Effects of walking speed, strength and range of motion on gait stability in healthy older adults

Falls pose a tremendous risk to those over 65 and most falls occur during locomotion. Older adults commonly walk slower, which many believe helps improve walking stability. While increased gait variability predicts future fall risk, increased variability is also caused by walking slower. Thus, we need to better understand how differences in age and walking speed independently affect dynamic stability during walking. We investigated if older adults improved their dynamic stability by walking slower, and how leg strength and flexibility (passive range of motion (ROM)) affected this relationship. Eighteen active healthy older and 17 healthy younger adults walked on a treadmill for 5min each at each of 5 speeds (80-120% of preferred). Local divergence exponents and maximum Floquet multipliers (FM) were calculated to quantify each subject's inherent local dynamic stability. The older subjects walked with the same preferred walking speeds as the younger subjects (p=0.860). However, these older adults still exhibited greater local divergence exponents (p<0.0001) and higher maximum FM (p<0.007) than the younger adults at all walking speeds. These older adults remained more locally unstable (p<0.04) even after adjusting for declines in both strength and ROM. In both age groups, local divergence exponents decreased at slower speeds and increased at faster speeds (p<0.0001). Maximum FM showed similar changes with speed (p<0.02). Both younger and older adults exhibited decreased instability by walking slower, in spite of increased variability. These increases in dynamic instability might be more sensitive indicators of future fall risk than changes in gait variability.     

The effects of sensory loss and walking speed on the orbital dynamic stability of human walking

Peripheral sensory feedback is believed to contribute significantly to maintaining walking stability. Patients with diabetic peripheral neuropathy have a greatly increased risk of falling. Previously, we demonstrated that slower walking speeds in neuropathic patients lead to improved local dynamic stability. However, all subjects exhibited significant local instability during walking, even though no subject fell or stumbled during testing. The present study was conducted to determine if and how significant changes in peripheral sensation and walking speed affect orbital stability during walking. Trunk and lower extremity kinematics were examined from two prior experiments that compared patients with significant neuropathy to healthy controls and walking at multiple different speeds in young healthy subjects. Maximum Floquet multipliers were computed for each time series to quantify the orbital stability of these movements. All subjects exhibited orbitally stable walking kinematics, even though these same kinematics were previously shown to be locally unstable. Differences in orbital stability between neuropathic and control subjects were small and, with the exception of knee joint movements (p=0.001), not statistically significant (0.380p0.946). Differences in knee orbital stability were not mediated by differences in walking speed. This was supported by our finding that although orbital stability improved slightly with slower walking speeds, the correlations between walking speed and orbital stability were generally weak (r(2)16.7%). Thus, neuropathic patients do not gain improved orbital stability as a result of slowing down and do not experience any loss of orbital stability because of their sensory deficits.     

Dynamic stability of passive dynamic walking on an irregular surface

Falls that occur during walking are a significant health problem. One of the greatest impediments to solve this problem is that there is no single obviously "correct" way to quantify walking stability. While many people use variability as a proxy for stability, measures of variability do not quantify how the locomotor system responds to perturbations. The purpose of this study was to determine how changes in walking surface variability affect changes in both locomotor variability and stability. We modified an irreducibly simple model of walking to apply random perturbations that simulated walking over an irregular surface. Because the model's global basin of attraction remained fixed, increasing the amplitude of the applied perturbations directly increased the risk of falling in the model. We generated ten simulations of 300 consecutive strides of walking at each of six perturbation amplitudes ranging from zero (i.e., a smooth continuous surface) up to the maximum level the model could tolerate without falling over. Orbital stability defines how a system responds to small (i.e., "local") perturbations from one cycle to the next and was quantified by calculating the maximum Floquet multipliers for the model. Local stability defines how a system responds to similar perturbations in real time and was quantified by calculating short-term and long-term local exponential rates of divergence for the model. As perturbation amplitudes increased, no changes were seen in orbital stability (r(2)=2.43%; p=0.280) or long-term local instability (r(2)=1.0%; p=0.441). These measures essentially reflected the fact that the model never actually "fell" during any of our simulations. Conversely, the variability of the walker's kinematics increased exponentially (r(2)>or=99.6%; p<0.001) and short-term local instability increased linearly (r(2)=88.1%; p<0.001). These measures thus predicted the increased risk of falling exhibited by the model. For all simulated conditions, the walker remained orbitally stable, while exhibiting substantial local instability. This was because very small initial perturbations diverged away from the limit cycle, while larger initial perturbations converged toward the limit cycle. These results provide insight into how these different proposed measures of walking stability are related to each other and to risk of falling.     

Dynamic stability of human walking in visually and mechanically destabilizing environments

Understanding how humans remain stable during challenging locomotor activities is critical to developing effective tests to diagnose patients with increased fall risk. This study determined if different continuous low-amplitude perturbations would induce specific measureable changes in measures of dynamic stability during walking. We applied continuous pseudo-random oscillations of either the visual scene or support surface in either the anterior-posterior or mediolateral directions to subjects walking in a virtual environment with speed-matched optic flow. Floquet multipliers and short-term local divergence exponents both increased (indicating greater instability) during perturbed walking. These responses were generally much stronger for body movements occurring in the same directions as the applied perturbations. Likewise, subjects were more sensitive to both visual and mechanical perturbations applied in the mediolateral direction than to those applied in the anterior-posterior direction, consistent with previous experiments and theoretical predictions. These responses were likewise consistent with subjects' anecdotal perceptions of which perturbation conditions were most challenging. Contrary to the Floquet multipliers and short-term local divergence exponents, which both increased, long-term local divergence exponents decreased during perturbed walking. However, this was consistent with specific changes in the mean log divergence curves, which indicated that subjects' movements reached their maximum local divergence limits more quickly during perturbed walking. Overall, the Floquet multipliers were less sensitive, but reflected greater specificity in their responses to the different perturbation conditions. Conversely, the short-term local divergence exponents exhibited less specificity in their responses, but were more sensitive measures of instability in general.     

Dynamics and stability of muscle activations during walking in healthy young and older adults

To facilitate stable walking, humans must generate appropriate motor patterns and effective corrective responses to perturbations. Yet most EMG analyses do not address the continuous nature of muscle activation dynamics over multiple strides. We compared muscle activation dynamics in young and older adults by defining a multivariate state space for muscle activity. Eighteen healthy older and 17 younger adults walked on a treadmill for 2 trials of 5 min each at each of 5 controlled speeds (80–120% of preferred). EMG linear envelopes of v. lateralis, b. femoris, gastrocnemius, and t. anterior of the left leg were obtained. Interstride variability, local dynamic stability (divergence exponents), and orbital stability (maximum Floquet multipliers; FM) were calculated. Both age groups exhibited similar preferred walking speeds (p=0.86). Amplitudes and variability of individual EMG linear envelopes increased with speed (p<0.01) in all muscles but gastrocnemius. Older adults also exhibited greater variability in b. femoris and t. anterior (p<0.004). When comparing continuous multivariate EMG dynamics, older adults demonstrated greater local and orbital instability of their EMG patterns (p<0.01). We also compared how muscle activation dynamics were manifested in kinematics. Local divergence exponents were strongly correlated between kinematics and EMG, independent of age and walking speed, while variability and max FM were not. These changes in EMG dynamics may be related to increased neuromotor noise associated with aging and may indicate subtle deterioration of gait function that could lead to future functional declines.     

Effects of perturbation magnitude on dynamic stability when walking in destabilizing environments

External perturbations applied to the walking surface or visual field can challenge an individual's ability to maintain stability during walking. Accurately quantifying and predicting changes in stability during walking will further our understanding of how individuals respond to challenges encountered during daily life and guide the development of assessments and rehabilitation interventions for individuals at increased risk of falling. This study is the first to determine how orbital and local dynamic stability metrics, including maximum Floquet multipliers and local divergence exponents, change in response to continuous mediolateral visual and surface perturbations of different amplitudes. Eleven healthy individuals walked in a fully immersive virtual environment. Participants completed two 3-min walking trials each under the following nine conditions: no perturbations, surface perturbations at each of 3 amplitudes, and visual perturbations at each of 5 amplitudes. All perturbations were applied as continuous pseudo-random oscillations. During both surface and visual perturbations, individuals were significantly more orbitally and locally unstable compared to un-perturbed walking. As walking surface perturbation amplitudes increased, individuals were more orbitally (but not locally) unstable. As visual perturbation amplitudes increased, individuals were more locally (but not orbitally) unstable between lower and higher amplitudes. Overall, these dynamic stability metrics were much less sensitive to changes in perturbation amplitudes than to differences between un-perturbed and perturbed walking, or to differences between mechanical and visual perturbations. This suggests that the type of perturbation(s) applied has a far greater impact than the magnitude of those perturbations in determining the response that will be elicited.     

Local dynamic stability versus kinematic variability of continuous overground and treadmill walking

This study quantified the relationships between local dynamic stabiliht and variabilitr during continuous overground and treadmill walking. Stride-to-stride standard deviations were computed from temporal and kinematic data. Marimum finite-time Lyapunov exponents were estimated to quantify local dynamic stability. Local stability of gait kinematics was shown to be achieved over multiple consecutive strides. Traditional measures of variability poorly predicted local stability. Treadmill walking was associated with significant changes in both variability and local stability. Thus, motorized treadmills may produce misleading or erroneous results in situations where changes in neuromuscular control are likely to affect the variability and/or stability of locomotion.     

Improved Assessment of Orbital Stability of Rhythmic Motion with Noise

Mathematical techniques have provided tools to quantify the stability of rhythmic movements of humans and machines as well as mathematical models. One archetypal example is the use of Floquet multipliers: assuming periodic motion to be a limit-cycle of a nonlinear oscillator, local stability has been assessed by evaluating the rate of convergence to the limit-cycle. However, the accuracy of the assessment in experiments is questionable: Floquet multipliers provide a measure of orbital stability for deterministic systems, but various components of biological systems and machines involve inevitable noise. In this study, we show that the conventional estimate of orbital stability, which depends on regression, has bias in the presence of noise. We quantify the bias, and devise a new method to estimate orbital stability more accurately. Compared with previous methods, our method substantially reduces the bias, providing acceptable estimates of orbital stability with an order-of-magnitude fewer cycles.     

Influence of Input Parameters on Dynamic Orbital Stability of Walking: In-Silico and Experimental Evaluation

Many measures aiming to assess the stability of human motion have been proposed in the literature, but still there is no commonly accepted way to define or quantify locomotor stability. Among these measures, orbital stability analysis via Floquet multipliers is still under debate. Some of the controversies concerning the use of this technique could lie in the absence of a standard implementation. The aim of this study was to analyse the influence of i) experimental measurement noise, ii) variables selected for the construction of the state space, and iii) number of analysed cycles on the outputs of orbital stability applied to walking. The analysis was performed on a 2-dimensional 5-link walking model and on a sample of 10 subjects performing long over-ground walks. Noise resulting from stereophotogrammetric and accelerometric measurement systems was simulated in the in-silico analysis. Maximum Floquet multipliers resulted to be affected by both number of analysed strides and state space composition. The effect of experimental noise was found to be slightly more potentially critical when analysing stereophotogrammetric data then when dealing with acceleration data. Experimental and model results were comparable in terms of overall trend, but a difference was found in the influence of the number of analysed cycles.     

Effect of stable and unstable load carriage on walking gait variability,dynamic stability and muscle activity of older adults

Load carriage perturbs the neuromuscular system, which can be impaired due to ageing. The ability to counteract perturbations is an indicator of neuromuscular function but if the response is insufficient the risk of falls will increase. However, it is unknown how load carriage affects older adults. Fourteen older adults (65 ± 6 years) attended a single visit during which they performed 4 min of walking in 3 conditions, unloaded, stable backpack load and unstable backpack load. During each walking trial, 3-dimensional kinematics of the lower limb and trunk movements and electromyographic activity of 6 lower limb muscles were recorded. The local dynamic stability (local divergence exponents), joint angle variability and spatio-temporal variability were determined along with muscle activation magnitudes. Medio-lateral dynamic stability was lower (p = 0.018) and step width (p = 0.019) and step width variability (p = 0.015) were greater in unstable load walking and step width variability was greater in stable load walking (p = 0.009) compared to unloaded walking. However, there was no effect on joint angle variability. Unstable load carriage increased activity of the Rectus Femoris (p = 0.001) and Soleus (p = 0.043) and stable load carriage increased Rectus Femoris activity (p = 0.006). These results suggest that loaded walking alters the gait of older adults and that unstable load carriage reduces dynamic stability compared to unloaded walking. This can potentially increase the risk of falls, but also offers the potential to use unstable loads as part of fall prevention programmes.     

Local dynamic stability in turning and straight-line gait

Successful community and household ambulation require the ability to navigate corners and maneuver around obstacles, posing unique challenges compared to straight-line walking. The challenges associated with turning may contribute to an increased incidence of falling and the occurrence of fall-related injuries. A measure of stability applied to turning gait may be able to quantify a system's response to naturally occurring disturbances associated with turning and identify subjects at greater risk of falling. An index of stability has been used previously to assess the rate of kinematic separation (local dynamic stability) during straight-line gait. The purpose of this study was to determine if local dynamic stability during constant speed turning is reduced compared to straight-line treadmill walking. Maximum finite-time Lyapunov exponents (λ) were used to estimate the local stability of able-bodied subjects’ (n=19) sagittal plane hip, knee, and ankle trajectories for turning compared to straight-line walking at two different walking speeds. Turning λ was greater than straight λ for the hip, right knee, and ankle (p<0.05). Turning λ for the left knee angle was similar to straight λ. There were no differences in λ between left and right limbs for the hip and ankle and also no differences between the inside and outside limbs during turning for all joints. These findings indicate able-bodied subjects’ hip, right knee, and ankle kinematics are less locally stable while turning than walking in a straight line and may be used as a comparative tool for determining the efficacy of therapeutic interventions for mobility-impaired populations.     

Floquet theory: a useful tool for understanding nonequilibrium dynamics

Many ecological systems experience periodic variability. Theoretical investigation of population and community dynamics in periodic environments has been hampered by the lack of mathematical tools relative to equilibrium systems. Here, I describe one such mathematical tool that has been rarely used in the ecological literature but has widespread use: Floquet theory. Floquet theory is the study of the stability of linear periodic systems in continuous time. Floquet exponents/multipliers are analogous to the eigenvalues of Jacobian matrices of equilibrium points. In this paper, I describe the general theory, then give examples to illustrate some of its uses: it defines fitness of structured populations, it can be used for invasion criteria in models of competition, and it can test the stability of limit cycle solutions. I also provide computer code to calculate Floquet exponents and multipliers. Electronic supplementary material  The online version of this article (doi:) contains supplementary material, which is available to authorized users.     

The validity of stability measures: A modelling approach

Measures calculated from unperturbed walking patterns, such as variability measures and maximum Floquet multipliers, are often used to study the stability of walking. However, it is unknown if, and to what extent, these measures correlate to the probability of falling.We studied whether in a simple model of human walking, i.e., a passive dynamic walker, the probability of falling could be predicted from maximum Floquet multipliers, kinematic state variability, and step time variability. We used an extended version of the basic passive dynamic walker with arced feet and a hip spring. The probability of falling was manipulated by varying the foot radius and hip spring stiffness, or varying these factors while co-varying the slope to keep step length constant.The simulation data indicated that Floquet multipliers and kinematic state variability correlated inconsistently with probability of falling. Step time variability correlated well with probability of falling, but a more consistent correlation with the probability of falling was found by calculating the variability of the log transform of the step time. Our findings speak against the use of maximum Floquet multipliers and suggest instead that variability of critical variables may be a good predictor of the probability to fall.     

The effect of walking speed on local dynamic stability is sensitive to calculation methods

Local dynamic stability has been assessed by the short-term local divergence exponent (λ_S), which quantifies the average rate of logarithmic divergence of infinitesimally close trajectories in state space. Both increased and decreased local dynamic stability at faster walking speeds have been reported. This might pertain to methodological differences in calculating λ_S. Therefore, the aim was to test if different calculation methods would induce different effects of walking speed on local dynamic stability. Ten young healthy participants walked on a treadmill at five speeds (60%, 80%, 100%, 120% and 140% of preferred walking speed) for 3 min each, while upper body accelerations in three directions were sampled. From these time-series, λ_S was calculated by three different methods using: (a) a fixed time interval and expressed as logarithmic divergence per stride-time (λ_S−a), (b) a fixed number of strides and expressed as logarithmic divergence per time (λ_S−b) and (c) a fixed number of strides and expressed as logarithmic divergence per stride-time (λ_S−c). Mean preferred walking speed was 1.16±0.09 m/s. There was only a minor effect of walking speed on λ_S−a. λ_S−b increased with increasing walking speed indicating decreased local dynamic stability at faster walking speeds, whereas λ_S−c decreased with increasing walking speed indicating increased local dynamic stability at faster walking speeds. Thus, the effect of walking speed on calculated local dynamic stability was significantly different between methods used to calculate local dynamic stability. Therefore, inferences and comparisons of studies employing λ_S should be made with careful consideration of the calculation method.     

Older adults have unstable gait kinematics during weight transfer

The present article investigates gait stability of healthy older persons during weight transfer. Ten healthy older persons and ten younger persons walked 10 min each on a treadmill at 3 different gait speeds. The intra-stride change in gait stability was defined by the local divergence exponent λ(t) estimated by a newly developed method. The intra-stride changes in λ(t) during weight transfer were identified by separating each stride into a single and double support phase. The intra-stride changes in λ(t) were also compared to changes in the variation of the gait kinematics, i.e., SD(t). The healthy older persons walked at the same preferred walking speed as the younger persons. However, they exhibited significantly larger λ(t) (p<0.001) during weight transfer in the double support phase. Local divergence was closely related to intra-stride changes in SD(t) of the feet in the anterior-posterior direction. Furthermore, a high correlation was found between local divergence and the variation in step length and step width for both older (R>0.67, p<0.05) and younger persons (R>0.67, p<0.05). The present results indicate that the gait kinematics of older adults are more dynamical unstable during the weight transfer compared to younger persons. Furthermore, a close relationship exists between intra-stride changes in dynamical stability and variation in step length and step width. Further work will validate the results of the present study using real-life perturbations of the gait kinematics of both younger and older adults.     

Phase-dependent changes in local dynamic stability of human gait

Several methods derived from nonlinear time series analysis have been suggested to quantify stability in human gait kinematics. One of these methods is the definition of the maximum finite time Lyapunov exponent (λ) that quantifies how the system responds to infinitesimal perturbations. However, there are fundamental limitations to the conventional definition of λ for gait kinematics. First, exponential increase in initial perturbations cannot be assumed since real-life perturbations of gait kinematics are finite sized. Second, the transitions between single and double support phase within each stride cycle define two distinct dynamical regimes that may not be captured by a single λ. The present article presents a new method to quantify intra-stride changes λ(t) in local dynamical stability and employs the method to 3D lower extremity gait kinematics in 10 healthy adults walking on a treadmill at 3 different speeds. All participants showed an intra-stride change in λ(t) in the transition between single and double support phase. The intra-stride change reflected an both a increase and decrease in λ(t) at heel strike and toe off, respectively, with increased gait speed. Furthermore, a close relationship was found between the intra-stride change in standard deviation of foot velocity in the anterior-posterior direction and the intra-stride change of the initial perturbations. The present results indicate that local dynamical stability has gait phase-dependent changes that are not identified by conventional computation of a single λ.     

The effects of gait strategy on metabolic rate and indicators of stability during downhill walking

When walking at a given speed, humans often appear to prefer gait patterns that minimize metabolic rate, thereby maximizing metabolic economy. However, recent experiments have demonstrated that humans do not maximize economy when walking downhill. The purpose of this study was to investigate whether this non-metabolically optimal behavior is the result of a trade-off between metabolic economy and gait stability. We hypothesized that humans have the ability to modulate their gait strategy to increase either metabolic economy or stability, but that increase in one measure will be accompanied by decrease in the other. Subjects walked downhill using gait strategies ranging from risky to conservative, which were either prescribed by verbal instructions or induced by the threat of perturbations. We quantified spatiotemporal gait characteristics, metabolic rate and several indicators of stability previously associated with fall risk: stride period variability; step width variability; Lyapunov exponents; Floquet multipliers; and stride period fractal index. When subjects walked using conservative gait strategies, stride periods and lengths decreased, metabolic rate increased, and anteroposterior maximum Lyapunov exponents increased, which has previously been interpreted as an indicator of decreased stability. These results do not provide clear support for the proposed trade-off between economy and stability, particularly when stability is approximated using complex metrics. However, several gait pattern changes previously linked to increased fall risk were observed when our healthy subjects walked with a conservative strategy, suggesting that these changes may be a response to, rather than a cause of, increased fall risk.     

Can stability really predict an impending slip-related fall among older adults?

The primary purpose of this study was to systematically evaluate and compare the predictive power of falls for a battery of stability indices, obtained during normal walking among community-dwelling older adults. One hundred and eighty seven community-dwelling older adults participated in the study. After walking regularly for 20 strides on a walkway, participants were subjected to an unannounced slip during gait under the protection of a safety harness. Full body kinematics and kinetics were monitored during walking using a motion capture system synchronized with force plates. Stability variables, including feasible-stability-region measurement, margin of stability, the maximum Floquet multiplier, the Lyapunov exponents (short- and long-term), and the variability of gait parameters (including the step length, step width, and step time), were calculated for each subject. Sensitivity of predicting slip outcome (fall vs. recovery) was examined for each stability variable using logistic regression. Results showed that the feasible-stability-region measurement predicted fall incidence among these subjects with the highest sensitivity (68.4%). Except for the step width (with an sensitivity of 60.2%), no other stability variables could differentiate fallers from those who did not fall for the sample included in this study. The findings from the present study could provide guidance to identify individuals at increased risk of falling using the feasible-stability-region measurement or variability of the step width.     

A direct comparison of patient and force-controlled simulator total knee replacement kinematics

The need to critically evaluate the efficacy of current total knee replacement (TKR) wear testing methodologies is great. Proposed international standards for TKR wear simulation have been drafted, yet their methods continue to be debated. The "gold standard" to which all TKR wear testing methodologies should be compared is measured in vivo TKR performance in patients. The current study compared patient TKR kinematics from fluoroscopic analysis and simulator TKR kinematics from force-controlled wear testing to quantify similarities in clinical ranges of motion and contact bearing kinematics and to evaluate the proposed ISO force-controlled wear testing methodology. The treadmill walking kinematics from eight well-functioning, 13 month average post-op patients were compared to the 2 million cycle interval walking cycle kinematics from a force-controlled (Instron/Stanmore Knee Joint Simulator, Instron, Canton, MA) knee simulator using identical implant designs (Natural Knee II, Standard Congruent, Zimmer, Warsaw, IN). The in vivo and simulator data showed good agreement in kinematic patterns and ranges of clinical motion. Tribologically the data sets showed similar contact pathway ranges of motion and wear travel distances per cycle. Surgical and simulator alignments of the implant systems were determined to be a contributing factor in observed kinematic differences. This study's statistical findings offer supporting evidence that the simulation of in vivo walking cycle wear kinematics can be accurately reproduced with a force controlled testing methodology.     

Slower speeds in patients with diabetic neuropathy lead to improved local dynamic stability of continuous overground walking

Patients with diabetic peripheral neuropathy are significantly more likely to fall while walking than subjects with intact sensation. While it has been suggested that these patients walk slower to improve locomotor stability, slower speeds are also associated with increased locomotor variability, and increased variability has traditionally been equated with loss of stability. If the latter were true, this would suggest that slowing down, as a locomotor control strategy, should be completely antithetical to the goal of maintaining stability. The present study resolves these seemingly paradoxical findings by using methods from nonlinear time series analysis to directly quantify the sensitivity of the locomotor system to local perturbations that are manifested as natural kinematic variability. Fourteen patients with severe peripheral neuropathy and 12 gender-, age-, height-, and weight-matched non-diabetic controls participated. Sagittal plane angles of the right hip, knee, and ankle joints and tri-axial accelerations of the trunk were measured during 10 min of continuous overground walking at self-selected speeds. Maximum finite-time Lyapunov exponents were computed for each time series to quantify the local dynamic stability of these movements. Neuropathic patients exhibited slower walking speeds and better local dynamic stability of upper body movements in the horizontal plane than did control subjects. The differences in local dynamic stability were significantly predicted by differences in walking speed, but not by differences in sensory status. These results support the hypothesis that reductions in walking speed are a compensatory strategy used by neuropathic patients to maintain dynamic stability of the upper body during level walking.