LDDMM stochastic interpolants: an application to domain uncertainty quantification in hemodynamics

2026-03-30

AI Summary

This work addresses the impact of vascular geometric domain uncertainty—arising from medical image segmentation—on the estimation of hemodynamic biomarkers. To this end, the authors propose a Large Deformation Diffeomorphic Metric Mapping (LDDMM)-based conditional stochastic interpolation framework. This approach extends LDDMM stochastic interpolation to irregular three-dimensional biological shapes for the first time, modeling conditional drift over complex aortic geometries through pullback and pushforward operators. Implicit geometric conditioning is achieved by integrating centerline trajectories with inscribed sphere radii. The method enables controlled generation of three-dimensional aortic shapes with prescribed perturbation magnitudes, thereby providing an efficient tool for data augmentation and perturbation analysis in hemodynamic simulations under domain uncertainty.

Abstract

We introduce a novel conditional stochastic interpolant framework for generative modeling of three-dimensional shapes. The method builds on a recent LDDMM-based registration approach to learn the conditional drift between geometries. By leveraging the resulting pull-back and push-forward operators, we extend this formulation beyond standard Cartesian grids to complex shapes and random variables defined on distinct domains. We present an application in the context of cardiovascular simulations, where aortic shapes are generated from an initial cohort of patients. The conditioning variable is a latent geometric representation defined by a set of centerline points and the radii of the corresponding inscribed spheres. This methodology facilitates both data augmentation for three-dimensional biomedical shapes, and the generation of random perturbations of controlled magnitude for a given shape. These capabilities are essential for quantifying the impact of domain uncertainties arising from medical image segmentation on the estimation of relevant biomarkers.

Problem

• domain uncertainty quantification
• hemodynamics
• 3D shape generation
• medical image segmentation
• biomarker estimation

Innovation

• LDDMM
• stochastic interpolants
• conditional generative modeling
• domain uncertainty quantification
• shape perturbation