Predicting curvature evolution on biological surfaces from clinical imaging-derived area dilation: a closed-form...

Area of Science:

• Computational geometry and biomechanics
• Medical imaging analysis
• Cardiovascular disease modeling

Background:

• Curvature evolution on biological surfaces is difficult to predict from 3D imaging due to lost shear information.
• Thoracic aorta curvature changes are critical indicators of disease progression.
• Existing imaging methods provide incomplete data for precise curvature evolution prediction.

Purpose of the Study:

• To derive a closed-form equation predicting integrated Gaussian curvature change in the thoracic aorta.
• To develop a multi-level predictor combining analytic equations and machine learning for curvature evolution.
• To assess the equation's accuracy on synthetic and real patient data.

Main Methods:

• Derived a closed-form equation relating integrated Gaussian curvature change to area dilation and initial geometry.
• Developed a four-level predictor incorporating conformal terms, anisotropy correction, spatial features, and a graph neural network.
• Validated the model on synthetic geometries and 236 paired thoracic aortic CT scans.

Main Results:

• The derived equation exactly recovered analytic predictions on synthetic isotropic expansion.
• The model achieved R² ≥ 0.71 across a spectrum from pure expansion to pure shear.
• On patient data, the equation recovered within-surface curvature change patterns with a pooled R² = +0.238, matching a graph neural network.

Conclusions:

• A closed-form equation can predict thoracic aorta curvature change from area dilation and initial geometry.
• The derived predictor offers interpretable insights into geometric mechanisms driving aortic deformation.
• The residual of the model quantifies deviations from conformality, potentially indicating disease-specific growth patterns.