Estimating Dynamic Gait Stability Using Data from Non-aligned Inertial Sensors

Recently, two methods for quantifying the stability of a dynamical system have been applied to human locomotion: local stability (quantified by finite time maximum Lyapunov exponents, λs and λL) and orbital stability (quantified by maximum Floquet multipliers, MaxFm). In most studies published to date, data from optoelectronic measurement systems were used to calculate these measures. However, using wireless inertial sensors may be more practical as they are easier to use, also in ambulatory applications. While inertial sensors have been employed in some studies, it is unknown whether they lead to similar stability estimates as obtained with optoelectronic measurement systems. In the present study, we compared stability measures of human walking estimated from an optoelectronic measurement system with those calculated from an inertial sensor measurement system. Subjects walked on a treadmill at three different speeds while kinematics were recorded using both measurement systems. From the angular velocities and linear accelerations, λs, λL, and MaxFm were calculated. Both measurement systems showed the same effects of walking speed for all variables. Estimates from both measurement systems correlated high for λs and λL, (R > 0.85) but less strongly for MaxFm (R = 0.66). These results indicate that inertial sensors constitute a valid alternative for an optoelectronic measurement system when assessing dynamic stability in human locomotion, and may thus be used instead, which paves the way to studying gait stability during natural, everyday walking

Sensitivity of Local Dynamic Stability of Over-Ground Walking to Balance Impairment Due to Galvanic Vestibular Stimulation

Impaired balance control during gait can be detected by local dynamic stability measures. For clinical applications, the use of a treadmill may be limiting. Therefore, the aim of this study was to test sensitivity of these stability measures collected during short episodes of over-ground walking by comparing normal to impaired balance control. Galvanic vestibular stimulation (GVS) was used to impair balance control in 12 healthy adults, while walking up and down a 10 m hallway. Trunk kinematics, collected by an inertial sensor, were divided into episodes of one stroll along the hallway. Local dynamic stability was quantified using short-term Lyapunov exponents (λs), and subjected to a bootstrap analysis to determine the effects of number of episodes analysed on precision and sensitivity of the measure. λs increased from 0.50 ± 0.06 to 0.56 ± 0.08 (p = 0.0045) when walking with GVS. With increasing number of episodes, coefficients of variation decreased from 10 ± 1.3% to 5 ± 0.7% and the number of p values >0.05 from 42 to 3.5%, indicating that both precision of estimates of λs and sensitivity to the effect of GVS increased. λs calculated over multiple episodes of over-ground walking appears to be a suitable measure to calculate local dynamic stability on group level

Kinematic variability, fractal dynamics and local dynamic stability of treadmill walking

<p>Abstract</p> <p>Background</p> <p>Motorized treadmills are widely used in research or in clinical therapy. Small kinematics, kinetics and energetics changes induced by Treadmill Walking (TW) as compared to Overground Walking (OW) have been reported in literature. The purpose of the present study was to characterize the differences between OW and TW in terms of stride-to-stride variability. Classical (Standard Deviation, SD) and non-linear (fractal dynamics, local dynamic stability) methods were used. In addition, the correlations between the different variability indexes were analyzed.</p> <p>Methods</p> <p>Twenty healthy subjects performed 10 min TW and OW in a random sequence. A triaxial accelerometer recorded trunk accelerations. Kinematic variability was computed as the average SD (MeanSD) of acceleration patterns among standardized strides. Fractal dynamics (scaling exponent α) was assessed by Detrended Fluctuation Analysis (DFA) of stride intervals. Short-term and long-term dynamic stability were estimated by computing the maximal Lyapunov exponents of acceleration signals.</p> <p>Results</p> <p>TW did not modify kinematic gait variability as compared to OW (multivariate T², p = 0.87). Conversely, TW significantly modified fractal dynamics (t-test, p = 0.01), and both short and long term local dynamic stability (T²p = 0.0002). No relationship was observed between variability indexes with the exception of significant negative correlation between MeanSD and dynamic stability in TW (3 × 6 canonical correlation, r = 0.94).</p> <p>Conclusions</p> <p>Treadmill induced a less correlated pattern in the stride intervals and increased gait stability, but did not modify kinematic variability in healthy subjects. This could be due to changes in perceptual information induced by treadmill walking that would affect locomotor control of the gait and hence specifically alter non-linear dependencies among consecutive strides. Consequently, the type of walking (i.e. treadmill or overground) is important to consider in each protocol design.</p

Effects of an attention demanding task on dynamic stability during treadmill walking

<p>Abstract</p> <p>Background</p> <p>People exhibit increased difficulty balancing when they perform secondary attention-distracting tasks while walking. However, a previous study by Grabiner and Troy (<it>J. Neuroengineering Rehabil</it>., 2005) found that young healthy subjects performing a concurrent Stroop task while walking on a motorized treadmill exhibited <it>decreased </it>step width variability. However, measures of variability do not directly quantify how a system responds to perturbations. This study re-analyzed data from Grabiner and Troy 2005 to determine if performing the concurrent Stroop task directly affected the dynamic stability of walking in these same subjects.</p> <p>Methods</p> <p>Thirteen healthy volunteers walked on a motorized treadmill at their self-selected constant speed for 10 minutes both while performing the Stroop test and during undisturbed walking. This Stroop test consisted of projecting images of the name of one color, printed in text of a different color, onto a wall and asking subjects to verbally identify the color of the text. Three-dimensional motions of a marker attached to the base of the neck (C5/T1) were recorded. Marker velocities were calculated over 3 equal intervals of 200 sec each in each direction. Mean variability was calculated for each time series as the average standard deviation across all strides. Both "local" and "orbital" dynamic stability were quantified for each time series using previously established methods. These measures directly quantify how quickly small perturbations grow or decay, either continuously in real time (local) or discretely from one cycle to the next (orbital). Differences between Stroop and Control trials were evaluated using a 2-factor repeated measures ANOVA.</p> <p>Results</p> <p>Mean variability of trunk movements was significantly reduced during the Stroop tests compared to normal walking. Conversely, local and orbital stability results were mixed: some measures showed slight increases, while others showed slight decreases. In many cases, different subjects responded differently to the Stroop test. While some of our comparisons reached statistical significance, many did not. In general, measures of variability and dynamic stability reflected different properties of walking dynamics, consistent with previous findings.</p> <p>Conclusion</p> <p>These findings demonstrate that the decreased movement variability associated with the Stroop task did <it>not </it>translate to greater dynamic stability.</p

Describing Robotic Bat Flight with Stable Periodic Orbits

From a dynamic system point of view, bat locomotion stands out among other forms of flight. During a large part of bat wingbeat cycle the moving body is not in a static equilibrium. This is in sharp contrast to what we observe in other simpler forms of flight such as insects, which stay at their static equilibrium. Encouraged by biological examinations that have revealed bats exhibit periodic and stable limit cycles, this work demonstrates that one effective approach to stabilize articulated flying robots with bat morphology is locating feasible limit cycles for these robots; then, designing controllers that retain the closed-loop system trajectories within a bounded neighborhood of the designed periodic orbits. This control design paradigm has been evaluated in practice on a recently developed bio-inspired robot called Bat Bot (B2)

Do Humans Optimally Exploit Redundancy to Control Step Variability in Walking?

It is widely accepted that humans and animals minimize energetic cost while walking. While such principles predict average behavior, they do not explain the variability observed in walking. For robust performance, walking movements must adapt at each step, not just on average. Here, we propose an analytical framework that reconciles issues of optimality, redundancy, and stochasticity. For human treadmill walking, we defined a goal function to formulate a precise mathematical definition of one possible control strategy: maintain constant speed at each stride. We recorded stride times and stride lengths from healthy subjects walking at five speeds. The specified goal function yielded a decomposition of stride-to-stride variations into new gait variables explicitly related to achieving the hypothesized strategy. Subjects exhibited greatly decreased variability for goal-relevant gait fluctuations directly related to achieving this strategy, but far greater variability for goal-irrelevant fluctuations. More importantly, humans immediately corrected goal-relevant deviations at each successive stride, while allowing goal-irrelevant deviations to persist across multiple strides. To demonstrate that this was not the only strategy people could have used to successfully accomplish the task, we created three surrogate data sets. Each tested a specific alternative hypothesis that subjects used a different strategy that made no reference to the hypothesized goal function. Humans did not adopt any of these viable alternative strategies. Finally, we developed a sequence of stochastic control models of stride-to-stride variability for walking, based on the Minimum Intervention Principle. We demonstrate that healthy humans are not precisely “optimal,” but instead consistently slightly over-correct small deviations in walking speed at each stride. Our results reveal a new governing principle for regulating stride-to-stride fluctuations in human walking that acts independently of, but in parallel with, minimizing energetic cost. Thus, humans exploit task redundancies to achieve robust control while minimizing effort and allowing potentially beneficial motor variability

Persistent fluctuations in stride intervals under fractal auditory stimulation

Copyright @ 2014 Marmelat et al. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.Stride sequences of healthy gait are characterized by persistent long-range correlations, which become anti-persistent in the presence of an isochronous metronome. The latter phenomenon is of particular interest because auditory cueing is generally considered to reduce stride variability and may hence be beneficial for stabilizing gait. Complex systems tend to match their correlation structure when synchronizing. In gait training, can one capitalize on this tendency by using a fractal metronome rather than an isochronous one? We examined whether auditory cues with fractal variations in inter-beat intervals yield similar fractal inter-stride interval variability as isochronous auditory cueing in two complementary experiments. In Experiment 1, participants walked on a treadmill while being paced by either an isochronous or a fractal metronome with different variation strengths between beats in order to test whether participants managed to synchronize with a fractal metronome and to determine the necessary amount of variability for participants to switch from anti-persistent to persistent inter-stride intervals. Participants did synchronize with the metronome despite its fractal randomness. The corresponding coefficient of variation of inter-beat intervals was fixed in Experiment 2, in which participants walked on a treadmill while being paced by non-isochronous metronomes with different scaling exponents. As expected, inter-stride intervals showed persistent correlations similar to self-paced walking only when cueing contained persistent correlations. Our results open up a new window to optimize rhythmic auditory cueing for gait stabilization by integrating fractal fluctuations in the inter-beat intervals.Commission of the European Community and the Netherlands Organisation for Scientific Research

Toe clearance and velocity profiles of young and elderly during walking on sloped surfaces

Background Most falls in older adults are reported during locomotion and tripping has been identified as a major cause of falls. Challenging environments (e.g., walking on slopes) are potential interventions for maintaining balance and gait skills. The aims of this study were: 1) to investigate whether or not distributions of two important gait variables [minimum toe clearance (MTC) and foot velocity at MTC (VelMTC)] and locomotor control strategies are altered during walking on sloped surfaces, and 2) if altered, are they maintained at two groups (young and elderly female groups). Methods MTC and VelMTC data during walking on a treadmill at sloped surfaces (+3°, 0° and -3°) were analysed for 9 young (Y) and 8 elderly (E) female subjects. Results MTC distributions were found to be positively skewed whereas VelMTC distributions were negatively skewed for both groups on all slopes. Median MTC values increased (Y = 33%, E = 7%) at negative slope but decreased (Y = 25%, E = 15%) while walking on the positive slope surface compared to their MTC values at the flat surface (0°). Analysis of VelMTC distributions also indicated significantly (p < 0.05) lower minimum and 25th percentile (Q1) values in the elderly at all slopes. Conclusion The young displayed a strong positive correlation between MTC median changes and IQR (interquartile range) changes due to walking on both slopes; however, such correlation was weak in the older adults suggesting differences in control strategies being employed to minimize the risk of tripping

Use of Motor Abundance in Young and Older Adults during Dual-Task Treadmill Walking

Contains fulltext : 110120.pdf (publisher's version ) (Open Access)Motor abundance allows individuals to perform any task reliably while being variable in movement's particulars. The study investigated age-related differences in this feature when young adults (YA) and older adults (OA) performed challenging tasks, namely treadmill walking alone and while performing a cognitive task. A goal function for treadmill walking was first defined, i.e., maintain constant speed at each step, which led to a goal equivalent manifold (GEM) containing all combinations of step time and step length that equally satisfied the function. Given the GEM, amounts of goal-equivalent and non-goal-equivalent variability were afterwards determined and used to define an index providing information about the set of effective motor solutions relative to the GEM. The set was limited in OA compared to YA in treadmill walking alone, indicating that OA made less flexible use of motor abundance than YA. However, this differentiation between YA and OA disappeared when concurrently performing the cognitive task. It is proposed that OA might have benefited from cognitive compensation

Fractal analyses reveal independent complexity and predictability of gait

Locomotion is a natural task that has been assessed for decades and used as a proxy to highlight impairments of various origins. So far, most studies adopted classical linear analyses of spatio-temporal gait parameters. Here, we use more advanced, yet not less practical, non-linear techniques to analyse gait time series of healthy subjects. We aimed at finding more sensitive indexes related to spatio-temporal gait parameters than those previously used, with the hope to better identify abnormal locomotion. We analysed large-scale stride interval time series and mean step width in 34 participants while altering walking direction (forward vs. backward walking) and with or without galvanic vestibular stimulation. The Hurst exponent α and the Minkowski fractal dimension D were computed and interpreted as indexes expressing predictability and complexity of stride interval time series, respectively. These holistic indexes can easily be interpreted in the framework of optimal movement complexity. We show that α and D accurately capture stride interval changes in function of the experimental condition. Walking forward exhibited maximal complexity (D) and hence, adaptability. In contrast, walking backward and/or stimulation of the vestibular system decreased D. Furthermore, walking backward increased predictability (α) through a more stereotyped pattern of the stride interval and galvanic vestibular stimulation reduced predictability. The present study demonstrates the complementary power of the Hurst exponent and the fractal dimension to improve walking classification. Our developments may have immediate applications in rehabilitation, diagnosis, and classification procedures