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Intrinsic shape measures have been shown to complement diameter, but their utility depends critically on the observation scale imposed during quantification. We aim to identify scales at which a size-invariant shape descriptor, specifically the normalized fluctuation in total integrated Gaussian curvature\n \n \n $$\\widetilde{\\delta K}$$<\/jats:tex-math>\n \n \n \n \u03b4<\/mml:mi>\n K<\/mml:mi>\n <\/mml:mrow>\n ~<\/mml:mo>\n <\/mml:mover>\n <\/mml:math>\n <\/jats:alternatives>\n <\/jats:inline-formula>\n , most robustly captures thoracic aortic disease state and to relate the tuned\n \n \n $$\\widetilde{\\delta K}$$<\/jats:tex-math>\n \n \n \n \u03b4<\/mml:mi>\n K<\/mml:mi>\n <\/mml:mrow>\n ~<\/mml:mo>\n <\/mml:mover>\n <\/mml:math>\n <\/jats:alternatives>\n <\/jats:inline-formula>\n signal to clinically relevant markers of chronicity in aortic dissection.\n <\/jats:p>\n <\/jats:sec>\n \n \n Methods<\/jats:bold>\n <\/jats:title>\n \n We construct a scale space of aortic surface representations from CTA images via a factorial sweep across smoothing intensity, mesh density, and mesh partitioning (coarse-graining) size. For each construction we compute\n \n \n $$\\widetilde{\\delta K}$$<\/jats:tex-math>\n \n \n \n \u03b4<\/mml:mi>\n K<\/mml:mi>\n <\/mml:mrow>\n ~<\/mml:mo>\n <\/mml:mover>\n <\/mml:math>\n <\/jats:alternatives>\n <\/jats:inline-formula>\n , quantify signal robustness and predictive clinical value, and identify a \u201cstable zone\u201d of scales where performance stabilizes. We then model clinical progression using Gaussian Process Regression and relate\n \n \n $$\\widetilde{\\delta K}$$<\/jats:tex-math>\n \n \n \n \u03b4<\/mml:mi>\n K<\/mml:mi>\n <\/mml:mrow>\n ~<\/mml:mo>\n <\/mml:mover>\n <\/mml:math>\n <\/jats:alternatives>\n <\/jats:inline-formula>\n to markers of aortic chronicity in dissection, testing whether\n \n \n $$\\widetilde{\\delta K}$$<\/jats:tex-math>\n \n \n \n \u03b4<\/mml:mi>\n K<\/mml:mi>\n <\/mml:mrow>\n ~<\/mml:mo>\n <\/mml:mover>\n <\/mml:math>\n <\/jats:alternatives>\n <\/jats:inline-formula>\n behaves as a proxy for phase transitions in disease progression.\n <\/jats:p>\n <\/jats:sec>\n \n \n Results<\/jats:bold>\n <\/jats:title>\n \n A reproducible stable zone emerges in which centimeter-scale partitioning consistently maximizes the informativeness of\n \n \n $$\\widetilde{\\delta K}$$<\/jats:tex-math>\n \n \n \n \u03b4<\/mml:mi>\n K<\/mml:mi>\n <\/mml:mrow>\n ~<\/mml:mo>\n <\/mml:mover>\n <\/mml:math>\n <\/jats:alternatives>\n <\/jats:inline-formula>\n while remaining resilient to smoothing, meshing, and acquisition (CT resolution) variability. Within this zone,\n \n \n $$\\widetilde{\\delta K}$$<\/jats:tex-math>\n \n \n \n \u03b4<\/mml:mi>\n K<\/mml:mi>\n <\/mml:mrow>\n ~<\/mml:mo>\n <\/mml:mover>\n <\/mml:math>\n <\/jats:alternatives>\n <\/jats:inline-formula>\n augments preoperative risk stratification and, when coupled with Gaussian Process Regression, delineates a nonstationary regime consistent with progressive remodeling in dissection, suggesting linkage to chronicity beyond diameter alone.\n <\/jats:p>\n <\/jats:sec>\n \n \n Conclusion<\/jats:bold>\n <\/jats:title>\n \n Optimizing scale space yields a tuned, size-invariant shape signal that is both robust and clinically interpretable. The observed association between\n \n \n $$\\widetilde{\\delta K}$$<\/jats:tex-math>\n \n \n \n \u03b4<\/mml:mi>\n K<\/mml:mi>\n <\/mml:mrow>\n ~<\/mml:mo>\n <\/mml:mover>\n <\/mml:math>\n <\/jats:alternatives>\n <\/jats:inline-formula>\n and chronicity supports its use as a complementary marker to diameter and motivates prospective validation of shape-aware, curvature-based decision tools.\n <\/jats:p>\n <\/jats:sec>","DOI":"10.1007\/s13239-026-00827-z","type":"journal-article","created":{"date-parts":[[2026,3,30]],"date-time":"2026-03-30T17:57:14Z","timestamp":1774893434000},"page":"343-356","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":7,"title":["Shape and Scale in Quantifying Aortic Morphology Evolution and Chronicity"],"prefix":"10.1007","volume":"17","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-3295-5664","authenticated-orcid":false,"given":"Joseph A.","family":"Pugar","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"David","family":"Jiang","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Junsung","family":"Kim","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Luka","family":"Pocivavsek","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2026,3,30]]},"reference":[{"key":"827_CR1","doi-asserted-by":"publisher","first-page":"e895","DOI":"10.1161\/CIR.0000000000001063","volume":"145","author":"PA Heidenreich","year":"2022","unstructured":"Heidenreich, P. 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