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：规范建模通过将受试者与参考人群而非群体平均值进行比较，实现对结构性脑偏差的个体化表征。现有的大多数实现将脑区视为独立变量，且仍为横截面设计，尽管重复神经影像测量已可用，且神经解剖变异的空间组织已有充分文献记载。我们提出了一种贝叶斯纵向空间规范模型，该模型在统一的层次化框架内联合捕获受试者内时间依赖性和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基于原理的贝叶斯估计量，而非特设的残差汇总。在涵盖不同空间依赖性、非线性轨迹、不规则访视计划和缺失随访的六种模拟场景下，与独立的横截面和纵向非空间基准相比，所提模型在保持稳定校准的同时，持续降低了偏差图重建误差。在应用于OASIS-3结构性MRI数据时，该模型相对于独立横截面模型将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、颞下回、后扣带回和海马旁回，这与早期阿尔茨海默型神经退行性变所涉及的脑区一致。受试者层面轮廓揭示了区域异常模式的显著异质性，包括在全局认知评分保持正常情况下出现显著的多区域偏差。