A manipulability analysis of human walking

From the literature of biomechanics, it is now clear that humans use elevating, lowering and delayed-lowering strategies in order to maintain stability during perturbed walking. The main purpose of this study is to provide insights into the role of manipulability in selection of these strategies. A 37 degrees of freedom (DoFs) model of the human body is developed to evaluate the manipulability indices during walking. The model is considered as a tree-like structure and its forward kinematics equations and the Jacobian are derived based on the Denavit-Hartenberg (DH) convention. A hybrid genetic algorithm (HGA) is then employed to map the experimental kinematics of a human to the model. The kinematic and dynamic manipulability indices of the swing phase of walking are evaluated concentrating on early, mid and late swing phases. The results indicate that the manipulability indices can characterize well the selection of elevating, lowering and delayed-lowering strategies at different stages of the swing phase. The results kinematically describe the reason of selecting delayed-lowering strategy at mid-swing phase that was not obvious in previous studies. Moreover, the results show that at mid-swing phase of walking the kinematic maneuverability is lower than that of the early and late swing phases.     

Stepping boundary of external force-controlled perturbations of varying durations: Comparison of experimental data and model simulations

This study investigated the stepping boundary – the force that can be resisted without stepping – for force-controlled perturbations of different durations. Twenty-two healthy young adults (19–37 years old) were instructed to try not to step in response to 86 different force/time combinations of forward waist-pulls. The forces at which 50% of subjects stepped (F₅₀) were identified for each tested perturbation durations. Results showed that F₅₀ decreased hyperbolically when the perturbation’s duration increased and converged toward a constant value (about 10% BW) for longer perturbations (over 1500 ms). The effect of perturbation duration was critical for the shortest perturbations (less than 1 s).In parallel, a simple function was proposed to estimate this stepping boundary. Considering the dynamics of a linear inverted pendulum + foot model and simple balance recovery reactions, we could express the maximum pulling force that can be withstood without stepping as a simple function of the perturbation duration. When used with values of the main model parameters determined experimentally, this function replicated adequately the experimental results.This study demonstrates for the first time that perturbation duration has a major influence on the outcomes of compliant perturbations such as force-controlled pulls. The stepping boundary corresponds to a constant perturbation force-duration product and is largely explained by only two parameters: the reaction time and the displacement of the center of pressure within the functional base of support. Future work should investigate pathological populations and additional parameters characterizing the perturbation time-profile such as the time derivative of the perturbation.     

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.     

Mechanical model of the recovery from stumbling

Several strategies have been described as a reaction to a stumble during gait. The elevating strategy, which tries to proceed with the perturbed step, was executed as a response to a perturbation during early swing. The lowering strategy, bringing the perturbed leg to the ground and overtaking the obstacle with the contralateral limb, was executed more frequently when the perturbation appeared at mid or late swing. The goal of this paper is to analyze which mechanical factors determine the most advantageous strategy. In order to determine these factors, a mechanical model of the recovery was developed and used to analyze a series of perturbation experiments. It was assumed that the goal of the recovery reaction was to control the trunk as an inverted pendulum during the double-stance phase. In order to be able to control the trunk angle, one foot should be up front and one foot should be behind the hips; otherwise it would be impossible to generate the required trunk torques. The trunk dynamics were expressed in terms of the ground reaction forces and their application point. A larger step (elevation strategy) gives the opportunity to dissolve the perturbation in one step. A small step (lowering strategy) necessarily results in a second quick step, after which the perturbation energy can be dissipated in the second double-stance phase. If a recovery step is too slow, it becomes impossible to counteract the forward flexion of the trunk. It is suggested that a measure of the ability to recover from a stumble could be based on the ability to perform quick steps.     

A neurobiological model of the recovery strategies from perturbed walking

This paper proposes a human mimetic neuro-musculo-skeletal model to simulate the recovery reactions from perturbations during walking. The computational model incorporates nonlinear viscoelastic muscular mechanics, supraspinal control of the center-of-mass, spinal pattern generator including muscle synergy network, spinal reflexes, and long-loop reflexes. Especially the long-loop reflexes specify recovery strategies based on the experimental observations [Schillings, A.M., van Wezel, B.M.H., Mulder, T.H., Duysen, J., 2000. Muscular responses and movement strategies during stumbling over obstacles. J. Neurophysiol. 83, 2093–2102; Eng, J.J., Winter, D.A., Patla, A.E., 1994. Strategies for recovery from a trip in early and late swing during human walking. Exp. Brain Res. 102, 339–349]. The model demonstrates two typical recovery strategies, i.e., elevating and lowering strategies against pulling over a swing leg. Sensed perturbation triggers a simple tonic pulse from the cortex. Depending on the swing phase, the tonic pulse activates a different compound of muscles over lower limbs. The compound induces corresponding recovery strategies. The reproduction of principal recovery behaviors may support the model's proposed functional and/or anatomical correspondence.     

A neurobiological model of the recovery strategies from perturbed walking

This paper proposes a human mimetic neuro-musculo-skeletal model to simulate the recovery reactions from perturbations during walking. The computational model incorporates nonlinear viscoelastic muscular mechanics, supraspinal control of the center-of-mass, spinal pattern generator including muscle synergy network, spinal reflexes, and long-loop reflexes. Especially the long-loop reflexes specify recovery strategies based on the experimental observations [Schillings, A.M., van Wezel, B.M.H., Mulder, T.H., Duysen, J., 2000. Muscular responses and movement strategies during stumbling over obstacles. J. Neurophysiol. 83, 2093–2102; Eng, J.J., Winter, D.A., Patla, A.E., 1994. Strategies for recovery from a trip in early and late swing during human walking. Exp. Brain Res. 102, 339–349]. The model demonstrates two typical recovery strategies, i.e., elevating and lowering strategies against pulling over a swing leg. Sensed perturbation triggers a simple tonic pulse from the cortex. Depending on the swing phase, the tonic pulse activates a different compound of muscles over lower limbs. The compound induces corresponding recovery strategies. The reproduction of principal recovery behaviors may support the model's proposed functional and/or anatomical correspondence.     

Anticipation of direction and time of perturbation modulates the onset latency of trunk muscle responses during sitting perturbations

Trunk muscles are responsible for maintaining trunk stability during sitting. However, the effects of anticipation of perturbation on trunk muscle responses are not well understood. The objectives of this study were to identify the responses of trunk muscles to sudden support surface translations and quantify the effects of anticipation of direction and time of perturbation on the trunk neuromuscular responses. Twelve able-bodied individuals participated in the study. Participants were seated on a kneeling chair and support surface translations were applied in the forward and backward directions with and without direction and time of perturbation cues. The trunk started moving on average approximately 40 ms after the perturbation. During unanticipated perturbations, average latencies of the trunk muscle contractions were in the range between 103.4 and 117.4 ms. When participants anticipated the perturbations, trunk muscle latencies were reduced by 16.8 ± 10.0 ms and the time it took the trunk to reach maximum velocity was also reduced, suggesting a biomechanical advantage caused by faster muscle responses. These results suggested that trunk muscles have medium latency responses and use reflexive mechanisms. Moreover, anticipation of perturbation decreased trunk muscles latencies, suggesting that the central nervous system modulated readiness of the trunk based on anticipatory information.     

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.     

A biomechanical study of balance recovery during the fall forward

The study deals with the biomechanics of balance recovery of human subjects in a falling forward situation. Eight subjects took part in the experiment. The subject, held in the initial leaning forward position, was released without his knowledge. The instruction was to recover the induced disequilibrium by walking. The biomechanical analysis shows two phases in the balance recovery. The first phase—preparation phase—is characterized by three events at fixed timing whatever the initial inclination. (i) Dynamic reaction time, showing no significant inter-individual variation (mean VALUE = 90.8 ms). (ii) Braking of the forward fall, between 184 ms and 237.2 ms, depending on the subject. (iii) Beginning of the swing phase—i.e. toe-off instant—between 235.9 ms and 328.3 ms, depending on the subject. The second phase—gait execution phase—is characterized by the duration of the swing phase, the duration of the stance phase, the stride length and execution speed. The durations diminish whereas the stride length and the execution speed increase with respect to the initial inclination. For the same execution speed, the stride length is shorter than in normal walking.

It has been concluded that balance recovery following an induced fall forward begins with an invariable preparation process which is followed by an adaptable recovery one.     

L'augmentation de la contraction du muscle soléaire du membre d'appui chez l'homme ne retarde pas la phase pendulaire au cours de pas déclenchés par la chute en avant

In this study it was examined in man whether tension increase in the extensor muscles of the stance foot delays the stance to swing transition, as suggested by some observations made in cats. Steps reproducibly elicited by forward fall were studied. Increase in muscle tension was obtained by electrical stimulation of the tibial nerve during the last third of the first step stance phase with trains of five rectangular pulses, 1 ms in duration, at 20 Hz, whose intensity was sufficient for eliciting maximal responses in the stance Soleus muscle (e.m.g. M responses). Trials with and without electrical stimulation were randomly carried out in five healthy subjects who had consented to take part in the experimentation. The stance to swing transition was characterized by the time of activation of the Tibialis anterior muscle of the stance foot and by the time of clearance of this foot from the ground. It was found that maximal contractions of the stance Soleus muscle did not change these times. Thus, in contradiction to some observations made in spinal and decerebrated cats, tension increase in the stance Soleus in man during steps elicited by a forward fall does not delay the transition to the swing phase.     

Ankle extensor proprioceptors contribute to the enhancement of the soleus EMG during the stance phase of human walking

A rapid plantar flexion perturbation applied to the ankle during the stance phase of the step cycle during human walking unloads the ankle extensors and produces a marked decline in the soleus EMG. This demonstrates that sensory activity contributes importantly to the enhancement of the ankle extensor muscle activation during human walking. On average, the EMG begins to decline approximately 52 ms after the perturbation. In contrast, a rapid dorsi flex ion perturbation produces a group Ia mediated short-latency stretch reflex burst with an onset latency of approximately 36 ms. The transmission of sensory traffic from the foot and ankle was suppressed in 10 subjects by an anaesthetic nerve block produced with local injections of lidocaine hydrochloride. The anaesthetic block had no effect on the stance phase soleus EMG, the latencies of the EMG responses, or the magnitude of the EMG decline following the plantar flexion perturbation. Therefore, it is more likely that proprioceptive afferents, rather than cutaneous afferents, contribute to the background soleus EMG during the late stance phase of the step cycle. The large difference in onset latencies between the short-latency reflex and unload responses suggests that the largest of the active group Ia afferents might not contribute strongly to the background soleus EMG, although it remains to be determined which of the proprioceptive pathways provide the more important contributions.     

The effect of perturbing body segment parameters on calculated joint moments and muscle forces during gait

This study examined the effect of body segment parameter (BSP) perturbations on joint moments calculated using an inverse dynamics procedure and muscle forces calculated using computed muscle control (CMC) during gait. BSP (i.e. segment mass, center of mass location (com) and inertia tensor) of the left thigh, shank and foot of a scaled musculoskeletal model were perturbed. These perturbations started from their nominal value and were adjusted to ±40% in steps of 10%, for both individual as well as combined perturbations in BSP. For all perturbations, an inverse dynamics procedure calculated the ankle, knee and hip moments based on an identical inverse kinematics solution. Furthermore, the effect of applying a residual reduction algorithm (RRA) was investigated. Muscle excitations and resulting muscle forces were calculated using CMC. The results show only a limited effect of an individual parameter perturbation on the calculated moments, where the largest effect is found when perturbing the shank com (MS_com,shank, the ratio of absolute difference in torque and relative parameter perturbation, is maximally −7.81 N m for hip flexion moment). The additional influence of perturbing two parameters simultaneously is small (MS_{mass+com,thigh} is maximally 15.2 N m for hip flexion moment). RRA made small changes to the model to increase the dynamic consistency of the simulation (after RRA MS_com,shank is maximally 5.01 N m). CMC results show large differences in muscle forces when BSP are perturbed. These result from the underlying forward integration of the dynamic equations.     

Factors influencing the quick onset of stepping following postural perturbation.

It has been shown that the stepping to recover balance following a forward fall occurs at a constant time (on average 293 ms) (Do et al. Journal of Biomechanics 15, 1982, 933-939). In this study, we tested the hypothesis according to which programming to make fast movement could trigger the movement earlier than when programming self-pace movement. The same experimental paradigm of forward fall was used (see Do et al., 1982) to induce stepping. Different extents of stepping were manipulated by instructions: Subjects were instructed to step to recover their balance naturally (control condition); to make shorter steps than in the control condition; longer steps; faster steps. Lastly, a fast step was also induced by the biomechanical constraint on the initial posture, i.e. by inclining the subject forward at his maximum capacity. Data were collected from 12 subjects. The variables analyzed were the onset latency of step execution and other classical parameters (time of heel-contact, duration of the swing phase, step length, center of mass progression velocity, and step velocity). The results showed that the onset of stepping was unchanged in the longer- and faster-step conditions, relative to the control condition (mean control value = 280 ms). In contrast, the onset of stepping was significantly earlier in the short-step condition, and when the initial inclination was greater (250 and 252 ms, respectively). The swing phase duration in these two conditions averaged 140 and 185 ms, was significantly shorter than in the other conditions, whereas step length was obviously expected to be shorter in the shorter-step condition and longer in the longer-step condition than in the other conditions. Step length was similar between the other conditions. We conclude that neither step length or step velocity programming could induce an earlier onset latency of stepping. Step programming in relation to these specific instructions seemed to concern the extent of step execution and not the time of triggering of the stepping. We suggest that the control of short swing phase duration resulted in an earlier onset latency of stepping to recover the balance. This control depends on the combination of biomechanical constraints and cognitive processes, including subject's interpretation of the instructions and evaluation of the risk of fall.     

Hip recovery strategy used by below-knee amputees following mediolateral foot perturbations

Lower-limb amputees have a higher risk of falling compared to non-amputees. Proper regulation of whole-body angular momentum is necessary to prevent falls, particularly in the frontal plane where individuals are most unstable. However, the balance recovery mechanisms used by lower-limb amputees when recovering from a perturbation are not well-understood. This study sought to understand the balance recovery mechanisms used by lower-limb amputees in response to mediolateral foot perturbations by examining changes to frontal plane whole-body angular momentum and hip joint work. These metrics provide a quantitative measure of frontal plane dynamic balance and associated joint contributions required to maintain balance during gait. Nine amputees and 11 non-amputees participated in this study where an unexpected medial or lateral foot placement perturbation occurred immediately prior to heel strike on the residual, sound or non-amputee limbs. Lateral perturbations of all limbs resulted in a reduced range of whole-body angular momentum and increased positive frontal plane hip work in the first half of single limb support. Medial perturbations for all limbs resulted in increased range of whole-body angular momentum and decreased positive frontal plane hip work, also in the first half of single limb support. These results suggest that medial foot placement perturbations are particularly challenging and that hip strategies play an important role in balance recovery. Thus, rehabilitation interventions that focus on hip muscles that regulate mediolateral balance, particularly the hip abductors, and the use of prostheses with active ankle control, may reduce the risk of falls.     

The response of GS-NS0 myeloma cells to single and multiple pH perturbations

Animal cells are cultured in several types of vessels at laboratory and industrial scale the most common being the stirred tank and the air-lift. Economically, it is preferable to culture animal cells at the largest possible scale but the perceived sensitivity of animal cells to hydrodynamic shear has, until now, limited the aeration and agitation rates used. This has been reported to cause inhomogeneities in operational parameters such as dissolved oxygen concentration, temperature and pH. pH is of special interest during the latter stages of many animal cell fermentation because alkali additions, used for pH control, can cause large local pH perturbations of varying size and duration. The effect of single and multiple pH perturbations on the cell growth of a widely used GS-NS0 mouse myeloma cell line grown in batch culture was investigated. The effect of perturbation amplitude and duration was investigated using a single stirred tank reactor (STR). In the single STR system cells were subjected to one pH 8.0 or 9.0 perturbation ranging in duration from 0-90 minutes. No measurable decrease in viable cell number was seen for pH 8.0 perturbations of any duration whereas pH 9.0 perturbations lasting for 10 minutes caused a 15% decrease in viable cell number. The proportion of viable cells decreased with increasing perturbation time and a 90-minute exposure killed all of the cells. The effect of multiple pH perturbations on GS-NS0 cells was investigated using two connected STR's. More specifically the number of perturbations and the perturbation frequency were investigated. Cells were subjected to between 0 and 100 perturbations at pH 8.0; the time between each perturbation (frequency) was 6 minutes and each perturbation lasted for 200 seconds. Viable cell number decreased with increasing perturbation number, with 100 perturbations causing death of 27.5% of cells. Cells were also exposed to 10 perturbations at pH 9.0, each of 200 second duration at frequencies of either 6, 18 or 60 minutes. Approximately 8 times more cells were killed with perturbations at a 6-minute frequency (28.3% cell death) than at a 60-minute frequency (3.4% cell death).     

Adaptive trunk sway velocities following repeated perturbations in subjects with and without low back pain

Faster trunk motions could be a strategy to prevent loss of balance and fall injuries due to unexpected perturbations. However, it is unclear how trunk sway velocities can be compensated during stepping in subjects with low back pain (LBP). The purpose of this study was to investigate lower limb reaction, swing, and step times, as well as trunk sway velocities at heel strike and toe-off, following repeated step perturbations between subjects with and without LBP. There were 30 subjects with LBP and 42 control subjects who were exposed to treadmill-induced perturbations at a velocity of 0.12 m/sec for 0.62 m. The treadmill-induced steps caused subjects to walk forward for 4.90 sec after the perturbation. The groups demonstrated significant interactions on the lower limb reaction times and on the number of repeated perturbations (F = 4.83, p = 0.03) due to a decreased step time at the first perturbation (t = 2.52, p = 0.01) in the LBP group. For the trunk sway velocities, the repeated perturbations demonstrated a significant interaction between groups (F = 4.65, p = 0.03). This adaptive trunk strategy for gait stability increased step times with repeated perturbations in the LBP group. The group interactions on the trunk sway velocities also indicated a possible somatosensory integration for step time adjustments to avoid potential fall hazards. This adaptive response with repeated step perturbations could result in compensatory trunk sway for gait stability.     

Instantaneous kinematic phase reflects neuromechanical response to lateral perturbations of running cockroaches

Instantaneous kinematic phase calculation allows the development of reduced-order oscillator models useful in generating hypotheses of neuromechanical control. When perturbed, changes in instantaneous kinematic phase and frequency of rhythmic movements can provide details of movement and evidence for neural feedback to a system-level neural oscillator with a time resolution not possible with traditional approaches. We elicited an escape response in cockroaches (Blaberus discoidalis) that ran onto a movable cart accelerated laterally with respect to the animals’ motion causing a perturbation. The specific impulse imposed on animals (0.50 $\pm $ 0.04 m s $^{-1}$ ; mean, SD) was nearly twice their forward speed (0.25 $\pm $ 0.06 m s $^{-1})$ . Instantaneous residual phase computed from kinematic phase remained constant for 110 ms after the onset of perturbation, but then decreased representing a decrease in stride frequency. Results from direct muscle action potential recordings supported kinematic phase results in showing that recovery begins with self-stabilizing mechanical feedback followed by neural feedback to an abstracted neural oscillator or central pattern generator. Trials fell into two classes of forward velocity changes, while exhibiting statistically indistinguishable frequency changes. Animals pulled away from the side with front and hind legs of the tripod in stance recovered heading within 300 ms, whereas animals that only had a middle leg of the tripod resisting the pull did not recover within this period. Animals with eight or more legs might be more robust to lateral perturbations than hexapods.     

Muscle response times between shoe and no-shoe conditions following a weight-bearing rotary perturbation are similar in females

The purpose of this study was to compare the muscle response times (MRTs) of select lower extremity muscles following a weight bearing rotary perturbation in single-leg stance with and without shoes. Ten recreationally active females volunteered for this study. Each subject received a rotary perturbation in single-leg stance under two conditions: with shoes and without shoes. The outcomes measured were response times of the medial and lateral quadriceps, hamstrings and gastrocnemius. The results demonstrated that significant differences in MRTs were not apparent for either the medial or lateral perturbation between conditions. While a main effect for muscle was evident for both medial and lateral perturbations, a muscle by shoe interaction was not present for either the medial or lateral perturbation. Our findings suggest that wearing shoes does not alter MRTs during single-limb rotary perturbations. These data indicate that lower extremity perturbation device testing may be done with or without shoes and comparisons between works are permissible as response times are unaffected.     

Effects of a single-session stance-slip perturbation training program on reducing risk of slip-related falls

The purpose of this pilot study was to establish the efficacy and feasibility of a single-session treadmill-based stance-slip perturbation program on preventing slip-related falls while walking over the ground among young adults. Two groups (training vs. control) of healthy young participants were respectively exposed to a treadmill-based stance-slip perturbation training protocol and a placebo training protocol. Post training, both groups experienced an unexpected overground gait-slip. Our results indicated that 28.6% of individuals in the training group and 55.0% of controls fell when responding to the overground slip. In comparison with the control group, the training group exhibited better control over the compensatory step and dynamic stability at the instant immediately prior to recovery touchdown. The improved dynamic stability control in the training group likely resulted from the enhanced capability of harnessing the slip kinematics of the base of support. Dynamic stability did not display any significant group-associated difference at slipping foot touchdown and recovery foot liftoff. This implies that a stance-slip perturbation training protocol with eight slips may not provide enough and very task-specific incentive to the Central Nervous System to form the capability of sufficiently modifying regular gait pattern after an unexpected gait slip. However, given its ease of use, stance-perturbation could be a practical option to train individuals in clinical settings as a simple push or pull could exert a perturbation to a standing individual. The findings from this study provide information for developing future studies based on large-scale samples.