arXiv:2608.05132cs.CVcs.LG2026-08

用图神经网络预测大脑结构随时间的形状演变,精度显著优于现有方法。

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

论文配图:Predicting Brain Morphometry with MT-GNN: Mesh Evolution in Continuous Time with Graph-Based Metric Tensor Embeddings
图 1 · 摘自论文原文
  • 基于图神经网络建模表面内在几何,直接预测连续时间下的度量张量
  • 在ADNI数据集上14个脑区均实现最低顶点误差,领先于对比方法
  • 适合需长期追踪脑结构变化的神经退行性疾病研究者使用

从少量前期扫描预测皮层下结构的形态演变,有助于疾病预后与临床试验人群筛选。现有纵向网格预测方法要么通过高维嵌入外推形状轨迹,要么直接回归顶点形变。本文提出一种新方法:基于图网络预测任意因果多访视历史与任意预测时长下的连续时间表面内在几何——即每个结构的逐顶点第一基本形式(度量张量),并采用傅里叶编码对领先时间进行条件建模。预测的度量张量通过可微的尽量刚性算法解码为表面,模型在刚性对齐顶点误差上端到端训练。重建过程确保解码结果为有效表面,并持续优化。在来自ADNI数据集的14个皮层下结构上,所提模型(MT-GNN)在所有预测时长下表现最佳,平均顶点误差比时间均值低2.29%(p=6.1×10⁻⁵),在全部14个结构上超越地心测地线回归(DCM,-0.19%)和网格变换器(TransforMesh,-0.45%;p=1.2×10⁻⁴),且领先优势随预测时长增加而扩大。

原文摘要 · Abstract (English)

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.

脑形态预测图神经网络连续时间建模

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