Principal Component Analysis Reveals the Proximal to Distal Pattern in Vertical Jumping Is Governed by Two Functional Degrees of Freedom

Abstract

The successful completion of motor tasks requires effective control of multiple degrees of freedom (DOF), with adaptations occurring as a function of varying performance constraints. In this study we sought to compare the emergent coordination strategies employed in vertical jumping under different task constraints [countermovement jump (CMJ) with arm swing-CMJas and no arm swing-CMJnas]. In order to achieve this, principal component analysis (PCA) was conducted on joint moment waveform data from the hip, knee and ankle. This statistical approach has the advantage of analyzing the whole movement within a time series and reduces multidimensional datasets to lower dimensions for analysis. Both individual and group analyses were conducted. For individual analysis, PCA was conducted on combined hip, knee, and ankle joint moment data for each individual across both CMJnas (thirty-eight participants), and CMJas (twenty-two participants) conditions. PCA was also performed comparing all data from each individual across CMJnas and CMJas conditions. The results revealed a maximum of three principal components (PC) explained over 90% of the variance in the data sets for both conditions and within individual and group analyses. For individual analysis, no more than 2PCs were required for both conditions. For group analysis, CMJas required 3PCs to explain over 90% of the variance within the dataset and CMJnas only required 2PCs. Reconstruction of the original NJM waveforms from the PCA output demonstrates a greater loading of hip and knee joint moments to PC1, with PC2 showing a greater loading to ankle joint moment. The reduction in dimensions of the original data shows the proximal to distal extension pattern in the sagittal plane, typical of vertical jumping tasks, is governed by only 2 functional DOF, at both a group, and individual level, rather than the typically reported 3 mechanical DOF in some forms of jumping.

Muscular coordination during vertical jumping

“…In this study we found that the three-dimensional inter-segmental moments of 34 subjects performing a vertical jump can be represented by just 3 PCs. This is similar to our recent work where we showed that the sagittal plane inter-segmental moments during jumping could be described by 2 PCs [12]. It is notable here that only one further PC is required to capture 90% of the variance in the joint moments, despite the fact that the addition of the remaining two planes effectively triples the number of kinetic DOF in the input data.…”

“…One tool that is useful for this purpose is principal component analysis (PCA) a data reduction technique that can be used to establish the effective DOF present within a data set. We have recently employed PCA to demonstrate that the sagittal plane moments impressed by the lower limb during vertical jumping exhibit only 2 functional DOF [12]. The purpose of this study was therefore two-fold: firstly, to expand on our previous work by examining the moment production in all 3 dimensions, and secondly, to use PCA to evaluate the functional DOF present within the muscular control problem.…”

A Correlational Analysis of Shuttlecock Speed Kinematic Determinants in the Badminton Jump Smash

“…It must also be acknowledged that the present study relies on investigation of joint kinematics at discrete time points (i.e., key instants). Future studies may therefore extend the current work using methodologies to investigate the continuous time series of kinematic data, such as statistical parametric mapping [40], vector coding [41] or principal component analysis [42], as well as considering other biomechanical principles not explored within this study. Additionally, differences in anthropometric data were not accounted for, where the same angular velocities and joint angles may lead to different linear velocities.…”

On the use and abuse of principal component analysis in biomechanics

“…This raw data was used to calculate the knee joint moments generated by each participant during the vertical jump using a publicly available model of the lower limb (Cleather and Bull, 2015). A detailed description of the processing of this data is provided in Cushion et al (2019). To facilitate comparison of different time-series the data was time-normalised.…”