# The Effect of Neuromuscular Fatigue on the Spatiotemporal Coordination of Rowing
## 2 Materials and Methods
### Data Processing and Analysis  
Following HD reprocessing (XSens MVN Analyze, software version 2021.0.1), joint angles were exported into MATLAB (v. R2021b, The MathWorks Inc., Natick, MA, USA), and the shoulder, lumbar, hip, knee, and ankle flexion-extension joint angles were taken for further analysis and were trimmed to the first 10-50 cycles (PRE) and the final 40 cycles (POST) of the rowing trial to represent periods of minimal and maximal neuromuscular fatigue. The first 10 cycles were excluded from any analyses to ensure that all the participants had reached a steady-state rowing movement. Further, all joint flexion-extension time-series data were segmented, with each stroke time-normalized to 101 frames (i.e., 0-100%) to facilitate further analyses. Time-normalized joint angle time series data were used to extract the average maximum, average minimum, and average range (i.e., maximum-minimum) joint angles across each 40-cycle pre- and post-fatigue timepoint.  
For each of the joint angles, an amplitude-normalized joint angle was plotted against an amplitude-normalized joint angular velocity to yield the extraction of a phase angle. Amplitude normalization is a critical step, and the relative amplitude was observed to differ across segments and derivatives [16]. As such, these signals were amplitude-normalized from \(-1\) (minimum) to \(+1\) (maximum) using Equation (1) to ensure that the two phase portraits being compared were identical and comparable [14].  
\[\theta i,\ norm=\frac{2\times\theta i-\min(\theta)}{\max(\theta)-\min(\theta)}-1 \tag{1}\]  
Once amplitude-normalized, the phase angle between adjacent points within the phase plot was calculated for each time point across the cycle [10]. The difference was then taken between each point in time between the two phase angles to yield a time-varying CRP angle (Equation (2)) [14].  
\[CRPi=1\,\varphi i,proximal\,-\varphi i,distal\,| \tag{2}\]  
Joint pairs of interest included three pairs of neighboring joints: hip-knee (HK), lumbar-hip (LH), shoulder-lumbar (SL), and four joint pairs referenced to the movement of the ankle: shoulder-ankle (SA), lumbar-ankle (LA), hip-ankle (HA), and knee-ankle (KA). Once calculated, the time-varying CRP angles were further reduced into estimates of the mean absolute relative phase (MARP) and deviation phase (DP) to provide a better understanding of the spatiotemporal differences between segments/joints [11]. The MARP was calculated by taking the mean absolute value across all CRP cycles (Equation (3)), while the DP was calculated by taking the mean standard deviation obtained across all 40 cycles (Equation (4)) [14].  
\[MARP=\sum_{i=1}^{101}|\,\varphi\,relative\,phase|\,i/101 \tag{3}\]  
\[DP=\sum_{i=1}^{101}\,SDi/101 \tag{4}\]  
To complement the CRP analyses, cross-correlations (R\({}_{XY}\)) were also computed to infer the mean time lag between joint pairs [17]. This was completed to provide additional detail surrounding the relative timing of joint flexion-extension movement across each stroke(i.e., drive-recovery) cycle. For all R\({}_{\rm XY}\) analyses, the joint pairs mirrored those used for any CRP analyses.