Vector field statistical analysis of kinematic and force trajectories

When investigating the dynamics of three-dimensional multi-body biomechanical systems it is often difficult to derive spatiotemporally directed predictions regarding experimentally induced effects. A paradigm of 'non-directed' hypothesis testing has emerged in the literature as a result. Non-directed analyses typically consist of ad hoc scalar extraction, an approach which substantially simplifies the original, highly multivariate datasets (many time points, many vector components). This paper describes a commensurately multivariate method as an alternative to scalar extraction. The method, called 'statistical parametric mapping' (SPM), uses random field theory to objectively identify field regions which co-vary significantly with the experimental design. We compared SPM to scalar extraction by re-analyzing three publicly available datasets: 3D knee kinematics, a ten-muscle force system, and 3D ground reaction forces. Scalar extraction was found to bias the analyses of all three datasets by failing to consider sufficient portions of the dataset, and/or by failing to consider covariance amongst vector components. SPM overcame both problems by conducting hypothesis testing at the (massively multivariate) vector trajectory level, with random field corrections simultaneously accounting for temporal correlation and vector covariance. While SPM has been widely demonstrated to be effective for analyzing 3D scalar fields, the current results are the first to demonstrate its effectiveness for 1D vector field analysis. It was concluded that SPM offers a generalized, statistically comprehensive solution to scalar extraction's over-simplification of vector trajectories, thereby making it useful for objectively guiding analyses of complex biomechanical systems.

Understanding how an arm swing enhances performance in the vertical jump

This investigation was conducted to examine the various theories that have been proposed to explain the enhancement of jumping performance when using an arm swing compared to when no arm swing is used. Twenty adult males were asked to perform a series of maximal vertical jumps while using an arm swing and again while holding their arms by their sides. Force, motion and electromyographical data were recorded during each performance. Participants jumped higher (0.086 m) in the arm swing compared to the no-arm swing condition and was due to increased height (28%) and velocity (72%) of the center of mass at take-off. The increased height at take-off was due to the elevation of the arm segments. The increased velocity of take-off stemmed from a complex series of events which allowed the arms to build up energy early in the jump and transfer it to the rest of the body during the later stages of the jump. This energy came from the shoulder and elbow joints as well as from extra work done at the hip. This energy was used to (i) increase the kinetic and potential energy of the arms at take-off, (ii) store and release energy from the muscles and tendons around the ankle, knee and hip joint, and (iii) 'pull' on the body through an upward force acting on the trunk at the shoulder. It was concluded that none of the prevailing theories exclusively explains the enhanced performance in the arm swing jump, but rather the enhanced performance is based on several mechanisms operating together.

Region-of-interest analyses of one-dimensional biomechanical trajectories: bridging 0D and 1D theory, augmenting statistical power

One-dimensional (1D) kinematic, force, and EMG trajectories are often analyzed using zero-dimensional (0D) metrics like local extrema. Recently whole-trajectory 1D methods have emerged in the literature as alternatives. Since 0D and 1D methods can yield qualitatively different results, the two approaches may appear to be theoretically distinct. The purposes of this paper were (a) to clarify that 0D and 1D approaches are actually just special cases of a more general region-of-interest (ROI) analysis framework, and (b) to demonstrate how ROIs can augment statistical power. We first simulated millions of smooth, random 1D datasets to validate theoretical predictions of the 0D, 1D and ROI approaches and to emphasize how ROIs provide a continuous bridge between 0D and 1D results. We then analyzed a variety of public datasets to demonstrate potential effects of ROIs on biomechanical conclusions. Results showed, first, that a priori ROI particulars can qualitatively affect the biomechanical conclusions that emerge from analyses and, second, that ROIs derived from exploratory/pilot analyses can detect smaller biomechanical effects than are detectable using full 1D methods. We recommend regarding ROIs, like data filtering particulars and Type I error rate, as parameters which can affect hypothesis testing results, and thus as sensitivity analysis tools to ensure arbitrary decisions do not influence scientific interpretations. Last, we describe open-source Python and MATLAB implementations of 1D ROI analysis for arbitrary experimental designs ranging from one-sample t tests to MANOVA.

The probability of false positives in zero-dimensional analyses of one-dimensional kinematic, force and EMG trajectories

A false positive is the mistake of inferring an effect when none exists, and although α controls the false positive (Type I error) rate in classical hypothesis testing, a given α value is accurate only if the underlying model of randomness appropriately reflects experimentally observed variance. Hypotheses pertaining to one-dimensional (1D) (e.g. time-varying) biomechanical trajectories are most often tested using a traditional zero-dimensional (0D) Gaussian model of randomness, but variance in these datasets is clearly 1D. The purpose of this study was to determine the likelihood that analyzing smooth 1D data with a 0D model of variance will produce false positives. We first used random field theory (RFT) to predict the probability of false positives in 0D analyses. We then validated RFT predictions via numerical simulations of smooth Gaussian 1D trajectories. Results showed that, across a range of public kinematic, force/moment and EMG datasets, the median false positive rate was 0.382 and not the assumed α=0.05, even for a simple two-sample t test involving N=10 trajectories per group. The median false positive rate for experiments involving three-component vector trajectories was p=0.764. This rate increased to p=0.945 for two three-component vector trajectories, and to p=0.999 for six three-component vectors. This implies that experiments involving vector trajectories have a high probability of yielding 0D statistical significance when there is, in fact, no 1D effect. Either (a) explicit a priori identification of 0D variables or (b) adoption of 1D methods can more tightly control α.

The trajectory of the centre of pressure during barefoot running as a potential measure for foot function

The main purpose of this study was to describe and interpret the COP trajectory during barefoot running in a large cohort of young adults with no history of injury. COP data were collected from 215 subjects, who ran at 3.3 ms(-1) over a 16.5m long track, with a built in Footscan pressure platform. COP data were filtered using a 50 Hz lowpass butterworth filter and normalised. Reliability was then studied and mean curves were calculated for medial-lateral displacement (COP(x)) and velocity (v(x)COP), anterior-posterior displacement (COP(y)) and velocity (v(y)COP) as well as for the resultant velocity (v(xy)COP). Displacement and velocity of the COP provided insight over functional foot behaviour. A medially oriented peak in v(x)COP was found, which may reflect the fast initial pronation. A laterally oriented second peak in v(x)COP, together with a second peak in v(y)COP, indicated a fast forward shift of the COP over the lateral border of the foot during forefoot contact phase. During the forefoot push off phase, at the level of the metatarsals, anterior velocities of the COP were low and reflected the importance of the forefoot during push off. Finally, the COP course was studied for high arch, normal and low arch feet and indicated, a more lateral COP course for the low arch feet.

Solutions for representing the whole-body centre of mass in side cutting manoeuvres based on data that is typically available for lower limb kinematics

While studying detailed lower limb mechanics of dynamic sports manoeuvres like side cutting it is often desirable but practically difficult to directly measure velocity profiles of the whole-body centre of mass (CoM). In the current study, representations of CoM, either based on a single marker placed on the pelvis or thorax, or based on segment kinematics of lower limbs with or without inclusion of trunk, were evaluated against whole-body CoM representation. Using the 95% limits of agreement method for comparison of two methods, strongest agreement was found between velocity of whole-body CoM and CoM representation based on lower limbs with the addition of the trunk. The CoM representation based on lower limbs only showed weaker agreement, but this representation was still markedly superior to single marker representations.

A functional foot type classification with cluster analysis based on plantar pressure distribution during jogging

The purpose of this study was to establish a reference dataset for peak pressures and pressure-time integrals during jogging, to compare this reference dataset with existing walking data and to develop a foot type classification, all based on plantar pressure data obtained from 215 healthy young adults. The subjects ran at 3.3 m s(-1) over a 16.5 m long running track, with a built-in pressure platform mounted on top of a force platform. Peak pressures, regional impulses and relative regional impulses were measured. These variables were found to be reliable (all intra class correlation coefficients above 0.75) and, except for the heel areas, gender and asymmetry effects could be neglected. Highest peak pressures were found under the heel due to large impact forces during initial contact phase (ICP). In the forefoot, the highest peak pressure was found under the second metatarsal (64.2 +/- 21.1 N cm(-2)). Compared to walking data, overall higher peak pressures and impulses and difference in hallux loading were found during barefoot jogging. Four pressure loading patterns were identified using a K-means cluster analysis, based on the relative regional impulses underneath the forefoot: medial M1 pattern, medial M2 pattern, central pattern and central-lateral pattern. These four pressure loading patterns could help in the functional interpretation of the foot behaviour during the stance phase in slow running.

A systematic review on biomechanical characteristics of walking in children and adolescents with overweight/obesity: Possible implications for the development of musculoskeletal disorders

It is known that obesity is associated with biomechanical alterations during locomotor tasks, which is considered a potential risk factor for the development of musculoskeletal disorders (MSKD). However, the association of obesity with biomechanical alterations of walking in the early stages of life have not yet been systematically reviewed. Thus, this review aims to summarize the biomechanical characteristics of walking in children and adolescents with overweight/obesity (OW/OB) versus their normal-weight (NW) counterparts. PubMed and Web of Science were systematically searched until November 2018. We found strong and moderate evidence supporting biomechanical differences in the gait pattern of OW/OB with respect to NW. Based on strong evidence, the gait patterns of OW/OB present greater pelvis transversal plane motion, higher hip internal rotation, higher hip flexion, extension and abduction moments and power generation/absorption, greater knee abduction/adduction motion, and higher knee abduction/adduction moments and power generation/absorption. Based on moderate evidence, OW/OB walk with greater step width, longer stance phase, higher tibiofemoral contact forces, higher ankle plantarflexion moments and power generation, and greater gastrocnemius and soleus activation/forces. These biomechanical alterations during walking in OW/OB could play a major role in the onset and progression of MSKD.

Performing the vertical jump: Movement adaptations for submaximal jumping

The purpose of this study was to gain insight into the kinematics and kinetics of the vertical jump when jumping for different heights and to investigate movement effectiveness as a criterion for movement control in submaximal jumping. In order to jump high a countermovement is used and large body segments are rotated, both of which consume energy which is not directly used to gain extra jump height. It was hypothesized that the energy used to reach a specified jump height is minimized by limiting the non-effective energy consumed. Standing vertical jumps attempting 100%, 75%, 50%, and 25% of maximal height were performed by a group of 10 subjects. Force and motion data were recorded simultaneously during each performance. We found that jump height increased due to increasing vertical velocity at take off. This was primarily related to an increase in countermovement amplitude. As such, flexion amplitude of the hip joint increased with jump height whereas the ankle and knee joint flexion did not. These findings revealed that for submaximal jumping a consistent strategy was used of maximizing the contribution of distal joints and minimizing the contribution of proximal joints. Taking into account the high inertia of proximal segments, the potential energy deficit due to countermovement prior to joint extension, the advantageous horizontal orientation of the foot segment during stance and the tendon lengths in distal muscles, it was concluded that movement effectiveness is a likely candidate for the driving criterion of this strategy.

Multi-segment foot landing kinematics in subjects with chronic ankle instability

BACKGROUND

Chronic ankle instability has been associated with altered joint kinematics at the ankle, knee and hip. However, no studies have investigated possible kinematic deviations at more distal segments of the foot. The purpose of this study was to evaluate if subjects with ankle instability and copers show altered foot and ankle kinematics and altered kinetics during a landing task when compared to controls.

METHODS

Ninety-six subjects (38 subjects with chronic ankle instability, 28 copers and 30 controls) performed a vertical drop and side jump task. Foot kinematics were obtained using the Ghent Foot Model and a single-segment foot model. Group differences were evaluated using statistical parametric mapping and analysis of variance.

RESULTS

Subjects with ankle instability had a more inverted midfoot position in relation to the rearfoot when compared to controls during the side jump. They also had a greater midfoot inversion/eversion range of motion than copers during the vertical drop. Copers exhibited less plantar flexion/dorsiflexion range of motion in the lateral and medial forefoot. Furthermore, the ankle instability and coper group exhibited less ankle plantar flexion at touchdown. Additionally, the ankle instability group demonstrated a decreased plantar flexion/dorsiflexion range of motion at the ankle compared to the control group. Analysis of ground reaction forces showed a higher vertical peak and loading rate during the vertical drop in subjects with ankle instability.

INTERPRETATION

Subjects with chronic ankle instability displayed an altered, stiffer kinematic landing strategy and related alterations in landing kinetics, which might predispose them for episodes of giving way and actual ankle sprains.

Impact of knee modeling approach on indicators and classification of anterior cruciate ligament injury risk

INTRODUCTION

The aim of this study was to determine whether using a direct kinematic (DK) or inverse kinematic (IK) modeling approach could influence the estimation of knee joint kinematics, kinetics, and ACL injury risk classification during unanticipated side cutting.

METHODS

The three-dimensional motion and force data of 34 amateur Australian rules footballers conducting unanticipated side-cutting maneuvers were collected. The model used during the DK modeling approach was an eight-segment lower body model with the hip, knee, and ankle free to move in six degrees of freedom. During the IK modeling approach, the same eight-segment model was used; however, translational constraints were imposed on the hip, knee, and ankle joints. The similarity between kinematic and kinetic waveforms was evaluated using the root mean square difference (RMSD) and the one-dimensional statistical parametric mapping (SPM1D). The classification of an athlete's ACL injury risk was determined by correlating their peak knee moments with a predefined injury risk threshold.

RESULTS

The greatest RMSD occurred in the frontal plane joint angles (RMSD = 10.86°) and moments (RMSD = 0.67 ± 0.18 N·m·kg(-1)), which were also shown to be significantly different throughout the stance phase in the SPM1D analysis. Both DK and IK modeling approaches classified the same athletes as being at risk of ACL injury.

CONCLUSIONS

The choice of a DK or an IK modeling approach affected frontal plane estimates of knee joint angles and peak knee moments during the weight acceptance phase of unanticipated side cutting. However, both modeling approaches were similar in their classification of an athlete's ACL injury risk.

Necessary precautions in measuring correct vertical jumping height by means of force plate measurements

The present study was designed to investigate the determination of vertical jumping height by means of force plate measurements. Four different sources of error influence this determination: the measurement of body mass, the determination of take off, the integration frequency, and the assessment of the initial conditions influencing the determination of the start of the movement. A theoretical model was utilized to simulate the vertical ground reaction forces in vertical jumping and to compare the outcome of analytical and numerical double integration of the vertical acceleration of the body centre of mass. A high integration frequency and an optimizing loop for body mass determination were found to be important and should be taken into account when determining jumping height parameters.

Vector field statistics for objective center-of-pressure trajectory analysis during gait, with evidence of scalar sensitivity to small coordinate system rotations

Center of pressure (COP) trajectories summarize the complex mechanical interaction between the foot and a contacted surface. Each trajectory itself is also complex, comprising hundreds of instantaneous vectors over the duration of stance phase. To simplify statistical analysis often a small number of scalars are extracted from each COP trajectory. The purpose of this paper was to demonstrate how a more objective approach to COP analysis can avoid particular sensitivities of scalar extraction analysis. A previously published dataset describing the effects of walking speed on plantar pressure (PP) distributions was re-analyzed. After spatially and temporally normalizing the data, speed effects were assessed using a vector-field paired Hotelling's T2 test. Results showed that, as walking speed increased, the COP moved increasingly posterior at heel contact, and increasingly laterally and anteriorly between ∼60 and 85% stance, in agreement with previous independent studies. Nevertheless, two extracted scalars disagreed with these results. Furthermore, sensitivity analysis found that a relatively small coordinate system rotation of 5.5° reversed the mediolateral null hypothesis rejection decision. Considering that the foot may adopt arbitrary postures in the horizontal plane, these sensitivity results suggest that non-negligible uncertainty may exist in mediolateral COP effects. As compared with COP scalar extraction, two key advantages of the vector-field approach are: (i) coordinate system independence, (ii) continuous statistical data reflecting the temporal extents of COP trajectory changes.

Knee and Hip Joint Kinematics Predict Quadriceps and Hamstrings Neuromuscular Activation Patterns in Drop Jump Landings

Purpose

The purpose was to assess if variation in sagittal plane landing kinematics is associated with variation in neuromuscular activation patterns of the quadriceps-hamstrings muscle groups during drop vertical jumps (DVJ).

Methods

Fifty female athletes performed three DVJ. The relationship between peak knee and hip flexion angles and the amplitude of four EMG vectors was investigated with trajectory-level canonical correlation analyses over the entire time period of the landing phase. EMG vectors consisted of the {vastus medialis(VM),vastus lateralis(VL)}, {vastus medialis(VM),hamstring medialis(HM)}, {hamstring medialis(HM),hamstring lateralis(HL)} and the {vastus lateralis(VL),hamstring lateralis(HL)}. To estimate the contribution of each individual muscle, linear regressions were also conducted using one-dimensional statistical parametric mapping.

Results

The peak knee flexion angle was significantly positively associated with the amplitudes of the {VM,HM} and {HM,HL} during the preparatory and initial contact phase and with the {VL,HL} vector during the peak loading phase (p<0.05). Small peak knee flexion angles were significantly associated with higher HM amplitudes during the preparatory and initial contact phase (p<0.001). The amplitudes of the {VM,VL} and {VL,HL} were significantly positively associated with the peak hip flexion angle during the peak loading phase (p<0.05). Small peak hip flexion angles were significantly associated with higher VL amplitudes during the peak loading phase (p = 0.001). Higher external knee abduction and flexion moments were found in participants landing with less flexed knee and hip joints (p<0.001).

Conclusion

This study demonstrated clear associations between neuromuscular activation patterns and landing kinematics in the sagittal plane during specific parts of the landing. These findings have indicated that an erect landing pattern, characterized by less hip and knee flexion, was significantly associated with an increased medial and posterior neuromuscular activation (dominant hamstrings medialis activity) during the preparatory and initial contact phase and an increased lateral neuromuscular activation (dominant vastus lateralis activity) during the peak loading phase.

Sample size estimation for biomechanical waveforms: Current practice, recommendations and a comparison to discrete power analysis

Testing a prediction is fundamental to scientific experiments. Where biomechanical experiments involve analysis of 1-Dimensional (waveform) data, sample size estimation should consider both 1D variance and hypothesised 1D effects. This study exemplifies 1D sample size estimation using typical biomechanical signals and contrasts this with 0D (discrete) power analysis. For context, biomechanics papers from 2018 and 2019 were reviewed to characterise current practice. Sample size estimation occurred in approximately 4% of 653 papers and reporting practice was mixed. To estimate sample sizes, common biomechanical signals were sourced from the literature and 1D effects were generated artificially using the open-source power1d software. Smooth Gaussian noise was added to the modelled 1D effect to numerically estimate the sample size required. Sample sizes estimated using 1D power procedures varied according to the characteristics of the dataset, requiring only small-to-moderate sample sizes of approximately 5-40 to achieve target powers of 0.8 for reported 1D effects, but were always larger than 0D sample sizes (from N + 1 to >N + 20). The importance of a priori sample size estimation is highlighted and recommendations are provided to improve the consistency of reporting. This study should enable researchers to construct 1D biomechanical effects to address adequately powered, hypothesis-driven, predictive research questions.

Kinematic response characteristics of the CAREN moving platform system for use in posture and balance research

The CAREN system is a new and unique device for use in postural and balance research in clinical settings due to its ability to independently perturb the support surface in each of six degrees of freedom. Users of this system need knowledge of its technical performance which is not available. The aim of this study was to determine the technical performance of the CAREN system by defining its kinematic response characteristics to two commonly used input functions (sine and ramp) for each of its six translational and rotational axes. The translational and rotational displacement, velocity and acceleration limits of the CAREN system suggest that it is a mid-range system with regard to single degree of freedom moving platform devices reported in the literature. The maximum average displacement cross-talk was 1.5% of the viable working range in any specified direction. The maximum average velocity cross-talk was 3.3% of its maximum velocity in any specified direction. The CAREN system was able to respond to ramp input functions within its displacement and velocity limits although, for short duration ramps, there was evidence that target velocity was not reached. It is concluded that the CAREN system is an appropriate device for postural and balance research with some unique features. This specification of its technical performance should help researchers to identify the tasks for which it is most suitable.

Whole-body biomechanical load in running-based sports: The validity of estimating ground reaction forces from segmental accelerations

OBJECTIVES

Unlike physiological loads, the biomechanical loads of training in running-based sports are still largely unexplored. This study, therefore, aimed to assess the validity of estimating ground reaction forces (GRF), as a measure of external whole-body biomechanical loading, from segmental accelerations.

METHODS

Fifteen team-sport athletes performed accelerations, decelerations, 90° cuts and straight running at different speeds including sprinting. Full-body kinematics and GRF were recorded with a three-dimensional motion capture system and a single force platform respectively. GRF profiles were estimated as the sum of the product of all fifteen segmental masses and accelerations, or a reduced number of segments.

RESULTS

Errors for GRF profiles estimated from fifteen segmental accelerations were low (1-2Nkg^-1) for low-speed running, moderate (2-3Nkg^-1) for accelerations, 90° cuts and moderate-speed running, but very high (>4Nkg^-1) for decelerations and high-speed running. Similarly, impulse (2.3-11.1%), impact peak (9.2-28.5%) and loading rate (20.1-42.8%) errors varied across tasks. Moreover, mean errors increased from 3.26±1.72Nkg^-1 to 6.76±3.62Nkg^-1 across tasks when the number of segments was reduced.

CONCLUSIONS

Accuracy of estimated GRF profiles and loading characteristics was dependent on task, and errors substantially increased when the number of segments was reduced. Using a direct mechanical approach to estimate GRF from segmental accelerations is thus unlikely to be a valid method to assess whole-body biomechanical loading across different dynamic and high-intensity activities. Researchers and practitioners should, therefore, be very cautious when interpreting accelerations from one or several segments, as these are unlikely to accurately represent external whole-body biomechanical loads.

External and internal loads during the competitive season in professional female soccer players according to their playing position: differences between training and competition

The aim of this study was to compare external (EL) and internal loads (IL) during training sessions compared to official matches between elite female soccer players according to their playing position.Training and match data were obtained during the 2017/18 season from eighteen players (age: 26.5±5.7 years; height: 164.4±5.3 cm; body mass: 58.56±5.58 kg) from a first Division Spanish team. The EL (total distance covered; high-speed running distance; number of accelerations and decelerations) was assessed with a Global Positioning System (GPS) and triaxial accelerometer. The IL was assessed with ratings of perceived exertion (RPE; and session-RPE).The EL and the IL from official matches were higher compared to training sessions (p<0.05; effect size [ES]:0.6-5.4). In matches, the EL was greater in Attackers (AT) and Central Midfielders (CM) versus Central Backs (p<0.05; ES:0.21-1.74). During training sessions, the EL was similar between playing positions (p>0.05; ES:0.03-0.87). The EL and the IL are greater in matches compared to training sessions, with greater match-related EL in AT and CM players. Current results may help practitioners to better understand and modulate training session's loads according to playing position, potentially contributing to their performance readiness and injury risk reduction.