Principal Component Analysis of the Running Ground Reaction Forces With Different Speeds.
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ABSTRACT: Ground reaction force (GRF) is a key metric in biomechanical research, including parameters of loading rate (LR), first impact peak, second impact peak, and transient between first and second impact peaks in heel strike runners. The GRFs vary over time during stance. This study was aimed to investigate the variances of GRFs in rearfoot striking runners across incremental speeds. Thirty female and male runners joined the running tests on the instrumented treadmill with speeds of 2.7, 3.0, 3.3, and 3.7 m/s. The discrete parameters of vertical average loading rate in the current study are consistent with the literature findings. The principal component analysis was modeled to investigate the main variances (95%) in the GRFs over stance. The females varied in the magnitude of braking and propulsive forces (PC1, 84.93%), whereas the male runners varied in the timing of propulsion (PC1, 53.38%). The female runners dominantly varied in the transient between the first and second peaks of vertical GRF (PC1, 36.52%) and LR (PC2, 33.76%), whereas the males variated in the LR and second peak of vertical GRF (PC1, 78.69%). Knowledge reported in the current study suggested the difference of the magnitude and patterns of GRF between male and female runners across different speeds. These findings may have implications for the prevention of sex-specific running-related injuries and could be integrated with wearable signals for the in-field prediction and estimation of impact loadings and GRFs.
Project description:Twenty-seven methods of estimating vertical ground reaction force first peak, loading rate, second peak, average, and/or time series from a single wearable accelerometer worn on the shank or approximate center of mass during running were compared. Force estimation errors were quantified for 74 participants across different running surfaces, speeds, and foot strike angles and biases, repeatability coefficients, and limits of agreement were modeled with linear mixed effects to quantify the accuracy, reliability, and precision. Several methods accurately and reliably estimated the first peak and loading rate, however, none could do so precisely (the limits of agreement exceeded ±65% of target values). Thus, we do not recommend first peak or loading rate estimation from accelerometers with the methods currently available. In contrast, the second peak, average, and time series could all be estimated accurately, reliably, and precisely with several different methods. Of these, we recommend the 'Pogson' methods due to their accuracy, reliability, and precision as well as their stability across surfaces, speeds, and foot strike angles.
Project description:During running at a constant speed, the optimal stride frequency (SF) can be derived from the u-shaped relationship between SF and heart rate (HR). Changing SF towards the optimum of this relationship is beneficial for energy expenditure and may positively change biomechanics of running. In the current study, the effects of speed on the optimal SF and the nature of the u-shaped relation were empirically tested using Generalized Estimating Equations. To this end, HR was recorded from twelve healthy (4 males, 8 females) inexperienced runners, who completed runs at three speeds. The three speeds were 90%, 100% and 110% of self-selected speed. A self-selected SF (SFself) was determined for each of the speeds prior to the speed series. The speed series started with a free-chosen SF condition, followed by five imposed SF conditions (SFself, 70, 80, 90, 100 strides·min-1) assigned in random order. The conditions lasted 3 minutes with 2.5 minutes of walking in between. SFself increased significantly (p<0.05) with speed with averages of 77, 79, 80 strides·min-1 at 2.4, 2.6, 2.9 m·s-1, respectively). As expected, the relation between SF and HR could be described by a parabolic curve for all speeds. Speed did not significantly affect the curvature, nor did it affect optimal SF. We conclude that over the speed range tested, inexperienced runners may not need to adapt their SF to running speed. However, since SFself were lower than the SFopt of 83 strides·min-1, the runners could reduce HR by increasing their SFself.
Project description:Background:Monitoring the external ground reaction forces (GRF) acting on the human body during running could help to understand how external loads influence tissue adaptation over time. Although mass-spring-damper (MSD) models have the potential to simulate the complex multi-segmental mechanics of the human body and predict GRF, these models currently require input from measured GRF limiting their application in field settings. Based on the hypothesis that the acceleration of the MSD-model's upper mass primarily represents the acceleration of the trunk segment, this paper explored the feasibility of using measured trunk accelerometry to estimate the MSD-model parameters required to predict resultant GRF during running. Methods:Twenty male athletes ran at approach speeds between 2-5 m s-1. Resultant trunk accelerometry was used as a surrogate of the MSD-model upper mass acceleration to estimate the MSD-model parameters (ACCparam) required to predict resultant GRF. A purpose-built gradient descent optimisation routine was used where the MSD-model's upper mass acceleration was fitted to the measured trunk accelerometer signal. Root mean squared errors (RMSE) were calculated to evaluate the accuracy of the trunk accelerometry fitting and GRF predictions. In addition, MSD-model parameters were estimated from fitting measured resultant GRF (GRFparam), to explore the difference between ACCparam and GRFparam. Results:Despite a good match between the measured trunk accelerometry and the MSD-model's upper mass acceleration (median RMSE between 0.16 and 0.22 g), poor GRF predictions (median RMSE between 6.68 and 12.77 N kg-1) were observed. In contrast, the MSD-model was able to replicate the measured GRF with high accuracy (median RMSE between 0.45 and 0.59 N kg-1) across running speeds from GRFparam. The ACCparam from measured trunk accelerometry under- or overestimated the GRFparam obtained from measured GRF, and generally demonstrated larger within parameter variations. Discussion:Despite the potential of obtaining a close fit between the MSD-model's upper mass acceleration and the measured trunk accelerometry, the ACCparam estimated from this process were inadequate to predict resultant GRF waveforms during slow to moderate speed running. We therefore conclude that trunk-mounted accelerometry alone is inappropriate as input for the MSD-model to predict meaningful GRF waveforms. Further investigations are needed to continue to explore the feasibility of using body-worn micro sensor technology to drive simple human body models that would allow practitioners and researchers to estimate and monitor GRF waveforms in field settings.
Project description:Despite being a key concept in rehabilitation, controlling weight-bearing load while walking, following lower limb injury is very hard to achieve. Walking in water provides an opportunity to prescribe load for people who have pain, weakness or weight bearing restrictions related to stages of healing. The aim of this experimental study was to evaluate and validate regression models for predicting ground reaction forces while walking in water. One hundred and thirty seven individuals (24±5 years, 1.71±0.08 m and 68.7±12.5 kg) were randomly assigned to a regression group (n = 113) and a validation group (n = 24). Trials were performed at a randomly assigned water depth (0.75 to 1.35 m), and at a self-selected speed. Independent variables were: immersion ratio, velocity, body mass, and waist, thigh and leg circumferences. Stepwise regression was used for the prediction of ground reaction forces and validation included agreement and consistency statistical analyses. Data from a force plate were compared with predicted data from the created model in the validation group. Body mass, immersion ratio, and velocity independently predicted 95% of the vertical and resultant ground reaction force variability, while, together, velocity and thigh circumference explained 81% of antero-posterior ground reaction force variability. When tested against the data measured in validation samples, the models output resulted in statistically similar values, intraclass correlation coefficients ranging from 0.88 to 0.90 and standard errors of measurement, 11.8 to 42.3 N. The models introduced in this study showed good predictive performance in our evaluation procedures and may be considered valid in the prediction of vertical, antero-posterior and resultant ground reaction forces while walking in water. All predictive variables can be easily determined in clinical practice. Future studies should focus on the validation of these models in specific populations.
Project description:Although principal component analysis is frequently used in multivariate/ analysis, it has disadvantages when applied to experimental or diagnostic data. First, the identified principal components have poor generality; since the size and directions of the components are dependent on the particular data set, the components are valid only within the set. Second, the method is sensitive to experimental noise and bias between sample groups, since it cannot reflect the design of experiments; rather, it estimates the same weight and independence of all the samples in the matrix. Third, the resulting components are often difficult to interpret. To address these issues, several options were introduced to the methodology. The resulting components were scaled to unify their size unit. Also, the principal axes were identified using training data sets and shared among experiments. This training data reflects the design of experiments, and its preparation allows noise to be reduced and group bias to be removed. The effects of these options were observed in microarray experiments, and showed an improvement in the separation of groups and robustness to noise. Additionally, unknown samples were appropriately classified using pre-arranged axes, and principal axes well reflected the characteristics of groups in the experiments. This SuperSeries is composed of the SubSeries listed below.
Project description:BackgroundMetabolism and its regulation constitute a large fraction of the molecular activity within cells. The control of cellular metabolic state is mediated by numerous molecular mechanisms, which in effect position the metabolic network flux state at specific locations within a mathematically-definable steady-state flux space. Post-translational regulation constitutes a large class of these mechanisms, and decades of research indicate that achieving a network flux state through post-translational metabolic regulation is both a complex and complicated regulatory problem. No analysis method for the objective, top-down assessment of such regulation problems in large biochemical networks has been presented and demonstrated.ResultsWe show that the use of Monte Carlo sampling of the steady-state flux space of a cell-scale metabolic system in conjunction with Principal Component Analysis and eigenvector rotation results in a low-dimensional and biochemically interpretable decomposition of the steady flux states of the system. This decomposition comes in the form of a low number of small reaction sets whose flux variability accounts for nearly all of the flux variability in the entire system. This result indicates an underlying simplicity and implies that the regulation of a relatively low number of reaction sets can essentially determine the flux state of the entire network in the given growth environment.ConclusionWe demonstrate how our top-down analysis of networks can be used to determine key regulatory requirements independent of specific parameters and mechanisms. Our approach complements the reductionist approach to elucidation of regulatory mechanisms and facilitates the development of our understanding of global regulatory strategies in biological networks.
Project description:Human runners have long been thought to have the ability to consume a near-constant amount of energy per distance traveled, regardless of speed, allowing speed to be adapted to particular task demands with minimal energetic consequence.1-3 However, recent and more precise laboratory measures indicate that humans may in fact have an energy-optimal running speed.4-6 Here, we characterize runners' speeds in a free-living environment and determine if preferred speed is consistent with task- or energy-dependent objectives. We analyzed a large-scale dataset of free-living runners, which was collected via a commercial fitness tracking device, and found that individual runners preferred a particular speed that did not change across commonly run distances. We compared the data from lab experiments that measured participants' energy-optimal running speeds with the free-living preferred speeds of age- and gender-matched runners in our dataset and found the speeds to be indistinguishable. Human runners prefer a particular running speed that is independent of task distance and is consistent with the objective of minimizing energy expenditure. Our findings offer an insight into the biological objectives that shape human running preferences in the real world-an important consideration when examining human ecology or creating training strategies to improve performance and prevent injury.
Project description:Impaired control of mediolateral body motion during walking is an important health concern. Developing treatments to improve mediolateral control is challenging, partly because the mechanisms by which muscles modulate mediolateral ground reaction force (and thereby modulate mediolateral acceleration of the body mass center) during unimpaired walking are poorly understood. To investigate this, we examined mediolateral ground reaction forces in eight unimpaired subjects walking at four speeds and determined the contributions of muscles, gravity, and velocity-related forces to the mediolateral ground reaction force by analyzing muscle-driven simulations of these subjects. During early stance (0-6% gait cycle), peak ground reaction force on the leading foot was directed laterally and increased significantly (p<0.05) with walking speed. During early single support (14-30% gait cycle), peak ground reaction force on the stance foot was directed medially and increased significantly (p<0.01) with speed. Muscles accounted for more than 92% of the mediolateral ground reaction force over all walking speeds, whereas gravity and velocity-related forces made relatively small contributions. Muscles coordinate mediolateral acceleration via an interplay between the medial ground reaction force contributed by the abductors and the lateral ground reaction forces contributed by the knee extensors, plantarflexors, and adductors. Our findings show how muscles that contribute to forward progression and body-weight support also modulate mediolateral acceleration of the body mass center while weight is transferred from one leg to another during double support.
Project description:Motivated by modern observational studies, we introduce a class of functional models that expand nested and crossed designs. These models account for the natural inheritance of the correlation structures from sampling designs in studies where the fundamental unit is a function or image. Inference is based on functional quadratics and their relationship with the underlying covariance structure of the latent processes. A computationally fast and scalable estimation procedure is developed for high-dimensional data. Methods are used in applications including high-frequency accelerometer data for daily activity, pitch linguistic data for phonetic analysis, and EEG data for studying electrical brain activity during sleep.
Project description:We propose localized functional principal component analysis (LFPCA), looking for orthogonal basis functions with localized support regions that explain most of the variability of a random process. The LFPCA is formulated as a convex optimization problem through a novel Deflated Fantope Localization method and is implemented through an efficient algorithm to obtain the global optimum. We prove that the proposed LFPCA converges to the original FPCA when the tuning parameters are chosen appropriately. Simulation shows that the proposed LFPCA with tuning parameters chosen by cross validation can almost perfectly recover the true eigenfunctions and significantly improve the estimation accuracy when the eigenfunctions are truly supported on some subdomains. In the scenario that the original eigenfunctions are not localized, the proposed LFPCA also serves as a nice tool in finding orthogonal basis functions that balance between interpretability and the capability of explaining variability of the data. The analyses of a country mortality data reveal interesting features that cannot be found by standard FPCA methods.