Sjoerd M. Bruijn

Assessing the stability of human locomotion: A review of current measures

Falling poses a major threat to the steadily growing population of the elderly in modern-day society. A major challenge in the prevention of falls is the identification of individuals who are at risk of falling owing to an unstable gait. At present, several methods are available for estimating gait stability, each with its own advantages and disadvantages. In this paper, we review the currently available measures: the maximum Lyapunov exponent (λS and λL), the maximum Floquet multiplier, variability measures, long-range correlations, extrapolated centre of mass, stabilizing and destabilizing forces, foot placement estimator, gait sensitivity norm and maximum allowable perturbation. We explain what these measures represent and how they are calculated, and we assess their validity, divided up into construct validity, predictive validity in simple models, convergent validity in experimental studies, and predictive validity in observational studies. We conclude that (i) the validity of variability measures and λS is best supported across all levels, (ii) the maximum Floquet multiplier and λL have good construct validity, but negative predictive validity in models, negative convergent validity and (for λL) negative predictive validity in observational studies, (iii) long-range correlations lack construct validity and predictive validity in models and have negative convergent validity, and (iv) measures derived from perturbation experiments have good construct validity, but data are lacking on convergent validity in experimental studies and predictive validity in observational studies. In closing, directions for future research on dynamic gait stability are discussed.

Is slow walking more stable

Several efforts have been made to study gait stability using measures derived from nonlinear time-series analysis. The maximum finite time Lyapunov exponent (lambda(max)) quantifies how a system responds to an infinitesimally small perturbation. Recent studies suggested that slow walking leads to lower lambda(max) values, and thus is more stable than fast walking, but these studies suffer from methodological limitations. We studied the effects of walking speed on the amount of kinematic variability and stability in human walking. Trunk motions of 15 healthy volunteers were recorded in 3D during 2 min of treadmill walking at different speeds. From those time series, maximum Lyapunov exponents, indicating short-term and long-term divergence (lambda(S-stride) and lambda(L-stride)), and mean standard deviation (MeanSD) were calculated. lambda(S-stride) showed a linear decrease with increasing speed for forward-backward (AP) movements and quadratic effects (inverted U-shaped) for medio-lateral (ML) and up-down (VT) movements. lambda(L-stride) showed a quadratic effect (inverted U-shaped) of walking speed for AP movements, a linear decrease for ML movements, and a linear increase for VT movements. Moreover, positive correlations between lambda(S) and MeanSD were found for all directions, while lambda(L-stride) and MeanSD were correlated negatively in the AP direction. The different effects of walking speed on lambda(S-stride) and lambda(L-stride) for the different planes suggest that slow walking is not necessarily more stable than fast walking. The absence of a consistent pattern of correlations between lambda(L-stride) and MeanSD over the three directions suggests that variability and stability reflect, at least to a degree, different properties of the dynamics of walking.

Statistical precision and sensitivity of measures of dynamic gait stability.

Recently, two methods for quantifying a systems dynamic stability have been applied to human locomotion: local stability (quantified by finite time maximum Lyapunov exponents, lambda(S-stride) and lambda(L-stride)) and orbital stability (quantified as maximum Floquet multipliers, MaxFm). Thus far, however, it has remained unclear how many data points are required to obtain precise estimates of these measures during walking, and to what extent these estimates are sensitive to changes in walking behaviour. To resolve these issues, we collected long data series of healthy subjects (n=9) walking on a treadmill in three conditions (normal walking at 0.83 m/s (3 km/h) and 1.38 m/s (5 km/h), and walking at 1.38 m/s (5 km/h) while performing a Stroop dual task). Data series from 0.83 and 1.38 m/s trials were submitted to a bootstrap procedure and paired t-tests for samples of different data series lengths were performed between 0.83 and 1.38 m/s and between 1.38 m/s with and without Stroop task. Longer data series led to more precise estimates for lambda(S-stride), lambda(L-stride), and MaxFm. All variables showed an effect of data series length. Thus, when estimating and comparing these variables across conditions, data series covering an equal number of strides should be analysed. lambda(S-stride), lambda(L-stride), and MaxFm were sensitive to the change in walking speed while only lambda(S-stride) and MaxFm were sensitive enough to capture the modulations of walking induced by the Stroop task. Still, these modulations could only be detected when using a substantial number of strides (>150).

The effects of arm swing on human gait stability

SUMMARY Arm swing during human gait has been shown to reduce both angular momentum about the vertical and energy expenditure, and has been hypothesized to enhance gait stability. To examine this hypothesis, we studied the effect of arm swing on the local and global stability of steady-state gait, as well as the ability to perform adequate recovery actions following a perturbation. Trunk kinematics of 11 male subjects was measured in treadmill walking with normal and with restricted arm swing. In half of the trials, gait was perturbed by a position-controlled forward pull to the trunk. We constructed state spaces using data recorded from the unperturbed steady-state walking trials, and quantified local gait stability by calculating maximum Lyapunov exponents. In addition, we analyzed perturbation forces, the distance from the unperturbed gait pattern, and the return toward the normal gait pattern following an external perturbation. Walking without arm swing led to a non-significantly lower Lyapunov exponent (P=0.06), significantly higher perturbation forces (P<0.05), and significantly slower movements away from the attractor (P<0.01). These results suggest that gait without arm swing is characterized by similar local stability to gait with arm swing and a higher perturbation resistance. However, return towards the normal gait pattern was significantly slower (P<0.05) when walking with restricted arms, suggesting that the arms play an important role in the recovery from a perturbation. Collectively, the results suggest that arm swing as such does not enhance gait stability, but rather that recovery movements of the arms contribute to the overall stability of human gait.

The how and why of arm swing during human walking.

Humans walk bipedally, and thus, it is unclear why they swing their arms. In this paper, we will review the mechanisms and functions of arm swinging in human gait. First, we discuss the potential advantages of having swinging arms. Second, we go into the detail on the debate whether arm swing is arising actively or passively, where we will conclude that while a large part of arm swinging is mechanically passive, there is an active contribution of muscles (i.e. an activity that is not merely caused by stretch reflexes). Third, we describe the possible function of the active muscular contribution to arm swinging in normal gait, and discuss the possibility that a Central Pattern Generator (CPG) generates this activity. Fourth, we discuss examples from pathological cases, in which arm swinging is affected. Moreover, using the ideas presented, we suggest ways in which arm swing may be used as a therapeutic aid. We conclude that (1) arm swing should be seen as an integral part of human bipedal gait, arising mostly from passive movements, which are stabilized by active muscle control, which mostly originates from locomotor circuits in the central nervous system (2) arm swinging during normal bipedal gait most likely serves to reduce energy expenditure and (3) arm swinging may be of therapeutic value.

Sensitivity of trunk variability and stability measures to balance impairments induced by galvanic vestibular stimulation during gait

For targeted prevention of falls, it is necessary to identify individuals with balance impairments. To test the sensitivity of measures of variability, local stability and orbital stability of trunk kinematics to balance impairments during gait, we used galvanic vestibular stimulation (GVS) to impair balance in 12 young adults while walking on a treadmill at different speeds. Inertial sensors were used to measure trunk accelerations, from which variability in the medio-lateral direction and local and orbital stability were calculated. The short-term Lyapunov exponent and variability reflected the destabilizing effect of GVS, while the long-term Lyapunov exponent and Floquet multipliers suggested increased stability. Therefore, we concluded that only short-term Lyapunov exponents and variability can be used to asses stability of gait. In addition, to investigate the feasibility of using these measures in screening for fall risk, the presence or absence of GVS was predicted with variability and the short-term Lyapunov exponent. Predictions were good at all walking speeds, but best at preferred walking speed, with a correct classification in 83.3% of the cases.

Mechanical coupling between transverse plane pelvis and thorax rotations during gait is higher in people with low back pain

This study investigated whether people with low back pain (LBP) reduce variability of movement between the pelvis and thorax (trunk) in the transverse plane during gait at different speeds compared to healthy controls. Thirteen people with chronic LBP and twelve healthy controls walked on a treadmill at speeds from 0.5 to 1.72 m/s, with increments of 0.11 m/s. Step-to-step variability of the trunk, pelvis, and thorax rotations were calculated. Step-to-step deviations of pelvis and thorax rotations from the average pattern (residual rotations) were correlated to each other, and the linear regression coefficients between these deviations calculated. Spectral analysis was used to determine the frequencies of the residual rotations, to infer the relation of reduced trunk variability to trunk stiffness and/or damping. Variability of trunk motion (thorax relative to pelvis) was lower (P=0.02), covariance between the residual rotations of pelvis and thorax motions was higher (P=0.03), and the linear regression coefficients were closer to 1 (P=0.05) in the LBP group. Most power of segmental residual rotations was below stride frequency (~1 Hz). In this frequency range, trunk residual rotations had less power than pelvis or thorax residual rotations. These data show that people with LBP had lower variability of trunk rotations, as a result of the coupling of deviations of residual rotations in one segment to deviations of a similar shape (correlation) and amplitude (regression coefficient) in the other segment. These results support the argument that people with LBP adopt a protective movement strategy, possibly by increased trunk stiffness.

Gait in Pregnancy-related Pelvic girdle Pain: amplitudes, timing, and coordination of horizontal trunk rotations

Walking is impaired in Pregnancy-related Pelvic girdle Pain (PPP). Walking velocity is reduced, and in postpartum PPP relative phase between horizontal pelvis and thorax rotations was found to be lower at higher velocities, and rotational amplitudes tended to be larger. While attempting to confirm these findings for PPP during pregnancy, we wanted to identify underlying mechanisms. We compared gait kinematics of 12 healthy pregnant women and 12 pregnant women with PPP, focusing on the amplitudes of transverse segmental rotations, the timing and relative phase of these rotations, and the amplitude of spinal rotations. In PPP during pregnancy walking velocity was lower than in controls, and negatively correlated with fear of movement. While patients’ rotational amplitudes were larger, with large inter-individual differences, spinal rotations did not differ between groups. In the patients, peak thorax rotation occurred earlier in the stride cycle at higher velocities, and relative phase was lower. The earlier results on postpartum PPP were confirmed for PPP during pregnancy. Spinal rotations remained unaffected, while at higher velocities the peak of thorax rotations occurred earlier in the stride cycle. The latter change may serve to avoid excessive spine rotations caused by the larger segmental rotations.

Optimal inertial sensor location for ambulatory measurement of trunk inclination

Trunk inclination (TI) is used often to quantify back loading in ergonomic workplace evaluation. The aim of the present study was to determine whether TI can be obtained using a single inertial sensor (IS) on the back, and to determine the optimal IS location on the back for the estimation of TI. Gold standard TI, the angle between the vertical and the line connecting the L5/S1 joint and the trunk centre of mass, was measured using an optoelectronic system. Ten subjects performed experimental trials, each consisting of a symmetric and an asymmetric lifting task, and of a left-right lateral flexion movement. Trials were repeated and, in between trials, the IS was shifted in small steps from a location on the thorax towards a location on the sacrum. Optimal IS location was defined as the IS location with minimum root-mean-square (RMS) error between the gold standard TI and the IS TI. Averaged over subjects, the optimal IS location for symmetric and asymmetric lifting was at about 25% of the distance from the midpoint between the posterior superior iliac spines (MPSIS) to the C7 spinous process. The RMS error at this location, averaged over subjects, was 4.6+/-2.9 degrees. For the left-right lateral flexion task, the optimal IS location was at about 30% of the MPSIS to C7 distance. Because in most activities of daily living, pure lateral flexion does not occur often, it is recommended place the IS at 25% of the distance from the MPSIS to C7.

Is interlimb coordination during walking preserved in children with cerebral palsy

Arm movements during gait in children with cerebral palsy (CP) are altered compared to typically developing children (TD). We investigated whether these changes in arm movements alter interlimb coordination in CP gait. 3D gait analysis was performed in CP (diplegia [DI]: N = 15 and hemiplegia [HE]: N = 11) and TD (N = 24) children at preferred and fast walking speeds. Mean Relative Phase (MRP, i.e. mean over the gait cycle of the Continuous Relative Phase or CRP) was calculated as a measure of coordination, standard deviation of CRP was used as a measure of coordinative stability, and the sign of MRP indicated which limb was leading (for all pair combinations of the four limbs). In HE, coordination was significantly altered, less stable and a different leading limb was found compared to TD whenever the most affected arm was included in the studied limb pair. In DI, coordination deteriorated significantly when any of the two legs was included in the studied limb pair, and coordinative stability was significantly affected when any of the two arms was included. In almost all limb pair combinations, a different limb was leading in DI compared to TD. Increasing walking speed significantly improved coordination and coordinative stability of several limb pairs in DI. Coordination and limb-leading deficits were mostly linked to the affected limb. The compensating (non-affected) arm primarily affected coordinative stability, which underlines the importance of active arm movements in HE. Increasing walking speed may be used to improve interlimb coordination in DI.