Background: Minute-level accelerometer data capture rich diurnal physical activity (PA) patterns, but conventional summary metrics obscures clinically meaningful changes accumulated across a day. Building on Riemannian framework, we integrate multivariate functional principal component analysis (MFPCA) to identify main modes of PA change in older women and examine associations with physical function (PF). Method: A subset participant from OPACH as baseline and two WHISH follow-ups (W1, W2), yielded 3 accelerometer measurements; each participant's diurnal PA at each visit was represented as a smooth curve. Change between consecutive visits (defined as periods: baseline-W1, W1-W2) was modeled as a Riemannian deformation (RD) jointly capturing changes in PA timing and magnitude. Deformations were parameterized by initial momenta and summarized using MFPCA; participant-level changes were characterized by principal component (PC) scores and deformation energy (DE), a metric of overall pattern change. Associations with PF were assessed using linear mixed models. Results: Mean deformation in both periods showed overall downward shifts in PA magnitude with temporal redistribution between 10am and 7pm. Top 15 PCs explained >= 90% of variability in both periods; PC1 represented a pattern of PA increase/decrease throughout the day, explaining 22.4% (baseline-W1) and 20.8% (W1-W2). Among complete data (N=1157), an increase in PA in the mode of PC1 was positively associated with PF (p <0.0001). The interaction between DE and period was significantly associated with PF (p=0.003). Conclusions: Modeling longitudinal PA change as RDs and summarizing variability via MFPCA produced clinically interpretable phenotypes of diurnal PA change beyond standard metrics. The leading deformation mode was significantly associated with PF, and DE showed a stronger association with PF in the later period.

翻译：背景：分钟级加速度计数据可捕捉丰富的日间身体活动（PA）模式，但传统汇总指标掩盖了一天内积累的临床意义变化。基于黎曼框架，我们整合多元函数主成分分析（MFPCA）以识别老年女性PA变化的主要模式，并探究其与身体功能（PF）的关联。方法：来自OPACH研究的基线参与者及两次WHISH随访（W1、W2）数据提供3次加速度计测量；每位参与者每次访视的日间PA被表示为光滑曲线。连续两次访视间的变化（定义为时段：基线-W1、W1-W2）通过联合捕捉PA时间与幅度变化的黎曼形变（RD）进行建模。形变由初始动量参数化，并利用MFPCA进行汇总；参与者水平的变化通过主成分（PC）得分和形变能量（DE）（反映整体模式变化的指标）进行表征。采用线性混合模型评估其与PF的关联。结果：两个时段的平均形变均显示PA幅度整体下降，且在上午10点至晚上7点之间存在时间再分布。前15个PC在两个时段均解释≥90%的变异性；PC1代表全天PA增加/减少的模式，分别解释22.4%（基线-W1）和20.8%（W1-W2）的变异。在完整数据（N=1157）中，PC1模式下的PA增加与PF呈正相关（p <0.0001）。DE与时段的交互作用与PF显著相关（p=0.003）。结论：将纵向PA变化建模为RD并通过MFPCA汇总变异性，可产生超越标准指标的临床可解释的日间PA变化表型。主导形变模式与PF显著相关，且DE在后期时段与PF的关联更强。