The geometric evolution of aortic dissections: Predicting surgical success using fluctuations in integrated Gaussian curvature
Fig 7
Aortic Topological Invariance and Aortic Clustering in -space.
A. The eight canonical representative aortas along the normal-to-diseased axis (left to right): a 3-year-old child, healthy adults, and type B aortic dissection (TBAD) patients at varying degrees of aneurysmal degeneration. Two clinical regimes exist: shape preserving growth and growth with shape changes. B. shows the topologic equivalence of all aortic shapes to tori (red stars) and cylinders (red diamonds); the yellow symbols correspond to specific aortic shapes along the normal-to-diseased axis (A.). Red circles correspond to perfect spheres of varying size; pseudospheres and catenoids are depicted as red rightward-pointing triangles and upward-pointing triangles, respectively. C. shows the optimal two-dimensional aortic geometric feature space with independent axes for size and shape. The solid red curve is a best fit to the data. The power-like behavior is further supported by the probability distribution of δK (Fig 8). The aortas separate into shape invariant (normal) and shape fluctuating (diseased) populations. Furthermore, this feature space defines decision boundaries that correctly classify diseased patients based on success of TEVAR.