Our main goal is to study and quantify the evolution of multiple sclerosis lesions observed longitudinally over many years in multi-sequence structural magnetic resonance imaging (sMRI). To achieve that, we propose a class of functional models for capturing the temporal dynamics and spatial distribution of the voxel-specific intensity trajectories in all sMRI sequences. To accommodate the hierarchical data structure (observations nested within voxels, which are nested within lesions, which, in turn, are nested within study participants), we use structured functional principal component analysis. We propose and evaluate the finite sample properties of hypothesis tests of therapeutic intervention effects on lesion evolution while accounting for the multilevel structure of the data. Using this novel testing strategy, we found statistically significant differences in lesion evolution between treatment groups.

中文翻译：

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用于模拟多发性硬化症病变发展过程的矩阵分解。

我们的主要目标是研究和量化多年来在多序列结构磁共振成像 (sMRI) 中纵向观察到的多发性硬化病变的演变。为了实现这一点，我们提出了一类功能模型，用于捕获所有 sMRI 序列中体素特定强度轨迹的时间动态和空间分布。为了适应分层数据结构（嵌套在体素中的观察，嵌套在病变中，而病变又嵌套在研究参与者中），我们使用结构化功能主成分分析。我们提出并评估了治疗干预对病变演变影响的假设检验的有限样本特性，同时考虑了数据的多级结构。使用这种新颖的测试策略，