Estimating Knee Movement Patterns of Recreational Runners Across Training Sessions Using Multilevel Functional Regression Models

Modern wearable monitors and laboratory equipment allow the recording of high-frequency data that can be used to quantify human movement. However, currently, data analysis approaches in these domains remain limited. This article proposes a new framework to analyze biomechanical patterns in sport training data recorded across multiple training sessions using multilevel functional models. We apply the methods to subsecond-level data of knee location trajectories collected in 19 recreational runners during a medium-intensity continuous run (MICR) and a high-intensity interval training (HIIT) session, with multiple steps recorded in each participant-session. We estimate functional intra-class correlation coefficient to evaluate the reliability of recorded measurements across multiple sessions of the same training type. Furthermore, we obtained a vectorial representation of the three hierarchical levels of the data and visualize them in a low-dimensional space. Finally, we quantified the differences between genders and between two training types using functional multilevel regression models that incorporate covariate information. We provide an overview of the relevant methods and make both data and the R code for all analyses freely available online on GitHub. Thus, this work can serve as a helpful reference for practitioners and guide for a broader audience of researchers interested in modeling repeated functional measures at different resolution levels in the context of biomechanics and sports science applications.

现代可穿戴监测设备与实验室仪器可采集高频数据，用于量化人体运动状态。然而当前该领域的数据分析方法仍存在局限。本文提出一种全新框架，借助多层功能模型（multilevel functional models）分析多训练会话中采集的运动训练数据内的生物力学模式。本研究将所提方法应用于19名休闲跑者在中等强度持续跑（medium-intensity continuous run，MICR）与高强度间歇训练（high-intensity interval training，HIIT）过程中采集的膝关节位置轨迹亚秒级数据，每名受试者的每次训练会话均记录了多组步态步幅。我们通过估算功能型组内相关系数（functional intra-class correlation coefficient），评估同一训练类型下多次训练所获测量数据的可靠性。此外，我们获取了该数据三类层级的向量表示，并将其可视化于低维空间中。最后，我们借助融入协变量信息的多层功能回归模型（functional multilevel regression models），量化了不同性别以及两种训练类型之间的差异。我们对相关方法进行了综述，并将所有分析所用的数据集与R代码公开上传至GitHub平台，供免费获取。因此，本研究可为从业者提供实用参考，同时也可为众多关注生物力学与运动科学领域中不同分辨率层级下重复功能测量数据建模的研究人员提供指导。