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

Predicting future structural MRI of a brain is challenging because longitudinal changes are often subtle and confined to specific anatomical regions, while most subject-specific brain structure remains stable over time. An effective model should therefore preserve global brain structural consistency while remaining sensitive to fine-grained disease progression. Existing latent-space-based methods improve computational efficiency, but suffer from information loss during their compression-reconstruction procedure. In contrast, direct voxel-space methods avoid latent reconstruction but commonly use a unified prediction pathway to model brain structure and progression-related changes. Subtle local changes may therefore be overshadowed by the dominant stable brain structure. To address these challenges, we propose ProgFormer, a hierarchical voxel-space Diffusion Transformer for longitudinal brain MRI prediction. ProgFormer uses a coarse pathway to perform the primary volumetric prediction from 3D patch tokens. This pathway models overall brain structure and longitudinal context. The fine pathway then uses the coarse representations as spatio-temporal grounding for voxel-level refinement within individual patches. The two pathways jointly estimate a velocity field directly in voxel space through conditional flow matching, enabling end-to-end prediction without a separately learned image autoencoder. The predicted future scan is then generated from Gaussian noise by integrating the estimated velocity field over a sequence of Euler steps. Extensive experimental results on three widely used benchmarks, ADNI, AIBL, and OASIS, under both pairwise and trajectory settings demonstrate favourable performance compared against several state-of-the-art methods.

Tracking neurite morphology over time helps characterize structural changes during neuronal development and deterioration, but long-term time-lapse imaging is resource-intensive and difficult to scale. Forecasting future morphology could reduce this burden. Existing neurite digital-twin models such as gated spatiotemporal attention (gSTA) produce a single deterministic forecast without representing variability among plausible futures. We introduce Morphology-Gated Residual Diffusion (MGRD), a compact stochastic surrogate that jointly forecasts twenty future neurite-morphology frames from ten observed frames while conditioning on morphology features derived from the latest observation. On controlled phase-field trajectories, MGRD reduces trajectory-wise mean MAE by 9.7% relative to a matched control while updating 4.46 times fewer parameters. On human iPSC-derived neuron microscopy, MGRD improves all four reported metrics over gSTA, including a 39.6% reduction in trajectory-wise mean MAE and a 45.3% increase in skeleton F1. Without mouse-domain retraining or fine-tuning, MGRD also improves MAE and skeleton F1 on mouse cortical-neurosphere microscopy across 10-40-min sampling intervals and forecast horizons beyond 13 hours. Repeated sampling provides a case-level variance score for ranking forecast difficulty. Retaining approximately 60% of the lowest-variance cases reduces mean MAE by 17.6% on iPSC microscopy and 16.8% on simulation data. MGRD uses 1.01% of gSTA's parameters, requires less than one tenth of its training-update time, and generates a 50-step DDIM trajectory 7.9% faster when morphology features are cached. These results establish MGRD as a compact stochastic surrogate for neurite-morphology forecasting and case prioritization across simulation and microscopy datasets.

Forecasting the future anatomy of slow-evolving neurodegenerative diseases could enable earlier, more targeted intervention and improve clinical trial design, but it remains challenging because true progression signals are subtle in longitudinal MRI. In this low-signal regime, transferring modern generative sequence models directly is unreliable: training is dominated by stable baseline anatomy and confounded by dense, sample-specific nuisance variation. We first provide a theoretical analysis that explains these failures through two modes. Identity collapse occurs when optimization is driven toward reproducing the current anatomy, which prevents the model from learning faint temporal change. The continuous interpolation trap arises when standard smooth networks cannot separate localized biological drift from pervasive noise, which leads to spurious changes that diffuse across the volume. To address both issues, we propose Latent Drift, a progressive generative framework that learns change in a compressed semantic representation rather than synthesizing full-resolution anatomy. This design removes pixel-level identity from the prediction target and concentrates model capacity on progression-relevant dynamics. We further apply Finite Scalar Quantization to the learned change representation, which suppresses small, high-frequency nuisance fluctuations while preserving consistent structural drift. Experiments on longitudinal 3D brain MRI show that Latent Drift improves patient-specific neuro-forecasting over diffusion and autoregressive transformer baselines across generative fidelity and clinically relevant evaluation metrics. Project page: \href{https://cutepkq.github.io/latent-drift}{https://cutepkq.github.io/latent-drift}.