Interpolation of segment Euler angles can provide a robust estimation of segment angular trajectories during asymmetric lifting tasks

Video-based field methods that estimate L5/S1 net joint moments from kinematics based on interpolation in the sagittal plane of joint angles alone can introduce a significant error on the interpolated joint angular trajectory when applied to asymmetric dynamic lifts. Our goal was to evaluate interpolation of segment Euler angles for a wide range of dynamic asymmetric lifting tasks using cubic spline methods by comparing the interpolated values with the continuous measured ones. For most body segments, the estimated trajectories of segment Euler angles have less than 5° RMSE (in each dimension) with 5-point cubic spline interpolation when there is no measurement error of interpolation points. Sensitivity analysis indicates that when the measurement error exists, the root mean square error (RMSE) of estimated trajectories increases. Comparison among different lifting conditions showed that lifting a load from a high initial position yielded a smaller RMSE than lifting from a low initial position. In conclusion, interpolation of segment Euler angles can provide a robust estimation of segment angular trajectories during asymmetric lifting when measurement error of interpolation points can be controlled at a low level.     

Quantitative assessment of the accuracy for three interpolation techniques in kinematic analysis of human movement

Marker obstruction during human movement analyses requires interpolation to reconstruct missing kinematic data. This investigation quantifies errors associated with three interpolation techniques and varying interpolated durations. Right ulnar styloid kinematics from 13 participants performing manual wheelchair ramp ascent were reconstructed using linear, cubic spline and local coordinate system (LCS) interpolation from 11-90% of one propulsive cycle. Elbow angles (flexion/extension and pronation/supination) were calculated using real and reconstructed kinematics. Reconstructed kinematics produced maximum elbow flexion/extension errors of 37.1 (linear), 23.4 (spline) and 9.3 (LCS) degrees. Reconstruction errors are unavoidable [minimum errors of 6.7?mm (LCS); 0.29?mm (spline); 0.42?mm (linear)], emphasising careful motion capture system setup must be performed to minimise data interpolation. For the observed movement, LCS-based interpolation (average error of 14.3?mm; correlation of 0.976 for elbow flexion/extension) was most suitable for reconstructing durations longer than 200?ms. Spline interpolation was superior for shorter durations.     

Quantitative assessment of the accuracy for three interpolation techniques in kinematic analysis of human movement

Marker obstruction during human movement analyses requires interpolation to reconstruct missing kinematic data. This investigation quantifies errors associated with three interpolation techniques and varying interpolated durations. Right ulnar styloid kinematics from 13 participants performing manual wheelchair ramp ascent were reconstructed using linear, cubic spline and local coordinate system (LCS) interpolation from 11–90% of one propulsive cycle. Elbow angles (flexion/extension and pronation/supination) were calculated using real and reconstructed kinematics. Reconstructed kinematics produced maximum elbow flexion/extension errors of 37.1 (linear), 23.4 (spline) and 9.3 (LCS) degrees. Reconstruction errors are unavoidable [minimum errors of 6.7 mm (LCS); 0.29 mm (spline); 0.42 mm (linear)], emphasising careful motion capture system setup must be performed to minimise data interpolation. For the observed movement, LCS-based interpolation (average error of 14.3 mm; correlation of 0.976 for elbow flexion/extension) was most suitable for reconstructing durations longer than 200 ms. Spline interpolation was superior for shorter durations.     

Evidence for a role of antagonistic cocontraction in controlling trunk stiffness during lifting

Activity of the abdominal muscles during symmetric lifting has been a consistent finding in many studies. It has been hypothesized that this antagonistic coactivation increases trunk stiffness to provide stability to the spine. To test this, we investigated whether abdominal activity in lifting is increased in response to destabilizing conditions.

Ten healthy male subjects lifted 35 l containers containing 15 l of water (unstable condition), or ice (stable condition). 3D-kinematics, ground reaction forces, and EMG of selected trunk muscles were recorded. Euler angles of the thorax relative to the pelvis were determined. Inverse dynamics was used to calculate moments about L5S1. Averaged normalized abdominal EMG activity was calculated to express coactivation and an EMG-driven trunk muscle model was used to estimate the flexor moment produced by these muscles and to estimate the L5S1 compression force.

Abdominal coactivation was significantly higher when lifting the unstable load. This coincided with significant increases in estimated moments produced by the antagonist muscles and in estimated compression forces on the L5S1 disc, except at the instant of the peak moment about L5S1. The lifting style was not affected by load instability as evidenced by the absence of effects on moments about L5S1 and angles of the thorax relative to the pelvis. The data support the interpretation of abdominal cocontraction during lifting as subserving spinal stability. An alternative function of the increased trunk stiffness due to cocontraction might be to achieve more precise control over the trajectory of lifted weight in order to avoid sloshing of the water mass in the box and the consequent perturbations.     

Estimating the L5S1 flexion/extension moment in symmetrical lifting using a simplified ambulatory measurement system

Mechanical loading of the spine has been shown to be an important risk factor for the development of low-back pain. Inertial motion capture (IMC) systems might allow measuring lumbar moments in realistic working conditions, and thus support evaluation of measures to reduce mechanical loading. As the number of sensors limits applicability, the objective of this study was to investigate the effect of the number of sensors on estimates of L5S1 moments.Hand forces, ground reaction forces (GRF) and full-body kinematics were measured using a gold standard (GS) laboratory setup. In the ambulatory setup, hand forces were estimated based on the force plates measured GRF and body kinematics that were measured using (subsets of) an IMC system. Using top-down inverse dynamics, L5S1 flexion/extension moments were calculated.RMSerrors (Nm) were lowest (16.6) with the full set of 17 sensors and increased to 20.5, 22 and 30.6, for 8, 6 and 4 sensors. Absolute errors in peak moments (Nm) ranged from 17.7 to 16.4, 16.9 and 49.3 Nm, for IMC setup’s with 17, 8, 6 and 4 sensors, respectively. When horizontal GRF were neglected for 6 sensors, RMSerrors and peak moment errors decreased from 22 to 17.3 and from 16.9 to 13 Nm, respectively.In conclusion, while reasonable moment estimates can be obtained with 6 sensors, omitting the forearm sensors led to unacceptable errors. Furthermore, vertical GRF information is sufficient to estimate L5S1 moments in lifting.     

Estimation of musculotendon kinematics in large musculoskeletal models using multidimensional B-splines

We present a robust and computationally inexpensive method to estimate the lengths and three-dimensional moment arms for a large number of musculotendon actuators of the human lower limb. Using a musculoskeletal model of the lower extremity, a set of values was established for the length of each musculotendon actuator for different lower limb generalized coordinates (joint angles). A multidimensional spline function was then used to fit these data. Muscle moment arms were obtained by differentiating the musculotendon length spline function with respect to the generalized coordinate of interest. This new method was then compared to a previously used polynomial regression method. Compared to the polynomial regression method, the multidimensional spline method produced lower errors for estimating musculotendon lengths and moment arms throughout the whole generalized coordinate workspace. The fitting accuracy was also less affected by the number of dependent degrees of freedom and by the amount of experimental data available. The spline method only required information on musculotendon lengths to estimate both musculotendon lengths and moment arms, thus relaxing data input requirements, whereas the polynomial regression requires different equations to be used for both musculotendon lengths and moment arms. Finally, we used the spline method in conjunction with an electromyography driven musculoskeletal model to estimate muscle forces under different contractile conditions, which showed that the method is suitable for the integration into large scale neuromusculoskeletal models.     

A new method for gravity correction of dynamometer data and determining passive elastic moments at the joint

Moments measured by a dynamometer in biomechanics testing often include the gravitational moment and the passive elastic moment in addition to the moment caused by muscle contraction. Gravitational moments result from the weight of body segments and dynamometer attachment, whereas passive elastic moments are caused by the passive elastic deformation of tissues crossing the joint being assessed. Gravitational moments are a major potential source of error in dynamometer measurements and must be corrected for, a procedure often called gravity correction. While several approaches to gravity correction have been presented in the literature, they generally assume that the gravitational moment can be adequately modeled as a simple sine or cosine function. With this approach, a single passive data point may be used to specify the model, assuming that passive elastic moments are negligible at that point. A new method is presented here for the gravity correction of dynamometer data. Gravitational moment is represented using a generalized sinusoid, which is fit to passive data obtained over the entire joint range of motion. The model also explicitly accounts for the presence of passive elastic moments. The model was tested for cases of hip flexion-extension, knee flexion-extension, and ankle plantar flexion-dorsiflexion, and provided good fits in all cases.     

Walking on high heels changes muscle activity and the dynamics of human walking significantly

The aim of the study was to investigate the distribution of net joint moments in the lower extremities during walking on high-heeled shoes compared with barefooted walking at identical speed. Fourteen female subjects walked at 4 km/h across three force platforms while they were filmed by five digital video cameras operating at 50 frames/second. Both barefooted walking and walking on high-heeled shoes (heel height: 9 cm) were recorded. Net joint moments were calculated by 3D inverse dynamics. EMG was recorded from eight leg muscles. The knee extensor moment peak in the first half of the stance phase was doubled when walking on high heels. The knee joint angle showed that high-heeled walking caused the subjects to flex the knee joint significantly more in the first half of the stance phase. In the frontal plane a significant increase was observed in the knee joint abductor moment and the hip joint abductor moment. Several EMG parameters increased significantly when walking on high-heels. The results indicate a large increase in bone-on-bone forces in the knee joint directly caused by the increased knee joint extensor moment during high-heeled walking, which may explain the observed higher incidence of osteoarthritis in the knee joint in women as compared with men.     

Lower extremity control and dynamics during backward angular impulse generation in forward translating tasks

Observation of complex whole body movements suggests that the nervous system coordinates multiple operational subsystems using some type of hierarchical control. When comparing two forward translating tasks performed with and without backward angular impulse, we have learned that both trunk-leg coordination and reaction force-time characteristics are significantly different between tasks. This led us to hypothesize that differences in trunk-leg coordination and reaction force generation would induce between-task differences in the control of the lower extremity joints during impulse generation phase of the tasks. Eight highly skilled performers executed a series of forward jumps with and without backward rotation (reverse somersault and reverse timer, respectively). Sagittal plane kinematics, reaction forces, and electromyograms of lower extremity muscles were acquired during the take-off phase of both tasks. Lower extremity joint kinetics were calculated using inverse dynamics. The results demonstrated between-task differences in the relative angles between the lower extremity segments and the net joint forces/reaction force and the joint angular velocity profiles. Significantly less knee extensor net joint moments and net joint moment work and greater hip extensor net joint moments and net joint moment work were observed during the push interval of the reverse somersault as compared to the reverse timer. Between-task differences in lower extremity joint kinetics were regulated by selectively activating the bi-articular muscles crossing the knee and hip. These results indicate that between-task differences in the control of the center of mass relative to the reaction force alters control and dynamics of the multijoint lower extremity subsystem.     

Joint axes of rotation and body segment parameters of pig limbs

To enable a quantification of net joint moments and joint reaction forces, indicators of joint loading, this study aimed to locate the mediolateral joint axes of rotation and establish the body segment parameters of the limbs of pigs (Sus scrofa). To locate the joint axes of rotation the scapulohumeral, humeroradial, carpal complex, metacarpophalangeal, coxofemoral, femorotibial, tarsal, and metatarsophalangeal joints from 12 carcasses were studied. The joints were photographed in three positions, bisecting lines drawn at fixed landmarks with their intersection marking the joint axes of rotation. The body segment parameters, i.e. the segment mass, center of mass and moment of inertia were measured on the humerus, radius/ulna, metacarpus, forepastern, foretoe, femur, tibia, metatarsus, hindpastern, and hindtoe segments from five carcasses. The segments were weighed, and their center of mass was found by balancing them. The moments of inertia of the humerus, radius/ulna, femur and tibia were found by rotating the segments. The moments of inertia of the remaining segments were calculated. Generally, the joint axes of rotation were near the attachment site of the lateral collateral ligaments. The forelimb, with segments taken as one, was significantly lighter and shorter than the hindlimb (P < 0.001). In all segments the center of mass was located 31 to 50% distal to the proximal segment end. The segment mass decreased with distance from the trunk, as did the segment moment of inertia. The results may serve as reference on the location of the joint axes of rotation and on the body segment parameters for inverse dynamic modeling of pigs.     

Discrepancies in knee joint moments using common anatomical frames defined by different palpable landmarks

The aim was to investigate the effects of three anatomical frames using palpable anatomical landmarks of the knee on the net knee joint moments. The femoral epicondyles, femoral condyles, and tibial ridges were used to define the different anatomical frames and the segment end points of the distal femur and proximal tibia, which represent the origin of the tibial coordinate system. Gait data were then collected using the calibrated anatomical system technique (CAST), and the external net knee joint moments in the sagittal, coronal, and transverse planes were calculated based upon the three anatomical frames. Peak knee moments were found to be significantly different in the sagittal plane by approximately 25% (p 相似文献   

Mechanical analysis of the landing phase in heel-toe running.

Results of mechanical analyses of running may be helpful in the search for the etiology of running injuries. In this study a mechanical analysis was made of the landing phase of three trained heel-toe runners, running at their preferred speed and style. The body was modeled as a system of seven linked rigid segments, and the positions of markers defining these segments were monitored using 200 Hz video analysis. Information about the ground reaction force vector was collected using a force plate. Segment kinematics were combined with ground reaction force data for calculation of the net intersegmental forces and moments. The vertical component of the ground reaction force vector Fz was found to reach a first peak approximately 25 ms after touch-down. This peak occurs because, in the support leg, the vertical acceleration of the knee joint is not reduced relative to that of the ankle joint by rotation of the lower leg, so that the support leg segments collide with the floor. Rotation of the support upper leg, however, reduces the vertical acceleration of the hip joint relative to that of the knee joint, and thereby plays an important role in limiting the vertical forces during the first 40 ms. Between 40 and 100 ms after touch-down, the vertical forces are mainly limited by rotation of the support lower leg. At the instant that Fz reaches its first peak, net moments about ankle, knee and hip joints of the support leg are virtually zero. The net moment about the knee joint changed from -100 Nm (flexion) at touch-down to +200 Nm (extension) 50 ms after touch-down. These changes are too rapid to be explained by variations in the muscle activation levels and were ascribed to spring-like behavior of pre-activated knee flexor and knee extensor muscles. These results imply that the runners investigated had no opportunity to control the rotations of body segments during the first part of the contact phase, other than by selecting a certain geometry of the body and muscular (co-)activation levels prior to touch-down.     

Coordination of the leg muscles in backlift and leglift.

Net joint moments are often used to quantify the loading of structures (e.g. the intervertebral disc at L5S1) during lifting. This quantification method is also used to evaluate the loading of the knee, for instance, to determine the effect of backlifting as opposed to leglifting. However, the true loading of the joint as derived from net joint moments can be obscured by a possible co-contraction of antagonists. To unravel the mechanisms that determine the net joint moments in the knee, the leglift was compared to the backlift. Although a completely different net knee moment curve was found when comparing the two lifting techniques, it appeared to be closely related to the ground reaction force vector and its orientation with respect to the joint centre of rotation (R > 0.995). This close relation was established by co-contraction of both flexors and extensors of the knee. Furthermore, a close relation appeared to exist between the joint moment difference between hip and knee and the activity difference between rectus femoris muscle and hamstring (R = 0.72 and 0.83 in leglift and backlift, respectively). The knee-ankle joint moment difference and the activity of the gastrocnemius showed a close relation as well (R = -0.89 and 0.96 in leglift and backlift, respectively). These relations can be interpreted as a mechanism to distribute net moments across joints. It is concluded that during lifting tasks the intermuscular coordination is aimed at coupling of joint moments, such that the ground reaction force points in a direction that provides balance during the movement. The use of net joint moments as direct indicators for joint loading (e.g. knee) seems, therefore, questionable.     

Interpolating three-dimensional kinematic data using quaternion splines and hermite curves

Kinematic interpolation is an important tool in biomechanics. The purpose of this work is to describe a method for interpolating three-dimensional kinematic data, minimizing error while maintaining ease of calculation. This method uses cubic quaternion and hermite interpolation to fill gaps between kinematic data points. Data sets with a small number of samples were extracted from a larger data set and used to validate the technique. Two additional types of interpolation were applied and then compared to the cubic quaternion interpolation. Displacement errors below 2% using the cubic quaternion method were achieved using 4% of the total samples, representing a decrease in error over the other algorithms.     

A computer program for the analysis of dental arch form using the cubic spline function.

This paper presents the details and logic of a FORTRAN computer program which fits a cubic interpolatory spline to a set of data points digitized from an exact size photographic reproduction of a dental model. It also measures the length of the arc and computes a set of normals to the curve to be used in evaluating the error in the fit of the spline. The program is used in studies of dental arch form and is useful in evaluating changes in the form of the arches due to orthodontic treatment. The measurement of the arc length provides an adequate assessment of space available in the dental arch, which is of importance to the orthodontist.     

Relationship between moments at the L5/S1 level, hip and knee joint when lifting

A study was performed to determine the influence of load magnitude on the self selected technique of lifting. Specifically, it was hypothesized that with heavier weights a tendency would occur to lift more with the back and less with the legs. Flexion-extension moments at the L5/S1 level, hip and knee joints were calculated for subjects when lifting boxes weighing from 50 to 250 N. Lifts were performed using a freestyle technique at normal speed. The moment profiles (moment plotted vs time) were analyzed kinematically and as a function of the weight lifted. The kinematics of the lift changed as the weight increased. The moment at the L5/S1 level increased with increasing weight, however, the corresponding knee moment decreased. Thus, an inverse relationship was found between the moment at the L5/S1 level and the knee joint moment. An increase in weight lifted was also associated with an increase in the angular velocity at the knee while lifting. Apparently with heavier weights there is a tendency to extend the knees earlier during the lift than with lighter weights, confirming our hypothesis. This explains the reduced knee moment. Our findings lead to the hypothesis that quadriceps muscle strength limits the subjects' ability to lift with their knees flexed.     

Invariant hip moment pattern while walking with a robotic hip exoskeleton

Robotic lower limb exoskeletons hold significant potential for gait assistance and rehabilitation; however, we have a limited understanding of how people adapt to walking with robotic devices. The purpose of this study was to test the hypothesis that people reduce net muscle moments about their joints when robotic assistance is provided. This reduction in muscle moment results in a total joint moment (muscle plus exoskeleton) that is the same as the moment without the robotic assistance despite potential differences in joint angles. To test this hypothesis, eight healthy subjects trained with the robotic hip exoskeleton while walking on a force-measuring treadmill. The exoskeleton provided hip flexion assistance from approximately 33% to 53% of the gait cycle. We calculated the root mean squared difference (RMSD) between the average of data from the last 15 min of the powered condition and the unpowered condition. After completing three 30-min training sessions, the hip exoskeleton provided 27% of the total peak hip flexion moment during gait. Despite this substantial contribution from the exoskeleton, subjects walked with a total hip moment pattern (muscle plus exoskeleton) that was almost identical and more similar to the unpowered condition than the hip angle pattern (hip moment RMSD 0.027, angle RMSD 0.134, p<0.001). The angle and moment RMSD were not different for the knee and ankle joints. These findings support the concept that people adopt walking patterns with similar joint moment patterns despite differences in hip joint angles for a given walking speed.     

Lifting over an obstacle: effects of one-handed lifting and hand support on trunk kinematics and low back loading

Mechanical loading of the low back during lifting is a common cause of low back pain. In this study two-handed lifting is compared to one-handed lifting (with and without supporting the upper body with the free hand) while lifting over an obstacle. A 3-D linked segment model was combined with an EMG-assisted trunk muscle model to quantify kinematics and joint loads at the L5S1 joint. Peak total net moments (i.e., the net moment effect of all muscles and soft tissue spanning the joint) were found to be 10+/-3% lower in unsupported one-handed lifting compared to two-handed lifting, and 30+/-8% lower in supported compared to unsupported one-handed lifting. L5S1 joint forces also showed reductions, but not of the same magnitude (18+/-8% and 15+/-10%, respectively, for compression forces, and 15+/-17% and 11+/-14% respectively, for shear forces). Those reductions of low back load were mainly caused by a reduction of trunk and load moment arms relative to the L5S1 joint during peak loading, and, in the case of hand support, by a support force of about 250 N. Stretching one leg backward did not further reduce low back load estimates. Furthermore, one-handed lifting caused an 6+/-8 degrees increase in lateral flexion, a 9+/-5 degrees increase in twist and a 6+/-6 degrees decrease in flexion. Support with the free hand caused a small further increase in lumbar twisting. It is concluded that one-handed lifting, especially with hand support, reduces L5S1 loading but increases asymmetry in movements and moments about the lumbar spine.     

Joint moments and contact forces in the foot during walking

The net force and moment of a joint have been widely used to understand joint disease in the foot. Meanwhile, it does not reflect the physiological forces on muscles and contact surfaces. The objective of the study is to estimate active moments by muscles, passive moments by connective tissues and joint contact forces in the foot joints during walking. Joint kinematics and external forces of ten healthy subjects (all males, 24.7 ± 1.2 years) were acquired during walking. The data were entered into the five-segment musculoskeletal foot model to calculate muscle forces and joint contact forces of the foot joints using an inverse dynamics-based optimization. Joint reaction forces and active, passive and net moments of each joint were calculated from muscle and ligament forces. The maximum joint reaction forces were 8.72, 4.31, 2.65, and 3.41 body weight (BW) for the ankle, Chopart’s, Lisfranc and metatarsophalangeal joints, respectively. Active and passive moments along with net moments were also obtained. The maximum net moments were 8.6, 8.4, 5.4 and 0.8%BW∙HT, respectively. While the trend of net moment was very similar between the four joints, the magnitudes and directions of the active and passive moments varied between joints. The active and passive moments during walking could reveal the roles of muscles and ligaments in each of the foot joints, which was not obvious in the net moment. This method may help narrow down the source of joint problems if applied to clinical studies.     

Modeling the stance leg in two-dimensional analyses of sprinting: inclusion of the MTP joint affects joint kinetics

Two-dimensional analyses of sprint kinetics are commonly undertaken but often ignore the metatarsalphalangeal (MTP) joint and model the foot as a single segment. Due to the linked-segment nature of inverse dynamics analyses, the aim of this study was to investigate the effect of ignoring the MTP joint on the calculated joint kinetics at the other stance leg joints during sprinting. High-speed video and force platform data were collected from four to five trials for each of three international athletes. Resultant joint moments, powers, and net work at the stance leg joints during the first stance phase after block clearance were calculated using three different foot models. By ignoring the MTP joint, peak extensor moments at the ankle, knee, and hip were on average 35% higher (p < .05 for each athlete), 40% lower (p < .05), and 9% higher (p > .05), respectively, than those calculated with the MTP joint included. Peak ankle and knee joint powers and net work at all joints were also significantly (p < .05) different. By ignoring a genuine MTP joint plantar flexor moment, artificially high peak ankle joint moments are calculated, and these also affect the calculated joint kinetics at the knee.