Longitudinal magnetic resonance imaging data is used to model trajectories of change in brain regions of interest to identify areas susceptible to atrophy in those with neurodegenerative conditions like Alzheimer's disease. Most methods for extracting brain regions are applied to scans from study participants independently, resulting in wide variability in shape and volume estimates of these regions over time in longitudinal studies. To address this problem, we propose a longitudinal principal manifold estimation method, which seeks to recover smooth, longitudinally meaningful manifold estimates of shapes over time. The proposed approach uses a smoothing spline to smooth over the coefficients of principal manifold embedding functions estimated at each time point. This mitigates the effects of random disturbances to the manifold between time points. Additionally, we propose a novel data augmentation approach to enable principal manifold estimation on self-intersecting manifolds. Simulation studies demonstrate performance improvements over naive applications of principal manifold estimation and principal curve/surface methods. The proposed method improves the estimation of surfaces of hippocampuses and thalamuses using data from participants of the Alzheimer's Disease Neuroimaging Initiative. An analysis of magnetic resonance imaging data from 236 individuals shows the advantages of our proposed methods that leverage regional longitudinal trends for segmentation.

翻译：纵向磁共振成像数据用于建模感兴趣脑区随时间变化的轨迹，以识别阿尔茨海默病等神经退行性疾病患者中易发生萎缩的区域。现有提取脑区的方法大多独立应用于研究参与者的扫描图像，导致纵向研究中这些区域的形状和体积估计随时间出现较大变异。为解决此问题，我们提出一种纵向主流形估计方法，旨在恢复随时间变化的、平滑且具有纵向意义的形状流形估计。该方法采用平滑样条对每个时间点估计的主流形嵌入函数系数进行平滑处理，从而减轻时间点间流形随机扰动的影响。此外，我们提出一种新颖的数据增强方法，使自相交流形上的主流形估计成为可能。仿真研究表明，相较于直接应用主流形估计及主曲线/曲面方法，本方法性能显著提升。利用阿尔茨海默病神经影像计划参与者的数据，该方法改进了海马体和丘脑表面的估计。对236名个体磁共振成像数据的分析表明，所提方法通过利用区域纵向趋势进行分割具有显著优势。