用潜在空间线性建模，让脑部MRI随年龄自然演化，预测更准且可动态更新。

Simulating aging in 3D brain MRI scans can reveal disease progression patterns in neurological disorders such as Alzheimer's disease. Current deep learning-based generative models typically approach this problem by predicting future scans from a single observed scan. We investigate modeling brain aging via linear models in the latent space of convolutional autoencoders (MRExtrap). Our approach, MRExtrap, is based on our observation that autoencoders trained on brain MRIs create latent spaces where aging trajectories appear approximately linear. We train autoencoders on brain MRIs to create latent spaces, and investigate how these latent spaces allow predicting future MRIs through linear extrapolation based on age, using an estimated latent progression rate $\boldsymbolβ$. For single-scan prediction, we propose using population-averaged and subject-specific priors on linear progression rates. We also demonstrate that predictions in the presence of additional scans can be flexibly updated using Bayesian posterior sampling, providing a mechanism for subject-specific refinement. On the ADNI dataset, MRExtrap predicts aging patterns accurately and beats a GAN-based baseline for single-volume prediction of brain aging. We also demonstrate and analyze multi-scan conditioning to incorporate subject-specific progression rates. Finally, we show that the latent progression rates in MRExtrap's linear framework correlate with disease and age-based aging patterns from previously studied structural atrophy rates. MRExtrap offers a simple and robust method for the age-based generation of 3D brain MRIs, particularly valuable in scenarios with multiple longitudinal observations.