Onno G. Meijer

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.

Deficits in the coordination of agonist and antagonist muscles in stroke patients: implications for normal motor control

Movement impairments about a single joint in stroke patients may be related to deficits in the central regulation of stretch reflex (SR) thresholds of agonist and antagonist muscles. One boundary of the SR threshold range for elbow flexor and extensor muscles was measured in hemiparetic subjects by analysing electromyographic activity during stretching of relaxed muscles at seven different velocities. For each velocity, dynamic SR thresholds were measured as angles at which electromyographic activity appeared. These data were used to determine the sensitivity of the threshold to velocity and the static SR thresholds for flexors and extensors. In contrast to relaxed muscles in healthy subjects, static flexor and extensor thresholds lay within the physiological range in 11/12 and 4/12 subjects, respectively. This implies that, in the range between the static SR threshold and one of the physiological joint limits, relaxation of the muscle was impossible. Subjects then made slow movements against different loads to determine their ranges of active movement. Maximal flexor and extensor torques were lower in hemiparetic subjects throughout the angular range. In some subjects, ranges were found in which no active torque could be produced in either extensor or both muscle groups. These ranges were related to the boundary values of SR thresholds found during passive muscle stretch. The range in which reciprocally organized agonist and antagonist muscle activity could be generated was limited in all but one subject. When attempting to produce torque from positions outside their measured range of movement, excessive muscle coactivation occurred, typically producing no or paradoxical motion in the opposite direction. Results suggest a relationship between spasticity measured at rest and the movement deficit in stroke by demonstrating a link between motor deficits and control deficits in the central regulation of individual SR thresholds.

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).

Pelvis-thorax coordination in the transverse plane during walking in persons with nonspecific low back pain

Study Design. Transverse pelvis and thorax rotations were studied during walking in 39 patients with nonspecific low back pain and 19 healthy participants. Objectives. To gain insight into the consequences of low back pain for gait and to identify clinically useful measures for characterizing the quality of walking in patients with low back pain. Summary of Background Data. Gait studies in patients with low back pain have reported a decrease in walking velocity. In normal gait, in-phase pelvis-thorax coordination (synchronicity) evolves toward antiphase coordination (counterrotation) as walking velocity increases. This study examined the effect of walking velocity on pelvis and thorax rotations in patients with low back pain. Methods. Amplitudes of pelvis and thorax rotations were calculated, and spectral analyses were performed. Pelvis-thorax coordination was characterized in terms of relative Fourier phase, and coupling strength was assessed by means of cross-spectral analysis. Results. In comparison with healthy participants, relative Fourier phase was significantly smaller in low back pain patients for walking velocities of 3.8 km/h and higher, whereas coupling strength was significantly higher for velocities from 1.4 to 3.0 km/h. No significant group differences were found in amplitude or spectral content of individual pelvis and thorax rotations. Conclusion. In comparison with healthy participants, the gait of patients with low back pain was characterized by a more rigid, less flexible pelvis-thorax coordination in the absence of significant differences in the kinematics of the component rotations. This result suggests that coordination measures are more adequate in assessing quality of walking in patients with low back pain than are kinematic measures pertaining to the individual segment rotations, and that conservative therapy should use methods aimed at improving intersegmental coordination.

Pelvis-thorax coordination in the transverse plane during gait

The coordination between horizontal pelvic and thoracic rotations during treadmill walking was studied in ten subjects. Previous studies have considered the relative phase using the mean to characterize coordination mode, and the S.D. as an index of its stability. However, to use S.D. of relative phase as a measure for coordinative stability, the underlying oscillations have to be phase-locked at a certain value. Random fluctuations around this value can then be viewed as stochastic perturbations of a stable fixed point, resulting in a unimodal distribution of relative phase. Using methods of circular statistics this study shows that these conditions were not met in pelvis-thorax coordination. Spectral analyses revealed that, as walking velocity increased, a triphasic component emerged in the pelvic rotations, while the thoracic rotations remained harmonic across all walking velocities. These findings refute the use of standard relative phase measures to capture pelvis-thorax coordination. An alternative measure is introduced, namely the difference between the continuous Fourier phases of the component oscillations as determined for the main frequency of the thorax oscillation. With this measure, pelvis-thorax coordination was found to evolve from in-phase coordination towards antiphase coordination as walking velocity increased. This method may be used to assess reliably the properties of pelvis-thorax coordination in both healthy and pathological gait patterns in the future.

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.

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.