Gaussian Surface Curvature Mapping Indicating High Risk Type B Thoracic Aortic Dissections

Background: Identifying fragile aortas that are more likely to lead to adverse clinical outcomes would provide surgeons with a better sense of how to balance the risks of surgical versus medical management in patients with type B dissections. We examine the progression of a type B dissection into a type A dissection in a patient and analyze changes in the Gaussian surface curvature distribution, as well as the response of the stress distribution at the lesser curve in response to pressurization. We hypothesize that examining the Gaussian curvature will provide us with a link between aortic surface geometry and the stress distribution, which is crucial to understanding the process driving aortic dissection.Methods: Computed tomography scans of a patient before and after the type A dissection are obtained. These are segmented in Simpleware ScanIP. Centerline curvatures are calculated on segmented models in ScanIP. Models are then pressurized in the finite element analysis software Abaqus. The Gaussian curvature is calculated by exporting segmentations into the computational program Matlab and applying a modified previously published algorithm.Results: The centerlines generated in ScanIP fail to capture the change in the acuity of the lesser curve before and after the type A dissection. Instead, Gaussian curvature analysis shows that the curvature distribution before the type A dissection is much wider compared with the distribution after the type A dissection. In addition, analyzing the stress distribution in response to pressurization reveals that before the type A dissection there is a large divergence in the principal stress vectors at the lesser curve but this transitions to a more uniform hoop stress after the type A dissection.Conclusions: Our analysis demonstrates that Gaussian surface curvature analysis captures changes in aortic geometry that are otherwise silent in centerline curvature analysis. Here, we show that as the aorta develops a type A dissection it is able to more smoothly handle the hoop stress at the lesser curve compared with the stress focusing seen in the before type A geometry. We propose that the geometric focusing before type A creates a higher energy stress state, which is relaxed on retrograde dissection. Thus, Gaussian curvature analysis may provide a window to capture underlying geometric instability in type B dissections.