Influence of the 3D inverse dynamic method on the joint forces and moments during gait

The joint forces and moments are commonly used in gait analysis. They can be computed by four different 3D inverse dynamic methods proposed in the literature, either based on vectors and Euler angles, wrenches and quaternions, homogeneous matrices, or generalized coordinates and forces. In order to analyze the influence of the inverse dynamic method, the joint forces and moments were computed during gait on nine healthy subjects. A ratio was computed between the relative dispersions (due to the method) and the absolute amplitudes of the gait curves. The influence of the inverse dynamic method was negligible at the ankle (2%) but major at the knee and the hip joints (40%). This influence seems to be due to the dynamic computation rather than the kinematic computation. Compared to the influence of the joint center location, the body segment inertial parameter estimation, and more, the influence of the inverse dynamic method is at least of equivalent importance. This point should be confirmed with other subjects, possibly pathologic, and other movements.     

The effect of perturbing body segment parameters on calculated joint moments and muscle forces during gait

This study examined the effect of body segment parameter (BSP) perturbations on joint moments calculated using an inverse dynamics procedure and muscle forces calculated using computed muscle control (CMC) during gait. BSP (i.e. segment mass, center of mass location (com) and inertia tensor) of the left thigh, shank and foot of a scaled musculoskeletal model were perturbed. These perturbations started from their nominal value and were adjusted to ±40% in steps of 10%, for both individual as well as combined perturbations in BSP. For all perturbations, an inverse dynamics procedure calculated the ankle, knee and hip moments based on an identical inverse kinematics solution. Furthermore, the effect of applying a residual reduction algorithm (RRA) was investigated. Muscle excitations and resulting muscle forces were calculated using CMC. The results show only a limited effect of an individual parameter perturbation on the calculated moments, where the largest effect is found when perturbing the shank com (MS_com,shank, the ratio of absolute difference in torque and relative parameter perturbation, is maximally −7.81 N m for hip flexion moment). The additional influence of perturbing two parameters simultaneously is small (MS_{mass+com,thigh} is maximally 15.2 N m for hip flexion moment). RRA made small changes to the model to increase the dynamic consistency of the simulation (after RRA MS_com,shank is maximally 5.01 N m). CMC results show large differences in muscle forces when BSP are perturbed. These result from the underlying forward integration of the dynamic equations.     

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.     

Simultaneous prediction of muscle and contact forces in the knee during gait

Musculoskeletal models are currently the primary means for estimating in vivo muscle and contact forces in the knee during gait. These models typically couple a dynamic skeletal model with individual muscle models but rarely include articular contact models due to their high computational cost. This study evaluates a novel method for predicting muscle and contact forces simultaneously in the knee during gait. The method utilizes a 12 degree-of-freedom knee model (femur, tibia, and patella) combining muscle, articular contact, and dynamic skeletal models. Eight static optimization problems were formulated using two cost functions (one based on muscle activations and one based on contact forces) and four constraints sets (each composed of different combinations of inverse dynamic loads). The estimated muscle and contact forces were evaluated using in vivo tibial contact force data collected from a patient with a force-measuring knee implant. When the eight optimization problems were solved with added constraints to match the in vivo contact force measurements, root-mean-square errors in predicted contact forces were less than 10 N. Furthermore, muscle and patellar contact forces predicted by the two cost functions became more similar as more inverse dynamic loads were used as constraints. When the contact force constraints were removed, estimated medial contact forces were similar and lateral contact forces lower in magnitude compared to measured contact forces, with estimated muscle forces being sensitive and estimated patellar contact forces relatively insensitive to the choice of cost function and constraint set. These results suggest that optimization problem formulation coupled with knee model complexity can significantly affect predicted muscle and contact forces in the knee during gait. Further research using a complete lower limb model is needed to assess the importance of this finding to the muscle and contact force estimation process.     

Ground reaction forces during termination of human gait.

This is the first published report of the ground reaction forces during gait termination. Two mechanisms appear to be used to stop walking: increased braking forces and decreased push-off force. There appears to be a short interval of time during the gait cycle in which a decision to take an additional step is to be made.     

Comparison of shear forces and ligament loading in the healthy and ACL-deficient knee during gait

The purpose of this study was to predict and explain the pattern of shear force and ligament loading in the ACL-deficient knee during walking, and to compare these results to similar calculations for the healthy knee. Musculoskeletal modeling and computer simulation were combined to calculate ligament forces in the ACL-deficient knee during walking. Joint angles, ground-reaction forces, and the corresponding lower-extremity muscle forces obtained from a whole-body dynamic optimization simulation of walking were input into a second three-dimensional model of the lower extremity that represented the knee as a six degree-of-freedom spatial joint. Anterior tibial translation (ATT) increased throughout the stance phase of gait when the model ACL was removed. The medial collateral ligament (MCL) was the primary restraint to ATT in the ACL-deficient knee. Peak force in the MCL was three times greater in the ACL-deficient knee than in the ACL-intact knee; however, peak force sustained by the MCL in the ACL-deficient knee was limited by the magnitude of the total anterior shear force applied to the tibia. A decrease in anterior tibial shear force was brought about by a decrease in the patellar tendon angle resulting from the increase in ATT. These results suggest that while the MCL acts as the primary restraint to ATT in the ACL-deficient knee, changes in patellar tendon angle reduce total anterior shear force at the knee.     

Normalization of joint moments during gait: a comparison of two techniques

Joint moments are commonly used to characterize gait. Factors like height and weight influence these moments. This study determined which of two commonly used normalization methods, body mass or body weight times height, most reduced the effects of height and weight on peak hip, knee, and ankle external moments during walking. The effectiveness of each normalization method in reducing gender differences was then tested. Gait data from 158 normal subjects were analyzed using unnormalized values, body mass normalized values, and body weight times height normalized values. Without normalization, height or weight accounted for 7-82% of the variance in all 10 peak components of the moments. With normalization, height and weight accounted for at most 6% of the variance with the exception of the hip adduction moment normalized by body weight times height and the ankle dorsiflexion moment normalized by body mass. For the hip adduction moment normalized by body weight times height, height still accounted for 13% of the variance (p<0.001) and for the ankle dorsiflexion moment normalized by body mass, 22% of the variance (p<0.001). After normalization, significant differences between males and females remained for only two out of 10 moments with the body weight times height method compared to six out of 10 moments with the body mass method. When compared to the unnormalized data, both normalization methods were highly effective in reducing height and weight differences. Even for the two cases where one normalization method was less effective than the other (hip adduction-body weight times height; ankle dorsiflexion-body mass) the normalization process reduced the variance ascribed to height or weight by 48% and 63%, respectively, as compared to the unnormalized data.     

A new parametric approach for modeling hip forces during gait

An analytical parametric model was developed to estimate the natural biological variations in muscle forces and their effect on the hip forces subject only to physiological constraints and not predefined optimization criterion. Force predictions are based on the joint kinematics and kinetics of each subject, a previously published muscle model, and physiological constraints on the muscle force distributions. The model was used to determine the hip contact forces throughout the stance phase of gait of a subject with a total hip replacement (THR). The parametrically modeled peak hip force without antagonistic muscle activity varied from 2.7 to 3.2 Body Weights (mean 2.9 Body Weights), which agreed well with published in vivo measurements from instrumented THRs in other subjects. For every 10% increase in antagonistic activity, the mean peak hip force increased by 0.2 Body Weights. The parametric model allows one to examine the effect of specific muscle weaknesses or increased antagonistic muscle activity on the hip forces. The model also provides a tool for studying the effect of gait adaptations on hip forces, as predictions are based on each individual's gait data. Differences in peak forces between subjects can then be evaluated relative to the uncertainty in not knowing the precise muscle force distributions.     

Prediction of ground reaction forces and moments during various activities of daily living

Inverse dynamics based simulations on musculoskeletal models is a commonly used method for the analysis of human movement. Due to inaccuracies in the kinematic and force plate data, and a mismatch between the model and the subject, the equations of motion are violated when solving the inverse dynamics problem. As a result, dynamic inconsistency will exist and lead to residual forces and moments. In this study, we present and evaluate a computational method to perform inverse dynamics-based simulations without force plates, which both improves the dynamic consistency as well as removes the model?s dependency on measured external forces. Using the equations of motion and a scaled musculoskeletal model, the ground reaction forces and moments (GRF&Ms) are derived from three-dimensional full-body motion. The method entails a dynamic contact model and optimization techniques to solve the indeterminacy problem during a double contact phase and, in contrast to previously proposed techniques, does not require training or empirical data. The method was applied to nine healthy subjects performing several Activities of Daily Living (ADLs) and evaluated with simultaneously measured force plate data. Except for the transverse ground reaction moment, no significant differences (P>0.05) were found between the mean predicted and measured GRF&Ms for almost all ADLs. The mean residual forces and moments, however, were significantly reduced (P>0.05) in almost all ADLs using our method compared to conventional inverse dynamic simulations. Hence, the proposed method may be used instead of raw force plate data in human movement analysis using inverse dynamics.     

Subject-specific hip geometry affects predicted hip joint contact forces during gait

Hip loading affects bone remodeling and implant fixation. In this study, we have analyzed the effect of subject-specific modeling of hip geometry on muscle activation patterns and hip contact forces during gait, using musculoskeletal modeling, inverse dynamic analysis and static optimization. We first used sensitivity analysis to analyze the effect of isolated changes in femoral neck-length (NL) and neck-shaft angle (NSA) on calculated muscle activations and hip contact force during the stance phase of gait. A deformable generic musculoskeletal model was adjusted incrementally to adopt a physiological range of NL and NSA. In a second similar analysis, we adjusted hip geometry to the measurements from digitized radiographs of 20 subjects with primary hip osteoarthrosis. Finally, we studied the effect of hip abductor weakness on muscle activation patterns and hip contact force. This analysis showed that differences in NL (41-74 mm) and NSA (113-140 degrees ) affect the muscle activation of the hip abductors during stance phase and hence hip contact force by up to three times body weight. In conclusion, the results from both the sensitivity and subject-specific analysis showed that at the moment of peak contact force, altered NSA has only a minor effect on the loading configuration of the hip. Increased NL, however, results in an increase of the three hip contact-force components and a reduced vertical loading. The results of these analyses are essential to understand modified hip joint loading, and for planning hip surgery for patients with osteoarthrosis.     

A novel gait platform to measure isolated plantar metatarsal forces during walking

A new gait platform described in this report allows an isolated measurement of the vertical and shear forces under an individual metatarsal head during barefoot walking. The apparatus incorporated a customized tactile force sensor and a high-speed camera system, which enabled easy identification of a single anatomical landmark at the forefoot’s plantar surface that is in contact with the sensor throughout stance. After calibration, the measured peak forces under the 2nd MTH showed variability of 3.7%, 9.2%, and 8.9% in vertical, anterior–posterior, and medial–lateral directions, respectively. The device therefore provides information about the magnitude and timing of such local metatarsal forces, and has been shown to be of significant research and clinical interest. Its ability to achieve this with a high degree of accuracy ensures its potential as a valuable research tool.     

Potential of lumbodorsal fascia forces to generate back extension moments during squat lifts

The lumbodorsal fascia (LDF) has been implicated in numerous biomechanical interpretations of low back mechanics as a tissue that provides support to the lumbar spine during demanding load bearing. One hypothesis is that oblique obdominal muscle forces contribute to trunk extensor moment by transforming lateral abdominal tension into longitudinal tension via the LDF. However, a review of the anatomical literature supports the hypothesis that extensor forces in the LDF result from tension within the latissimus dorsi muscle. The purpose of our work was to evaluate the potential of the LDF to generate trunk extensor moment using two mathematical models: one that activated the LDF with the abdominals and another that activated the LDF with the latissimus dorsi. Efforts were made to represent the anatomy as accurately as possible. The results from three subjects performing six squat lifts each, suggested that the potential of the LDF to contribute significant extensor moment has been overestimated. In fact, the issue of whether the LDF is activated by the abdominals or the latissimus dorsi is irrelevant because neither strategy appeared able to generate sizable extensor moments in the type of lift studied.     

Multi-segment foot kinematics and ground reaction forces during gait of individuals with plantar fasciitis

Background

Clinically, plantar fasciitis (PF) is believed to be a result and/or prolonged by overpronation and excessive loading, but there is little biomechanical data to support this assertion. The purpose of this study was to determine the differences between healthy individuals and those with PF in (1) rearfoot motion, (2) medial forefoot motion, (3) first metatarsal phalangeal joint (FMPJ) motion, and (4) ground reaction forces (GRF).

Methods

We recruited healthy (n=22) and chronic PF individuals (n=22, symptomatic over three months) of similar age, height, weight, and foot shape (p>0.05). Retro-reflective skin markers were fixed according to a multi-segment foot and shank model. Ground reaction forces and three dimensional kinematics of the shank, rearfoot, medial forefoot, and hallux segment were captured as individuals walked at 1.35 ms⁻¹.

Results

Despite similarities in foot anthropometrics, when compared to healthy individuals, individuals with PF exhibited significantly (p<0.05) (1) greater total rearfoot eversion, (2) greater forefoot plantar flexion at initial contact, (3) greater total sagittal plane forefoot motion, (4) greater maximum FMPJ dorsiflexion, and (5) decreased vertical GRF during propulsion.

Conclusion

These data suggest that compared to healthy individuals, individuals with PF exhibit significant differences in foot kinematics and kinetics. Consistent with the theoretical injury mechanisms of PF, we found these individuals to have greater total rearfoot eversion and peak FMPJ dorsiflexion, which may put undue loads on the plantar fascia. Meanwhile, increased medial forefoot plantar flexion at initial contact and decreased propulsive GRF are suggestive of compensatory responses, perhaps to manage pain.     

Prediction of ground reaction forces during gait based on kinematics and a neural network model

Kinetic information during human gait can be estimated with inverse dynamics, which is based on anthropometric, kinematic, and ground reaction data. While collecting ground reaction data with a force plate is useful, it is costly and requires regulated space. The goal of this study was to propose a new, accurate methodology for predicting ground reaction forces (GRFs) during level walking without the help of a force plate. To predict GRFs without a force plate, the traditional method of Newtonian mechanics was used for the single support phase. In addition, an artificial neural network (ANN) model was applied for the double support phase to solve statically indeterminate structure problems. The input variables of the ANN model, which were selected to have both dependency and independency, were limited to the trajectory, velocity, and acceleration of the whole segment's mass centre to minimise errors. The predicted GRFs were validated with actual GRFs through a ten-fold cross-validation method, and the correlation coefficients (R) for the ground forces were 0.918 in the medial–lateral axis, 0.985 in the anterior–posterior axis, and 0.991 in the vertical axis during gait. The ground moments were 0.987 in the sagittal plane, 0.841 in the frontal plane, and 0.868 in the transverse plane during gait. The high correlation coefficients(R) are due to the improvement of the prediction rate in the double support phase. This study also proved the possibility of calculating joint forces and moments based on the GRFs predicted with the proposed new hybrid method. Data generated with the proposed method may thus be used instead of raw GRF data in gait analysis and in calculating joint dynamic data using inverse dynamics.     

Effect of alignment changes on socket reaction moments during gait in transfemoral and knee-disarticulation prostheses: Case series

The alignment of a lower-limb prosthesis is critical to the successful prosthetic fitting and utilization by the wearer. Loads generated by the socket applied to the residual limb while walking are thought to be different in transfemoral and knee-disarticulation prostheses. The aim of this case series was to compare the socket reaction moments between transfemoral and knee-disarticulation prostheses and to investigate the effect of alignment changes on them. Two amputees, one with a transfemoral prosthesis and another with a knee-disarticulation prosthesis, participated in this study. A Smart Pyramid™ was used to measure socket reaction moments while walking under 9 selected alignment conditions; including nominally aligned, angle malalignments of 6° (flexion, extension, abduction and adduction) and translation malalignments of 15 mm (anterior, posterior, medial and lateral) of the socket relative to the foot. This study found that the pattern of the socket reaction moments was similar between transfemoral and knee-disarticulation prostheses. An extension moment in the sagittal plane and a varus moment in the coronal plane were dominant during stance under the nominally aligned condition. This study also demonstrated that alignment changes might have consistent effects on the socket reaction moments in transfemoral and knee-disarticulation prostheses. Extension and posterior translation of the socket resulted in increases in an extension moment, while abduction and lateral translation of the socket resulted in increases in a varus moment. The socket reaction moments may potentially serve as useful biomechanical parameters to evaluate alignment in transfemoral and knee-disarticulation prostheses.     

The effects of electromyography-assisted modelling in estimating musculotendon forces during gait in children with cerebral palsy

Neuro-musculoskeletal modelling can provide insight into the aberrant muscle function during walking in those suffering cerebral palsy (CP). However, such modelling employs optimization to estimate muscle activation that may not account for disturbed motor control and muscle weakness in CP. This study evaluated different forms of neuro-musculoskeletal model personalization and optimization to estimate musculotendon forces during gait of nine children with CP (GMFCS I-II) and nine typically developing (TD) children. Data collection included 3D-kinematics, ground reaction forces, and electromyography (EMG) of eight lower limb muscles. Four different optimization methods estimated muscle activation and musculotendon forces of a scaled-generic musculoskeletal model for each child walking, i.e. (i) static optimization that minimized summed-excitation squared; (ii) static optimization with maximum isometric muscle forces scaled to body mass; (iii) an EMG-assisted approach using optimization to minimize summed-excitation squared while reducing tracking errors of experimental EMG-linear envelopes and joint moments; and (iv) EMG-assisted with musculotendon model parameters first personalized by calibration. Both static optimization approaches showed a relatively low model performance compared to EMG envelopes. EMG-assisted approaches performed much better, especially in CP, with only a minor mismatch in joint moments. Calibration did not affect model performance significantly, however it did affect musculotendon forces, especially in CP. A model more consistent with experimental measures is more likely to yield more physiologically representative results. Therefore, this study highlights the importance of calibrated EMG-assisted modelling when estimating musculotendon forces in TD children and even more so in children with CP.     

Differences in lower limb transverse plane joint moments during gait when expressed in two alternative reference frames

When comparing previous studies that have measured the three-dimensional moments acting about the lower limb joints (either external moments or opposing internal joint moments) during able-bodied adult gait, significant variation is apparent in the profiles of the reported transverse plane moments. This variation cannot be explained on the basis of adopted convention (i.e. external versus internal joint moment) or inherent variability in gait strategies. The aim of the current study was to determine whether in fact the frame in which moments are expressed has a dominant effect upon transverse plane moments and thus provides a valid explanation for the observed inconsistency in the literature. Kinematic and ground reaction force data were acquired from nine able-bodied adult subjects walking at a self-selected speed. Three-dimensional hip, knee and ankle joint moments during gait were calculated using a standard inverse dynamics approach. In addition to calculating internal joint moments, the components of the external moment occurring in the transverse plane at each of the lower limb joints were calculated to determine their independent effects. All moments were expressed in both the laboratory frame (LF) as well as the anatomical frame (AF) of the distal segment. With the exception of the ankle rotation moment in the foot AF, lower limb transverse plane joint moments during gait were found to display characteristic profiles that were consistent across subjects. Furthermore, lower limb transverse plane joint moments during gait differed when expressed in the distal segment AF compared to the LF. At the hip, the two alternative reference frames produced near reciprocal joint moment profiles. The components of the external moment revealed that the external ground reaction force moment was primarily responsible for this result. Lower limb transverse plane joint moments during gait were therefore found to be highly sensitive to a change in reference frame. These findings indicate that the different transverse plane joint moment profiles during able-bodied adult gait reported in the literature are likely to be explained on this basis.     

Controlling propulsive forces in gait initiation in transfemoral amputees

During prosthetic gait initiation, transfemoral (TF) amputees control the spatial and temporal parameters that modulate the propulsive forces, the positions of the center of pressure (CoP), and the center of mass (CoM). Whether their sound leg or the prosthetic leg is leading, the TF amputees reach the same end velocity. We wondered how the CoM velocity build up is influenced by the differences in propulsive components in the legs and how the trajectory of the CoP differs from the CoP trajectory in able bodied (AB) subjects. Seven TF subjects and eight AB subjects were tested on a force plate and on an 8 m long walkway. On the force plate, they initiated gait two times with their sound leg and two times with their prosthetic leg. Force measurement data were used to calculate the CoM velocity curves in horizontal and vertical directions. Gait initiated on the walkway was used to determine the leg preference. We hypothesized that because of the differences in propulsive components, the motions of the CoP and the CoM have to be different, as ankle muscles are used to help generate horizontal ground reaction force components. Also, due to the absence of an active ankle function in the prosthetic leg, the vertical CoM velocity during gait initiation may be different when leading with the prosthetic leg compared to when leading with the sound leg. The data showed that whether the TF subjects initiated a gait with their prosthetic leg or with their sound leg, their horizontal end velocity was equal. The subjects compensated the loss of propulsive force under the prosthesis with the sound leg, both when the prosthetic leg was leading and when the sound leg was leading. In the vertical CoM velocity, a tendency for differences between the two conditions was found. When initiating gait with the sound leg, the downward vertical CoM velocity at the end of the gait initiation was higher compared to when leading with the prosthetic leg. Our subjects used a gait initiation strategy that depended mainly on the active ankle function of the sound leg; therefore, they changed the relative durations of the gait initiation anticipatory postural adjustment phase and the step execution phase. Both legs were controlled in one single system of gait propulsion. The shape of the CoP trajectories, the applied forces, and the CoM velocity curves are described in this paper.