Bivariate functional principal components analysis: considerations for use with multivariate movement signatures in sports biomechanics

Analyzing Key Factors on Training Days within a Standard Microcycle for Young Sub-Elite Football Players: A Principal Component Approach

Utilizing techniques for reducing multivariate data is essential for comprehensively understanding the variations and relationships within both biomechanical and physiological datasets in the context of youth football training. Therefore, the objective of this study was to identify the primary factors influencing training sessions within a standard microcycle among young sub-elite football players. A total of 60 male Portuguese youth sub-elite footballers (15.19 ± 1.75 years) were continuous monitored across six weeks during the 2019-2020 in-season, comprising the training days from match day minus (MD-) 3, MD-2, and MD-1. The weekly training load was collected by an 18 Hz global positioning system (GPS), 1 Hz heart rate (HR) monitors, the perceived exertion (RPE) and the total quality recovery (TQR). A principal component approach (PCA) coupled with a Monte Carlo parallel analysis was applied to the training datasets. The training datasets were condensed into three to five principal components, explaining between 37.0% and 83.5% of the explained variance (proportion and cumulative) according to the training day (p < 0.001). Notably, the eigenvalue for this study ranged from 1.20% to 5.21% within the overall training data. The PCA analysis of the standard microcycle in youth sub-elite football identified that, across MD-3, MD-2, and MD-1, the first was dominated by the covered distances and sprinting variables, while the second component focused on HR measures and training impulse (TRIMP). For the weekly microcycle, the first component continued to emphasize distance and intensity variables, with the ACC and DEC being particularly influential, whereas the second and subsequent components included HR measures and perceived exertion. On the three training days analyzed, the first component primarily consisted of variables related to the distance covered, running speed, high metabolic load, sprinting, dynamic stress load, accelerations, and decelerations. The high intensity demands have a high relative weight throughout the standard microcycle, which means that the training load needs to be carefully monitored and managed.

Bivariate functional principal component analysis of barbell trajectories during the snatch

The purpose of this study was to use bivariate functional principal components analysis (bfPCA) to quantify patterns in barbell trajectories during the snatch and to investigate whether these patterns correlate with weightlifting performance and biomechanical characteristics that characterise weightlifting technique. A motion capture system was used to record three-dimensional barbell trajectories as six weightlifters performed three snatch lifts during a weightlifting competition. Horizontal and vertical barbell positions of all lifts were used as input to a bfPCA. Weightlifting performance was quantified through the ratio of barbell mass/body-mass, whereas biomechanical variables were quantified through peak vertical barbell velocity and acceleration. The bfPCA extracted barbell trajectory patterns related to variations in general forward/backward motion (pattern 1), peak height (pattern 2), and crossing of the vertical reference line during the first pull (pattern 3). Spearman rank correlations showed that pattern 1 correlated positively with weightlifting performance and negatively with peak barbell velocity and acceleration. The opposite results were found for pattern 3. Interpretation of the extracted barbell trajectory patterns and statistical results suggest that better weightlifting performances were characterised by snatch lifts that exhibited general backward shifts and limited forward motions during the first and second pull, regardless of peak heights.

Resultant equations for training load monitoring during a standard microcycle in sub-elite youth football: a principal components approach

Applying data-reduction techniques to extract meaningful information from electronic performance and tracking systems (EPTS) has become a hot topic in football training load (TL) monitoring. The aim of this study was to reduce the dimensionality of the internal and external load measures, by a principal component approach, to describe and explain the resultant equations for TL monitoring during a standard in-season microcycle in sub-elite youth football. Additionally, it is intended to identify the most representative measure for each principal component. A principal component analysis (PCA) was conducted with a Monte Carlo parallel analysis and VariMax rotation to extract baseline characteristics, external TL, heart rate (HR)-based measures and perceived exertion. Training data were collected from sixty sub-elite young football players during a 6-week training period using 18 Hz global positioning system (GPS) with inertial sensors, 1 Hz short-range telemetry system, total quality recovery (TQR) and rating of perceived exertion (RPE). Five principal components accounted for 68.7% of the total variance explained in the training data. Resultant equations from PCA was subdivided into: (1) explosiveness, accelerations and impacts (27.4%); (2) high-speed running (16.2%); (3) HR-based measures (10.0%); (4) baseline characteristics (8.3%); and (5) average running velocity (6.7%). Considering the highest factor in each principal component, decelerations (PCA 1), sprint distance (PCA 2), average HR (PCA 3), chronological age (PCA 4) and maximal speed (PCA 5) are the conditional dimension to be considered in TL monitoring during a standard microcycle in sub-elite youth football players. Current research provides the first composite equations to extract the most representative components during a standard in-season microcycle in sub-elite youth football players. Futures research should expand the resultant equations within training days, by considering other well-being measures, technical-tactical skills and match-related contextual factors.

Determining jumping performance from a single body-worn accelerometer using machine learning

External peak power in the countermovement jump is frequently used to monitor athlete training. The gold standard method uses force platforms, but they are unsuitable for field-based testing. However, alternatives based on jump flight time or Newtonian methods applied to inertial sensor data have not been sufficiently accurate for athlete monitoring. Instead, we developed a machine learning model based on characteristic features (functional principal components) extracted from a single body-worn accelerometer. Data were collected from 69 male and female athletes at recreational, club or national levels, who performed 696 jumps in total. We considered vertical countermovement jumps (with and without arm swing), sensor anatomical locations, machine learning models and whether to use resultant or triaxial signals. Using a novel surrogate model optimisation procedure, we obtained the lowest errors with a support vector machine when using the resultant signal from a lower back sensor in jumps without arm swing. This model had a peak power RMSE of 2.3 W·kg^-1 (5.1% of the mean), estimated using nested cross validation and supported by an independent holdout test (2.0 W·kg^-1). This error is lower than in previous studies, although it is not yet sufficiently accurate for a field-based method. Our results demonstrate that functional data representations work well in machine learning by reducing model complexity in applications where signals are aligned in time. Our optimisation procedure also was shown to be robust can be used in wider applications with low-cost, noisy objective functions.

Volleyball Competition on Consecutive Days Modifies Jump Kinetics but Not Height

PURPOSE

In volleyball, jump execution is critical for the match outcome. Game-play-related neuromuscular impairments may manifest as decreased jump height (JH) or increased jump total duration, both of which are pivotal for performance. To investigate changes in JH and kinetics with game play, the authors conducted a prospective exploratory analysis using minimal-effect testing (MET) and equivalence testing with the 2 one-sided tests procedure, univariate, and bivariate functional principal component analysis, respectively.

METHODS

Twelve male varsity athletes completed 3-set matches on 2 consecutive days. Countermovement jumps were performed on a force platform immediately prematch and postmatch on days 1 and 2 and once on days 3 and 4.

RESULTS

Across sessions, JH was equivalent (P < .022, equivalence test), while total duration reported inconclusive changes (P > .227). After match 2, MET indicated that relative force at zero velocity (P = .036) decreased, while braking duration (P = .040) and time to peak force (P = .048) increased compared with baseline. With the first and second functional principal components, these alterations, together with decreased relative braking rate of force development (P = .092), were already evident after match 1. On day 4, MET indicated that relative peak force (P = .049), relative force at zero velocity (P = .023), and relative braking rate of force development (P = .021) decreased, whereas braking duration (P = .025) increased from baseline.

CONCLUSIONS

Impairments in jump kinetics were evident from variables related to the countermovement-jump braking phase, while JH was equivalent. In addition to these experimental findings, the present research provides information for the choice of sample size and smallest effect size of interest when using MET and 1- and 2-dimensional analyses for countermovement-jump height and kinetics.

Maximal Strength in Relation to Force and Velocity Patterns During Countermovement Jumps

Maximal strength is important for the performance of dynamic athletic activities, such as countermovement jumps (CMJ). Although measures of maximal strength appear related to discrete CMJ variables, such as peak ground reaction forces (GRF) and center-of-mass (COM) velocity, knowledge about the association between strength and the time series patterns during CMJ will help characterize changes that can be expected in dynamic movement with changes in maximal strength.

PURPOSE

To investigate the associations between maximal strength and GRF and COM velocity patterns during CMJ.

METHODS

Nineteen female college lacrosse players performed 3 maximal-effort CMJs and isometric midthigh pull. GRF and COM velocity time series data from the CMJ were time normalized and used as inputs to principal-components analyses. Associations between isometric midthigh pull peak force and CMJ principal-component scores were investigated with a correlational analysis.

RESULTS

Isometric midthigh pull peak force was associated with several GRF and COM velocity patterns. Correlations indicated that stronger players exhibited a GRF pattern characterized by greater eccentric-phase rate of force development, greater peak GRF, and a unimodal GRF profile (P = .016). Furthermore, stronger athletes exhibited a COM velocity pattern characterized by higher velocities during the concentric phase (P = .004).

CONCLUSIONS

Maximal strength is correlated to specific GRF and COM velocity patterns during CMJ in female college lacrosse athletes. Since maximal strength was not correlated with discrete CMJ variables, the patterns extracted via principal-components analyses may provide information that is more beneficial for performance coaches and researchers.

Individuals with gluteal tendon repair display similar hip biomechanics to those of a healthy cohort during a sit-to-stand task

BACKGROUND

Gluteal-tendon repair (GTR) is reported to be effective for relieving pain and improving clinical function in patients with gluteal-tendon tears. The sit-to-stand (STS) task is an important activity of daily living and is often used to assess functional capacity in clinical populations. Understanding if and how STS performance is altered in individuals with gluteal tendon repair may be an effective marker of GTR outcomes as well as a possible therapeutic target for post-operative rehabilitation.

RESEARCH QUESTION

Do biomechanical parameters during STS differ between age- and sex-matched participants with and without gluteal-tendon repair?

METHODS

27 participants with a GTR and 29 healthy participants performed the STS task. Data were acquired using the three-dimensional motion capture system and forceplates. Outcomes of interest were task duration, rate of force development, trunk, pelvis, and hip joint angles, moments and powers. Differences were assessed using Generalised linear multivariate models and statistical parametric mapping.

RESULTS

GTR patients performed the STS movement significantly slower (1.4+/- 0.40 s) compared to controls (1.1+/ -0.2 s) with a significantly lower rate of force development (35.1+/- 5.7 N/kg/ms vs 30.3+/- 8.5 N/kg/ms). There were no group differences for hip, pelvis, or trunk angle over the movement cycle or for maximal or minimal values. Furthermore, there were no significant differences detected in hip joint kinetics. However, there appeared to be substantial between-subject variability indicating different patient-specific movements patterns.

SIGNIFICANCE

Individuals with a GTR performed the STS task about 20 % slower than healthy controls with a lower rate of force development. The individual variations indicate that participants likely employed different movement strategies to achieve STS. While the lack of differences between groups could suggest that GTR helps restore function and corrects the proposed underlying aetiology, it is possible that the STS task was not sufficiently challenging to discriminate between groups.

Whole-body energy transfer strategies during football instep kicking: implications for training practices

Knowledge of whole-body energy transfer strategies during football instep kicking can help inform empirically grounded training practices. The aim of this study was thus to investigate energy transfer strategies of 15 semi-professional players performing kicks for speed and accuracy. Three-dimensional kinematics and GRFs (both 1000 Hz) were incorporated into segment power analyses to derive energy transfers between the support leg, torso, pelvis and kick leg throughout the kick. Energy transferred from support leg (r = 0.62, P = 0.013) and torso (r = 0.54, P = 0.016) into the pelvis during tension arc formation and leg cocking was redistributed to the kick leg during the downswing (r = 0.76, P < 0.001) and were associated with faster foot velocities at ball contact. This highlights whole-body function during instep kicking. Of particular importance were: (a) regulating support leg energy absorption, (b) eccentric formation and concentric release of a 'tension arc' between the torso and kicking hip, and (c) coordinated proximal to distal sequencing of the kick leg. Resistance exercises that replicate the demands of these interactions may help develop more powerful kicking motions and varying task and/or environmental constraints might facilitate development of adaptable energy transfer strategies.

Test-retest reliability of entire time-series data from hip, knee and ankle kinematics and kinetics during one-leg hops for distance: Analyses using integrated pointwise indices

Motion capture systems enable in-depth interpretations of human movements based on data from three-dimensional joint angles and moments. Such analyses carry important bearings for evaluation of movement control during for instance hop landings among sports-active individuals from a performance perspective but also in rehabilitation. Recent statistical development allows analysis of entire time-series of angle and moment during hops using functional data analysis, but the reliability of such multifaceted data is not established. We used integrated pointwise indices (intra-class correlation, ICC; standard error of measurement, SEM) to establish the test-retest reliability of three-dimensional hip, knee and ankle angle and moment curves during landings of one-leg hop for distance (OLHD) in 23 asymptomatic individuals aged 18-28. We contrasted these findings to reliability of discrete variables extracted at specific events (initial contact, peak value). We extended the calculations of ICC and SEM to handle unbalanced situations (varying number of repetitions) to include all available data. Hip and knee angle curves proved reliable with stable ICC curves throughout the landing, with integrated ICCs ≥ 0.71 for all planes except for knee internal/external rotation (ICC = 0.57). Hip and knee moment curves and ankle angle and moments were less reliable and less stable, particularly in the first ~ 10-25% of the landing (integrated ICCs 0.44-0.57). Curve data were generally not in agreement with the results for discrete event data, thus advocating analysis of curve data which contains more information. To conclude, hip and knee angle curve data during OLHD landings can reliably be evaluated, while moment curves necessitate careful consideration.

Effects of acute wearable resistance loading on overground running lower body kinematics

Field-based sports require athletes to run sub-maximally over significant distances, often while contending with dynamic perturbations to preferred coordination patterns. The ability to adapt movement to maintain performance under such perturbations appears to be trainable through exposure to task variability, which encourages movement variability. The aim of the present study was to investigate the extent to which various wearable resistance loading magnitudes alter coordination and induce movement variability during running. To investigate this, 14 participants (three female and 11 male) performed 10 sub-maximal velocity shuttle runs with either no weight, 1%, 3%, or 5% of body weight attached to the lower limbs. Sagittal plane lower limb joint kinematics from one complete stride cycle in each run were assessed using functional data analysis techniques, both across the participant group and within-individuals. At the group-level, decreases in ankle plantarflexion following toe-off were evident in the 3% and 5% conditions, while increased knee flexion occurred during weight acceptance in the 5% condition compared with unloaded running. At the individual-level, between-run joint angle profiles varied, with six participants exhibiting increased joint angle variability in one or more loading conditions compared with unloaded running. Loading of 5% decreased between-run ankle joint variability among two individuals, likely in accordance with the need to manage increased system load or the novelty of the task. In terms of joint coordination, the most considerable alterations to coordination occurred in the 5% loading condition at the hip-knee joint pair, however, only a minority of participants exhibited this tendency. Coaches should prescribe wearable resistance individually to perturb preferred coordination patterns and encourage movement variability without loading to the extent that movement options become limited.

Over 50 Years of Researching Force Profiles in Rowing: What Do We Know?

There has been substantial interest in the mechanisms underpinning the skilled movements of on-water rowing for more than 150 years. Contemporary attention from biomechanical research has focused on the important relationship between kinetics (such as force application at the oar) and performance. A range of instrumentation systems have been developed and used in both academic and applied training contexts to better understand this relationship. Both qualitative and quantitative analytical approaches have been used in conjunction with these instrumentation systems for observing differences in propulsive force patterns between rowers. Despite the use of these analytical approaches, there is still limited consensus surrounding which characteristics of force profiles are associated with better rowing performance. Newell's model of constraints is provided as a framework for understanding why this lack of clarity exists surrounding force profile characteristics and performance. Further to this, direction for further research is provided by a framework that outlines two main streams: (1) exploration of constraints and how they are related to force profile characteristics; and (2) after controlling for constraints, exploration of performance and how it is related to force profile characteristics. These two steps are sequential, with an understanding of constraints influencing how we understand the interaction of force profiles and performance.