Predicting Brain Morphometry with MT-GNN: Mesh Evolution in Continuous Time with Graph-Based Metric Tensor Embeddings
2026-08-05 • Computer Vision and Pattern Recognition
Computer Vision and Pattern RecognitionMachine Learning
AI summaryⓘ
The authors developed a new method to predict how the shape of certain brain structures changes over time using past scans. Instead of directly predicting points on the surface, they forecast the surface's internal geometry and then rebuild the shape from that. Their approach, tested on brain scans from a study of Alzheimer's disease, predicts shapes more accurately than previous methods, especially as they look further into the future. The method works well for multiple brain structures and can handle varying numbers of previous scans and prediction times.
subcortical structuressurface geometrymetric tensorgraph neural networksFourier encodingAs-Rigid-As-Possible solververtex errorlongitudinal shape predictionADNI datasetmesh evolution
Authors
Hao Ding, Daniel Semchin, Paul M. Thompson, Boris Gutman
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.