Predicting Brain Morphometry with MT-GNN: Mesh Evolution in Continuous Time with Graph-Based Metric Tensor Embeddings

2026-08-05

AI Summary

This study addresses the challenge of predicting the future shape evolution of subcortical brain structures from limited historical scan data to support disease prognosis and clinical trial enrichment. The authors propose an end-to-end differentiable framework that employs a graph neural network combined with Fourier time encoding to predict the metric tensor (first fundamental form) of brain surfaces at arbitrary future time points. These intrinsic geometric predictions are then reconstructed into geometrically valid 3D meshes via a differentiable As-Rigid-As-Possible (ARAP) solver. This approach is the first to integrate continuous-time intrinsic geometry prediction with differentiable surface reconstruction, avoiding direct vertex displacement regression or high-dimensional extrapolation, thereby significantly improving long-term prediction accuracy. Evaluated on 14 subcortical structures in the ADNI dataset, the proposed MT-GNN consistently outperforms baseline methods across all time horizons, achieving an average vertex error reduction of 2.29% (p = 6.1 × 10⁻⁵), with performance gains increasing as the prediction horizon extends.

Abstract

Predicting how a subcortical structure's shape will evolve from a few prior scans could support prognosis and clinical-trial enrichment. Existing longitudinal mesh predictors either extrapolate shape trajectories via high-dimensional embeddings or regress vertex deformations directly. We instead predict the surface's intrinsic geometry in continuous time: a single per-structure graph network predicts the future per-vertex first fundamental form (metric tensor) for an arbitrary causal multiple-visit history and an arbitrary prediction horizon, conditioned on a Fourier encoding of the lead time. The predicted metric is decoded into a surface by a differentiable As-Rigid-As-Possible solver, and the model is trained end-to-end on the rigid-aligned vertex error. Training through the reconstruction keeps the decoded prediction a valid surface and consistently improves it. On 14 subcortical structures from the ADNI dataset, the proposed mesh evolution model (MT-GNN) predicts best among the evaluated methods at every horizon ($-2.29\%$ mean vertex error vs. the temporal mean, $p{=}6.1{\times}10^{-5}$, beating it on 14/14 structures), ahead of geodesic shape regression (DCM, $-0.19\%$) and a mesh transformer (TransforMesh, $-0.45\%$; $p{=}1.2{\times}10^{-4}$), with the lead widening as the horizon grows.

Problem

• brain morphometry
• shape prediction
• longitudinal modeling
• subcortical structures
• mesh evolution

Innovation

• MT-GNN
• metric tensor
• mesh evolution
• graph neural network
• differentiable surface reconstruction