Calculate Joint Moments Research Articles

THE USE OF MODEL DISTRIBUTIONS IN THE ANALYSIS OF QUEUING SYSTEMS WITH CORRELATED ARRIVALS

The article considers the task of determining the waiting time for a request in a queue in a general-type single-channel queueing system when time intervals between incoming requests are correlated. For solving the task, it is proposed to carry out decorrelation of specified time intervals using the discrete cosine transform. Generally, to analyze arbitrary distributions included in the expression for a decorrelated sequence, one can suggest an approach based on the approximation of unknown densities by a model distribution. The calculation of cumulants and moments of random variables is very simple compared to the analytical methods. Based on the found final set of cumulants, a model probability density can always be reproduced with a certain error. Generally, to calculate the average waiting time of a request in a queue, it is necessary to determine the correlation properties and one-dimensional probability density of time intervals between incoming requests, synthesize a two-dimensional probability density of a sequence of given intervals that has a measured correlation function, and, further, calculate joint moments and cumulants for correlated values, on which their model density is built.

Analysis of maximum joint moment during infant lifting-up motion.

BACKGROUND: Infant care activities can induce musculoskeletal disease. However, little is known about the biomechanical joint load during lifting-up of an infant.OBJECTIVE: The aim of this study was to investigate normalized maximum moment during lifting-up of infant dummies weighing 4.6 kg, 7.6 kg, and 9.8 kg.METHODS: Six healthy young subjects participated in our study. All subjects performed lifting-up activities of dummies to shoulder height with their feet apart and natural postures in their comfortable speed. Three-dimensional reflective marker trajectories and ground reaction forces were used as input to calculate joint moments using a full body musculoskeletal model. Joint moments were normalized by each subject’s body mass. Friedman’s test was performed to compare mean differences of normalized joint moments for lifting up three dummy weights.RESULTS: Lumbar joint had the greatest normalized joint moment. Lumbar and hip extension moments were significantly increased with dummy weight ( 0.05). In contrast, knee extension and ankle plantarflexion moment were not significantly affected by dummy weight ( 0.05).CONCLUSIONS: These results indicate that the lumbar joint plays the most important role in infant lifting-up motion and that the load of lumbar and hip joint should be reduced when lifting a heavier infant. These results could contribute to the development of an effective lifting strategy and an assisting device for lifting an infant.

Design of a wearable upper limb rehabilitation robot and its motion simulation and dynamics analysis

<p><strong>Objective:</strong> A new wearable upper limb rehabilitation robot is designed to address the disadvantages of the current desktop upper limb rehabilitation robot, which is bulky and inconvenient to move, and the rationality of the design is verified through the analysis of its motion characteristics and the calculation of joint moments. <strong>Methods:</strong> Firstly, according to the principle of modular design, the overall structure was designed. Secondly, the SOILDWORKS is used for three-dimensional modeling, and the SOILDWORKS Motion is used to simulate the elbow flexion/extension movement, shoulder flexion/extension movement and shoulder-elbow joint linkage movement of the robot. Finally, the dynamic equation of the system is established based on Lagrange method, and the change curve of the joint torque of the manipulator is calculated by MATLAB software. <strong>Results:</strong> The simulation results confirmed that the motion simulation curves of shoulder joint, elbow joint and wrist joint were smooth. The dynamic analysis confirmed that the joint torque variation curve was smooth and the maximum joint torque was less than the rated torque of the motor after deceleration. <strong>Conclusion:</strong> The design of wearable upper limb rehabilitation robot is reasonable, which lays a theoretical foundation for the subsequent research on upper limb rehabilitation robot.</p>

A fair and EMG-validated comparison of recruitment criteria, musculotendon models and muscle coordination strategies, for the inverse-dynamics based optimization of muscle forces during gait

Experimental studies and EMG collections suggest that a specific strategy of muscle coordination is chosen by the central nervous system to perform a given motor task. A popular mathematical approach for solving the muscle recruitment problem is optimization. Optimization-based methods minimize or maximize some criterion (objective function or cost function) which reflects the mechanism used by the central nervous system to recruit muscles for the movement considered. The proper cost function is not known a priori, so the adequacy of the chosen function must be validated according to the obtained results. In addition of the many criteria proposed, several physiological representations of the musculotendon actuator dynamics (that prescribe constraints for the forces) along with different musculoskeletal models can be found in the literature, which hinders the selection of the best neuromusculotendon model for each application. Seeking to provide a fair base for comparison, this study measures the efficiency and accuracy of: (i) four different criteria within the static optimization approach (where the physiological character of the muscle, which affects the constraints of the forces, is not considered); (ii) three physiological representations of the musculotendon actuator dynamics: activation dynamics with elastic tendon, simplified activation dynamics with rigid tendon and rigid tendon without activation dynamics; (iii) a synergy-based method; all of them within the framework of inverse-dynamics based optimization. Motion/force/EMG gait analyses were performed on ten healthy subjects. A musculoskeletal model of the right leg actuated by 43 Hill-type muscles was scaled to each subject and used to calculate joint moments, musculotendon kinematics and moment arms. Muscle activations were then estimated using the different approaches, and these estimates were compared with EMG measurements. Although no significant differences were obtained with all the methods at statistical level, it must be pointed out that a higher complexity of the method does not guarantee better results, as the best correlations with experimental values were obtained with two simplified approaches: the static optimization and the physiological approach with simplified activation dynamics and rigid tendon, both using the sum of the squares of muscle forces as objective function.

Do Muscle Synergies Improve Optimization Prediction of Muscle Activations During Gait?

Determination of muscle forces during motion can help to understand motor control, assess pathological movement, diagnose neuromuscular disorders, or estimate joint loads. Difficulty of in vivo measurement made computational analysis become a common alternative in which, as several muscles serve each degree of freedom, the muscle redundancy problem must be solved. Unlike static optimization (SO), synergy optimization (SynO) couples muscle activations across all time frames, thereby altering estimated muscle co-contraction. This study explores whether the use of a muscle synergy structure within an SO framework improves prediction of muscle activations during walking. A motion/force/electromyography (EMG) gait analysis was performed on five healthy subjects. A musculoskeletal model of the right leg actuated by 43 Hill-type muscles was scaled to each subject and used to calculate joint moments, muscle–tendon kinematics, and moment arms. Muscle activations were then estimated using SynO with two to six synergies and traditional SO, and these estimates were compared with EMG measurements. Synergy optimization neither improved SO prediction of experimental activation patterns nor provided SO exact matching of joint moments. Finally, synergy analysis was performed on SO estimated activations, being found that the reconstructed activations produced poor matching of experimental activations and joint moments. As conclusion, it can be said that, although SynO did not improve prediction of muscle activations during gait, its reduced dimensional control space could be beneficial for applications such as functional electrical stimulation or motion control and prediction.

COMPARING METHODS FOR 3D INVERSE DYNAMICS ANALYSIS OF SQUAT LIFTING USING A FULL BODY LINKED SEGMENT MODEL

Objective: The main objective of this study was to assess the accuracy of bottom-up solution for three-dimensional (3D) inverse dynamics analysis of squat lifting using a 3D full body linked segment model. Least squares solution was used in this study as reference for assessment of the accuracy of bottom-up solution. Findings of this study may clarify how much the bottom-up solution can be reliable for calculating the joint kinetics in 3D inverse dynamics problems. Methods: Ten healthy males volunteered to perform squat lifting of a box with a load of one-tenth of their body weights. The joint moments were calculated using 110 reflective passive markers (46 anatomical markers and 64 tracking markers) and a 3D full body linked segment model. Ground reaction forces and kinematics data were recorded using a Vicon system with two parallel Kistler force plates. Three-dimensional Newton–Euler equations of motion with bottom-up and least squares solutions were applied to calculate joint moments. The peak and mean values of the joint moments were determined to check the quantitative differences as well as the time-to-peak value of the moment curves was determined to check the temporal differences between the two inverse dynamics solutions. Results: Significant differences (all [Formula: see text]-[Formula: see text]) between the two inverse dynamics solutions were detected for the peak values of the hip (right and left sides) and L5–S1 joint moments in the lateral anatomical direction as well significant differences (all [Formula: see text]-[Formula: see text]) were detected for the peak and mean values of the L5–S1 joint moment in all anatomical directions. Moreover, small differences (all [Formula: see text]) were detected between the two inverse dynamic solutions for the calculated lower body joint moments. Conclusions: The findings of this study clarified the disadvantages of the straightforward solutions and demonstrated that the bottom-up solution may not be accurate for more distal measures from the force plate (for hip and S1–L5) but it may be accurate for more proximal joints (ankle and knee) in 3D inverse dynamics analysis.

Between-Limb Differences in Patellofemoral Joint Forces During Running at 12 to 24 Months After Unilateral Anterior Cruciate Ligament Reconstruction

Background: Patellofemoral joint (PFJ) osteoarthritis may occur after anterior cruciate ligament reconstruction (ACLR). The mechanisms underpinning the development of PFJ osteoarthritis are not known but may relate to altered PFJ loading. Few studies have assessed PFJ loads during high-impact tasks, such as running, beyond the acute rehabilitation phase (ie, >12 months) after ACLR. Purpose/Hypothesis: The purpose was to compare between-limb joint angles, joint moments, and PFJ contact force during running in individuals at 12 to 24 months after unilateral ACLR. We hypothesized that peak knee flexion angle, knee extension moment, and PFJ contact force during stance would be lower in the ACLR limb compared with the uninjured limb. Study Design: Controlled laboratory study. Methods: A total of 55 participants (mean ± SD age, 28 ± 7 years), 12 to 24 months after ACLR, ran at a self-selected speed (2.9 ± 0.3 m/s). Measured kinematics and ground-reaction forces were input into musculoskeletal models to calculate joint moments and muscle forces. These values were subsequently input into a PFJ model to calculate contact force peak and impulse. Outcome measures were compared between the ACLR and uninjured limbs. Results: In the ACLR limb, compared with the uninjured limb, the PFJ contact force displayed a lower peak (ACLR, 6.1 ± 1.3 body weight [BW]; uninjured, 6.7 ± 1.4 BW; P < .001) and impulse (ACLR, 0.72 ± 0.17 BW*seconds [BWs]; uninjured, 0.81 ± 0.17 BWs; P < .001). At the time of the peak PFJ contact force, the knee extension moment was lower in the ACLR limb (ACLR, 14.0 ± 2.4 %BW*height [%BW*HT]; uninjured, 15.5 ± 2.5 %BW*HT; P < .001). The opposite was true for the ankle plantarflexion moment (ACLR, 12.1 ± 2.6 %BW*HT; uninjured, 11.5 ± 2.7 %BW*HT; P = .019) and the hip extension moment (ACLR, 2.3 ± 2.5 %BW*HT; uninjured, 1.6 ± 2.3 %BW*HT; P = .013). The foot-ground center of pressure was located more anteriorly with respect to the ankle joint center (ACLR, 5.8 ± 0.9 %height [%HT]; uninjured, 5.4 ± 1.0 %HT; P = .001). No differences were found for the sagittal plane hip, knee, and ankle angles. Conclusion: The ACLR limb experienced lower peak PFJ loads during running, explained by a small anterior shift in the foot-ground center of pressure during stance that offloaded the torque demand away from the ACLR knee. Clinical Relevance: Lower net PFJ loading during running in the ACLR limb more than 12 months after ACLR suggests that underloading might play a role in the onset of PFJ osteoarthritis after ACLR.

COMPARING METHODS FOR 3D INVERSE DYNAMICS ANALYSIS OF SQUAT LIFTING USING A FULL BODY LINKED SEGMENT MODEL

Objective: The main objective of this study was to assess the accuracy of bottom-up solution for three-dimensional (3D) inverse dynamics analysis of squat lifting using a 3D full body linked segment model. Least squares solution was used in this study as reference for assessment of the accuracy of bottom-up solution. Findings of this study may clarify how much the bottom-up solution can be reliable for calculating the joint kinetics in 3D inverse dynamics problems. Methods: Ten healthy males volunteered to perform squat lifting of a box with a load of one-tenth of their body weights. The joint moments were calculated using 110 reflective passive markers (46 anatomical markers and 64 tracking markers) and a 3D full body linked segment model. Ground reaction forces and kinematics data were recorded using a Vicon system with two parallel Kistler force plates. Three-dimensional Newton–Euler equations of motion with bottom-up and least squares solutions were applied to calculate joint moments. The peak and mean values of the joint moments were determined to check the quantitative differences as well as the time-to-peak value of the moment curves was determined to check the temporal differences between the two inverse dynamics solutions. Results: Significant differences (all [Formula: see text]-values [Formula: see text]) between the two inverse dynamics solutions were detected for the peak values of the hip (right and left sides) and L5–S1 joint moments in the lateral anatomical direction as well significant differences (all [Formula: see text]-values [Formula: see text]) were detected for the peak and mean values of the L5–S1 joint moment in all anatomical directions. Moreover, small differences (all RMSEs [Formula: see text]%) were detected between the two inverse dynamic solutions for the calculated lower body joint moments. Conclusions: The findings of this study clarified the disadvantages of the straightforward solutions and demonstrated that the bottom-up solution may not be accurate for more distal measures from the force plate (for hip and S1–L5) but it may be accurate for more proximal joints (ankle and knee) in 3D inverse dynamics analysis.

Flatter ground reaction force patterns are associated with incident knee pain over two years: the multicenter osteoarthritis study (MOST)

Purpose: Identifying modifiable risk factors related to knee osteoarthritis (OA) progression could be key to reducing the burden of knee OA. Prior studies have reported that features of knee joint moments during walking are associated with symptomatic and structural worsening of knee OA. Measurement of joint moments is resource and time-intensive, therefore, prior longitudinal studies have been relatively small (n∼20-200). Ground reaction forces (GRF), which are one component of joint moment calculations, can be measured with relative ease in large cohorts.

The effects of tai chi chuan exercise training on countermovement jump performance in the elderly

ABSTRACT This study sought to compare the biomechanical parameters of the lower extremities during a countermovement jump in elderly people who are engaged in frequent practice of tai chi chuan (TCG) and in the general population of healthy elderly people (HG). Each group included 12 participants. Ten Vicon Motion System infrared cameras and two Kistler force plates were employed for measurement. The jump height, duration, centre of mass (COM) displacement, joint ROM, and upward velocity were analysed in this study. Motion analysis and force platform data were combined to calculate joint moments and powers during the takeoff phase. The data were analysed using independent sample t-tests. The results showed that the tai chi chuan practitioner group (0.13 m) achieved 44% higher jump heights (p < 0.05). The COM displacement during squatting was lower in the TCG (0.25 m) than in the HG (0.19 m) (p < 0.05). The knee and ankle ROMs of the TCG were higher than those of the HG (p < 0.05). Peak knee moment 23% and peak knee power 32% higher in TCG compared to the HG (p < 0.05), suggesting that frequent practice of tai chi chuan may slow the rate of knee degeneration.

Clinical Applicability of an Existing Proportionality Scheme in Three-Segment Kinetic Foot Models.

An important methodological challenge in multi-segment kinetic foot models is to partition the total ground reaction force across different foot segments. Several studies applied a proportionality scheme based on the combination of a pressure- and force platform. A recent study highlighted distinct errors in the partitioning of shear forces when using this proportionality scheme. To date, the impact of this shear force partitioning error analysis on joint moment calculations using inverse dynamic calculations in pathological gait is not known. Hence, the goal of this study was to investigate the clinical applicability of an existing proportionality scheme by extending the shear force partitioning error analysis towards joint moment calculations. Both healthy (n = 10) and pathological gait (n = 10) was assessed using (I) an adjacent force plate method and (II) the estimation method based on an existing proportionality scheme. A correction factor matrix was developed to compensate for the shear force partitioning errors in the estimation method. Extending the shear force partitioning error analysis towards joint moments using inverse dynamic calculations, did not reveal significant differences when comparing corrected joint moments with the estimated joint moments in both healthy and pathological gait.

Effects of aerial ladder rung spacing on firefighter climbing biomechanics

This study investigated the effects of aerial ladder rung spacing on firefighter climbing biomechanics. Ten female and 9 male firefighters ascended and descended instrumented ladders with rungs spaced at 356 mm (current design) and 305 mm in a laboratory setup. The climbing tests were performed at five ladder slope and handrail conditions: 30° with low (305 mm) and high (914 mm) handrails, 52.5° with and without a low handrail, and 75° without a handrail. Foot and hand forces and body movements were recorded and used to calculate joint moments of the upper and lower body. Reduced rung spacing resulted in reduced foot forces, reduced hand forces, and reduced ankle transverse moment. It was also associated with increased climbing speed for female climbers, and increased ankle vertical overshoot. The results indicate that reduced rung spacing on aerial ladders may lead to lower biomechanical stress; better climbing efficiency and safety; and reduced climbing speed disparity across sexes.

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.

DYNAMIC ANALYSIS OF THREE DIFFERENT HIGH BAR DISMOUNTS IN THE SIMMECHANICS ENVIRONMENT

This study compares certain kinematic and kinetic parameters in giant circles performed before twisting, double stretched and double tucked dismounts using the dynamic model in the SimMechanics environment. The joint moments calculated using the designed model were investigated for the three different dismounts. The study included a 13-year-old voluntary national gymnast with seven years of training history. Markers were placed on the wrist, elbow, shoulder, hip, knee and ankle joints of the gymnast. The gymnast was asked to perform twisting, double stretched and double tucked dismounts. MATLAB and SimMechanics were used to calculate joint moments. The moves were simulated and the joint moments during the moves were calculated using the SimMechanics toolbox. The study observed that the highest joint moment was in the wrist joint in all three dismounts, in line with the findings of previous studies. However, unlike other studies, higher joint moments were calculated in the accelerated giant circle performed together with thrusts, compared with the regular giant circle. While there were similar maximum moment values in twisting dismounts and double tucked dismounts, an almost three times higher moment was observed in double stretched dismounts. In terms of joint moments, stretched dismount is obviously the most difficult move, which is consistent with the difficulty levels. A recorded performance of the mechanical model created in the SimMechanics environment was investigated in terms of the twist angle and moments generated on the bar, and found to be sufficient and useful. However, there are certain restrictions regarding the methods employed in this study. We concluded that the mechanical model will allow for the performance of kinematic and kinetic analyses of different gymnasts and types of moves thanks to its flexible structure.

Estimation of foot joint kinetics in three and four segment foot models using an existing proportionality scheme: Application in paediatric barefoot walking

Recent studies which estimated foot segment kinetic patterns were found to have inconclusive data on one hand, and did not dissociate the kinetics of the chopart and lisfranc joint. The current study aimed therefore at reproducing independent, recently published three-segment foot kinetic data (Study 1) and in a second stage expand the estimation towards a four-segment model (Study 2).Concerning the reproducibility study, two recently published three segment foot models (Bruening et al., 2014; Saraswat et al., 2014) were reproduced and kinetic parameters were incorporated in order to calculate joint moments and powers of paediatric cohorts during gait. Ground reaction forces were measured with an integrated force/pressure plate measurement set-up and a recently published proportionality scheme was applied to determine subarea total ground reaction forces. Regarding Study 2, moments and powers were estimated with respect to the Instituto Ortopedico Rizzoli four-segment model. The proportionality scheme was expanded in this study and the impact of joint centre location on kinetic data was evaluated.Findings related to Study 1 showed in general good agreement with the kinetic data published by Bruening et al. (2014). Contrarily, the peak ankle, midfoot and hallux powers published by Saraswat et al. (2014) are disputed. Findings of Study 2 revealed that the chopart joint encompasses both power absorption and generation, whereas the Lisfranc joint mainly contributes to power generation.The results highlights the necessity for further studies in the field of foot kinetic models and provides a first estimation of the kinetic behaviour of the Lisfranc joint.

Effect of Running Speed on Achilles Tendon Injury Potential

: Previous literature has suggested that increasing running speed is associated with a reduction in cumulative load per distance traveled and thereby a decrease in injury risk. However, the tissue damage incurred by a bout of loading is a function of its stress-life (S-N) behavior which describes the exponential relationship between loading magnitude and cycles to failure. Current cumulative loading measures do not consider the S-N relationship which may in fact lead to erroneous conclusions about tissue damage and injury risk. PURPOSE: The purpose of this study was to examine the influence of running speed on an S-N weighted impulse measure at the Achilles tendon. METHODS: Ten participants ran overground at 2.5, 3.5, and 4.5 m/s while force and motion capture data were recorded. An inverse dynamics analysis was used to calculate joint moments and AT force was calculated from the ankle joint moment and the AT moment arm which was a function of ankle joint angle. AT impulse per step was calculated as the time integral of the AT force curve. A weighted impulse measure was quantified where AT force was raised to the power of 9. This value was derived from in vitro tendon testing and describes the slope of the S-N tendon curve. Impulse and weighted impulse per km were calculated as the respective impulse per step measures multiplied by the number of steps necessary to run 1km. A Friedman test examined the main effect of speed followed by Bonferroni adjusted pair-wise comparisons. RESULTS: A significant main effect of speed was observed for impulse per step (p=0.003), impulse per km (p<0.001) and weighted impulse per km (p<0.001). In general, the impulse per step and impulse per km decreased with running speed (p≤0.013); however, no significant differences were observed between 3.5 and 2.5 m/s (p≥0.047). On the other hand, the weighted impulse per km increased with running speed (p=0.005). CONCLUSION: Using a traditional measure of cumulative impulse suggests that running faster may decrease the risk of Achilles tendon injury. This counterintuitive conclusion is not reached when using a weighted impulse measure that considers the S-N behavior of the tendon.

Medial knee joint contact force in the intact limb during walking in recently ambulatory service members with unilateral limb loss: a cross-sectional study.

BackgroundIndividuals with unilateral lower limb amputation have a high risk of developing knee osteoarthritis (OA) in their intact limb as they age. This risk may be related to joint loading experienced earlier in life. We hypothesized that loading during walking would be greater in the intact limb of young US military service members with limb loss than in controls with no limb loss.MethodsCross-sectional instrumented gait analysis at self-selected walking speeds with a limb loss group (N = 10, age 27 ± 5 years, 170 ± 36 days since last surgery) including five service members with transtibial limb loss and five with transfemoral limb loss, all walking independently with their first prosthesis for approximately two months. Controls (N = 10, age 30 ± 4 years) were service members with no overt demographical risk factors for knee OA. 3D inverse dynamics modeling was performed to calculate joint moments and medial knee joint contact forces (JCF) were calculated using a reduction-based musculoskeletal modeling method and expressed relative to body weight (BW).ResultsPeak JCF and maximum JCF loading rate were significantly greater in limb loss (184% BW, 2,469% BW/s) vs. controls (157% BW, 1,985% BW/s), with large effect sizes. Results were robust to probabilistic perturbations to the knee model parameters.DiscussionAssuming these data are reflective of joint loading experienced in daily life, they support a “mechanical overloading” hypothesis for the risk of developing knee OA in the intact limb of limb loss subjects. Examination of the evolution of gait mechanics, joint loading, and joint health over time, as well as interventions to reduce load or strengthen the ability of the joint to withstand loads, is warranted.

FEASIBILITY STUDY FOR ANFIS AND EMG UTILIZATION IN MODELING PROSTHESIS FOR TRANS-FEMORAL CUT REHABILITATION AND GAIT CYCLE RESTORATION

Rehabilitation of lower limbs with high-level amputation (Trans-femoral Cut) requires an alternative method of inverse and forward dynamics to be employed. Inverse and forward dynamics are capable of solving the problem of redundancy of muscles in human lower limbs. Furthermore, inverse and forward dynamics can be used for estimating joints moments, predicting body segment kinematics, and estimating the distribution of forces between the agonist/antagonist muscle group with reasonable accuracy [Riener R, Lünenburger L, Colombo G, Human-Centered robotics applied to gait training and assessment robert, J Rehabil Res Dev43:679, 2006; Keller T, Perry JC, Rehabilitation robotics for outpatient clinical and domestic use, WC IFMBE Proc25:291, 2009; Crespo LM, Reinkensmeyer DJ, Review of control strategies for robotic movement training after neurologic injury, J Neuroeng Rehabil6:20, 2009; Hillman MI, Rehabilitation robotics from past to present — A historical prespective, Adv Rehabil Robotics, Lect Notes Contr Inf306:25, 2004.]. However, the application of these methods, in rehabilitation, is still limited due to their dependence on multiple input data that cannot be measured using conventional measurement tools. This study is aimed at verifying and validating new models which are capable of predicting body segment kinematics accurately using features obtained from electromyography (EMG) and adaptive neuro fuzzy inference system (ANFIS). These features are used to model a set of (input\output) dynamic data. EMG signals obtained from full gait cycle trials of a subject are used to calculate joint moments. Kinematics of the body segments are obtained by applying Euler numerical integration. The relative percentage root mean square (RMS) error between predicted kinematics from ANFIS and measured values for hip, knee, and ankle were 2.23%, 0.98%, and 0.69%, respectively. However, the achieved minimal reasonable accuracy for minimum number of measured inputs depends on the characteristics of the gait parameters such as cyclic nature and delayed symmetric activities between right and left leg about mid sagittal plane. Results of the combined model show that higher prediction accuracy of the gait cycle is achieved and so rehabilitation of lower limbs is feasible.

Sensitivity analysis of human lower extremity joint moments due to changes in joint kinematics

Despite the widespread applications of human gait analysis, causal interactions between joint kinematics and joint moments have not been well documented. Typical gait studies are often limited to pure multi-body dynamics analysis of a few subjects which do not reveal the relative contributions of joint kinematics to joint moments.This study presented a computational approach to evaluate the sensitivity of joint moments due to variations of joint kinematics. A large data set of probabilistic joint kinematics and associated ground reaction forces were generated based on experimental data from literature. Multi-body dynamics analysis was then used to calculate joint moments with respect to the probabilistic gait cycles. Employing the principal component analysis (PCA), the relative contributions of individual joint kinematics to joint moments were computed in terms of sensitivity indices (SI).Results highlighted high sensitivity of (1) hip abduction moment due to changes in pelvis rotation (SI = 0.38) and hip abduction (SI = 0.4), (2) hip flexion moment due to changes in hip flexion (SI = 0.35) and knee flexion (SI = 0.26), (3) hip rotation moment due to changes in pelvis obliquity (SI = 0.28) and hip rotation (SI = 0.4), (4) knee adduction moment due to changes in pelvis rotation (SI = 0.35), hip abduction (SI = 0.32) and knee flexion (SI = 0.34), (5) knee flexion moment due to changes in pelvis rotation (SI = 0.29), hip flexion (SI = 0.28) and knee flexion (SI = 0.31), and (6) knee rotation moment due to changes in hip abduction (SI = 0.32), hip flexion and knee flexion (SI = 0.31).Highlighting the “cause-and-effect” relationships between joint kinematics and the resultant joint moments provides a fundamental understanding of human gait and can lead to design and optimization of current gait rehabilitation treatments.

Inertial compensation for belt acceleration in an instrumented treadmill

Instrumented treadmills provide a convenient means for applying horizontal perturbations during gait or standing. However, varying the treadmill belt speed introduces inertial artifacts in the sagittal plane moment component of the ground reaction force. Here we present a compensation method based on a second-order dynamic model that predicts inertial pitch moment from belt acceleration. The method was tested experimentally on an unloaded treadmill at a slow belt speed with small random variations (1.20±0.10m/s) and at a faster belt speed with large random variations (2.00±0.50m/s). Inertial artifacts of up to 12Nm (root-mean-square, RMS) and 30Nm (peak) were observed. Coefficients of the model were calibrated on one trial and then used to predict and compensate the pitch moment of another trial with different random variations. Coefficients of determination (R2) were 72.08% and 96.75% for the slow and fast conditions, respectively. After compensation, the root-mean-square (RMS) of the inertial artifact was reduced by 47.37% for the slow speed and 81.98% for fast speed, leaving only 1.5Nm and 2.1Nm of artifact uncorrected, respectively. It was concluded that the compensation technique reduced inertial errors substantially, thereby improving the accuracy in joint moment calculations on an instrumented treadmill with varying belt speed.