Normative modeling enables individualized characterization of structural brain deviations by evaluating subjects against a reference population rather than a group average. Most existing implementations treat brain regions independently and remain cross-sectional, despite the availability of repeated neuroimaging measurements and the well-documented spatial organization of neuroanatomical variation. We propose a Bayesian longitudinal spatial normative model that jointly captures within-subject temporal dependence and spatially structured subject-specific deviations within a unified hierarchical framework. The individualized deviation map is treated as a latent spatial process with an explicit posterior distribution, yielding a principled Bayes estimator under squared error loss rather than an ad hoc residual summary. Across six simulation scenarios encompassing varying spatial dependence, nonlinear trajectories, irregular visit schedules, and missing follow-up, the proposed model consistently reduced deviation-map reconstruction error relative to independent cross-sectional and longitudinal non-spatial benchmarks while maintaining stable calibration. In an application to OASIS-3 structural MRI data, the model reduced RMSE by 54% relative to the independent cross-sectional model and by 45% relative to the longitudinal non-spatial model. Regional deviation burden was concentrated in the temporal pole, entorhinal cortex, inferior temporal cortex, posterior cingulate, and parahippocampal cortex, consistent with regions implicated in early Alzheimer-type neurodegeneration. Subject-level profiles revealed substantial heterogeneity in regional abnormality patterns, including marked multiregional deviation with preserved global cognitive scores.

翻译：规范模型能够通过将受试者与参考人群而非群体平均值进行比较，实现结构性脑偏差的个体化表征。现有的大多数实现方法将脑区域视为独立处理，且仍为横截面研究，尽管重复神经影像测量数据已可用，且神经解剖学变异的空间组织已有充分文献记载。我们提出一种贝叶斯纵向空间规范模型，在统一的层次化框架内联合捕获受试者内部的时间依赖性以及空间结构化的受试者特异性偏差。个体化偏差图被视为具有显式后验分布的潜在空间过程，在平方误差损失下产生具有原理性的贝叶斯估计量，而非临时性的残差汇总。在涵盖不同空间依赖性、非线性轨迹、不规则访视频次以及缺失随访数据的六种模拟情景中，相对于独立的横截面模型和纵向非空间基准模型，所提模型持续降低了偏差图的重建误差，同时保持稳定的校准。在应用于OASIS-3结构MRI数据时，相对于独立横截面模型，该模型将RMSE降低了54%，相对于纵向非空间模型降低了45%。区域偏差负荷集中在颞极、内嗅皮层、颞下皮层、后扣带回和海马旁皮层，这与早期阿尔茨海默型神经变性所涉及的区域一致。受试者层面特征揭示了区域异常模式的显著异质性，包括在保持全局认知评分的情况下出现明显的多区域偏差。