Purpose Decision-making in thoracic aortic disease primarily relies on diameter thresholds that compress rich three-dimensional morphology into a single length scale. 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 <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$\widetilde{\delta K}$</EquationSource> <EquationSource Format="MATHML"><math> <mover accent="true"> <mrow> <mi>δ</mi> <mi>K</mi> </mrow> <mo stretchy="true">~</mo> </mover> </math></EquationSource> </InlineEquation>, most robustly captures thoracic aortic disease state and to relate the tuned <InlineEquation ID="IEq2"> <EquationSource Format="TEX">$\widetilde{\delta K}$</EquationSource> <EquationSource Format="MATHML"><math> <mover accent="true"> <mrow> <mi>δ</mi> <mi>K</mi> </mrow> <mo stretchy="true">~</mo> </mover> </math></EquationSource> </InlineEquation> signal to clinically relevant markers of chronicity in aortic dissection. Methods 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 <InlineEquation ID="IEq3"> <EquationSource Format="TEX">$\widetilde{\delta K}$</EquationSource> <EquationSource Format="MATHML"><math> <mover accent="true"> <mrow> <mi>δ</mi> <mi>K</mi> </mrow> <mo stretchy="true">~</mo> </mover> </math></EquationSource> </InlineEquation>, quantify signal robustness and predictive clinical value, and identify a “stable zone” of scales where performance stabilizes. We then model clinical progression using Gaussian Process Regression and relate <InlineEquation ID="IEq4"> <EquationSource Format="TEX">$\widetilde{\delta K}$</EquationSource> <EquationSource Format="MATHML"><math> <mover accent="true"> <mrow> <mi>δ</mi> <mi>K</mi> </mrow> <mo stretchy="true">~</mo> </mover> </math></EquationSource> </InlineEquation> to markers of aortic chronicity in dissection, testing whether <InlineEquation ID="IEq5"> <EquationSource Format="TEX">$\widetilde{\delta K}$</EquationSource> <EquationSource Format="MATHML"><math> <mover accent="true"> <mrow> <mi>δ</mi> <mi>K</mi> </mrow> <mo stretchy="true">~</mo> </mover> </math></EquationSource> </InlineEquation> behaves as a proxy for phase transitions in disease progression. Results A reproducible stable zone emerges in which centimeter-scale partitioning consistently maximizes the informativeness of <InlineEquation ID="IEq6"> <EquationSource Format="TEX">$\widetilde{\delta K}$</EquationSource> <EquationSource Format="MATHML"><math> <mover accent="true"> <mrow> <mi>δ</mi> <mi>K</mi> </mrow> <mo stretchy="true">~</mo> </mover> </math></EquationSource> </InlineEquation> while remaining resilient to smoothing, meshing, and acquisition (CT resolution) variability. Within this zone, <InlineEquation ID="IEq7"> <EquationSource Format="TEX">$\widetilde{\delta K}$</EquationSource> <EquationSource Format="MATHML"><math> <mover accent="true"> <mrow> <mi>δ</mi> <mi>K</mi> </mrow> <mo stretchy="true">~</mo> </mover> </math></EquationSource> </InlineEquation> 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. Conclusion Optimizing scale space yields a tuned, size-invariant shape signal that is both robust and clinically interpretable. The observed association between <InlineEquation ID="IEq8"> <EquationSource Format="TEX">$\widetilde{\delta K}$</EquationSource> <EquationSource Format="MATHML"><math> <mover accent="true"> <mrow> <mi>δ</mi> <mi>K</mi> </mrow> <mo stretchy="true">~</mo> </mover> </math></EquationSource> </InlineEquation> and chronicity supports its use as a complementary marker to diameter and motivates prospective validation of shape-aware, curvature-based decision tools.

Shape and Scale in Quantifying Aortic Morphology Evolution and Chronicity

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2026年3月30日

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Joseph A. Pugar,
David Jiang,
Junsung Kim,
Luka Pocivavsek

摘要

Purpose

Decision-making in thoracic aortic disease primarily relies on diameter thresholds that compress rich three-dimensional morphology into a single length scale. 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 $\widetilde{\delta K}$ $\tilde{δ K}$ , most robustly captures thoracic aortic disease state and to relate the tuned $\widetilde{\delta K}$ $\tilde{δ K}$ signal to clinically relevant markers of chronicity in aortic dissection.

Methods

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 $\widetilde{\delta K}$ $\tilde{δ K}$ , quantify signal robustness and predictive clinical value, and identify a “stable zone” of scales where performance stabilizes. We then model clinical progression using Gaussian Process Regression and relate $\widetilde{\delta K}$ $\tilde{δ K}$ to markers of aortic chronicity in dissection, testing whether $\widetilde{\delta K}$ $\tilde{δ K}$ behaves as a proxy for phase transitions in disease progression.

Results

A reproducible stable zone emerges in which centimeter-scale partitioning consistently maximizes the informativeness of $\widetilde{\delta K}$ $\tilde{δ K}$ while remaining resilient to smoothing, meshing, and acquisition (CT resolution) variability. Within this zone, $\widetilde{\delta K}$ $\tilde{δ K}$ 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.

Conclusion

Optimizing scale space yields a tuned, size-invariant shape signal that is both robust and clinically interpretable. The observed association between $\widetilde{\delta K}$ $\tilde{δ K}$ and chronicity supports its use as a complementary marker to diameter and motivates prospective validation of shape-aware, curvature-based decision tools.