用拓扑方法分析脑萎缩，不依赖图像配准，可检测阿尔茨海默病早期变化。
Homology-based Morphometry of Brain Atrophy: Methods and Applications
- 基于持久同调的两个新方法，从多尺度几何特征量化脑结构变化。
- 在无非线性配准情况下，区分阿尔茨海默病与正常人准确率达89.5%。
- 适合跨组比较和纵向追踪，尤其适用于有病变或异常的个体。
理解脑结构及其随时间与疾病的变化是结构神经影像的核心目标。当前主流方法如体素形态学（VBM）依赖图像配准到标准模板，可能掩盖个体几何特征，且在存在显著病理、病变或解剖异常的群体间比较时存在问题。本文提出两种基于持久同调（PH）的互补分析流程，用于量化结构化T1加权MRI扫描的多尺度几何特征。流程一通过切片级欧氏距离变换对组织掩膜进行区域变薄量化；流程二利用α-过滤测量扫描对间的结构相似性，捕捉沟回增宽与脑室扩大。合成实验显示，流程一适用于组间分析，流程二更适于组内分析。在阿尔茨海默病神经影像计划（ADNI）真实数据上，流程一仅用单模态T1-MRI（无需非线性配准）即实现AD与认知正常（CN）人群分离（ROC-AUC = 0.895），峰值效应位于内侧颞叶；流程二成功捕捉疾病相关纵向变化，随访扫描仍最接近自身基线，且AD患者短周期变化显著大于CN者。两者共同提供可解释的拓扑生物标志物，适用于横断面组间比较与纵向追踪。
原文摘要 · Abstract (English)
Understanding the structure of the brain, and how it changes with time and disease, is a core goal of structural neuroimaging. Contemporary approaches to structural brain analysis are dominated by voxel-wise, mass-univariate methods such as voxel-based morphometry (VBM). However, these techniques require images to be normalized to a standard template, which can obscure subject-specific geometric features. Normalization to a common stereotactic space can also be problematic when comparing groups with substantial brain pathology, lesions, or other anatomical abnormalities. Here, we introduce two complementary pipelines based on persistent homology (PH), a tool from topological data analysis, to quantify multiscale geometric features of structural T1-weighted MRI scans. Pipeline 1 quantifies regional thinning by applying the Euclidean distance transform to tissue masks in a slice-wise manner. Pipeline 2 uses \(α\)-filtrations to measure structural similarity between pairs of scans, capturing sulcal widening and ventricular enlargement. Synthetic experiments with controlled induced lesions showed that Pipeline 1 is best suited to between-subject analyses, whereas Pipeline 2 is better suited to within-subject designs. Applied to real-world data from the Alzheimer's Disease Neuroimaging Initiative (ADNI), Pipeline 1 separated Alzheimer's disease (AD) from cognitively normal (CN) participants using single-modality T1-weighted MRI without nonlinear registration (ROC-AUC = 0.895), with peak effects localized to medial temporal regions. Pipeline 2 captured disease-related longitudinal change, with follow-up scans remaining closest to their own baselines and AD subjects showing greater short-interval change than CN subjects. Together, these pipelines provide interpretable topological biomarkers for cross-sectional group comparisons and longitudinal tracking.
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