Gait variability: methods, modeling and meaning

The study of gait variability, the stride-to-stride fluctuations in walking, offers a complementary way of quantifying locomotion and its changes with aging and disease as well as a means of monitoring the effects of therapeutic interventions and rehabilitation. Previous work has suggested that measures of gait variability may be more closely related to falls, a serious consequence of many gait disorders, than are measures based on the mean values of other walking parameters. The Current JNER series presents nine reports on the results of recent investigations into gait variability. One novel method for collecting unconstrained, ambulatory data is reviewed, and a primer on analysis methods is presented along with a heuristic approach to summarizing variability measures. In addition, the first studies of gait variability in animal models of neurodegenerative disease are described, as is a mathematical model of human walking that characterizes certain complex (multifractal) features of the motor control's pattern generator. Another investigation demonstrates that, whereas both healthy older controls and patients with a higher-level gait disorder walk more slowly in reduced lighting, only the latter's stride variability increases. Studies of the effects of dual tasks suggest that the regulation of the stride-to-stride fluctuations in stride width and stride time may be influenced by attention loading and may require cognitive input. Finally, a report of gait variability in over 500 subjects, probably the largest study of this kind, suggests how step width variability may relate to fall risk. Together, these studies provide new insights into the factors that regulate the stride-to-stride fluctuations in walking and pave the way for expanded research into the control of gait and the practical application of measures of gait variability in the clinical setting

Characteristics and coupling of cardiac and locomotor rhythms during treadmill walking tasks

Studying the variability of physiological subsystems (e.g., cardiac and locomotor control systems) has been insightful in understanding how functional and dysfunctional patterns emerge within their behaviors. The coupling of these subsystems (termed cardiolocomotor coupling) is believed to be important to maintain healthy functioning in the diverse conditions in which individuals must operate. Aging and pathology result in alterations to both the patterns of individual systems, as well as to how those systems couple to each other. By examining cardiac and locomotor rhythms concurrently during treadmill walking, it is possible to ascertain how these two rhythms relate to each other in different populations (i.e., younger and older adults) and with varying task constraints (i.e., a gait synchronization task or fast walking task). The purpose of this research was to simultaneously document the characteristics of cardiac and gait rhythms in younger (18-35 yrs) and older (63-80 yrs) healthy adults while walking and to establish the extent to which changes in these systems are coupled when gait is constrained. This study consisted of two repeated-measures experiments that participants completed on two separate days. Both experiments consisted of three 15-minute phases. During the first (baseline) and third (retention) phases of both experiments, participants walked with no cues or specific instructions at their preferred walking speed. During the second phase, participants were asked to synchronize their step falls to the timing of a visual cue (experiment 1) or to walk at 125% of their preferred walking speed (experiment 2). Fifty-one healthy adults (26 older, 67.67±4.70 yrs, 1.72±0.09 m, 70.13±14.30 kg; 25 younger, 24.57±4.29 yrs, 1.76±0.09 m, 73.34±15.35 kg) participated in this study. Participants’ cardiac rhythms (R-R interval time series) and locomotor rhythms (stride interval, step width, and step length time series) were measured while walking on a treadmill. Characteristics of variability in cardiac and locomotor rhythms and the coupling between cardiac and gait rhythms were measured. Results revealed that younger and older healthy adults alter gait patterns similarly when presented with a gait synchronization or fast walking task and that these tasks also alter cardiac patterns. Likewise, both groups exhibited enhanced cardiolocomotor coupling when tasked with a step timing constraint or increased speed during treadmill walking. Combined, these findings suggest that walking tasks likely alter both locomotor and cardiac dynamics and the coupling of physiological subsystems could be insightful in understanding the diverse effects aging and pathology have on individuals

Nonlinear dynamics indicates aging affects variability during gait

Objective. To investigate the nature of variability present in time series generated from gait parameters of two different age groups via a nonlinear analysis. Design. Measures of nonlinear dynamics were used to compare kinematic parameters between elderly and young females. Background. Aging may lead to changes in motor variability during walking, which may explain the large incidence of falls in the elderly. Methods. Twenty females, 10 younger (20–37 yr) and 10 older (71–79 yr) walked on a treadmill for 30 consecutive gait cycles. Time series from selected kinematic parameters of the right lower extremity were analyzed using nonlinear dynamics. The largest Lyapunov exponent and the correlation dimension of all time series, and the largest Lyapunov exponent of the original time series surrogated were calculated. Standard deviations and coefficient of variations were also calculated for selected discrete points from each gait cycle. Independent t-tests were used for statistical comparisons. Results. The Lyapunov exponents were found to be significantly different from their surrogate counterparts. This indicates that the fluctuations observed in the time series may reflect deterministic processes by the neuromuscular system. The elderly exhibited significantly larger Lyapunov exponents and correlation dimensions for all parameters evaluated indicating local instability. The linear measures indicated that the elderly demonstrated significantly higher variability. Conclusions. The nonlinear analysis revealed that fluctuations in the time series of certain gait parameters are not random but display a deterministic behavior. This behavior may degrade with physiologic aging resulting in local instability. Relevance Elderly show increased local instability or inability to compensate to the natural stride-to-stride variations present during locomotion. We hypothesized that this may be the one of the reasons for the increases in falling due to aging. Future efforts should attempt to evaluate this hypothesis by making comparisons to pathological subjects (i.e. elderly fallers), and examine the sensitivity and specificity of the nonlinear methods used in this study to aid clinical assessment

Gait variablility is altered in older adults when listening to auditory stimuli with differing temporal structures

Gait variability in the context of a deterministic dynamical system may be quantified using nonlinear time series analyses that characterize the complexity of the system. Pathological gait exhibits altered gait variability. It can be either too periodic and predictable, or too random and disordered, as it is the case with aging. While gait therapies often focus on restoration of linear measures such as gait speed or stride length, we propose that the goal of gait therapy should be to restore optimal gait variability, which exhibits chaotic fluctuations and is the balance between predictability and complexity. In this context, our purpose was to investigate how listening to different auditory stimuli affects gait variability. Twenty-seven young and 27 elderly subjects walked on a treadmill for 5 minutes while listening to white noise, a chaotic rhythm, a metronome, and with no auditory stimulus. Stride length, step width, and stride intervals were calculated for all conditions. Detrended Fluctuation Analysis was then performed on these time series. A quadratic trend analysis determined that an idealized inverted-U shape described the relationship between gait variability and the structure of the auditory stimuli for the elderly group, but not for the young group. This proof-of-concept study shows that the gait of older adults may be manipulated using auditory stimuli. Future work will investigate which structures of auditory stimuli lead to improvements in functional status in older adults

An Analysis of the Relationship Between Complexity and Gait Adaptability

The presented sequence of studies considers theoretical applications from Complexity Science and Chaos Theory for gait time-series analysis. The main goal of this research is to build on insights from a previous body of knowledge, which have identified measures derived from Complexity Science and Chaos Theory as critical markers of gait control. Specifically, the studies presented in this dissertation attempt to directly test whether characterizing gait complexity relates to an ability to flexibly adjust gait. The broader impact of this research is utilizing measures of complexity to characterize gait control, and as a tool for rehabilitation which have both gained momentum in fall prevention research. Through a series of four studies, this dissertation was designed to test the theoretical viewpoint that complexity is related to gait control, particularly gait adaptability. Firstly, I sought to develop a paradigm for reliably entraining gait complexity with the use of several auditory fluctuating timing imperatives which, differed based on specified fractal characteristics. I also sought to quantify the duration of the retention of gait complexity, following entrainment. Thirdly, I assessed whether attentional demands required during entrainment were affected by the fractal characteristics of a fluctuating timing imperative. Lastly, I applied the developed paradigm to evaluate the theoretical relationship between gait complexity and stepping performance. The findings from this dissertation have developed a framework for assessing gait control. This series of projects has determined that a fluctuating timing imperative can reliably prescribe the gait pattern of healthy individuals towards a particular complexity. The use of a fluctuating timing imperative leads to entrainment of the stimulus complexity. Furthermore, once the timing imperative has ceased, there is a brief period of complexity retention in the walking pattern. This dissertation has also confirmed that entraining complexity to a fluctuating timing imperative does not alter the attentional demands associated with entrainment. However, entraining gait to fluctuating timing imperatives of different complexities alters the stepping strategy that is adopted. Lastly, this dissertation has shown that synchronizing gait to a fixed-interval stimulus following entrainment, depends on the complexities of the gait pattern

Lyapunov Exponent and Surrogation Analysis of Patterns of Variability: Profiles in New Walkers With and Without Down Syndrome

In previous studies we found that preadolescents with Down syndrome (DS) produce higher amounts of variability (Smith et al., 2007) and larger Lyapunov exponent (LyE) values (indicating more instability) during walking than their peers with typical development (TD) (Buzzi & Ulrich, 2004). Here we use nonlinear methods to examine the patterns that characterize gait variability as it emerges, in toddlers with TD and with DS, rather than after years of practice. We calculated Lyapunov exponent (LyE) values to assess stability of leg trajectories. We also tested the use of 3 algorithms for surrogation analysis to investigate mathematical periodicity of toddlers’ strides. Results show that toddlers’ LyE values were not different between groups or with practice and strides of both groups become more periodic with practice. The underlying control strategies are not different between groups at this point in developmental time, although control strategies do diverge between the groups by preadolescence

Quantifying foot placement variability and dynamic stability of movement to assess control mechanisms during forward and lateral running

Research has indicated that human walking is more unstable in the secondary, rather than primary plane of progression. However, the mechanisms of controlling dynamic stability in different planes of progression during running remain unknown. The aim of this study was to compare variability (standard deviation and coefficient of variation) and dynamic stability (sample entropy and local divergence exponent) in anterior–posterior and medio-lateral directions in forward and lateral running patterns. For this purpose, fifteen healthy, male participants ran in a forward and lateral direction on a treadmill at their preferred running speeds. Coordinate data of passive reflective markers attached to body segments were recorded using a motion capture system. Results indicated that: (1) there is lower dynamic stability in the primary plane of progression during both forward and lateral running suggesting that, unlike walking, greater control might be required to regulate dynamic stability in the primary plane of progression during running, (2) as in walking, the control of stability in anterior–posterior and medio-lateral directions of running is dependent on the direction of progression, and (3), quantifying magnitude of variability might not be sufficient to understand control mechanisms in human movement and directly measuring dynamic stability could be an appropriate alternative

On the choice of multiscale entropy algorithm for quantification of complexity in gait data

The present study aimed at identifying a suitable multiscale entropy (MSE) algorithm for assessment of complexity in a stride-to-stride time interval time series. Five different algorithms were included (the original MSE, refine composite multiscale entropy (RCMSE), multiscale fuzzy entropy, generalized multiscale entropy and intrinsic mode entropy) and applied to twenty iterations of white noise, pink noise, or a sine wave with added white noise. Based on their ability to differentiate the level of complexity in the three different generated signal types, and their sensitivity and parameter consistency, MSE and RCMSE were deemed most appropriate. These two algorithms were applied to stride-to-stride time interval time series recorded from fourteen healthy subjects during one hour of overground and treadmill walking. In general, acceptable sensitivity and good parameter consistency were observed for both algorithms; however, they were not able to differentiate the complexity of the stride-to-stride time interval time series between the two walking conditions. Thus, the present study recommends the use of either MSE or RCMSE for quantification of complexity in stride-to-stride time interval time series

Movement Behavior of High-Heeled Walking: How Does the Nervous System Control the Ankle Joint during an Unstable Walking Condition?

The human locomotor system is flexible and enables humans to move without falling even under less than optimal conditions. Walking with high-heeled shoes constitutes an unstable condition and here we ask how the nervous system controls the ankle joint in this situation? We investigated the movement behavior of high-heeled and barefooted walking in eleven female subjects. The movement variability was quantified by calculation of approximate entropy (ApEn) in the ankle joint angle and the standard deviation (SD) of the stride time intervals. Electromyography (EMG) of the soleus (SO) and tibialis anterior (TA) muscles and the soleus Hoffmann (H-) reflex were measured at 4.0 km/h on a motor driven treadmill to reveal the underlying motor strategies in each walking condition. The ApEn of the ankle joint angle was significantly higher (p<0.01) during high-heeled (0.38±0.08) than during barefooted walking (0.28±0.07). During high-heeled walking, coactivation between the SO and TA muscles increased towards heel strike and the H-reflex was significantly increased in terminal swing by 40% (p<0.01). These observations show that high-heeled walking is characterized by a more complex and less predictable pattern than barefooted walking. Increased coactivation about the ankle joint together with increased excitability of the SO H-reflex in terminal swing phase indicates that the motor strategy was changed during high-heeled walking. Although, the participants were young, healthy and accustomed to high-heeled walking the results demonstrate that that walking on high-heels needs to be controlled differently from barefooted walking. We suggest that the higher variability reflects an adjusted neural strategy of the nervous system to control the ankle joint during high-heeled walking

A Method to Concatenate Multiple Short Time Series for Evaluating Dynamic Behaviour During Walking

Gait variability is a sensitive metric for assessing functional deficits in individuals with mobility impairments. To correctly represent the temporal evolution of gait kinematics, nonlinear measures require extended and uninterrupted time series. In this study, we present and validate a novel algorithm for concatenating multiple time-series in order to allow the nonlinear analysis of gait data from standard and unrestricted overground walking protocols. The fullbody gait patterns of twenty healthy subjects were captured during five walking trials (at least 5 minutes) on a treadmill under different weight perturbation conditions. The collected time series were cut into multiple shorter time series of varying lengths and subsequently concatenated using a novel algorithm that identifies similar poses in successive time series in order to determine an optimal concatenation time point. After alignment of the datasets, the approach then concatenated the data to provide a smooth transition. Nonlinear measures to assess stability (Largest Lyapunov Exponent, LyE) and regularity (Sample Entropy, SE) were calculated in order to quantify the efficacy of the concatenation approach using intra-class correlation coefficients, standard error of measurement and paired effect sizes. Our results indicate overall good agreement between the full uninterrupted and the concatenated time series for LyE. However, SE was more sensitive to the proposed concatenation algorithm and might lead to false interpretation of physiological gait signals. This approach opens perspectives for analysis of dynamic stability of gait data from physiological overground walking protocols, but also the re-processing and estimation of nonlinear metrics from previously collected datasets