Differences between local and orbital dynamic stability during human walking

Currently there is no commonly accepted way to define, much less quantify, locomotor stability. In engineering, "orbital stability" is defined using Floquet multipliers that quantify how purely periodic systems respond to perturbations discretely from one cycle to the next. For aperiodic systems, "local stability" is defined by local divergence exponents that quantify how the system responds to very small perturbations continuously in real time. Triaxial trunk accelerations and lower extremity sagittal plane joint angles were recorded from ten young healthy subjects as they walked for 10 min over level ground and on a motorized treadmill at the same speed. Maximum Floquet multipliers (Max FM) were computed at each percent of the gait cycle (from 0% to 100%) for each time series to quantify the orbital stability of these movements. Analyses of variance comparing Max FM values between walking conditions and correlations between Max FM values and previously published local divergence exponent results were computed. All subjects exhibited orbitally stable walking kinematics (i.e., magnitudes of Max FM < 1.0), even though these same kinematics were previously found to be locally unstable. Variations in orbital stability across the gait cycle were generally small and exhibited no systematic patterns. Walking on the treadmill led to small, but statistically significant improvements in the orbital stability of mediolateral (p = 0.040) and vertical (p = 0.038) trunk accelerations and ankle joint kinematics (p = 0.002). However, these improvements were not exhibited by all subjects (p < or = 0.012 for subject x condition interaction effects). Correlations between Max FM values and previously published local divergence exponents were inconsistent and 11 of the 12 comparisons made were not statistically significant (r2 < or = 19.8%; p > or = 0.049). Thus, the variability inherent in human walking, which manifests itself as local instability, does not substantially adversely affect the orbital stability of walking. The results of this study will allow future efforts to gain a better understanding of where the boundaries lie between locally unstable movements that remain orbitally stable and those that lead to global instability (i.e., falling).     

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.     

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.     

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.     

Influence of simulated neuromuscular noise on the dynamic stability and fall risk of a 3D dynamic walking model

Measures that can predict risk of falling are essential for enrollment of older adults into fall prevention programs. Local and orbital stability directly quantify responses to very small perturbations and are therefore putative candidates for predicting fall risk. However, research to date is not conclusive on whether and how these measures relate to fall risk. Testing this empirically would be time consuming or may require high risk tripping experiments. Simulation studies therefore provide an important tool to initially explore potential measures to predict fall risk. This study performed simulations with a 3D dynamic walking model to explore if and how dynamic stability measures predict fall risk. The model incorporated a lateral step controller to maintain lateral stability. Neuronal noise of increasing amplitude was added to this controller to manipulate fall risk. Short-term (λ(S)(*)) local instability did predict fall risk, but long-term (λ(L)(*)) local instability and orbital stability (maxFM) did not. Additionally, λ(S)(*) was an early predictor for fall risk as it started increasing before fall risk increased. Therefore, λ(S)(*) could be a very useful tool to identify older adults whose fall risk is about to increase, so they can be enrolled in fall prevention programs before they actually fall.     

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.     

Reliability and Minimum Detectable Change of Temporal-Spatial,Kinematic, and Dynamic Stability Measures during Perturbed Gait

Temporal-spatial, kinematic variability, and dynamic stability measures collected during perturbation-based assessment paradigms are often used to identify dysfunction associated with gait instability. However, it remains unclear which measures are most reliable for detecting and tracking responses to perturbations. This study systematically determined the between-session reliability and minimum detectable change values of temporal-spatial, kinematic variability, and dynamic stability measures during three types of perturbed gait. Twenty young healthy adults completed two identical testing sessions two weeks apart, comprised of an unperturbed and three perturbed (cognitive, physical, and visual) walking conditions in a virtual reality environment. Within each session, perturbation responses were compared to unperturbed walking using paired t-tests. Between-session reliability and minimum detectable change values were also calculated for each measure and condition. All temporal-spatial, kinematic variability and dynamic stability measures demonstrated fair to excellent between-session reliability. Minimal detectable change values, normalized to mean values ranged from 1–50%. Step width mean and variability measures demonstrated the greatest response to perturbations with excellent between-session reliability and low minimum detectable change values. Orbital stability measures demonstrated specificity to perturbation direction and sensitivity with excellent between-session reliability and low minimum detectable change values. We observed substantially greater between-session reliability and lower minimum detectable change values for local stability measures than previously described which may be the result of averaging across trials within a session and using velocity versus acceleration data for reconstruction of state spaces. Across all perturbation types, temporal-spatial, orbital and local measures were the most reliable measures with the lowest minimum detectable change values, supporting their use for tracking changes over multiple testing sessions. The between-session reliability and minimum detectable change values reported here provide an objective means for interpreting changes in temporal-spatial, kinematic variability, and dynamic stability measures during perturbed walking which may assist in identifying instability.     

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.     

Influence of simulated neuromuscular noise on movement variability and fall risk in a 3D dynamic walking model

People at risk of falling exhibit increased gait variability, which may predict future falls. However, the causal mechanisms underlying these correlations are not well known. Increased neuronal noise associated with aging likely leads to increased gait variability, which could in turn lead to increased fall risk. This paper presents a model of how changes in neuromuscular noise independently affect gait variability and probability of falling, and aims to determine the extent to which changes in gait variability directly predict fall risk. We used a dynamic walking model that incorporates a lateral step controller to maintain lateral stability. Noise was applied to this controller to approximate neuromuscular noise in humans. Noise amplitude was varied between low amplitudes that did not induce falls and high amplitudes for which the model always fell. With increases in noise amplitude, the model fell more often and after fewer steps. Gait variability increased with noise amplitude and predicted increased probability of falling. Importantly, these relationships were not linear. At either low gait variability or very high gait variability, small increases in noise and variability affected probability of falling very little. Conversely, at intermediate noise and/or variability levels, the same small increases resulted in large increases in probability of falling. Our results validate the idea that age-related increases in neuromuscular noise likely play a direct contributing role in increasing fall risk. However, neuromuscular noise remains only one of many important factors that need to be considered. These findings have important implications for fall prevention research and practice.     

Possible functional roles of phase resetting during walking

The walking rhythm is known to show phase shift or "reset" in response to external impulsive perturbations. We tried to elucidate functional roles of the phase reset possibly used for the neural control of locomotion. To this end, a system with a double pendulum as a simplified model of the locomotor control and a model of bipedal locomotion were employed and analyzed in detail. In these models, a movement corresponding to the normal steady-state walking was realized as a stable limit cycle solution of the system. Unexpected external perturbations applied to the system can push the state point of the system away from its limit cycle, either outside or inside the basin of attraction of the limit cycle. Our mathematical analyses of the models suggested functional roles of the phase reset during walking as follows. Function 1: an appropriate amount of the phase reset for a given perturbation can contribute to relocating the system's state point outside the basin of attraction of the limit cycle back to the inside. Function 2: it can also be useful to reduce the convergence time (the time necessary for the state point to return to the limit cycle). In experimental studies during walking of animals and humans, the reset of walking rhythm induced by perturbations was investigated using the phase transition curve (PTC) or the phase resetting curve (PRC) representing phase-dependent responses of the walking. We showed, for the simple double-pendulum model, the existence of the optimal phase control and the corresponding PTC that could optimally realize the aforementioned functions in response to impulsive force perturbations. Moreover, possible forms of PRC that can avoid falling against the force perturbations were predicted by the biped model, and they were compared with the experimentally observed PRC during human walking. Finally, physiological implications of the results were discussed.     

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.     

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.     

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.     

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.     

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.     

Faster walking speeds increase local instability among people with peripheral neuropathy

Individuals with peripheral neuropathy (PN) may compensate for decreased somatosensation by reducing walking speed. Predisposition to falls may therefore arise from an inability to adapt to challenging walking speeds. The purpose of this study was to examine the effects of PN on the magnitude of variability and local instability on walking at different speeds. Twelve individuals with PN and 12 controls completed a 6-min walk test to determine fast walking speed (FWS). Sagittal plane hip, knee, and ankle joint angles were then calculated during 3min of treadmill walking at 100%, 80%, and 60% FWS. The magnitudes of stride duration variability (SDvar), joint angle variability (JTvar), and both short- and long-term Lyapunov exponents (used to estimate local instability) were calculated. The PN group walked slower than the control group (p<.001). With groups combined, walking faster led to increased local instability and increased variability (p<.001). The PN group exhibited increased variability (SDvar, p=.02; JTvar, p=.01) over all speeds, and exaggerated local instability (p<.05) when walking at the fastest speed. PN leads to increased walking variability and local instability, particularly when walking at challenging speeds. These results are important to consider in future patient education and rehabilitation programs.     

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.     

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.     

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.     

Dynamic stability of superior vs. inferior body segments in individuals with transtibial amputation walking in destabilizing environments

Interestingly, young and highly active people with lower limb amputation appear to maintain a similar trunk and upper body stability during walking as able-bodied individuals. Understanding the mechanisms underlying how this stability is achieved after lower-leg amputation is important to improve training regimens for improving walking function in these patients. This study quantified how superior (i.e., head, trunk, and pelvis) and inferior (i.e., thigh, shank, and feet) segments of the body respond to continuous visual or mechanical perturbations during walking. Nine persons with transtibial amputation (TTA) and 12 able-bodied controls (AB) walked on a 2 m×3 m treadmill in a Computer Assisted Rehabilitation Environment (CAREN). Subjects were perturbed by continuous pseudo-random mediolateral movements of either the treadmill platform or the visual scene. TTA maintained a similar local and orbital stability in their superior body segments as AB throughout both perturbation types. However, for their inferior body segments, TTA subjects exhibited greater dynamic instability during perturbed walking. In TTA subjects, these increases in instability were even more pronounced in their prosthetic limb compared to their intact leg. These findings demonstrate that persons with unilateral lower leg amputation maintain upper body stability in spite of increased dynamic instability in their impaired lower leg. Thus, transtibial amputation does significantly impair sensorimotor function, leading to substantially altered dynamic movements of their lower limb segments. However, otherwise relatively healthy patients with unilateral transtibial amputation appear to retain sufficient remaining sensorimotor function in their proximal and contralateral limbs to adequately compensate for their impairment.