JcvPCA and JsvCRP : a set of metrics to evaluate changes in joint coordination strategies

TL;DR

This paper introduces two novel metrics for evaluating changes in inter-joint coordination: Joint Contribution Variation based on PCA (JcvPCA) and Joint Synchronization Variation based on Continuous Relative Phase (JsvCRP). JcvPCA uses a PCA reprojection framework where dataset $A$ serves as a reference and dataset $B$ is projected into $A$'s PCA space, with per-PC joint-load changes computed as $JcvPCA_{u,i} = |a_{u,i}| - |b_{u,i}^A|$, optionally weighted by explained variance. JsvCRP quantifies temporal coordination by computing the area between mean CRP curves, $JsvCRP_{A,B} = \\int_{0}^{t_{mvmt}} |CRP_{B}(t) - CRP_A(t)| \, dt$, with CRP phase angles derived from normalized $ heta_i$ and $\ heta_{i,norm}$ via $\\phi_i = \\tan^{-1} ( \\dot{\\theta}_{i,norm}/\\theta_{i,norm})$. Validation on simulated and experimental reaching tasks demonstrates that the metrics can differentiate distinct coordination strategies, with natural variability thresholds established from baseline data. Together, these metrics offer a practical, interpretable toolset for tracking evolution of joint coordination in ergonomics, rehabilitation, and assistive-device evaluation. The work suggests broad applicability for quantifying both spatial and temporal aspects of coordination changes and supports integration with clinical or performance-monitoring frameworks.

Abstract

Characterizing changes in inter-joint coordination presents significant challenges, as it necessitates the examination of relationships between multiple degrees of freedom during movements and their temporal evolution. Existing metrics are inadequate in providing physiologically coherent results that document both the temporal and spatial aspects of inter-joint coordination. In this article, we introduce two novel metrics to enhance the analysis of inter-joint coordination. The first metric, Joint Contribution Variation based on Principal Component Analysis (JcvPCA), evaluates the variation in each joint's contribution during series of movements. The second metric, Joint Synchronization Variation based on Continuous Relative Phase (JsvCRP), measures the variation in temporal synchronization among joints between two movement datasets. We begin by presenting each metric and explaining their derivation. We then demonstrate the application of these metrics using simulated and experimental datasets involving identical movement tasks performed with distinct coordination strategies. The results show that these metrics can successfully differentiate between unique coordination strategies, providing meaningful insights into joint collaboration during movement. These metrics hold significant potential for fields such as ergonomics and clinical rehabilitation, where a precise understanding of the evolution of inter-joint coordination strategies is crucial. Potential applications include evaluating the effects of upper limb exoskeletons in industrial settings or monitoring the progress of patients undergoing neurological rehabilitation.

Figures (7)

• Figure 1: Example of use of PCA and CRP metrics on simulated datasets. a) Example of use of PCA b) Example of use of CRP
• Figure 2: Experimental set-up. The participant is wearing the exoskeleton (in yellow) and can use shoulder flexion ($\Theta_1$) and elbow flexion ($\Theta_2$) to reach targets (in green) on the screen in front of them
• Figure 3: JcvPCA on simulated data. (A) datasets pertaining to kinematic time series for 2 joints. (B) Representation of joint positions using angle-angle plots. (C) PCA is computed on dataset A. (D) $PCA_A$ becomes the new reference frame and data of the second dataset are projected in this new reference frame. Another PCA is conducted on the projected data of dataset B. (E) Using equations at the bottom of C and D, the PCs of the second PCA can be expressed in terms of joint position. The coefficient before each joint can be extracted for each PC, this is the Joint Reprojection Weight (JRW). Each PC accounts for a percentage of the total variance of the dataset, but now the PCs of the 2 datasets account for the same percentage. (F) the results for the second dataset is subtracted from the reference dataset.
• Figure 4: JsvCRP on simulated datasets. (A) 2 datasets composed of a time series of 2 joint amplitudes. (B) joint velocities are computed and normalized to their range. (C) joint velocity is plotted with respect to position. (D) the angle between the velocity-position point and the horizontal (zero-velocity) axis is extracted for each timestamp. (E) The JsvCRP is calculated as the difference between the phase angles of two joints and the area between the 2 curves is computed.
• Figure 5: Four coordination strategies using shoulder flexion and elbow extension. (A) Physiological Coordination Strategy. (B) Desynchronization of the 2 joints. (C) Use of the shoulder only. (D) Overuse of the elbow. The mean trajectory as well as the standard deviation are presented