to demonstrate that k is independent of the specific size measure used to set the inner scale ℓ.