Inverse Dynamic Analysis Research Articles

An Enhanced Spine Model Validated for Simulating Dynamic Lifting Tasks in OpenSim.

A fully articulated thoracolumbar spine model had been previously developed in OpenSim and had been extensively validated against experimental data during various static tasks. In the present study, we enhanced this detailed musculoskeletal model by adding the role of passive structures and adding kinematic constraints to make it suitable for dynamic tasks. We validated the spinal forces estimated by this enhanced model during nine dynamic lifting/lowering tasks. Moreover, we recently developed and evaluated five approaches in OpenSim to model the external loads applied to the hands during lifting/lowering tasks, and in the present study, we assessed which approach results in more accurate spinal forces. Regardless of the external load modeling approach, the maximum forces predicted by our enhanced spine model across all tasks, as well as the pattern of estimated spinal forces within each task, showed strong correlations (r-values and cross-correlation coefficients > 0.9) with experimental data. Given the biofidelity of our enhanced model, its accessibility via the open-source OpenSim software, and the extent to which this model has been validated, we recommend it for applications requiring estimation of spinal forces during lifting/lowering tasks using multibody-based models and inverse dynamic analyses.

Elbow joint loads during simulated activities of daily living: implications for formulating recommendations after total elbow arthroplasty

Overloading of the elbow joint prosthesis following total elbow arthroplasty can lead to implant failure. Joint moments during daily activities are not well-contextualized for a prosthesis' failure limits and the effect of the current postoperative instruction on elbow joint loading is unclear. This study investigates the difference in elbow joint moments between simulated daily tasks and between flexion-extension, pronation-supination, varus-valgus movement directions. Additionally, the effect of the current postoperative instruction on elbow joint load is examined. Nine healthy participants (age 45.8 ± 17 years, 3 males) performed eight tasks; driving a car, opening a door, rising from chair, lifting, sliding, combing hair, drinking, emptying cup, without and with the instruction "not lifting more than 1 kg". Upper limb kinematics and hand contact forces were measured. Elbow joint angles and net moments were analyzed using inverse dynamic analysis, where the net moments are estimated from movement data and external forces. Peak elbow joint moments differed significantly between tasks (p < 0.01) and movement directions (p < 0.01). The most and least demanding tasks were, rising from a chair (13.4 Nm extension, 5.0 Nm supination, 15.2 Nm valgus) and sliding (4.3 Nm flexion, 1.7 Nm supination, 2.6 Nm varus). Net moments were significantly reduced after instruction only in the chair task (p < 0.01). This study analyzed elbow joint moments in different directions during daily tasks. The outcomes question whether postoperative instruction can lead to decreasing elbow loads. Future research might focus on reducing elbow loads in the flexion-extension and varus-valgus directions.

Joint kinematic and kinetic responses to added mass on the lower extremities during running

AimWe analyzed the biomechanical response (joint angles, moments, and powers) to running with added leg mass. These data may help guide the design of wearable locomotor assistive devices (i.e., exoskeletons), which are becoming more prevalent. Methods15 participants (7 females, 8 males) completed treadmill running trials (3m•s−1) normally and with lead mass (300–1350 g) attached to the thigh, shank, or foot, bilaterally. We quantified the lower limb biomechanics combining motion capture and ground reaction force data using standard inverse dynamics analysis. ResultsOnly moderate kinematic changes occurred in response to the distal added limb mass. Maximum hip flexion and maximum knee flexion angles during swing phase increased by approximately 9% and 6% respectively for each 1 kg added to each foot. However, adding even small masses made dramatic changes to the joint moments and powers, mostly during the swing phase. For example, adding 1 kg to each foot increased maximum joint moments by as much as 40% (knee extension in late swing) and maximum joint power by as much as 50% (hip generation in late swing). ConclusionLeg joint kinematics were largely conserved in response to adding mass to the legs. Adding mass to the leg distally increased joint power mainly at the knee and hip joints during the swing phase, whereas adding mass proximally mainly affected the ankle joint mechanics during the stance phase. These changes have implications for shoe designs, people who run with added mass on their legs for sport/strength training and for the design of wearable devices.

Influence of knee flexion on early femoral fracture healing: A combined analysis of musculoskeletal dynamics and finite elements

Background and ObjectivesKnee flexion causes a certain amount of misalignment and relative movement of the fractured ends of the femur fracture, and if the flexion angle is too large it will affect the stability of the fracture and the healing process, making it challenging to design a safe range of flexion. However, due to a lack of basic understanding of the effect of knee flexion on the mechanical environment at the fracture site, clinicians are often unable to provide an objective and safe range of motion in flexion based on subjective experience. The aim of this study was to evaluate the effect of knee flexion on plate and fracture healing using finite element analysis (FEA). MethodsA human musculoskeletal model was constructed based on CT scan data, and the mechanical properties of the fracture site were changed by adjusting the knee flexion angle. The joint forces, muscle forces and moments acting on the femur were obtained by inverse dynamics analysis, and the biomechanical properties of the fracture-plate system were analyzed using finite elements. A finite element model of the fracture-plate system without muscle loading was also constructed. The effect of knee flexion on the safety of plate fixation and fracture healing was evaluated in terms of the biomechanical properties of the plate and the interfragmentary motion of the fracture. ResultsAs the knee flexion angle increases, the von Mises stress of the locked compression plate (LCP) first increases, then decreases, then increases again. The deformation from compression bending to tension twisting occurs simultaneously. At 30° of flexion, shear interfragmentary motion (SIM) was dominant and inhibited fracture healing; at more than 45° of flexion, the plate was twisted and deformed to the lateral side of the body, and the fracture site underwent greater misalignment and relative motion, with destructive effects on bone scabs and healing tissues. If muscle loading is not taken into account, the plate will undergo predominantly bending deformation and will overestimate the interfragmentary strain in the far and near cortex. ConclusionsKnee flexion causes the plate to deform from compression bending to extension and torsion, which has an important impact on the safety and healing process of the fracture, and this study provides a biomechanical basis to guide the clinician in the post-operative rehabilitation of femoral fractures in the clinical setting.

Sex differences in the kinematics and kinetics of the foot and plantar aponeurosis during drop-jump

Plantar fasciitis is one of the most common musculoskeletal injuries in runners and jumpers, with a higher incidence in females. However, mechanisms underlying sex-associated differences in its incidence remain unclear. This study investigated the possible differences in landing and jumping kinematics and kinetics of the foot between sexes during drop-jump activities. Twenty-six participants, including 13 males and 13 females, performed drop-jumps from a platform onto force plates. Nineteen trials including ten males and nine females were selected for inverse dynamics analysis. The patterns of stretch and tensile force generated by the plantar aponeurosis (PA) were estimated using a multi-segment foot model incorporating the PA. Our results demonstrated that dorsiflexion, angular velocity, and normalized plantarflexion moment of the midtarsal joint right after the heel landed on the floor were significantly larger in females than in males. Consequently, the PA strain rate and tensile stress tended to be larger in females than in males. Such differences in the kinematics and kinetics of the foot and the PA between sexes could potentially lead to a higher prevalence of foot injuries such as plantar fasciitis in females.

A Bionic Control Method for Human–Exoskeleton Coupling Based on CPG Model

Exoskeleton robots are functioning in contexts with more complicated motion control needs as a result of the technology and applications for these robots rapidly developing. This calls for novel control techniques to accommodate their employment in a range of real-world settings. This paper proposes a bionic control method for a human–exoskeleton coupling dynamic model based on the CPG model, utilizing a model on the dynamics of the human–exoskeleton interaction. The CPG network is established as an oscillator by two neurons inhibiting one another, which approximates the torques simulated in the inverse dynamic analysis as the input to the exoskeleton robot. The findings of the simulation assessment suggest that the bionic control strategy may improve the robot’s ability to move quickly and steadily, as well as better adapt to challenging environments.

A comparison of five methods to normalize joint moments during running

BackgroundNet joint moments (NJM) are typically normalized for a (combination of) physical body characteristics such as mass, height, and limb length using ratio scaling to account for differences in body characteristics between individuals. Four assumptions must be met when normalizing NJM data this way to ensure valid conclusions. First, the relationship between the non-normalized NJM and participant characteristic should be linear. Second, the regression line between NJM and the characteristic(s) used should pass through the origin. Third, scaling should not significantly perturb the statistical distribution of the data. Fourth, normalizing a NJM should eliminate its correlation with the characteristic(s) normalized for. Research questionThis study assessed these assumptions using data collected among 59 individuals running at 10 km h−1. MethodsStandard inverse dynamics analyses were conducted, and ratios were computed between the sagittal-plane hip, knee and ankle NJM’s and the participant’s mass, height, leg length, mass × height, and mass × leg length. ResultsThe most important finding of this study was that none of the scaling variables fulfilled all assumptions across all joints. However, scaling by mass, mass*height and mass*leg length satisfied the assumptions for the knee joint moment and log-transformed hip joint moment, suggesting these methods generally performed best. SignificanceOur findings suggests that scaling by mass, mass*height and mass*leg length may be considered to normalize joint moments during running. Nevertheless, we urge researchers to check the statistical assumptions to ensure valid conclusions. We provide supplementary code to check the statistical assumptions, and discuss consequences of inappropriate scaling.

Mechanical upside of PAO mainstream fixations: co-simulation based on early postoperative gait characteristics of DDH patients.

Purpose: To investigate the early postoperative gait characteristics of patients who underwent periacetabular osteotomy (PAO) and predict the biomechanical performance of two commonly used PAO fixation methods: iliac screw (IS) and transverse screw (TS). Methods: A total of 12 patients with unilateral developmental dysplasia of the hip (DDH) (mean age 27.81 ± 4.64years, 42% male) that were scheduled to undergo PAO surgery were included in this study. Their preoperative CT images and pre- and postoperative gait data were used to create subject-specific musculoskeletal models and complete the inverse dynamics analysis (IDA). Two patients with typical gait characteristics were selected using clustering analysis, and their IDA data were incorporated into finite element (FE) models of IS and TS fixations. Failure simulation was performed by applying iterative steps with increasing gait load to predict yield load. Stress results and yield loads were calculated for each FE model at different phases of the gait cycle. Results: Postoperative gait showed improvement compared to preoperative gait but remained inferior to that of healthy individuals. Postoperative gait was characterized by a lower hip range of motion, lower peri-ilium muscle forces, particularly in the abductors, and a sharper initial peak and flatter second peak of hip joint reaction force (HRF). Finite element analysis (FEA) showed a trend of increasing stress during the second-fourth phases of the gait cycle, with lower stress levels in other phases. At high-stress gait phases, the mean stress of maximum differed significantly between IS and TS (p < 0.05) and between coupled and uncoupled muscle forces (p < 0.05). Failure analysis predicted a slightly larger yield load for TS configurations (6.21*BW) than that for IS (6.16*BW), but both were well above the gait load. Coupled and uncoupled groups showed similar results, but uncoupled groups had lower yield loads (5.9*BW). Conclusion: PAO early postoperative gait shows a normalized trend, but abnormalities persist. IS and TS are both capable of resisting mechanical strain failure, with no significant mechanical advantage found for transverse screw fixation during PAO early postoperative gait. Additionally, it is important to note that the TS may have a higher risk of cyclic fatigue failure due to the localized greater stress concentration. Furthermore, the most medial screw is crucial for pelvic stability.

Identification of track irregularities with the multi-sensor acceleration measurements of vehicle dynamic responses

Track irregularities induce potential risks to the safety and stability of railway track systems. This paper proposes a novel methodology to identify vertical and lateral track irregularities. The method involves measuring system-based attitude calculation and a model-based unknown input observer estimator, based on the dynamic responses of distributed multi-sensors on the vehicle and bogie. First, a mechanical model of wheel-rail contacts is built with dynamic methods. The model considers the different directions of motion for a railway vehicle and consists of two bogies and four wheelsets. Based on the multi-sensor acceleration measurement, the vertical and lateral acceleration signals of the vehicle and bogies are integrated into the displacement signal. Then a state-space description of the vehicle suspension model is established for inverse dynamical analysis to extract the input signals. A suitable unknown input observer is constructed to estimate the track irregularities by transforming the state space equations of the vehicle into an augmented system that can monitor the track irregularities in-service. This method provides an opportunity to reduce the costs of the monitoring infrastructure and provide quicker and more reliable information about the status of a track.

Recursive inverse dynamics sensitivity analysis of open-tree-type multibody systems

We present a first-order recursive approach to sensitivity analysis based on the application of the direct differentiation method to the inverse Lagrangian dynamics of rigid multibody systems. Our method is simple and efficient and is characterized by the following features. Firstly, it describes the kinematics of multibody systems using branch connectivity graphs and joint-branch connectivity matrices. For most mechanical systems with an open-tree kinematic structure, this method turns out to be more efficient compared to other kinematic descriptions employing joint or link connectivity graphs. Secondly, a recursive sensitivity analysis is presented for a dynamic system with an open-tree kinematic structure and inverse dynamic equations described in terms of the Lagrangian formalism. Thirdly, known approaches to recursive inverse dynamic and sensitivity analyses are modified to include dynamic systems with external forces and torques acting simultaneously at all joints. Finally, the proposed method for sensitivity analysis is easy to implement and computationally efficient. It can be utilized to evaluate the derivatives of the dynamic equations of multibody systems in gradient-based optimization algorithms. It also allows less experienced users to perform sensitivity analyses using the power of high-level programming languages such as MATLAB. To illustrate the method, simulation results for a human body model are discussed. The shortcomings of the method and possible directions for future work are outlined.

A gradient based numerical algorithm to solve inverse dynamic viscoelastic problems of multi-variable identification

A gradient based numerical method is put forward to solve the inverse dynamic viscoelastic problem with multi-variable identification for the constitutive and TKBC (third kind boundary conditions) related parameters. A three parameter model is employed to describe the time dependent TKBC concerned with structural interaction, and is formulated in the forward and inverse dynamic viscoelastic analysis. In addition to the reliable platform provided by TPAA-SBFEM to gain the solution of forward problems, a piecewise recursive adaptive algorithm is developed to obtain the derivatives required in the sensitivity analysis, which is able to provide a stable temporal solution accuracy for different step sizes. SBFEM (Scaled Boundary Finite Element Method) is stressed in the structural analysis with its own advantages, such as the efficient and convenient treatment of stress singularity problem and flexibility of mesh generation with polygonal elements and image based quadtree gridding. The inverse problem of identification is solved by the Levenberg-Marquardt method, and the regional inhomogeneity, crack, initial guess, location/number of measurement points, material contrast ratios, and noisy data are taken into account. Numerical examples are provided to verify the proposed approach, and the satisfactory results are achieved.

Powered Hip Exoskeleton Reduces Residual Hip Effort Without Affecting Kinematics and Balance in Individuals With Above-Knee Amputations During Walking.

A unilateral, lightweight powered hip exoskeleton has been shown to improve walking economy in individuals with above-knee amputations. However, the mechanism responsible for this improvement is unknown. In this study we assess the biomechanics of individuals with above-knee amputations walking with and without a unilateral, lightweight powered hip exoskeleton. We hypothesize that assisting the residual limb will reduce the net residual hip energy. Eight individuals with above-knee amputations walked on a treadmill at 1 m/s with and without a unilateral powered hip exoskeleton. Flexion/extension assistance was provided to the residual hip. Motion capture and inverse dynamic analysis were performed to assess gait kinematics, kinetics, center of mass, and center of pressure. The net energy at the residual hip decreased from 0.05±0.04 J/kg without the exoskeleton to -0.01±0.05 J/kg with the exoskeleton (p = 0.026). The cumulative positive energy of the residual hip decreased on average by 18.2% with 95% confidence intervals (CI) (0.20 J/kg, 0.24 J/kg) and (0.16 J/kg, 0.20 J/kg) without and with the exoskeleton, respectively. During stance, the hip extension torque of the residual limb decreased on average by 37.5%, 95% CI (0.28 Nm/kg, 0.36 Nm/kg), (0.17 Nm/kg, 0.23 Nm/kg) without and with the exoskeleton, respectively. Powered hip exoskeleton assistance significantly reduced the net residual hip energy, with concentric energy being the main contributor to this change. We believe that the reduction in residual hip extension torque during early stance is the main contributor to this reduction. This analysis shows that by assisting the residual hip, the exoskeleton significantly decreased the net hip energy produced by the residual limb, which may explain the improvements in walking economy previously observed.

A Deep Learning Model for 3D Ground Reaction Force Estimation Using Shoes with Three Uniaxial Load Cells

Ground reaction force (GRF) is essential for estimating muscle strength and joint torque in inverse dynamic analysis. Typically, it is measured using a force plate. However, force plates have spatial limitations, and studies of gaits involve numerous steps and thus require a large number of force plates, which is disadvantageous. To overcome these challenges, we developed a deep learning model for estimating three-axis GRF utilizing shoes with three uniaxial load cells. GRF data were collected from 81 people as they walked on two force plates while wearing shoes with three load cells. The three-axis GRF was calculated using a seq2seq approach based on long short-term memory (LSTM). To conduct the learning, validation, and testing, random selection was performed based on the subjects. The 60 selected participants were divided as follows: 37 were in the training set, 12 were in the validation set, and 11 were in the test set. The estimated GRF matched the force plate-measured GRF with correlation coefficients of 0.97, 0.96, and 0.90 and root mean square errors of 65.12 N, 15.50 N, and 9.83 N for the vertical, anterior-posterior, and medial-lateral directions, respectively, and there was a mid-stance timing error of 5.61% in the test dataset. A Bland-Altman analysis showed good agreement for the maximum vertical GRF. The proposed shoe with three uniaxial load cells and seq2seq LSTM can be utilized for estimating the 3D GRF in an outdoor environment with level ground and/or for gait research in which the subject takes several steps at their preferred walking speed, and hence can supply crucial data for a basic inverse dynamic analysis.

Dynamics analysis of the anterior cruciate ligament reconstruction surgery based on magnetic resonance imaging

ABSTRACT In clinical practice, anterior cruciate ligament (ACL) rupture is always repaired by the single-beam reconstruction method. Before the surgery, the surgeon made the diagnosis based on medical images, such as CT (computerized tomography) and MR (magnetic resonance) images. However, little is known about how biomechanics governs the biological nature for femoral tunnel position. In the present study, three volunteers’ motion trails were captured by six cameras when they were doing squat movement. The medical image can reconstruct the structure of the ligaments and bones and a left knee model was reconstructed by MIMICS by MRI data of DICOM format. Finally, the effects of different femoral tunnel positions on ACL biomechanics were characterized by the inverse dynamic analysis method. The results showed that there were significant differences in the direct mechanical effects of the anterior cruciate ligament at different locations of the femoral tunnel (p < 0.05), the peak stress of ACL in the low tension area was 1097.24 ± 25.55 N, and the peak stress of ACL in the distal femur was 356.81 ± 15.39 N, both of which were much higher than that in the direct fiber area (118.78 ± 20.68 N);

Equivalent system based inverse dynamics analysis of transfemoral prosthetic legs: Validation and application.

Inverse dynamics analysis of prosthetic legs with polycentric knees is complex due to increased number of links. The present work proposes a simple and general method called equivalent system (ES) analysis. The ES analysis provides forces and moment at hip joint as well as at the functional knee centre (FKC), the instant centre of the polycentric knee. The input to the ES analysis is the motion data. For validation of the proposed method, synthetic motion data for the swing phase of walking with prosthetic legs having different knees are generated by simulations using ADAMS. The hip kinetics evaluated by the proposed method is compared with that from ADAMS. The root mean square errors of the ES analysis are lower than 17 (10-6) N for hip reaction forces and 2.6 (10-6) Nm for the hip moments, thereby validating the proposed method. In order to demonstrate the application of the proposed methodology, the motion data of two transfemoral amputees using single-axis and four-bar knee prostheses are obtained during gait trials. The hip kinetics as well as kinetics at FKC are computed using ES analysis. Hip power during the swing phase is also evaluated and compared. The results are presented in this paper and discussed. The ES analysis is shown to be a versatile tool to provide insights into the human-mechanism interaction.

Present Status of Newborn Screening in Bangladesh through the Participation of Health Professionals

This paper suggests a biomechanical analysis of the joint motion of the arm based on the 3-dimensional motion analysis technique in the steering wheel action. The three-dimensional motion trajectory of the arm is obtained using the motion capture system, and the inverse kinematic analysis and inverse dynamics analysis are performed on the musculoskeletal model of the arm using this result. By doing this, the displacement of the arm joint and the magnitude of the joint torque are calculated. The rotational motion of each joint occurs simultaneously and in the joint motion, it can be confirmed that pronation-supination of the elbow joint, adduction-abduction of the shoulder joint, flexion-extension and flexion-extension of the wrist joint are the main movement parameters. Using this biomechanical motion analysis of joint segmental range of motion, it can be extended to analyze the behavior of passengers indoors in the autonomous vehicles.

A reduced-order closed-loop hybrid dynamic model for design and development of lower limb prostheses.

This manuscript presents a simplified dynamic human-prosthesis model and simulation framework for the purpose of designing and developing lower limb prosthesis hardware and controllers. The objective was to provide an offline design tool to verify the closed-loop behavior of the prosthesis with the human, in order to avoid relying solely on limiting kinematic and kinetic reference trajectories of (able-bodied) subjects and associated static or inverse dynamic analyses, while not having to resort to complete neuromusculoskeletal models of the human that require extensive optimizations to run. The presented approach employs a reduced-order model that includes only the prosthetic limb and trunk in a multi-body dynamic model. External forces are applied to the trunk during stance phase of the intact leg to represent its presence. Walking is realized by employing the well-known spring-loaded inverted pendulum model, which is shown to generate realistic dynamics on the prosthesis while maintaining a stable and modifiable gait. This simple approach is inspired from the rationale that the human is adaptive, and from the desire to facilitate modifications or inclusions of additional user actions. The presented framework is validated with two use cases, featuring a commercial and research knee prosthesis in combination with a passive ankle prosthesis, performing a continuous sequence of standing still, walking at different velocities and stopping.

Modeling and Simulation of a Wave Energy Converter: Multibody System Coupled to Fluid-Film Lubrication Model and Thermal Analysis

Sea wave energy is being increasingly regarded as one of the most promising sources of renewable energy. This paper deals with the modeling and simulation of an onshore wave energy converter system designed by UMBRA GROUP SpA. Several topics are addressed. Starting from the multibody modeling strategy, this paper delves more deeply into the mechanical efficiency evaluation of the ball-screw in the elastohydrodynamic lubrication regime, the core of the energy conversion process, as well as the thermal characterization of the power take-off module, based on the lumped-parameter and finite element method models. High values of ball-screw indirect efficiency have been observed, ranging from 73% to 97%; these results appear even more encouraging when compared to the performance of alternative energy-consuming technologies. Thermal analysis, on the other hand, provided a maximum temperature increase of 40 °C, allowing for the aversion of any structural collapse and the realistic identification of the lubrication regime, which turned out to be mostly mixed. Finally, an inverse multibody dynamic analysis is performed, and the most interesting simulation results are collected to prove the effectiveness of the proposed approach.

Inverse dynamic analysis for uncertain boundary condition parameters of a stepped beam subjected to an axial force

Generally, in engineering applications, the boundary condition parameters of axially loaded beam-like components with non-uniform cross-sections are unknown. This study investigates these uncertain parameters using inverse dynamic analysis of a stepped beam with elastic supports subjected to an axial force. A dynamic coefficient method is introduced in the dynamic analysis model to fundamentally overcome the numerical instability often encountered in traditional exact methods. Subsequently, a novel approach is proposed to evaluate the measurement error of the axial forces in an actual axially loaded beam-like component through inverse analysis of uncertain boundary condition parameters using two or only one observed natural frequency. The unknown rank orders of the measured natural frequencies can also be determined using the proposed method. Numerical examples are provided to verify the exactness and numerical robustness of the proposed method. Finally, during the construction of a real tied-arch bridge, the proposed approach was successfully applied to precisely control the tension forces of the bridge hangers.

A biomechanical analysis of skiing-related anterior cruciate ligament injuries based on biomedical imaging technology.

Alpine skiing is an attractive but highly risky sport, and the anterior cruciate ligament (ACL) tear is one of the most common diagnoses of skiing-related injuries. To better prevent such injuries among athletes and recreational skiers, we developed a facile and reliable biomechanical method to analyze the differences between "right" and "wrong" movements during skiing and their impacts on ACL stress loading. Unlike those conventional methods that are very difficult to implement and time-consuming, our method was developed based on inverse dynamics analyses and video capture, which were much easier to implement in the real-world setting. It is shown that, with a harmful skiing action, the knee joint's maximum reaction force significantly increases compared to nonharmful skiing actions. The peak front-and-rear force increased from 1242 N to 3105 N, and the peak axial force increased from 1023 N to 3443 N, which significantly exceeded the maximum tensile loading (2000 N) in the ACL. Our results are proven to be reliable and consistent with findings obtained with other methods. This method may substitute current complex analytical methods and be easier to apply in sports-related injury-prevention applications.