Considerations for the use of functional principal components analysis in sports biomechanics: examples from on-water rowing

The development of an automated assessment system for resistance training movement

Portable data collection devices and machine learning (ML) have been combined in autonomous movement analysis models for resistance training (RT) movements. However, input features for these models were mostly extracted empirically and subsequent models demonstrated limited interpretability and generalisability to real-world settings. This study aimed to investigate the utility of interpretable and generalisable modelling techniques and several data-driven feature extraction (FE) methods. This was achieved by developing machine learning movement analysis models for the barbell back squat and deadlift using markerless motion capture. 61 participants performed submaximal and maximal repetitions of both RT movements. Movement data was collected using two Azure Kinect cameras. Joint and segment kinematic variables were calculated from the collected depth imaging, and input features were extracted using traditional, manual FE methods and novel data-driven techniques. Classifiers were developed for several predefined technical deviations for both movements. Many of the addressed technical deviations could be classified with good levels of accuracy (≥70%) while the remainder were poor (55%-60%). Additionally, data-driven FE techniques were comparable to previous, traditional FE methods. Interpretable and generalisable modelling techniques can be utilised to good effect for certain classification tasks while data-driven FE techniques did not provide a consistent advantage over traditional FE methods.

Relationship between neck kinematics and neck dissability index. An approach based on functional regression

Numerous studies use numerical variables of neck movement to predict the level of severity of a pathology. However, the correlation between these numerical variables and disability levels is low, less than 0.4 in the best cases, even less in subjects with nonspecific neck pain. This work aims to use Functional Data Analysis (FDA), in particular scalar-on-function regression, to predict the Neck Disability Index (NDI) of subjects with nonspecific neck pain using the complete movement as predictors. Several functional regression models have been implemented, doubling the multiple correlation coefficient obtained when only scalar predictors are used. The best predictive model considers the angular velocity curves as a predictor, obtaining a multiple correlation coefficient of 0.64. In addition, functional models facilitate the interpretation of the relationship between the kinematic curves and the NDI since they allow identifying which parts of the curves most influence the differences in the predicted variable. In this case, the movement's braking phases contribute to a greater or lesser NDI. So, it is concluded that functional regression models have greater predictive capacity than usual ones by considering practically all the information in the curve while allowing a physical interpretation of the results.

Dynamical Analyses Show That Professional Archers Exhibit Tighter, Finer and More Fluid Dynamical Control Than Neophytes

Quantifying the dynamical features of discrete tasks is essential to understanding athletic performance for many sports that are not repetitive or cyclical. We compared three dynamical features of the (i) bow hand, (ii) drawing hand, and (iii) center of mass during a single bow-draw movement between professional and neophyte archers: dispersion (convex hull volume of their phase portraits), persistence (tendency to continue a trend as per Hurst exponents), and regularity (sample entropy). Although differences in the two groups are expected due to their differences in skill, our results demonstrate we can quantify these differences. The center of mass of professional athletes exhibits tighter movements compared to neophyte archers (6.3 < 11.2 convex hull volume), which are nevertheless less persistent (0.82 < 0.86 Hurst exponent) and less regular (0.035 > 0.025 sample entropy). In particular, the movements of the bow hand and center of mass differed more between groups in Hurst exponent analysis, and the drawing hand and center of mass were more different in sample entropy analysis. This suggests tighter neuromuscular control over the more fluid dynamics of the movement that exhibits more active corrections that are more individualized. Our work, therefore, provides proof of principle of how well-established dynamical analysis techniques can be used to quantify the nature and features of neuromuscular expertise for discrete movements in elite athletes.

Countermovement Jump and Squat Jump Force-Time Curve Analysis in Control and Fatigue Conditions

ABSTRACT

Hughes, S, Warmenhoven, J, Haff, GG, Chapman, DW, and Nimphius, S. Countermovement jump and squat jump force-time curve analysis in control and fatigue conditions. J Strength Cond Res 36(10): 2752-2761, 2022-This study aimed to reanalyze previously published discrete force data from countermovement jumps (CMJs) and squat jumps (SJs) using statistical parametric mapping (SPM), a statistical method that enables analysis of data in its native, complete state. Statistical parametric mapping analysis of 1-dimensional (1D) force-time curves was compared with previous zero-dimensional (0D) analysis of peak force to assess sensitivity of 1D analysis. Thirty-two subjects completed CMJs and SJs at baseline, 15 minutes, 1, 24, and 48 hours following fatigue and control conditions in a pseudo random cross-over design. Absolute (CMJ ABS /SJ ABS ) and time-normalized (CMJ NORM /SJ NORM ) force-time data were analyzed using SPM 2-way repeated measures analysis of variance with significance accepted at α = 0.05. The SPM indicated a magnitude of difference between force-time data with main effects for time ( p < 0.001) and interaction ( p < 0.001) observed in CMJ ABS , SJ ABS, and SJ NORM, whereas previously published 0D analysis reported no 2-way interaction in CMJ and SJ peak force. This exploratory research demonstrates the strength of SPM to identify changes between entire movement force-time curves. Continued development and use of SPM analysis techniques could present the opportunity for refined assessment of athlete fatigue and readiness with the analysis of complete force-time curves.

Hip and knee joint angle patterns and kicking velocity in female and male professional soccer players: A principal component analysis of waveforms approach

This study used principal component analysis (PCA) of waveforms to extract movement patterns from hip and knee angle time-series data; and determined if the extracted movement patterns were predictors of ball velocity during a soccer kick. Twenty-three female and nineteen male professional soccer players performed maximal effort instep kicks while motion capture and post-impact ball velocities data were recorded. Three-dimensional hip and knee joint angle time-series data were calculated from the beginning of the kicking leg's backswing phase until the end of the follow-through phase and entered into separate PCAs for females and males. Three principal components (PC) (i.e., movement patterns) were extracted and PC scores were calculated. Pearson correlation coefficients were calculated to establish correlations between hip and knee PC scores and kicking velocity. Results showed better kicking performance in male players was associated with a greater difference between the hip extension at the end of the backswing/beginning of the leg cocking phases and hip flexion at the end of the follow-through phase (r = -0.519, p = 0.023) and a delayed internal rotation of the hip (r = 0.475, p = 0.040). No significant correlations between ball velocity and hip and knee kinematics were found for female players.

The effects of curve registration on linear models of jump performance and classification based on vertical ground reaction forces

Functional principal components define modes of variation in time series, which represent characteristic movement patterns in biomechanical data. Their usefulness however depends on the prior choices made in data processing. Recent research showed that better curve alignment achieved with registration (dynamic time warping) reduces errors in linear models predicting jump height. However, the efficacy of registration in different preprocessing combinations, including time normalisation, padding and feature extraction, is largely unknown. A more comprehensive analysis is needed, given the potential value of registration to machine learning in biomechanics. We evaluated popular preprocessing methods combined with registration, creating 512 models based on ground reaction force data from 385 countermovement jumps. The models either predicted jump height or classified jumps into those performed with or without arm swing. Our results show that the classification models benefited from registration in various forms, particularly when landmarks were placed at critical points. The best classifier achieved a 5.5 percentage point improvement over the equivalent unregistered model. However, registration was detrimental to the jump height models, although this performance variable may be a special case given its direct relationship with impulse. Our meta-models revealed the relative contributions made by various preprocessing operations, highlighting that registration does not generalise so well to new data. Nonetheless, our analysis shows the potential for registration in further biomechanical applications, particularly in classification, when combined with the other appropriate preprocessing operations.

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.

Statistical kinematic modelling: concepts and model validity

Data reduction techniques are applied to reduce the volume of data while maintaining its integrity. For cyclic motion data, a reliable overview comparing these methods is lacking. Therefore, this study aims to evaluate the features of the different data reduction techniques by applying them to large public data sets. The periodicity of cyclic motion can be exploited by either analysing a single cycle or studying a series of cycles. Analysing single cycles requires a pre-processing step to isolate the amplitude variability. Three different alignment techniques were evaluated, namely Linear length normalisation (LLN), piecewise LLN (PLLN) and continuous registration (CR). CR showed to remove the most phase variation. For the data reduction, three techniques were assessed (i.e., principal component analysis (PCA), principal polynomial analysis (PPA) and multivariate functional PCA (MFPCA)) based on the in- and out-of-sample error, the compactness and the computation time. The differences were found to be minimal. From our results, PPA appeared to be most useful for data compression. Further, we recommend PCA and MFPCA for classification and feature extraction purposes. We suggest the use of PCA when computation time is key and we advise the use of MFPCA when the inclusion of different data sources is desired. In contrast, the analysis of a series of cycles requires a pre-processing step to decompose the series. Further, a regression model was used to compensate for the difference in fundamental frequency. PCA on FC and MFPCA with splines were applied on the frequency compensated curves. Both methods performed as good.

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.

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.

PCA of waveforms and functional PCA: A primer for biomechanics

Principal components analysis (PCA) of waveforms and functional PCA (fPCA) are statistical approaches used to explore patterns of variability in biomechanical curve data, with fPCA being an accepted statistical method grounded within the functional data analysis (FDA) statistical framework. This technical note demonstrates that PCA of waveforms is the most rudimentary form of FDA, and consequently can be rationalised within the FDA framework of statistical processes. Mathematical proofing applied demonstrations of both techniques, and an example of when fPCA may be of greater benefit to control over smoothing of functional principal components is provided using an open access motion sickness dataset. Finally, open access software is provided with this paper as means of priming the biomechanics community for using these methods as a part of future functional data explorations.

Development of Concise Physical Performance Test Batteries in Young Athletes

PURPOSE

This study aimed 1) to define the principal components of physical function assessed by 10 common lower extremity physical performance tests and 2) to derive a reduced-item set of physical performance tests that efficiently and accurately measures raw performance and limb symmetry on each underlying component in pediatric and adolescent athletes.

METHODS

This study included healthy, uninjured volunteers (n = 100) between the ages 6 and 18 yr (mean age = 11.7 ± 3.6 yr; 52 females). Subjects performed the stork balance, stork balance on BOSU® Balance Trainer, single leg squat (SLS), SLS on BOSU, clockwise and counterclockwise quadrant single leg hop (SLH), forward SLH, timed SLH, triple crossover SLH, and lower quarter Y-Balance Test™. Item reduction was performed using principal components analysis (PCA). We developed separate principal components analysis for average raw performance and side-to-side limb symmetry, with secondary analyses to evaluate consistency of results by age and sex.

RESULTS

We identified two components for average raw performance (accounting for 65.2% of the variance in total test battery) with a reduced-item set composed of five tests, and four components for limb symmetry (accounting for 62.9% of the variance in total test battery) with a reduced-item set of seven tests. The most parsimonious test suitable for screening both average raw performance and limb symmetry would consist of five tests (stork balance on BOSU, SLS on BOSU, forward SLH, timed SLH, and lower quarter Y-Balance Test™). Age- and sex-specific test batteries may be warranted.

CONCLUSION

Comprehensive screening for lower extremity average raw performance and limb symmetry is possible with short physical performance test batteries.

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.

Objective classification and scoring of movement deficiencies in patients with anterior cruciate ligament reconstruction

Motion analysis systems are widely employed to identify movement deficiencies-e.g. patterns that potentially increase the risk of injury or inhibit performance. However, findings across studies are often conflicting in respect to what a movement deficiency is or the magnitude of association to a specific injury. This study tests the information content within movement data using a data driven framework that was taught to classify movement data into the classes: NORM, ACLOP and ACLNO OP, without the input of expert knowledge. The NORM class was presented by 62 subjects (124 NORM limbs), while 156 subjects with ACL reconstruction represented the ACLOP and ACLNO OP class (156 limbs each class). Movement data from jumping, hopping and change of direction exercises were examined, using a variety of machine learning techniques. A stratified shuffle split cross-validation was used to obtain a measure of expected accuracy for each step within the analysis. Classification accuracies (from best performing classifiers) ranged from 52 to 81%, using up to 5 features. The exercise with the highest classification accuracy was the double leg drop jump (DLDJ; 81%), the highest classification accuracy when considering only the NORM class was observed in the single leg hop (81%), while the DLDJ demonstrated the highest classification accuracy when considering only for the ACLOP and ACLNO OP class (84%). These classification accuracies demonstrate that biomechanical data contains valuable information and that it is possible to differentiate normal from rehabilitating movement patterns. Further, findings highlight that a few features contain most of the information, that it is important to seek to understand what a classification model has learned, that symmetry measures are important, that exercises capture different qualities and that not all subjects within a normative cohort utilise 'true' normative movement patterns (only 27 to 71%).

Understanding the track and field sprint start through a functional analysis of the external force features which contribute to higher levels of block phase performance

This study aimed to identify the continuous ground reaction force (GRF) features which contribute to higher levels of block phase performance. Twenty-three sprint-trained athletes completed starts from their preferred settings during which GRFs were recorded separately under each block. Continuous features of the magnitude and direction of the resultant GRF signals which explained 90% of the variation between the sprinters were identified. Each sprinter's coefficient score for these continuous features was then input to a linear regression model to predict block phase performance (normalised external power). Four significant (p < 0.05) predictor features associated with GRF magnitude were identified; there were none associated with GRF direction. A feature associated with greater rear block GRF magnitudes from the onset of the push was the most important predictor (β = 1.185), followed by greater front block GRF magnitudes for the final three-quarters of the push (β = 0.791). Features which included a later rear block exit (β = 0.254) and greater front leg GRF magnitudes during the mid-push phase (β = 0.224) were also significant predictors. Sprint practitioners are encouraged, where possible, to consider the continuous magnitude of the GRFs produced throughout the block phase in addition to selected discrete values.