Static optimal estimation of joint accelerations for inverse dynamics problem solution

Errors in Estimating Lower-Limb Joint Angles and Moments during Walking Based on Pelvic Accelerations: Influence of Virtual Inertial Measurement Unit's Frontal Plane Misalignment

The accurate estimation of lower-limb joint angles and moments is crucial for assessing the progression of orthopedic diseases, with continuous monitoring during daily walking being essential. An inertial measurement unit (IMU) attached to the lower back has been used for this purpose, but the effect of IMU misalignment in the frontal plane on estimation accuracy remains unclear. This study investigated the impact of virtual IMU misalignment in the frontal plane on estimation errors of lower-limb joint angles and moments during walking. Motion capture data were recorded from 278 healthy adults walking at a comfortable speed. An estimation model was developed using principal component analysis and linear regression, with pelvic accelerations as independent variables and lower-limb joint angles and moments as dependent variables. Virtual IMU misalignments of -20°, -10°, 0°, 10°, and 20° in the frontal plane (five conditions) were simulated. The joint angles and moments were estimated and compared across these conditions. The results indicated that increasing virtual IMU misalignment in the frontal plane led to greater errors in the estimation of pelvis and hip angles, particularly in the frontal plane. For misalignments of ±20°, the errors in pelvis and hip angles were significantly amplified compared to well-aligned conditions. These findings underscore the importance of accounting for IMU misalignment when estimating these variables.

Bridging the sim2real gap. Investigating deviations between experimental motion measurements and musculoskeletal simulation results-a systematic review

Musculoskeletal simulations can be used to estimate biomechanical variables like muscle forces and joint torques from non-invasive experimental data using inverse and forward methods. Inverse kinematics followed by inverse dynamics (ID) uses body motion and external force measurements to compute joint movements and the corresponding joint loads, respectively. ID leads to residual forces and torques (residuals) that are not physically realistic, because of measurement noise and modeling assumptions. Forward dynamic simulations (FD) are found by tracking experimental data. They do not generate residuals but will move away from experimental data to achieve this. Therefore, there is a gap between reality (the experimental measurements) and simulations in both approaches, the sim2real gap. To answer (patho-) physiological research questions, simulation results have to be accurate and reliable; the sim2real gap needs to be handled. Therefore, we reviewed methods to handle the sim2real gap in such musculoskeletal simulations. The review identifies, classifies and analyses existing methods that bridge the sim2real gap, including their strengths and limitations. Using a systematic approach, we conducted an electronic search in the databases Scopus, PubMed and Web of Science. We selected and included 85 relevant papers that were sorted into eight different solution clusters based on three aspects: how the sim2real gap is handled, the mathematical method used, and the parameters/variables of the simulations which were adjusted. Each cluster has a distinctive way of handling the sim2real gap with accompanying strengths and limitations. Ultimately, the method choice largely depends on various factors: available model, input parameters/variables, investigated movement and of course the underlying research aim. Researchers should be aware that the sim2real gap remains for both ID and FD approaches. However, we conclude that multimodal approaches tracking kinematic and dynamic measurements may be one possible solution to handle the sim2real gap as methods tracking multimodal measurements (some combination of sensor position/orientation or EMG measurements), consistently lead to better tracking performances. Initial analyses show that motion analysis performance can be enhanced by using multimodal measurements as different sensor technologies can compensate each other's weaknesses.

Upper limb motor dysfunction is associated with fragmented kinetics after brain injury

BACKGROUND

Characterization of motor deficits after brain injury is important for rehabilitation personalization. While studies reported abnormalities in the kinematics of paretic and non-paretic elbow extension for patients with brain injuries, kinematic analysis is not sufficient to explore how patients deal with musculoskeletal redundancy and the energetic aspect of movement execution. Conversely, interarticular coordination and movement kinetics can reflect patients' motor strategies. This study investigates motor strategies of paretic and non-paretic upper limb after brain injury to highlight motor deficits or compensation strategies.

METHODS

26 brain-injured hemiplegic patients and 24 healthy controls performed active elbow extensions in the horizontal plane, with both upper limbs for patients and, with the dominant upper limb for controls. Elbow and shoulder kinematics, interarticular coordination, net joint kinetics were quantified.

FINDINGS

Results show alterations in kinematics, and a strong correlation between elbow and shoulder angles, as well as time to reach elbow and shoulder peak angular velocity in both upper limbs of patients. Net joint kinetics were lower for paretic limb and highlighted a fragmented motor strategy with increased number of transitions between concentric and eccentric phases.

INTERPRETATION

In complement to kinematic results, our kinetic results confirmed patients' difficulties to manage both spatially and temporally the joint degrees of freedom redundancy but revealed a fragmented compensatory motor strategy allowing patients upper limb extension despite quality alteration and decrease in energy efficiency. Motor rehabilitation should improve the management of this fragmentation strategy to improve the performance and the efficiency of active movement after brain injury.

Biomechanical modeling for the estimation of muscle forces: toward a common language in biomechanics, medical engineering, and neurosciences

Different research fields, such as biomechanics, medical engineering or neurosciences take part in the development of biomechanical models allowing for the estimation of individual muscle forces involved in motor action. The heterogeneity of the terminology used to describe these models according to the research field is a source of confusion and can hamper collaboration between the different fields. This paper proposes a common language based on lexical disambiguation and a synthesis of the terms used in the literature in order to facilitate the understanding of the different elements of biomechanical modeling for force estimation, without questioning the relevance of the terms used in each field or the different model components or their interest. We suggest that the description should start with an indication of whether the muscle force estimation problem is solved following the physiological movement control (from the nervous drive to the muscle force production) or in the opposite direction. Next, the suitability of the model for force production estimation at a given time or for monitoring over time should be specified. Authors should pay particular attention to the method description used to find solutions, specifying whether this is done during or after data collection, with possible method adaptations during processing. Finally, the presence of additional data must be specified by indicating whether they are used to drive, assist, or calibrate the model. Describing and classifying models in this way will facilitate the use and application in all fields where the estimation of muscle forces is of real, direct, and concrete interest.

Optimal estimation of complex aerial movements using dynamic optimisation

When estimating full-body motion from experimental data, inverse kinematics followed by inverse dynamics does not guarantee dynamical consistency of the resulting motion, especially in movements where the trajectory depends heavily on the initial state, such as in free-fall. Our objective was to estimate dynamically consistent joint kinematics and kinetics of complex aerial movements. A 42-degrees-of-freedom model with 95 markers was personalised for five elite trampoline athletes performing various backward and forward twisting somersaults. Using dynamic optimisation, our algorithm estimated joint angles, velocities and torques by tracking the recorded marker positions. Kinematics, kinetics, angular and linear momenta, and marker tracking difference were compared to results of an Extended Kalman Filter (EKF) followed by inverse dynamics. Angular momentum and horizontal linear momentum were conserved throughout the estimated motion, as per free-fall dynamics. Marker tracking difference went from 17 ± 4 mm for the EKF to 36 ± 11 mm with dynamic optimisation tracking the experimental markers, and to 49 ± 9 mm with dynamic optimisation tracking EKF joint angles. Joint angles from the dynamic optimisations were similar to those of the EKF, and joint torques were smoother. This approach satisfies the dynamics of complex aerial rigid-body movements while remaining close to the experimental 3D marker dataset.

Estimation of lower-limb sagittal joint moments during gait using vertical ground reaction force

Lower-limb sagittal joint moments during gait are important variables for evaluating the risk of disease progression, such as that of orthopedic diseases. Therefore, quantifying lower-limb sagittal joint moments during walking is important to continuously evaluate the risk of disease progression. A motion capture system and force plate are employed in the calculation of lower-limb sagittal joint moments during gait. However, they cannot be used during daily walking. Therefore, it is important to estimate these moments during walking from the vertical ground reaction force (vGRF), which can be measured using a wearable sensor, such as an insole device. Thus, this study aimed to estimate the lower-limb sagittal joint moments during gait using only the vGRF and confirmed its accuracy. This study included 188 healthy adults, and each participant walked at a comfortable speed (10 trials). We estimated the moments from the vGRF using a feedforward neural network. Our major findings are that our method can estimate lower-limb sagittal joint moments using the vGRF with accuracies of NRMSE¯ within 6.0-11.7% (NRMSEs¯ of the hip, knee, and ankle were 8.4, 11.7, and 6.0%, respectively). To the best of our knowledge, this study is the first to estimate lower-limb sagittal joint moments (including those of the hip, knee, and ankle joints) during gait using only the vGRF. Our method may be useful to estimate lower-limb sagittal joint moments during daily walking using only the vGRF, which can be measured by an insole device in the future.

Changes in intermuscular connectivity during active elbow extension reveal a functional simplification of motor control after stroke

Background

Stroke alters muscle co-activation and notably leads to exaggerated antagonist co-contraction responsible for impaired motor function. However, the mechanisms underlying this exaggerated antagonist co-contraction remain unclear. To fill this gap, the analysis of oscillatory synchronicity in electromyographic signals from synergistic muscles, also called intermuscular coherence, was a relevant tool.

Objective

This study compares functional intermuscular connectivity between muscle pairs of the paretic and non-paretic upper limbs of stroke subjects and the dominant limb of control subjects, concomitantly between two muscle pairs with a different functional role, through an intermuscular coherence analysis.

Methods

Twenty-four chronic stroke subjects and twenty-four healthy control subjects were included. Subjects performed twenty elbow extensions while kinematic data and electromyographic activity of both flexor and extensor elbow muscles were recorded. Intermuscular coherence was analyzed in the beta frequency band compared to the assessment of antagonist co-contraction.

Results

Intermuscular coherence was higher in the stroke subjects’ paretic limbs compared to control subjects. For stroke subjects, the intermuscular coherence of the antagonist-antagonist muscle pair (biceps brachii—brachioradialis) was higher than that of the agonist-antagonist muscle pair (triceps brachii—brachioradialis). For the paretic limb, intermuscular coherence of the antagonist-antagonist muscle pair presented a negative relationship with antagonist co-contraction.

Conclusion

Differences in intermuscular coherence between the paretic limbs of stroke subjects and control subjects suggest a higher common central drive during movement. Furthermore, results highlight the association between stroke-related alteration of intermuscular functional connectivity and the alteration of motor function.

Estimation of Joint Moments During Turning Maneuvers in Alpine Skiing Using a Three Dimensional Musculoskeletal Skier Model and a Forward Dynamics Optimization Framework

In alpine skiing, estimation of the joint moments acting onto the skier is essential to quantify the loading of the skier during turning maneuvers. In the present study, a novel forward dynamics optimization framework is presented to estimate the joint moments acting onto the skier incorporating a three dimensional musculoskeletal model (53 kinematic degrees of freedom, 94 muscles). Kinematic data of a professional skier performing a turning maneuver were captured and used as input data to the optimization framework. In the optimization framework, the musculoskeletal model of the skier was applied to track the experimental data of a skier and to estimate the underlying joint moments of the skier at the hip, knee and ankle joints of the outside and inside leg as well as the lumbar joint. During the turning maneuver the speed of the skier was about 14 m/s with a minimum turn radius of about 16 m. The highest joint moments were observed at the lumbar joint with a maximum of 1.88 Nm/kg for lumbar extension. At the outside leg, the highest joint moments corresponded to the hip extension moment with 1.27 Nm/kg, the knee extension moment with 1.02 Nm/kg and the ankle plantarflexion moment with 0.85 Nm/kg. Compared to the classical inverse dynamics analysis, the present framework has four major advantages. First, using a forward dynamic optimization framework the underlying kinematics of the skier as well as the corresponding ground reaction forces are dynamically consistent. Second, the present framework can cope with incomplete data (i.e., without ground reaction force data). Third, the computation of the joint moments is less sensitive to errors in the measurement data. Fourth, the computed joint moments are constrained to stay within the physiological limits defined by the musculoskeletal model.

Detecting differentially methylated regions using a fast wavelet-based approach to functional association analysis

Background

We present here a computational shortcut to improve a powerful wavelet-based method by Shim and Stephens (Ann Appl Stat 9(2):665–686, 2015. 10.1214/14-AOAS776) called WaveQTL that was originally designed to identify DNase I hypersensitivity quantitative trait loci (dsQTL).

Results

WaveQTL relies on permutations to evaluate the significance of an association. We applied a recent method by Zhou and Guan (J Am Stat Assoc 113(523):1362–1371, 2017. 10.1080/01621459.2017.1328361) to boost computational speed, which involves calculating the distribution of Bayes factors and estimating the significance of an association by simulations rather than permutations. We called this simulation-based approach “fast functional wavelet” (FFW), and tested it on a publicly available DNA methylation (DNAm) dataset on colorectal cancer. The simulations confirmed a substantial gain in computational speed compared to the permutation-based approach in WaveQTL. Furthermore, we show that FFW controls the type I error satisfactorily and has good power for detecting differentially methylated regions.

Conclusions

Our approach has broad utility and can be applied to detect associations between different types of functions and phenotypes. As more and more DNAm datasets are being made available through public repositories, an attractive application of FFW would be to re-analyze these data and identify associations that might have been missed by previous efforts. The full R package for FFW is freely available at GitHub https://github.com/william-denault/ffw.

Spastic co-contraction is directly associated with altered cortical beta oscillations after stroke

OBJECTIVE

Spastic co-contraction is a motor-disabling form of muscle overactivity occurring after a stroke, contributing to a limitation in active movement and a certain level of motor impairment. The cortical mechanisms underlying spastic co-contraction remain to be more fully elucidated, the present study aimed to investigate the role of the cortical beta oscillations in spastic co-contraction after a stroke.

METHOD

We recruited fifteen post-stroke participants and nine healthy controls. The participants were asked to perform active elbow extensions. In the study, multimodal analysis was performed to combine the evaluation of three-dimensional elbow kinematics, the elbow muscles electromyographic activations, and the cortical oscillatory activity.

RESULTS

The movement-related beta desynchronization was significantly decreased in post-stroke participants compared to healthy participants. We found a significant correlation between the movement-related beta desynchronization and the elbow flexors activation during the active elbow extension in post-stroke participants. When compared to healthy participants, post-stroke participants exhibited significant alterations in the elbow kinematics and greater muscle activation levels.

CONCLUSIONS

Cortical beta oscillation alterations may reflect an important neural mechanism underlying spastic co-contraction after a stroke.

SIGNIFICANCE

Measuring the cortical oscillatory activity could be useful to further characterize neuromuscular plasticity induced by recovery or therapeutic interventions.

Impact of the EMG normalization method on muscle activation and the antagonist-agonist co-contraction index during active elbow extension: Practical implications for post-stroke subjects

Electromyographic (EMG) raw signals are sensitive to intrinsic and extrinsic factors. Consequently, EMG normalization is required to draw proper interpretations of standardized data. Specific recommendations are needed regarding a relevant EMG normalization method for participants who show atypical EMG patterns, such as post-stroke subjects. This study compared three EMG normalization methods ("isometric MVC", "isokinetic MVC", "isokinetic MVC kinematic-related") on muscle activations and the antagonist-agonist co-contraction index. Fifteen post-stroke subjects and fifteen healthy controls performed active elbow extensions, followed by isometric and isokinetic maximum voluntary contractions (MVC). Muscle activations were obtained by normalizing EMG envelopes during active movement using a reference value determined for each EMG normalization method. The results showed no significant difference between the three EMG normalization methods in post-stroke subjects on muscle activation and the antagonist-agonist co-contraction index. We highlighted that the antagonist-agonist co-contraction index could underestimate the antagonist co-contraction in the presence of atypical EMG patterns. Based on its practicality and feasibility, we recommend the use of isometric MVC as a relevant procedure for EMG normalization in post-stroke subjects. We suggest combined analysis of the antagonist-agonist co-contraction index and agonist and antagonist activations to properly investigate antagonist co-contraction in the presence of atypical EMG patterns during movement.

Influence of body segment parameter estimation on calculated ground reaction forces in highly dynamic movements

The effect of body segment parameter estimation (BSP) on the inverse dynamics modelling results has not yet been demonstrated in specific groups during athletic movements with high segment accelerations. Therefore, the purpose of this study was to analyse this effect in ski-jumpers as representatives of a specific group (i.e. low body mass index) by comparing calculated and measured ground reaction forces during ski-jumping imitation jumps. Full body kinematics and vertical ground reaction forces were recorded of 9 ski-jumpers performing three imitation jumps each. BSP were estimated using three previously published, one individually optimized and one ski-jumper group specific model. Vertical ground reaction forces were calculated using the vertical acceleration of the segments as well as the BSP of the single models in a top-down approach. Statistical analysis revealed a main model effect concerning the root mean square error between the calculated and the measured ground reaction force with deviations between the models of 53%. Individual optimization and the application of the ski-jumper group specific model increased the accuracy of the calculated ground reaction forces by 11 and 7%, respectively, compared to the best performing published model. The results of inverse dynamics modelling are very sensitive to the BSP estimation for specific groups like ski-jumpers during movements incorporating high segment accelerations. This emphasizes the importance of selecting adequate BSP estimation models or methods when analysing specific groups in highly dynamic movements in order to increase the accuracy of the inverse dynamics analyses results.

Inverse dynamics of mechanical multibody systems: An improved algorithm that ensures consistency between kinematics and external forces

Inverse dynamics is a technique in which measured kinematics and, possibly, external forces are used to calculate net joint torques in a rigid body linked segment model. However, kinematics and forces are usually not consistent due to incorrect modelling assumptions and measurement errors. This is commonly resolved by introducing ‘residual forces and torques’ which compensate for this problem, but do not exist in reality. In this study a constrained optimization algorithm is proposed that finds the kinematics that are mechanically consistent with measured external forces and mimic the measured kinematics as closely as possible. The algorithm was tested on datasets containing planar kinematics and ground reaction forces obtained during human walking at three velocities (0.8 m/s, 1.25 and 1.8 m/s). Before optimization, the residual force and torque were calculated for a typical example. Both showed substantial values, indicating the necessity of developing a mechanically consistent algorithm. The proposed optimization algorithm converged to a solution in which the residual forces and torques were zero, without changing the ground reaction forces and with only minor changes to the measured kinematics. When using a rigid body approach, our algorithm ensures a consistent description of forces and kinematics, thereby improving the validity of calculated net joint torque and power values.

Estimation of muscle activation during different walking speeds with two mathematical approaches compared to surface EMG

BACKGROUND

Muscle force estimation could improve clinical gait analysis by enhancing insight into causes of impairments and informing targeted treatments. However, it is not currently standard practice to use muscle force models to augment clinical gait analysis, partly, because robust validations of estimated muscle activations, underpinning force modelling processes, against recorded electromyography (EMG) are lacking.

RESEARCH QUESTION

Therefore, in order to facilitate future clinical use, this study sought to validate estimated lower limb muscle activation using two mathematical models (static optimisation SO, computed muscle control CMC) against recorded muscle activations of ten healthy participants.

METHODS

Participants walked at five speeds. Visual agreement in activation onset and offset as well as linear correlation (r) and mean absolute error (MAE) between models and EMG were evaluated.

RESULTS

MAE between measured and recorded activations were variable across speeds (SO vs EMG 15-68%, CMC vs EMG 13-69%). Slower speeds resulted in smaller deviations (mean MAE < 30%) than faster speeds. Correlation was high (r > 0.5) for only 11/40 (CMC) and 6/40 (SO) conditions (muscles X speeds) compared to EMG.

SIGNIFICANCE

Modelling approaches do not yet show sufficient consistency of agreement between estimated and recorded muscle activation to support recommending immediate clinical adoption of muscle force modelling. This may be because assumptions underlying muscle activation estimations (e.g. muscles' anatomy and maximum voluntary contraction) are not yet sufficiently individualizable. Future research needs to find timely and cost efficient ways to scale musculoskeletal models for better individualisation to facilitate future clinical implementation.

Optimal Estimation of Anthropometric Parameters for Quantifying Multisegment Trunk Kinetics

Kinetics assessment of the human head-arms-trunk (HAT) complex via a multisegment model is a useful tool for objective clinical evaluation of several pathological conditions. Inaccuracies in body segment parameters (BSPs) are a major source of uncertainty in the estimation of the joint moments associated with the multisegment HAT. Given the large intersubject variability, there is currently no comprehensive database for the estimation of BSPs for the HAT. We propose a nonlinear, multistep, optimization-based, noninvasive method for estimating individual-specific BSPs and calculating joint moments in a multisegment HAT model. Eleven nondisabled individuals participated in a trunk-bending experiment and their body motion was recorded using cameras and a force plate. A seven-segment model of the HAT was reconstructed for each participant. An initial guess of the BSPs was obtained by individual-specific scaling of the BSPs calculated from the male visible human (MVH) images. The intersegmental moments were calculated using both bottom-up and top-down inverse dynamics approaches. Our proposed method adjusted the scaled BSPs and center of pressure (COP) offsets to estimate optimal individual-specific BSPs that minimize the difference between the moments obtained by top-down and bottom-up inverse dynamics approaches. Our results indicate that the proposed method reduced the error in the net joint moment estimation (defined as the difference between the net joint moment calculated via bottom-up and top-down approaches) by 79.3% (median among participants). Our proposed method enables an optimized estimation of individual-specific BSPs and, consequently, a less erroneous assessment of the three-dimensional (3D) kinetics of a multisegment HAT model.

Joint torque variability and repeatability during cyclic flexion-extension of the elbow

Background

Joint torques are generally of primary importance for clinicians to analyze the effect of a surgery and to obtain an indicator of functional capability to perform a motion. Given the current need to standardize the functional evaluation of the upper limb, the aim of this paper is to assess (1) the variability of the calculated maximal elbow joint torque during cyclic elbow flexion-extension movements and (2) participant test-retest repeatability in healthy young adults. Calculations were based on an existing non-invasive method including kinematic identification and inverse dynamics processes.

Methods

Twelve healthy young adults (male n = 6) performed 10 elbow flexion-extension movement carrying five different dumbbells (0, 1, 2, 3 and 4 kg) with several flexion-extension frequencies (½, ¹/₃, ¼ Hz) to evaluate peak elbow joint torques.

Results

Whatever the condition, the variability coefficient of trial peak torques remained under 4 %. Bland and Altman plot also showed good test-retest, whatever the frequency conditions for the 0, 1, 2, and 3 kg conditions.

Conclusion

The good repeatability of the flexion-extension peak torques represents a key step to standardize the functional evaluation of the upper limb.

Dynamically adjustable foot-ground contact model to estimate ground reaction force during walking and running

Human dynamic models have been used to estimate joint kinetics during various activities. Kinetics estimation is in demand in sports and clinical applications where data on external forces, such as the ground reaction force (GRF), are not available. The purpose of this study was to estimate the GRF during gait by utilizing distance- and velocity-dependent force models between the foot and ground in an inverse-dynamics-based optimization. Ten males were tested as they walked at four different speeds on a force plate-embedded treadmill system. The full-GRF model whose foot-ground reaction elements were dynamically adjusted according to vertical displacement and anterior-posterior speed between the foot and ground was implemented in a full-body skeletal model. The model estimated the vertical and shear forces of the GRF from body kinematics. The shear-GRF model with dynamically adjustable shear reaction elements according to the input vertical force was also implemented in the foot of a full-body skeletal model. Shear forces of the GRF were estimated from body kinematics, vertical GRF, and center of pressure. The estimated full GRF had the lowest root mean square (RMS) errors at the slow walking speed (1.0m/s) with 4.2, 1.3, and 5.7% BW for anterior-posterior, medial-lateral, and vertical forces, respectively. The estimated shear forces were not significantly different between the full-GRF and shear-GRF models, but the RMS errors of the estimated knee joint kinetics were significantly lower for the shear-GRF model. Providing COP and vertical GRF with sensors, such as an insole-type pressure mat, can help estimate shear forces of the GRF and increase accuracy for estimation of joint kinetics.

Residual Elimination Algorithm Enhancements to Improve Foot Motion Tracking During Forward Dynamic Simulations of Gait

Patient-specific gait optimizations capable of predicting post-treatment changes in joint motions and loads could improve treatment design for gait-related disorders. To maximize potential clinical utility, such optimizations should utilize full-body three-dimensional patient-specific musculoskeletal models, generate dynamically consistent gait motions that reproduce pretreatment marker measurements closely, and achieve accurate foot motion tracking to permit deformable foot-ground contact modeling. This study enhances an existing residual elimination algorithm (REA) Remy, C. D., and Thelen, D. G., 2009, “Optimal Estimation of Dynamically Consistent Kinematics and Kinetics for Forward Dynamic Simulation of Gait,” ASME J. Biomech. Eng., 131(3), p. 031005) to achieve all three requirements within a single gait optimization framework. We investigated four primary enhancements to the original REA: (1) manual modification of tracked marker weights, (2) automatic modification of tracked joint acceleration curves, (3) automatic modification of algorithm feedback gains, and (4) automatic calibration of model joint and inertial parameter values. We evaluated the enhanced REA using a full-body three-dimensional dynamic skeletal model and movement data collected from a subject who performed four distinct gait patterns: walking, marching, running, and bounding. When all four enhancements were implemented together, the enhanced REA achieved dynamic consistency with lower marker tracking errors for all segments, especially the feet (mean root-mean-square (RMS) errors of 3.1 versus 18.4 mm), compared to the original REA. When the enhancements were implemented separately and in combinations, the most important one was automatic modification of tracked joint acceleration curves, while the least important enhancement was automatic modification of algorithm feedback gains. The enhanced REA provides a framework for future gait optimization studies that seek to predict subject-specific post-treatment gait patterns involving large changes in foot-ground contact patterns made possible through deformable foot-ground contact models.

An algorithm to decompose ground reaction forces and moments from a single force platform in walking gait

In walking experimental conditions, subjects are sometimes unable to perform two steps on two different forceplates. This leads the authors to develop methods for discerning right and left ground reaction data while they are summed during the double support in walking. The aim of this study is to propose an adaptive transition function that considers the walking speed and ground reaction forces (GRF). A transition function is used to estimate left and right side GRF signals in double support. It includes a shape coefficient adjusted using single support GRF parameters. This shape coefficient is optimized by a non-linear least-square curve-fitting procedure to match the estimated signals with real GRF. A multiple regression is then performed to identify GRF parameters of major importance selected to compute the right and left GRF of the double support. Relative RMSE (RMSER), maximum GRF differences normalized to body mass and differences of center of pressure (CoP) are computed between real and decomposed signals. During double support, RMSER are 6%, 18%, 3.8%, 4.3%, 3%, and 12.3% for anterior force, lateral force, vertical force, frontal moment, sagittal moment and transverse moment, respectively. Maximum GRF differences normalized to body mass are lower than 1N/kg and mean CoP difference is 0.0135 m, when comparing real to decomposed signals during double support. This work shows the accuracy of an adaptive transition function to decompose GRF and moment of right and left sides. This method is especially useful to accurately discern right and left GRF data in single force platform configurations.

A dynamic finite element analysis of human foot complex in the sagittal plane during level walking

The objective of this study is to develop a computational framework for investigating the dynamic behavior and the internal loading conditions of the human foot complex during locomotion. A subject-specific dynamic finite element model in the sagittal plane was constructed based on anatomical structures segmented from medical CT scan images. Three-dimensional gait measurements were conducted to support and validate the model. Ankle joint forces and moment derived from gait measurements were used to drive the model. Explicit finite element simulations were conducted, covering the entire stance phase from heel-strike impact to toe-off. The predicted ground reaction forces, center of pressure, foot bone motions and plantar surface pressure showed reasonably good agreement with the gait measurement data over most of the stance phase. The prediction discrepancies can be explained by the assumptions and limitations of the model. Our analysis showed that a dynamic FE simulation can improve the prediction accuracy in the peak plantar pressures at some parts of the foot complex by 10%–33% compared to a quasi-static FE simulation. However, to simplify the costly explicit FE simulation, the proposed model is confined only to the sagittal plane and has a simplified representation of foot structure. The dynamic finite element foot model proposed in this study would provide a useful tool for future extension to a fully muscle-driven dynamic three-dimensional model with detailed representation of all major anatomical structures, in order to investigate the structural dynamics of the human foot musculoskeletal system during normal or even pathological functioning.

An optimization algorithm for joint mechanics estimate using inertial measurement unit data during a squat task

The use of dynamic optimization as a tool to estimate joint kinematics and kinetics, and ground reaction forces using data from a single inertial measurement unit (IMU) positioned on the lower trunk was investigated. The feasibility of this approach and its accuracy was explored for the analysis of a squat task, focusing on the ankle, knee and hip joints. An optimal motor control strategy aimed at minimizing the sum of the intersegmental couples and of their time derivatives was imposed to estimate the mechanics of a three-segment sagittal model. Moreover, in the optimization process constraints to the measured vertical acceleration, to the maximal vertical IMU excursion, and with regard to the maintenance of dynamic balance were imposed. Experiments were performed using 10 volunteers. Data were collected from the IMU, from a stereophotogrammetric system (SS) and from a force platform for validation purposes. Results showed a very good consistency of the model output with the lower limb joint trajectories, as obtained using the SS, and with the measured vertical component of the ground reaction (low root mean square differences (<10%) and high correlation coefficients (0.98)).

Comparative analysis of methods for estimating arm segment parameters and joint torques from inverse dynamics

A common problem in the analyses of upper limb unfettered reaching movements is the estimation of joint torques using inverse dynamics. The inaccuracy in the estimation of joint torques can be caused by the inaccuracy in the acquisition of kinematic variables, body segment parameters (BSPs), and approximation in the biomechanical models. The effect of uncertainty in the estimation of body segment parameters can be especially important in the analysis of movements with high acceleration. A sensitivity analysis was performed to assess the relevance of different sources of inaccuracy in inverse dynamics analysis of a planar arm movement. Eight regression models and one water immersion method for the estimation of BSPs were used to quantify the influence of inertial models on the calculation of joint torques during numerical analysis of unfettered forward arm reaching movements. Thirteen subjects performed 72 forward planar reaches between two targets located on the horizontal plane and aligned with the median plane. Using a planar, double link model for the arm with a floating shoulder, we calculated the normalized joint torque peak and a normalized root mean square (rms) of torque at the shoulder and elbow joints. Statistical analyses quantified the influence of different BSP models on the kinetic variable variance for given uncertainty on the estimation of joint kinematics and biomechanical modeling errors. Our analysis revealed that the choice of BSP estimation method had a particular influence on the normalized rms of joint torques. Moreover, the normalization of kinetic variables to BSPs for a comparison among subjects showed that the interaction between the BSP estimation method and the subject specific somatotype and movement kinematics was a significant source of variance in the kinetic variables. The normalized joint torque peak and the normalized root mean square of joint torque represented valuable parameters to compare the effect of BSP estimation methods on the variance in the population of kinetic variables calculated across a group of subjects with different body types. We found that the variance of the arm segment parameter estimation had more influence on the calculated joint torques than the variance of the kinematics variables. This is due to the low moments of inertia of the upper limb, especially when compared with the leg. Therefore, the results of the inverse dynamics of arm movements are influenced by the choice of BSP estimation method to a greater extent than the results of gait analysis.

Forward dynamics simulations provide insight into muscle mechanical work during human locomotion

Complex musculoskeletal models and computer simulations can provide critical insight into muscle mechanical work output during locomotion. Simulations provide both a consistent mechanical solution that can be interrogated at multiple levels (muscle fiber, musculotendon, net joint moment, and whole-body work) and an ideal framework to identify limitations with different estimates of muscle work and the resulting implications for metabolic cost and efficiency.

Optimal estimation of dynamically consistent kinematics and kinetics for forward dynamic simulation of gait

Forward dynamic simulation provides a powerful framework for characterizing internal loads and for predicting changes in movement due to injury, impairment or surgical intervention. However, the computational challenge of generating simulations has greatly limited the use and application of forward dynamic models for simulating human gait. In this study, we introduce an optimal estimation approach to efficiently solve for generalized accelerations that satisfy the overall equations of motion and best agree with measured kinematics and ground reaction forces. The estimated accelerations are numerically integrated to enforce dynamic consistency over time, resulting in a forward dynamic simulation. Numerical optimization is then used to determine a set of initial generalized coordinates and speeds that produce a simulation that is most consistent with the measured motion over a full cycle of gait. The proposed method was evaluated with synthetically created kinematics and force plate data in which both random noise and bias errors were introduced. We also applied the method to experimental gait data collected from five young healthy adults walking at a preferred speed. We show that the proposed residual elimination algorithm (REA) converges to an accurate solution, reduces the detrimental effects of kinematic measurement errors on joint moments, and eliminates the need for residual forces that arise in standard inverse dynamics. The greatest improvements in joint kinetics were observed proximally, with the algorithm reducing joint moment errors due to marker noise by over 20% at the hip and over 50% at the low back. Simulated joint angles were generally within 1 deg of recorded values when REA was used to generate a simulation from experimental gait data. REA can thus be used as a basis for generating accurate simulations of subject-specific gait dynamics.

Improving net joint torque calculations through a two-step optimization method for estimating body segment parameters

Two main sources of error in inverse dynamics based calculations of net joint torques are inaccuracies in segmental motions and estimates of anthropometric body segment parameters (BSPs). Methods for estimating BSP (i.e., segmental moment of inertia, mass, and center of mass location) have been previously proposed; however, these methods are limited due to low accuracies, cumbersome use, need for expensive medical equipment, and/or sensitivity of performance. This paper proposes a method for improving the accuracy of calculated net joint torques by optimizing for subject-specific BSP in the presence of characteristic and random errors in motion data measurements. A two-step optimization approach based on solving constrained nonlinear optimization problems was used. This approach minimized the differences between known ground reaction forces (GRFs), such as those measured by a force plate, and the GRF calculated via a top-down inverse dynamics approach. In step 1, a series of short calibration motions was used to compute first approximations of optimized segment motions and BSP for each motion. In step 2, refined optimal BSPs were derived from a combination of these motion profiles. We assessed the efficacy of this approach using a set of reference motions in which the true values for the BSP, segment motion, GRF, and net joint torques were known. To imitate real-world data, we introduced various noise conditions on the true motion and BSP data. We compared the root mean squared errors in calculated net joint torques relative to the true values due to the optimal BSP versus traditionally-derived BSP (from anthropometric tables derived from regression equations) and found that the optimized BSP reduced the error by 77%. These results suggest that errors in calculated net joint torques due to traditionally-derived BSP estimates could be reduced substantially using this optimization approach.

Whole body inverse dynamics over a complete gait cycle based only on measured kinematics

This paper presents a three-dimensional (3D) whole body multi-segment model for inverse dynamics analysis over a complete gait cycle, based only on measured kinematic data. The sequence of inverse dynamics calculations differs significantly from the conventional application of inverse dynamics using force plate data. A new validated "Smooth Transition Assumption" was used to solve the indeterminacy problem in the double support phase. Kinematic data is required for all major body segments and, hence, a whole body gait measurement protocol is presented. Finally, sensitivity analyses were conducted to evaluate the effects of digital filtering and body segment parameters on the accuracy of the prediction results. The model gave reasonably good estimates of sagittal plane ground forces and moment; however, the estimates in the other planes were less good, which we believe is largely due to their small magnitudes in comparison to the sagittal forces and moment. The errors observed are most likely caused by errors in the kinematic data resulting from skin movement artefact and by errors in the estimated body segment parameters. A digital filtering cut-off frequency of 4.5 Hz was found to produce the best results. It was also shown that errors in the mass properties of body segments can play a crucial role, with changes in properties sometimes having a disproportionate effect on the calculated ground reactions. The implication of these results is that, even when force plate data is available, the estimated joint forces are likely to suffer from similar errors.

Differences in the coordination of agonist and antagonist muscle groups in below-knee amputee and able-bodied children during dynamic exercise

A lack of co-contraction may predispose to knee instability or laxity, resulting in additional shear stress on the internal structures of the knee, especially in below-knee amputee (BKA) subjects. The purposes of this study were: (1) to provide information on how BKA children regulate agonist and antagonist muscle coordination, and (2) to quantify the level of knee co-contraction in able-bodied (AB) and BKA children during the stepping-in-place (SIP) task. Fourteen children (7 BKA vs. 7 AB), paired for age, weight and height, participated in this study. One-way ANOVA with Newman-Keuls post hoc tests (p<0.05) were used to compare peak power, the co-contraction index, and the resultant agonist and antagonist moments during different phases of SIP. Statistical analysis revealed that BKA children perform the task with similar kinematics than AB children while they generated less co-contraction in both their non-amputated limb and amputated limb, notably because the two groups of children used different agonist and antagonist muscles during the same periods of the SIP. This lack of co-contraction may reduce knee stability and may stress the internal structures of the knee in both the NAL and AL, and may lead to the development of premature knee osteoarthritis.

Uncertainties in inverse dynamics solutions: a comprehensive analysis and an application to gait

This paper presents a comprehensive analysis of the uncertainties in joint torque estimates derived through inverse dynamics. The analysis considered most of the quantifiable sources of inaccuracy in the input variables for inverse dynamics solutions (i.e., errors in body segment parameter estimates, joint center of rotation locations, force plate measurements, motion capture system measurements, and segment angle calculations due to skin movement artifacts). Estimates of inaccuracies were synthesized from existing literature and from a complementary set of experimental data. The analysis was illustrated and tested via an inverse dynamic analysis of gait, in which kinematic and force plate data from 10 adult subjects were recorded and used to calculate the planar (flexion/extension) torques at the ankle, knee, hip, elbow, shoulder, and bottom of torso. The results suggested that the uncertainties in torque estimates derived through inverse dynamics can be substantial (6-232% of the estimated torque magnitude); the time-varying uncertainty patterns do not resemble the torque profiles, and the magnitudes are smaller for more distal joints; the main contributors to these uncertainties were identified to be the inaccuracies in estimated segment angles and body segment parameters. The empirical test also showed that the uncertainty predicted by a more conservative (smaller) set of inaccuracy estimates was comparable to the statistical (3sigma) bound of the error. Implications in terms of how inverse dynamics solutions should be interpreted and improved, along with the limitations of the current work, are discussed.

Kinematic and kinetic analysis of a stepping-in-place task in below-knee amputee children compared to able-bodied children

It has been demonstrated that below-knee amputee (BKA) subjects use specific compensation strategies to overcome their physical limitations. Biomechanical studies emphasize that the motor strategies adopted by BKA adults differ between their amputated limb and their nonamputated limb and from those employed by able-bodied (AB) subjects. The purpose of this investigation was to compare the motor solutions used by control AB and BKA children during a stepping-in-place (SIP) task and to assess how they regulate the coordination of their nonamputated and amputated limbs during this task. Eight BKA children and eight AB children paired for gender, age, weight and height participated in our study. One-way analysis of variances (ANOVAs) were performed on peaks of angular excursion, moment, and power at the hip, knee, and ankle to compare motor strategies between the BKA and AB groups. The main results of our experiment showed that even if BKA and AB children did the task with almost the same kinematics, the kinetic data revealed completely different mechanisms of the two groups to achieve the SIP task, and BKA children had a symmetrical interlimb strategy. SIP, a simple task compared to gait at the level of neuro-musculoskeletal demands, could thus offer a transition task to physical therapists for below-knee recently-amputated children.

Posture Control and Complex Arm Coordination: Analysis of Multijoint Coordinative Movements and Stability of Stance

The authors addressed the interactions between control of bimanual multijoint coordination tasks and posture. Participants (N = 6) performed 8 coordination patterns that differed in degree of complexity by using their bilateral elbows and wrists under 3 scaled motion speeds while standing on 2 force plates. Results indicated that producing complex bimanual multijoint coordinative tasks affected postural sway, thus resulting in an increase of sway activity. Behavioral as well as mechanical factors accounted for the increased disturbance in postural sway. Those findings suggest that performing complex coordination tasks disrupts postural control in normal young adults.

Optimal Combination of Minimum Degrees of Freedom to be Actuated in the Lower Limbs to Facilitate Arm-Free Paraplegic Standing

Arm-free paraplegic standing via functional electrical stimulation (FES) has drawn much attention in the biomechanical field as it might allow a paraplegic to stand and simultaneously use both arms to perform daily activities. However, current FES systems for standing require that the individual actively regulates balance using one or both arms, thus limiting the practical use of these systems. The purpose of the present study was to show that actuating only six out of 12 degrees of freedom (12-DOFs) in the lower limbs to allow paraplegics to stand freely is theoretically feasible with respect to multibody stability and physiological torque limitations of the lower limb DOF. Specifically, the goal was to determine the optimal combination of the minimum DOF that can be realistically actuated using FES while ensuring stability and able-bodied kinematics during perturbed arm-free standing. The human body was represented by a three-dimensional dynamics model with 12-DOFs in the lower limbs. Nakamura’s method (Nakamura, Y., and Ghodoussi, U., 1989, “Dynamics Computation of Closed-Link Robot Mechanisms With Nonredundant and Redundant Actuators,” IEEE Trans. Rob. Autom., 5(3), pp. 294–302) was applied to estimate the joint torques of the system using experimental motion data from four healthy subjects. The torques were estimated by applying our previous finding that only 6 (6-DOFs) out of 12-DOFs in the lower limbs need to be actuated to facilitate stable standing. Furthermore, it was shown that six cases of 6-DOFs exist, which facilitate stable standing. In order to characterize each of these cases in terms of the torque generation patterns and to identify a potential optimal 6-DOF combination, the joint torques during perturbations in eight different directions were estimated for all six cases of 6-DOFs. The results suggest that the actuation of both ankle flexion∕extension, both knee flexion∕extension, one hip flexion∕extension, and one hip abduction∕adduction DOF will result in the minimum torque requirements to regulate balance during perturbed standing. To facilitate unsupported FES-assisted standing, it is sufficient to actuate only 6-DOFs. An optimal combination of 6-DOFs exists, for which this system can generate able-bodied kinematics while requiring lower limb joint torques that are producible using contemporary FES technology. These findings suggest that FES-assisted arm-free standing of paraplegics is theoretically feasible, even when limited by the fact that muscles actuating specific DOFs are often denervated or difficult to access.

Identification of human-generated forces on wheelchairs during total-body extensor thrusts

BACKGROUND

Involuntary extensor thrust experienced by wheelchair users with neurological disorders may cause injuries via impact with the wheelchair, lead to the occupant sliding out of the seat, and also damage the wheelchair. The concept of a dynamic seat, which allows movement of a seat with respect to the wheelchair frame, has been suggested as a potential solution to provide greater freedom and safety. Knowledge of the human-generated motion and forces during unconstrained extensor thrust events is of great importance in developing more comfortable and effective dynamic seats. The objective of this study was to develop a method to identify human-generated motions and forces during extensor thrust events. This information can be used to design the triggering system for a dynamic seat.

METHODS

An experimental system was developed to automatically track the motions of the wheelchair user using a video camera and also measure the forces at the footrest. An inverse dynamic approach was employed along with a three-link human body model and the experimental data to predict the human-generated forces.

FINDINGS

Two kinds of experiments were performed: the first experiment validated the proposed model and the second experiment showed the effects of the extensor thrust speed, the footrest angle, and the seatback angle. The proposed method was tested using a sensitivity analysis, from which a performance index was deduced to help indicate the robust region of the force identification.

INTERPRETATION

A system to determine human-generated motions and forces during unconstrained extensor thrusts was developed. Through experiments and simulations, the effectiveness and reliability of the developed system was established.