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

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

Influence of walking speed on gait parameters

Modern three-dimensional gait analysis systems give information on joint angles and moments in the sagittal and coronal planes, for which normal ranges may not be readily available in the literature. Since patients with joint disease tend to walk slowly and with a short stride, it is essential that normal ranges for gait parameters should be defined with reference to speed of walking. This we have done using a population of 10 normal male subjects agea from 18 to 63 years, walking at speeds which range from very slow to very fast. The ranges of knee angle and moment are given, together with the changes in these parameters with walking speed. Peak knee flexion moment is strongly related to walking speed, whereas coronal plane knee angle is virtually independent of it. The stride length is probably the best basis for deciding the normal range for a particular measurement.     

Upper extremity inverse dynamics model for crutch-assisted gait assessment

Current inverse dynamics models of the upper extremity (UE) are limited for the measurement of Lofstrand crutch-assisted gait. The objective of this study is to develop, validate, and demonstrate a three-dimensional (3-D) UE motion assessment system to quantify crutch-assisted gait in children. We propose a novel 3-D dynamic model of the UEs and crutches for quantification of joint motions, forces, and moments during Lofstrand crutch-assisted gait. The model is composed of the upper body (i.e., thorax, upper arms, forearms, and hands) and Lofstrand crutches to determine joint dynamics of the thorax, shoulders, elbows, wrists, and crutches. The model was evaluated and applied to a pediatric subject with myelomeningocele (MM) to demonstrate its effectiveness in the characterization of crutch gait during multiple walking patterns. The model quantified UE dynamics during reciprocal and swing-through crutch-assisted gait patterns. Joint motions and forces were greater during swing-through gait than reciprocal gait. The model is suitable for further application to pediatric crutch-user populations. This study has potential for improving the understanding of the biomechanics of crutch-assisted gait and may impact clinical intervention strategies and therapeutic planning of ambulation.     

Quantification of gait parameters with inertial sensors and inverse kinematics

Measuring human gait is important in medicine to obtain outcome parameter for therapy, for instance in Parkinson’s disease. Recently, small inertial sensors became available which allow for the registration of limb-position outside of the limited space of gait laboratories. The computation of gait parameters based on such recordings has been the subject of many scientific papers. We want to add to this knowledge by presenting a 4-segment leg model which is based on inverse kinematic and Kalman filtering of data from inertial sensors. To evaluate the model, data from four leg segments (shanks and thighs) were recorded synchronously with accelerometers and gyroscopes and a 3D motion capture system while subjects (n = 12) walked at three different velocities on a treadmill. Angular position of leg segments was computed from accelerometers and gyroscopes by Kalman filtering and compared to data from the motion capture system. The four-segment leg model takes the stance foot as a pivotal point and computes the position of the remaining segments as a kinematic chain (inverse kinematics). Second, we evaluated the contribution of pelvic movements to the model and evaluated a five segment model (shanks, thighs and pelvis) against ground-truth data from the motion capture system and the path of the treadmill.ResultsWe found the precision of the Kalman filtered angular position is in the range of 2–6° (RMS error). The 4-segment leg model computed stride length and length of gait path with a constant undershoot of 3% for slow and 7% for fast gait. The integration of a 5th segment (pelvis) into the model increased its precision. The advantages of this model and ideas for further improvements are discussed.     

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.     

Influence of body CO2 stores on ventilatory dynamics during exercise

Pulmonary CO2 flow (the product of cardiac output and mixed venous CO2 content) is purported to be an important determinant of ventilatory dynamics in moderate exercise. Depletion of body CO2 stores prior to exercise should thus slow these dynamics. We investigated, therefore, the effects of reducing the CO2 stores by controlled volitional hyperventilation on cardiorespiratory and gas exchange response dynamics to 100 W cycling in six healthy adults. The control responses of ventilation (VE), CO2 output (VCO2), O2 uptake (VO2), and heart rate were comprised of an abrupt increase at exercise onset, followed by a slower rise to the new steady state (t1/2 = 48, 43, 31, and 33 s, respectively). Following volitional hyperventilation (9 min, PETCO2 = 25 Torr), the steady-state exercise responses were unchanged. However, VE and VCO2 dynamics were slowed considerably (t1/2 = 76, 71 s) as PETCO2 rose to achieve the control exercise value. VO2 dynamics were slowed only slightly (t1/2 = 39 s), and heart rate dynamics were unaffected. We conclude that pulmonary CO2 flow provides a significant stimulus to the dynamics of the exercise hyperpnea in man.     

The influence of estimated body segment parameters on predicted joint kinetics during diplegic cerebral palsy gait

Inverse Dynamic calculations are routinely used in joint moment and power estimates during gait with anthropometric data often taken from published sources. Many biomechanical analyses have highlighted the need to obtain subject-specific anthropometric data (e.g. Mass, Centre of Mass, Moments of Inertia) yet the types of imaging techniques required to achieve this are not always available in the clinical setting. Differences in anthropometric sets have been shown to affect the reactive force and moment calculations in normal subjects but the effect on a paediatric diplegic cerebral palsy group has not been investigated. The aim of this study was to investigate the effect of using different anthropometric sets on predicted sagittal plane moments during normal and diplegic cerebral palsy gait. Three published anthropometric sets were applied to the reactive force and moment calculations of 14 Cerebral Palsy and 14 Control subjects. Statistically significant differences were found when comparing the different anthropometric sets but variability in the resulting sagittal plane moment calculations between sets was low (0.01–0.07 Nm/kg). In addition, the GDI-Kinetic, used as an outcome variable to assess whether differences were clinically meaningful, indicated no clinically meaningful difference between sets. The results suggest that the effects of using different anthropometric sets on the kinetic profiles of normal and diplegic cerebral palsy subjects are clinically insignificant.     

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.     

An upper extremity inverse dynamics model for pediatric Lofstrand crutch-assisted gait

The objective of this study was to develop an instrumented Lofstrand crutch system, which quantifies three-dimensional (3-D) upper extremity (UE) kinematics and kinetics using an inverse dynamics model. The model describes the dynamics of the shoulders, elbows, wrists, and crutches and is compliant with the International Society of Biomechanics (ISB) recommended standards. A custom designed Lofstrand crutch system with four, six-degree-of-freedom force transducers was implemented with the inverse dynamics model to obtain triaxial UE joint reaction forces and moments. The crutch system was validated statically and dynamically for accuracy of computing joint reaction forces and moments during gait. The root mean square (RMS) error of the system ranged from 0.84 to 5.20%. The system was demonstrated in children with diplegic cerebral palsy (CP), incomplete spinal cord injury (SCI), and type I osteogenesis imperfecta (OI). The greatest joint reaction forces were observed in the posterior direction of the wrist, while shoulder flexion moments were the greatest joint reaction moments. The subject with CP showed the highest forces and the subject with SCI demonstrated the highest moments. Dynamic quantification may help to elucidate UE joint demands in regard to pain and pathology in long-term assistive device users.     

Estimation of temporal gait parameters using Bayesian models on acceleration signals

The purpose of this study is to develop a system capable of performing calculation of temporal gait parameters using two low-cost wireless accelerometers and artificial intelligence-based techniques as part of a larger research project for conducting human gait analysis. Ten healthy subjects of different ages participated in this study and performed controlled walking tests. Two wireless accelerometers were placed on their ankles. Raw acceleration signals were processed in order to obtain gait patterns from characteristic peaks related to steps. A Bayesian model was implemented to classify the characteristic peaks into steps or nonsteps. The acceleration signals were segmented based on gait events, such as heel strike and toe-off, of actual steps. Temporal gait parameters, such as cadence, ambulation time, step time, gait cycle time, stance and swing phase time, simple and double support time, were estimated from segmented acceleration signals. Gait data-sets were divided into two groups of ages to test Bayesian models in order to classify the characteristic peaks. The mean error obtained from calculating the temporal gait parameters was 4.6%. Bayesian models are useful techniques that can be applied to classification of gait data of subjects at different ages with promising results     

Influence of gait parameters on the loading of the lower limb

The ground reaction force which acts on the foot during normal walking consists of the sum of two components: the support of the weight of the body and the acceleration of the body. The relationships between the initial loading rate of the lower limb (ignoring the contribution of the heelstrike transient) and the general gait parameters — cadence, stride length, and velocity — have been examined. Plots of the resultant ground reaction force were used to calculate the loading rate of the limb. A sample of 13 normal male subjects, aged from 18 to 63 years, walked at five different self-selected speeds. Velocity showed the highest correlation with loading rate (r = 0.95) and stride length the lowest (r = 0.85). The relationship between cadence and loading rate was non-linear.     

On the estimation of joint kinematics during gait.

In gait analysis, the concepts of Euler and helical (screw) angles are used to define the three-dimensional relative joint angular motion of lower extremities. Reliable estimation of joint angular motion depends on the accurate definition and construction of embedded axes within each body segment. In this paper, using sensitivity analysis, we quantify the effects of uncertainties in the definition and construction of embedded axes on the estimation of joint angular motion during gait. Using representative hip and knee motion data from normal subjects and cerebral palsy patients, the flexion-extension axis is analytically perturbed +/- 15 degrees in 5 degrees steps from a reference position, and the joint angles are recomputed for both Euler and helical angle definitions. For the Euler model, hip and knee flexion angles are relatively unaffected while the ab/adduction and rotation angles are significantly affected throughout the gait cycle. An error of 15 degrees in the definition of flexion-extension axis gives rise to maximum errors of 8 and 12 degrees for the ab/adduction angle, and 10-15 degrees for the rotation angles at the hip and knee, respectively. Furthermore, the magnitude of errors in ab/adduction and rotation angles are a function of the flexion angle. The errors for the ab/adduction angles increase with increasing flexion angle and for the rotation angle, decrease with increasing flexion angle. In cerebral palsy patients with flexed knee pattern of gait, this will result in distorted estimation of ab/adduction and rotation. For the helical model, similar results are obtained for the helical angle and associated direction cosines.(ABSTRACT TRUNCATED AT 250 WORDS)     

Influence of gait speed on the control of mediolateral dynamic stability during gait initiation

This study investigated the influence of gait speed on the control of mediolateral dynamic stability during gait initiation. Thirteen healthy young adults initiated gait at three self-selected speeds: Slow, Normal and Fast. The results indicated that the duration of anticipatory postural adjustments (APA) decreased from Slow to Fast, i.e. the time allocated to propel the centre of mass (COM) towards the stance-leg side was shortened. Likely as an attempt at compensation, the peak of the anticipatory centre of pressure (COP) shift increased. However, COP compensation was not fully efficient since the results indicated that the mediolateral COM shift towards the stance-leg side at swing foot-off decreased with gait speed. Consequently, the COM shift towards the swing-leg side at swing heel-contact increased from Slow to Fast, indicating that the mediolateral COM fall during step execution increased as gait speed rose. However, this increased COM fall was compensated by greater step width so that the margin of stability (the distance between the base-of-support boundary and the mediolateral component of the “extrapolated centre of mass”) at heel-contact remained unchanged across the speed conditions. Furthermore, a positive correlation between the mediolateral extrapolated COM position at heel-contact and step width was found, indicating that the greater the mediolateral COM fall, the greater the step width. Globally, these results suggest that mediolateral APA and step width are modulated with gait speed so as to maintain equivalent mediolateral dynamical stability at the time of swing heel-contact.     

Static optimal estimation of joint accelerations for inverse dynamics problem solution

In inverse dynamics computations, the accuracy of the solution strongly depends on the accuracy of the input data. In particular, estimated joint moments are highly sensitive to uncertainties in acceleration data. The aim of the present work was to improve classical inverse dynamics computations by providing an accurate estimation of accelerations. Accelerations are usually calculated from noise-polluted position data using numerical double differentiation, which amplifies measurement noise. The objective of the present paper is to use all available imperfect position and force measurements to extract optimum acceleration estimations. A weighted least-squares optimisation approach is used to provide optimal acceleration distributions most consistent with position and force data, and which account for the propagation of measurement uncertainties. The task chosen for comparing the solution methodology with other classical methods is a typical experimental postural movement, consisting in upper limb swings from an upright stance. The proposed method delivers a set of optimal accelerations well consistent with all available measurements. It also leads to an accurate prediction of ground reactions and it produces no residual moment at the top-most segment.     

An improved inverse dynamics formulation for estimation of external and internal loads during human sagittal plane movements

Planar musculoskeletal models are common in the inverse dynamics analysis of human movements such as walking, running and jumping. The continued interest in such models is justified by their simplicity and computational efficiency. Related to a human planar model, a unified formulation for both the flying and support phases of the sagittal plane movements is developed. The actuation involves muscle forces in the lower limbs and the resultant muscle torques in the other body joints. The dynamic equations, introduced in absolute coordinates of the segments, are converted into useful compact forms using the projective technique. The solution to a determinate inverse dynamics problem allows for the explicit determination of the external reactions (presumed to vanish during the flying phases) and the resultant muscle torques in all the model joints. The indeterminate inverse dynamics problem is then focused on the assessment of muscle forces and joint reaction forces selectively in the supporting lower limb. Numerical results of the inverse dynamics simulation of sample sagittal plane movements are reported to illustrate the validity and effectiveness of the improved formulation.     

Influence of head models on neuromagnetic fields and inverse source localizations

Background  

The magnetoencephalograms (MEGs) are mainly due to the source currents. However, there is a significant contribution to MEGs from the volume currents. The structure of the anatomical surfaces, e.g., gray and white matter, could severely influence the flow of volume currents in a head model. This, in turn, will also influence the MEGs and the inverse source localizations. This was examined in detail with three different human head models.     

Influence of head models on EEG simulations and inverse source localizations

Background  

The structure of the anatomical surfaces, e.g., CSF and gray and white matter, could severely influence the flow of volume currents in a head model. This, in turn, will also influence the scalp potentials and the inverse source localizations. This was examined in detail with four different human head models.     

Influence of gait speed on free vertical moment during walking

Free vertical moment (FVM) of ground reaction is recognized to be a meaningful indicator of torsional stress on the lower limbs when walking. The purpose of this study was to examine whether and how gait speed influences the FVM when walking. Fourteen young healthy adults performed a series of overground walking trials at three different speeds: low, preferred and fast. FVM was measured during the stance phase of the dominant leg using a force platform embedded in a 10 m-long walkway. Transverse plane kinematic parameters of the foot and pelvis were measured using a motion capture system. Results showed a significant decrease in peak abduction FVM (i.e., resisting internal foot rotation) and an increase in peak adduction FVM (i.e., resisting external foot rotation), together with an increase in gait speed. Concomitantly, we observed a decrease in the foot progression angle and an increase in the peak pelvis rotation velocity in the transverse plane with an increase in gait speed. A significant positive correlation was found between the pelvis rotation velocity and the peak adduction moment, suggesting that pelvis rotation influences the magnitude of adduction FVM. Furthermore, we also found significant correlations between the peak adduction FVM and both the step length and frequency, indicating that the alterations in FVM may be ascribed to changes in these two key variables of gait speed. These speed-related changes in FVM should be considered when this parameter is used in gait assessment, particularly when used as an index for rehabilitation and injury prevention.     

Influence of priors in Bayesian estimation of genetic parameters for multivariate threshold models using Gibbs sampling

Simulated data were used to investigate the influence of the choice of priors on estimation of genetic parameters in multivariate threshold models using Gibbs sampling. We simulated additive values, residuals and fixed effects for one continuous trait and liabilities of four binary traits, and QTL effects for one of the liabilities. Within each of four replicates six different datasets were generated which resembled different practical scenarios in horses with respect to number and distribution of animals with trait records and availability of QTL information. (Co)Variance components were estimated using a Bayesian threshold animal model via Gibbs sampling. The Gibbs sampler was implemented with both a flat and a proper prior for the genetic covariance matrix. Convergence problems were encountered in > 50% of flat prior analyses, with indications of potential or near posterior impropriety between about round 10 000 and 100 000. Terminations due to non-positive definite genetic covariance matrix occurred in flat prior analyses of the smallest datasets. Use of a proper prior resulted in improved mixing and convergence of the Gibbs chain. In order to avoid (near) impropriety of posteriors and extremely poorly mixing Gibbs chains, a proper prior should be used for the genetic covariance matrix when implementing the Gibbs sampler.