How to measure responses of the knee to lateral perturbations during gait? A proof-of-principle for quantification of knee instability

Knee instability is a major problem in patients with anterior cruciate ligament injury or knee osteoarthritis. A valid and clinically meaningful measure for functional knee instability is lacking. The concept of the gait sensitivity norm, the normalized perturbation response of a walking system to external perturbations, could be a sensible way to quantify knee instability. The aim of this study is to explore the feasibility of this concept for measurement of knee responses, using controlled external perturbations during walking in healthy subjects.Nine young healthy participants walked on a treadmill, while three dimensional kinematics were measured. Sudden lateral translations of the treadmill were applied at five different intensities during stance. Right knee kinematic responses and spatio-temporal parameters were tracked for the perturbed stride and following four cycles, to calculate perturbation response and gait sensitivity norm values (i.e. response/perturbation) in various ways.The perturbation response values in terms of knee flexion and abduction increased with perturbation intensity and decreased with an increased number of steps after perturbation. For flexion and ab/adduction during midswing, the gait sensitivity norm values were shown to be constant over perturbation intensities, demonstrating the potential of the gait sensitivity norm as a robust measure of knee responses to perturbations.These results show the feasibility of using the gait sensitivity norm concept for certain gait indicators based on kinematics of the knee, as a measure of responses during perturbed gait. The current findings in healthy subjects could serve as reference-data to quantify pathological knee instability.     

Retention of improvement in gait stability over 14 weeks due to trip-perturbation training is dependent on perturbation dose

Perturbation training is an emerging approach to reduce fall risk in the elderly. This study examined potential differences in retention of improvements in reactive gait stability over 14 weeks resulting from unexpected trip-like gait perturbations. Twenty-four healthy middle-aged adults (41–62 years) were assigned randomly to either a single perturbation group (SINGLE, n = 9) or a group subjected to eight trip-like gait perturbations (MULTIPLE, n = 15). While participants walked on a treadmill a custom-built brake-and-release system was used to unexpectedly apply resistance during swing phase to the lower right limb via an ankle strap. The anteroposterior margin of stability (MoS) was calculated as the difference between the anterior boundary of the base of support and the extrapolated centre of mass at foot touchdown for the perturbed step and the first recovery step during the first and second (MULTIPLE group only) perturbation trials for the initial walking session and retention-test walking 14 weeks later. Group MULTIPLE retained the improvements in reactive gait stability to the perturbations (increased MoS at touchdown for perturbed and first recovery steps; p < 0.01). However, in group SINGLE no differences in MoS were detected after 14 weeks compared to the initial walking session. These findings provide evidence for the requirement of a threshold trip-perturbation dose if adaptive changes in the human neuromotor system over several months, aimed at the improvement in fall-resisting skills, are to occur.     

Stability-normalised walking speed: A new approach for human gait perturbation research

In gait stability research, neither self-selected walking speeds, nor the same prescribed walking speed for all participants, guarantee equivalent gait stability among participants. Furthermore, these options may differentially affect the response to different gait perturbations, which is problematic when comparing groups with different capacities. We present a method for decreasing inter-individual differences in gait stability by adjusting walking speed to equivalent margins of stability (MoS). Eighteen healthy adults walked on a split-belt treadmill for two-minute bouts at 0.4 m/s up to 1.8 m/s in 0.2 m/s intervals. The stability-normalised walking speed (MoS = 0.05 m) was calculated using the mean MoS at touchdown of the final 10 steps of each speed. Participants then walked for three minutes at this speed and were subsequently exposed to a treadmill belt acceleration perturbation. A further 12 healthy adults were exposed to the same perturbation while walking at 1.3 m/s: the average of the previous group. Large ranges in MoS were observed during the prescribed speeds (6–10 cm across speeds) and walking speed significantly (P < 0.001) affected MoS. The stability-normalised walking speeds resulted in MoS equal or very close to the desired 0.05 m and reduced between-participant variability in MoS. The second group of participants walking at 1.3 m/s had greater inter-individual variation in MoS during both unperturbed and perturbed walking compared to 12 sex, height and leg length-matched participants from the stability-normalised walking speed group. The current method decreases inter-individual differences in gait stability which may benefit gait perturbation and stability research, in particular studies on populations with different locomotor capacities. [Preprint: https://doi.org/10.1101/314757]     

Dynamic stability of individuals with transtibial amputation walking in destabilizing environments

Lower limb amputation substantially disrupts motor and proprioceptive function. People with lower limb amputation experience considerable impairments in walking ability, including increased fall risk. Understanding the biomechanical aspects of the gait of these patients is crucial in improving their gait function and their quality of life. In the present study, 9 persons with unilateral transtibial amputation and 13 able-bodied controls walked on a large treadmill in a Computer Assisted Rehabilitation Environment (CAREN). While walking, subjects were either not perturbed, or were perturbed either by continuous mediolateral platform movements or by continuous mediolateral movements of the visual scene. Means and standard deviations of both step lengths and step widths increased significantly during both perturbation conditions (all p<0.001) for both groups. Measures of variability, local and orbital dynamic stability of trunk movements likewise exhibited large and highly significant increases during both perturbation conditions (all p<0.001) for both groups. Patients with amputation exhibited greater step width variability (p=0.01) and greater trunk movement variability (p=0.04) during platform perturbations, but did not exhibit greater local or orbital instability than healthy controls for either perturbation conditions. Our findings suggest that, in the absence of other co-morbidities, patients with unilateral transtibial amputation appear to retain sufficient sensory and motor function to maintain overall upper body stability during walking, even when substantially challenged. Additionally, these patients did not appear to rely more heavily on visual feedback to maintain trunk stability during these walking tasks.     

Responses in knee joint muscle activation patterns to different perturbations during gait in healthy subjects

PurposeTo compare the responses in knee joint muscle activation patterns to different perturbations during gait in healthy subjects.ScopeNine healthy participants were subjected to perturbed walking on a split-belt treadmill. Four perturbation types were applied, each at five intensities. The activations of seven muscles surrounding the knee were measured using surface EMG. The responses in muscle activation were expressed by calculating mean, peak, co-contraction (CCI) and perturbation responses (PR) values. PR captures the responses relative to unperturbed gait. Statistical parametric mapping analysis was used to compare the muscle activation patterns between conditions.ResultsPerturbations evoked only small responses in muscle activation, though higher perturbation intensities yielded a higher mean activation in five muscles, as well as higher PR. Different types of perturbation led to different responses in the rectus femoris, medial gastrocnemius and lateral gastrocnemius. The participants had lower CCI just before perturbation compared to the same phase of unperturbed gait.ConclusionsHealthy participants respond to different perturbations during gait with small adaptations in their knee joint muscle activation patterns. This study provides insights in how the muscles are activated to stabilize the knee when challenged. Furthermore it could guide future studies in determining aberrant muscle activation in patients with knee disorders.     

Reliability and sources of variability of 3D kinematics and electromyography measurements to assess newly-acquired gait in toddlers with typical development and unilateral cerebral palsy

The aim was to 1) determine intersession and intertrial reliability and 2) assess three sources of variability (intersubject, intersession and intertrial) of lower limb kinematic and electromyographic (EMG) variables during gait in toddlers with typical development (TD) and unilateral cerebral palsy (UCP) (age <3 years, independent walking experience ≤6 months). Gait kinematics and surface EMG were recorded in 30 toddlers (19 TD and 11 UCP), during two, 3D-motion capture sessions. Standard error of measurement (SEM) between trials (gait cycles) of the same session and between sessions was calculated to assess reliability. Standard deviations (SD) between subjects, sessions and trials were calculated to estimate sources of variability. Sixty-four percent of kinematic SEM-values were acceptable (2°-5°). Frontal plane measurements were most reliable (SEM 2°-4.6°). In toddlers with UCP, EMG variables were most reliable for affected side, distal muscles. Intrinsic (intertrial and intersubject) variability was high, reflecting both motor immaturity and the high variability of toddler gait patterns. In toddlers with UCP, variability was amplified by motor impairment and delayed motor development. 3D gait analysis and surface EMG are partially reliable tools to study individual gait patterns in toddlers in clinical practice and research, although some variables must be interpreted with caution.     

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.     

Walking speed and spatiotemporal step mean measures are reliable during feedback-controlled treadmill walking; however,spatiotemporal step variability is not reliable

The purpose of the study was to compare the effects of a feedback-controlled treadmill (FeedbackTM) to a traditional fixed-speed treadmill (FixedTM) on spatiotemporal gait means, variability, and dynamics. The study also examined inter-session reliability when using the FeedbackTM. Ten young adults walked on the FeedbackTM for a 5-minute familiarization followed by a 16-minute experimental trial. They returned within one week and completed a 5-minute familiarization followed by a 16-minute experimental trial each for FeedbackTM and FixedTM conditions. Mean walking speed and step time, length, width, and speed means and coefficient of variation were calculated from all experimental conditions. Step time, length, width, and speed gait dynamics were analyzed using detrended fluctuation analysis. Mean differences between experimental trials were determined using ANOVAs and reliability between FeedbackTM sessions was determined by intraclass correlation coefficient. No difference was found in mean walking speed nor spatiotemporal variables, with the exception of step width, between the experimental trials. All mean spatiotemporal variables demonstrated good to excellent reliability between sessions, while coefficient of variation was not reliable. Gait dynamics of step time, length, width, and speed were significantly more persistent during the FeedbackTM condition compared to FixedTM, especially step speed. However, gait dynamics demonstrated fair to poor reliability between FeedbackTM sessions. When walking on the FeedbackTM, users maintain a consistent set point, yet the gait dynamics around the mean are different when compared to walking on a FixedTM. In addition, spatiotemporal gait dynamics and variability may not be consistent across separate days when using the FeedbackTM.     

Kinematic variability and local dynamic stability of upper body motions when walking at different speeds

A ubiquitous characteristic of elderly and patients with gait disabilities is that they walk slower than healthy controls. Many clinicians assume these patients walk slower to improve their stability, just as healthy people slow down when walking across ice. However, walking slower also leads to greater variability, which is often assumed to imply deteriorated stability. If this were true, then slowing down would be completely antithetical to the goal of maintaining stability. This study sought to resolve this paradox by directly quantifying the sensitivity of the locomotor system to local perturbations that are manifested as natural kinematic variability. Eleven young healthy subjects walked on a motorized treadmill at five different speeds. Three-dimensional movements of a single marker placed over the first thoracic vertebra were recorded during continuous walking. Mean stride-to-stride standard deviations and maximum finite-time Lyapunov exponents were computed for each time series to quantify the variability and local dynamic stability, respectively, of these movements. Quadratic regression analyses of the dependent measures vs. walking speed revealed highly significant U shaped trends for all three mean standard deviations, but highly significant linear trends, with significant or nearly significant quadratic terms, for five of the six finite-time Lyapunov exponents. Subjects exhibited consistently better local dynamic stability at slower speeds for these five measures. These results support the clinically based intuition that people who are at increased risk of falling walk slower to improve their stability, even at the cost of increased variability.     

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.     

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.     

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.     

Walking variability during continuous pseudo-random oscillations of the support surface and visual field

Walking on uneven surfaces or while undergoing perturbations has been associated with increased gait variability in both modeling and human studies. Previous gait research involving continuous perturbations has focused on sinusoidal oscillations, which can result in individuals predicting the perturbation and/or entraining to it. Therefore, we examined the effects of continuous, pseudo-random support surface and visual field oscillations on 12 healthy, young participants. Participants walked in a virtual reality environment under no perturbation (NOP), anterior–posterior (AP) walking surface and visual oscillation and mediolateral (ML) walking surface and visual oscillation conditions. Participants exhibited shorter (p≤0.005), wider (p<0.001) and faster (p<0.001) steps relative to NOP during ML perturbations and shorter (p≤0.005) and wider (p<0.001) steps during AP perturbations. Step length variability and step width variability both increased relative to NOP during all perturbation conditions (p<0.001) but exhibited greater increases for the ML perturbations (p<0.001). Participants exhibited greater trunk position variability and trunk velocity variability in the ML direction than in the AP direction during ML perturbations relative to NOP (p<0.001). Significantly greater variability in the ML direction indicates that to maintain stability, participants needed to exert greater control in the ML direction. This observation is consistent with prior modeling predictions. The large and consistent responses observed during ML visual and walking surface perturbations suggest potential for application during gait training and patient assessment.     

A Simple State-Determined Model Reproduces Entrainment and Phase-Locking of Human Walking

Theoretical studies and robotic experiments have shown that asymptotically stable periodic walking may emerge from nonlinear limit-cycle oscillators in the neuro-mechanical periphery. We recently reported entrainment of human gait to periodic mechanical perturbations with two essential features: 1) entrainment occurred only when the perturbation period was close to the original (preferred) walking period, and 2) entrainment was always accompanied by phase locking so that the perturbation occurred at the end of the double-stance phase. In this study, we show that a highly-simplified state-determined walking model can reproduce several salient nonlinear limit-cycle behaviors of human walking: 1) periodic gait that is 2) asymptotically stable; 3) entrainment to periodic mechanical perturbations only when the perturbation period is close to the model''s unperturbed period; and 4) phase-locking to locate the perturbation at the end of double stance. Importantly, this model requires neither supra-spinal control nor an intrinsic self-sustaining neural oscillator such as a rhythmic central pattern generator. Our results suggest that several prominent limit-cycle features of human walking may stem from simple afferent feedback processes without significant involvement of supra-spinal control or a self-sustaining oscillatory neural network.     

Reproducibility and responsiveness of gait initiation in Parkinson’s disease

Persons with Parkinson’s disease (PD) have significant impairments in functional mobility, including the ability to initiate gait. Three-dimensional analysis of kinetic and kinematic outcomes has become one of the most powerful tools in evaluating abnormalities in gait initiation for persons with PD. Surprisingly however, the psychometric properties of spatial and temporal measures of gait initiation for persons with PD have not been established using force-platforms. The purposes of this study were to determine the reliability of kinetic and kinematic measures of gait initiation and to identify the minimal detectable change of these measures in persons with PD during On and Off medication conditions. Sixteen participants with idiopathic PD performed a series of 3 repeated trials of gait initiation by starting from a quiet stance position on 2 AMTI OR-6 force platforms, and walking forward across the floor following a signal from the investigators. Testing was performed first in the Off medication condition, after which participants took their medication and waited 60 min before repeating the gait initiation assessments. Relative test-retest reliability was good-to-excellent for most outcome measures (range 0.417–0.960). Bland-Altman analysis revealed no systematic variance in the majority of outcome measures when tested in distinct medication conditions (On vs. Off medication). Most outcome measures required low-to-moderate amounts of change (<50%) to indicate true change in individual participants. These results suggest that spatial and temporal measures of gait initiation using force-platforms are highly reliable and responsive to changes in performance for persons with PD, regardless of whether individuals are optimally medicated.     

Reliability of lower limb electromyography during overground walking: A comparison of maximal- and sub-maximal normalisation techniques

The purpose of this study was to determine the reliability of investigating electromyography (EMG) of selected leg muscles during walking. Tibialis posterior and peroneus longus EMG activity were recorded via intramuscular electrodes. Tibialis anterior and medial gastrocnemius EMG activity were recorded with surface electrodes. Twenty-eight young adults attended two test-sessions approximately 15 days apart. Relative and absolute measures of reliability were calculated for EMG timing and amplitude parameters during specific phases of the gait cycle. Maximum contractions and sub-maximal contractions were obtained via maximum isometric voluntary contractions and a very fast walking speed, respectively. Time of peak EMG amplitude for all muscles displayed relatively narrow limits of random error. However, reliability of peak and root mean square amplitude parameters for tibialis posterior and peroneus longus displayed unacceptably wide limits of random error, regardless of the normalisation reference technique. Whilst some amplitude parameters for tibialis anterior and medial gastrocnemius displayed good to excellent relative reliability, the corresponding values for absolute error were generally large.Timing and amplitude EMG parameters for all muscles displayed low to moderate coefficient of variation within each test session (range: 7–25%). Overall, between-participant variability was minimised with sub-maximal normalisation values. These results demonstrate that re-application of electrodes results in large random error between sessions, particularly with tibialis posterior and peroneus longus. Researchers planning studies of these muscles with a repeated-test design (e.g. to evaluate the effect of an intervention) must consider whether this level of error is acceptable.     

A shoe sole-based apparatus and method for randomly perturbing the stance phase of gait: test-retest reliability in young adults

Walking on an irregular surface is associated with an elevated risk for a fall at any age. Yet, relatively little is known about how a human responds to an unexpected underfoot perturbation during gait. This is partly due to the difficulty of generating an intermittent but repeatable, unexpected, underfoot perturbation whose size and location are precisely known. So we developed a shoe sole-embedded apparatus for randomly perturbing the stance phase of gait. Medial and lateral flaps were concealed in the soles of pairs of sandals, along with their actuators. Either flap could be deployed within 400ms in the parasagittal plane under a swing foot; this altered the resulting sagittal and frontal plane orientations of the foot during the next stance phase, whereafter the flap was retracted following toe-off for the rest of that gait trial. We tested six healthy young subjects by randomly presenting a single medial or lateral perturbation in 12 of 30 gait trials. Traditional step kinematic measures were used to evaluate the test-retest reliability of the response to the stimulus at two different walking speeds in 60 randomized trials conducted 1 week apart. The method was effective in systematically inducing an alteration in gait, reproducible across visits, as evidenced by acceptable intraclass correlation coefficients for step width, time and length. We conclude that the apparatus and method has potential for measuring the ability of humans to reject one or more unexpected underfoot perturbations during gait.     

Phase reset and dynamic stability during human gait

The human walking movement shows transient changes in response to single short-lived external perturbations, termed "stumbling reactions." During the stumbling reactions, the walking phase is reset. It has been considered that the reactions contribute to stabilizing the motion, but less evidence bridging between the rhythm reset and the dynamic stability of the gait has been provided. The present study tries to establish the relationship between them. To this end, we construct a simple dynamical system model of the human musculo-skeletal system interacting with the ground, whose joint kinematics during walking is constrained by a given periodic joint-angles-profile. We show first that the model can exhibit a stable limit cycle corresponding to the steady walking with no perturbations. The responses of the limit cycle oscillation are examined by applying a type of perturbations at various timings with various intensities, elucidating the stability of the model's walking when no phase reset is performed. We then observe that modifications of the periodic joint-angles-profile within a short time interval in response to the perturbation can alter the responses of the limit cycle oscillation and induce phase reset of the model's walking. It is shown that appropriate amounts of the phase reset can prevent the model from falling, even for the perturbation that induces falling in the case without the phase reset. This suggests that those phase resets can improve the dynamic stability of the gait. Moreover, the appropriate phase resets predicted by the model are compared with the experimentally observed phase resets during human stumbling reaction to show they share similar characteristics.     

Margins of stability in young adults with traumatic transtibial amputation walking in destabilizing environments

Understanding how lower-limb amputation affects walking stability, specifically in destabilizing environments, is essential for developing effective interventions to prevent falls. This study quantified mediolateral margins of stability (MOS) and MOS sub-components in young individuals with traumatic unilateral transtibial amputation (TTA) and young able-bodied individuals (AB). Thirteen AB and nine TTA completed five 3-min walking trials in a Computer Assisted Rehabilitation ENvironment (CAREN) system under each of three test conditions: no perturbations, pseudo-random mediolateral translations of the platform, and pseudo-random mediolateral translations of the visual field. Compared to the unperturbed trials, TTA exhibited increased mean MOS and MOS variability during platform and visual field perturbations (p<0.010). AB exhibited increased mean MOS during visual field perturbations and increased MOS variability during both platform and visual field perturbations (p<0.050). During platform perturbations, TTA exhibited significantly greater values than AB for mean MOS (p<0.050) and MOS variability (p<0.050); variability of the lateral distance between the center of mass (COM) and base of support at initial contact (p<0.005); mean and variability of the range of COM motion (p<0.010); and variability of COM peak velocity (p<0.050). As determined by mean MOS and MOS variability, young and otherwise healthy individuals with transtibial amputation achieved lateral stability similar to that of their able-bodied counterparts during unperturbed and visually-perturbed walking. However, based on mean and variability of MOS, unilateral transtibial amputation was shown to have affected lateral walking stability during platform perturbations.     

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.