发表机构
Texas Tech University（德克萨斯理工大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出一个多水平函数型框架，将脑MRI的持续同调摘要（Betti曲线）作为纵向响应建模，并用贝叶斯方法联合估计，应用于OASIS-2数据揭示脑拓扑与临床特征的关联。
AI 中文摘要
持续同调通过捕捉反映生物医学图像底层结构组织的高阶拓扑特征，提供其多尺度表示。然而，所得到的拓扑摘要通常被用作分类和组间比较的预测变量或特征，而非被视为感兴趣的主要变量。我们构建了一个广义多水平函数型框架，用于在重复的三维结构磁共振成像（MRI）中将持续同调摘要作为纵向函数型响应进行分析。具体而言，我们使用Betti曲线表示拓扑特征，并将这些曲线建模为计数型函数型响应。负二项分布适应Betti计数的离散性和潜在过度离散性，而多水平公式则考虑了重复测量引起的依赖性，并分离了受试者间和受试者内的函数型变异来源。函数型主成分分析进一步评估每个水平上的主要变异模式。采用贝叶斯方法对函数型回归和多水平函数型主成分进行联合估计。我们将此建模框架应用于OASIS-2研究的纵向结构MRI数据，以研究脑拓扑与人口统计学和临床特征（包括年龄、性别、随访时间和痴呆严重程度）之间的关联。结果表明，该框架能够捕捉沿过滤连续体上与协变量相关的变异，同时评估跨同调维度的纵向变异的独特来源和模式。
英文摘要
Persistent homology provides a multiscale representation of biomedical images by capturing higher-order topological features that reflect their underlying structural organization. However, the resulting topological summaries are typically used as predictors or features for classification and group comparisons rather than treated as primary variables of interest. We construct a generalized multilevel functional framework for analyzing persistent-homology summaries as longitudinal functional responses in repeated three-dimensional structural magnetic resonance imaging (MRI). Specifically, we represent topological features using Betti curves and model these curves as count-valued functional responses. A negative-binomial distribution accommodates the discrete and potentially overdispersed nature of Betti counts, while the multilevel formulation accounts for the dependence induced by repeated measurements and separates between-subject and within-subject sources of functional variation. Functional principal component analysis further evaluates the dominant modes of variation at each level. A Bayesian approach is used for joint estimation of the functional regression and multilevel functional principal components. We apply this modeling framework to longitudinal structural MRI data from the OASIS-2 study to investigate associations between brain topology and demographic and clinical characteristics, including age, gender, follow-up time, and dementia severity. The results demonstrate that the framework can capture covariate-associated variation across the filtration continuum while evaluating distinct sources and patterns of longitudinal variation across homology dimensions.
