Quantitative Shape Analysis Supports the Use of Aortic Arch Stent Grafts in Complex Aortic Geometries

Introduction: Traditional thoracic endovascular aortic repair (TEVAR) relies on distal landing zones beyond the left common carotid artery, which may underperform in patients with complex aortic anatomy. The Nexus Aortic Arch Stent Graft enables proximal landing zones in the ascending aorta, expanding endovascular options for challenging arch pathology. This study applies a geometrically focused framework using fluctuation in total integrated Gaussian curvature (𝛿𝐾), a size-invariant metric of surface topology, to evaluate Nexus performance across diverse aortic morphologies. Methods: Pre-operative CT imaging was analyzed for 27 patients treated with the Nexus device and 37 treated with traditional TEVAR (proximal landing zones 2/3). CT scans from 215 patients with non-pathologic aortas served as controls. Two-dimensional aortic surface meshes were constructed to calculate 𝛿𝐾 and mean aortic radius, while tortuosity index was derived from the centerline. Nexus data were mapped into a previously established size-shape feature space to assess predicted outcomes. TEVAR failure was defined as reintervention or death due to aneurysmal growth, endoleak, dissection extension, or rupture. Correlation and clustering analyses evaluated relationships between aortic morphology and outcomes. A scale-sampling approach captured the multiscale nature of aortic geometry while reducing sensitivity to mesh resolution and partitioning. Results: The Traditional TEVAR cohort had a significantly lower success rate than the Nexus cohort (51.4% vs. 85.2%, p = 0.005). Traditional TEVAR was particularly less effective in patients with elevated 𝛿𝐾 and large mean radius, whereas the Nexus device demonstrated favorable outcomes even in anatomically complex aortas with similarly elevated 𝛿𝐾 and radius values. Combining 𝛿𝐾 and radius demonstrated distinct clustering patterns by pathology: 78.3% of chronic dissections occupied the high 𝛿𝐾/radius zone, while 70.6% of isolated aneurysms fell in the low 𝛿𝐾/radius zone (p < 0.001). 𝛿𝐾 provided unique morphological insight beyond size, whereas tortuosity index was less discriminative. Conclusion: 𝛿𝐾 offers a quantitative framework for assessing device performance across variable aortic anatomy. Endovascular arch repair using proximal ascending aortic landing zones, exemplified by the Nexus device, may provide a viable option in patients with complex geometry. This shape-size framework represents a step toward personalized patient selection and improved long-term outcomes.