Predicted threshold against forward and backward loss of balance for perturbed walking

The biomechanical mechanisms of loss of balance have been studied before for slip condition but have not been investigated for arbitrary perturbation profiles under non-slip conditions in sagittal plane. This study aimed to determine the thresholds of center of mass (COM) velocity and position relative to the base of support (BOS) that predict forward and backward loss of balance during walking with a range of BOS perturbations. Perturbations were modeled as sinusoidal BOS motions in the vertical or anterior-posterior direction or as sagittal rotation. The human body was modeled using a seven-link model. Forward dynamics alongside with dynamic optimization were used to find the thresholds of initial COM velocity for each initial COM position that would predict forward or backward loss of balance. The effects of perturbation frequency and amplitude on these thresholds were modeled based on the simulation data. Experimental data were collected from 15 able-bodied individuals and three individuals with disability during perturbed walking. The simulation results showed similarity with the stability region reported for slip and non-slip conditions. The feasible stability region shrank when the perturbation frequency and amplitude increased, especially for larger initial COM velocities. 89.5% (70.9%) and 82.4% (68.2%) of the measured COM position and velocity combinations during low (high) perturbations were located inside the simulated limits of the stability region, for able-bodied and disabled individuals, respectively. The simulation results demonstrated the effects of different perturbation levels on the stability region. The obtained stability region can be used for developing rehabilitative programs in interactive environments.     

Effects of amplitude and predictability of perturbations to the arm on anticipatory and reactionary muscle responses to maintain balance

Disturbances to balance arising from forces applied to the upper limb have received relatively little attention compared to disturbances arising from support surface perturbations. In this study we applied fast ramp perturbations to the hand in anterior, posterior, medial and lateral directions. The effects of perturbation predictability and amplitude on the postural response of upper limb, trunk and lower limb muscles were investigated. Perturbations were applied either in blocks of constant amplitude and direction (predictable) or with direction and amplitude varying randomly (random) from trial to trial. The spatial-temporal patterns of anticipatory muscle activation under the predictable condition and the reactionary responses following the perturbation under both conditions were similarly organized. The size of the response increased systematically with the perturbation magnitude for both anticipatory and reactionary changes in muscle activation. However, the slope of the relation between perturbation amplitude and the magnitude of the change in muscle activation was greater when perturbations were predictable than when they were randomly selected. The timing of both the anticipatory and reactionary increases in muscle activation was invariant across perturbation amplitudes. The characteristics of the reactionary responses have a similar organization to the long latency muscle responses to support surface perturbations.     

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.     

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.     

Thresholds for step initiation induced by support-surface translation: a dynamic center-of-mass model provides much better prediction than a static model

The need to initiate a step in order to recover balance could, in theory, be predicted by a static model based solely on displacement of the center of mass (COM) with respect to the base of support (BOS), or by a dynamic model based on the interaction between COM displacement and velocity. The purpose of this study was to determine whether the dynamic model provides better prediction than the static model regarding the need to step in response to moving-platform perturbation. The COM phase plane trajectories were determined for 10 healthy young adults for trials where the supporting platform was translated at three different acceleration levels in anterior and posterior directions. These trajectories were compared with the thresholds for step initiation predicted by the static and dynamic COM models. A single-link-plus-foot biomechanical model was employed to mathematically simulate termination of the COM movement, without stepping, using the measured platform acceleration as the input. An optimization routine was used to determine the stability boundaries in COM state space so as to establish the dynamic thresholds where a compensatory step must be initiated in order to recover balance. In the static model, the threshold for step initiation was reached if the COM was displaced beyond the BOS limits. The dynamic model showed substantially better accuracy than the static model in predicting the need to step in order to recover balance: 71% of all stepping responses predicted correctly by the dynamic model versus only 11% by the static model. These results support the proposition that the central nervous system must react to and control dynamic effects, i.e. COM velocity, as well as COM displacement in order to maintain stability with respect to the existing BOS without stepping.     

Characteristics of postural corrective responses before and after long-term spaceflights

Balance function is dramatically deteriorated after exposure to microgravity. The purpose of the present study was to investigate the role and the contribution of different gravity sensory systems to the development of balance impairment after long-term spaceflights. Postural perturbations (pushes to the chest) of the threshold, medium, and sub-maximal intensities were produced in eight cosmonauts before, and on the day 3, 7, and 11 following spaceflight. Postural corrective responses were analyzed by anterior-posterior body sway fluctuation and electromyographic activity of leg muscles. The characteristics of the postural corrective responses changed significantly on the day 3 following spaceflight: the amplitude of posterior sway caused by perturbation of threshold intensity was increased reaching 135% of preflight value; the corrective responses lasted more than 6 s in 50% of all trials, while it did not last more than 4 s in 96% before spaceflight. The EMG responses were characterized by increased contribution of medium- and long-latency reactions. On the day 11 following spaceflight, most of the characteristics of postural corrective responses were close to preflight values. We assumed that the balance alterations after spaceflight are caused by changes in weightlessness of functions of two main gravity sensory systems, namely, weight-bearing and vestibular one. The deficit of weight-bearing afferentation triggers a decline of the extensors’ muscle tone, while changes of vestibular function cause a decline of accuracy of postural corrections.     

Characteristics of postural corrective responses before and after long-term spaceflight

Balance function is dramatically deteriorated after exposure to microgravity. The purpose of the present study was to investigate the role and the contribution of different gravity sensory systems to the development of balance impairment after long-term spaceflights. Postural perturbations (pushes to the chest) of the threshold, medium, and sub-maximal intensities were produced in eight cosmonauts before, and on the day 3, 7, and 11 following spaceflight. Postural corrective responses were analyzed by anterior-posterior body sway fluctuation and electromyographic activity of leg muscles. The characteristics of the postural corrective responses changed significantly on the day 3 following spaceflight: the amplitude of posterior sway caused by perturbation of threshold intensity was increased reaching 135% ofpreflight value; the corrective responses lasted more than 6 s in 50% of all trials, while it did not last more than 4 s in 96% before spaceflight. The EMG responses were characterized by increased contribution of medium- and long-latency reactions. On the day 11 following spaceflight, most of the characteristics of postural corrective responses were close to preflight values. We assumed that the balance alterations after spaceflight are caused by changes in weightlessness of functions of two main gravity sensory systems, namely, weight-bearing and vestibular one. The deficit of weight-bearing afferentation triggers a decline of the extensors' muscle tone, while changes of vestibular function cause a decline of accuracy of postural corrections.     

Human breathing pattern responses to loading with increased background impedance

We determined the influence of the background level of mechanical impedance on the respiratory responses to very small mechanical loads, at or below the threshold for conscious perception. We used a pseudorandom load application technique to estimate the immediate pattern responses from the zeroth lag of the cross correlation between the load application sequence and the respiratory pattern components of tidal volume (VT), inspiratory and expiratory time (TI and TE), and the instantaneous respiratory frequency (f), minute ventilation (VI), and mean inspiratory flow (VT/TI). Elevation of the background resistance served to reduce the TI and TE responses to small perturbations in resistance from those in the control background state, which resulted in generally smaller perturbations of f, VI, and VT/TI. Elevation of the background elastance, however, served to initiate a TI reduction not seen in the control state but did not appreciably affect the rest of the pattern responses to the load perturbations. Thus the neural reflexes involved in breath-by-breath pattern regulation are modulated by the background level of the respiratory impedance, as well as by the type and size of the load perturbation.     

Functional postural responses after perturbations in multiple directions in a standing man: a principle of decoupled control

The objective of this study was to assess functional postural responses by analyzing the net joint torques (NJT) in the ankles and the hips resulting from perturbations delivered in multiple directions to subjects standing quietly. A total of eight subjects were standing on two force platforms while an apparatus randomly delivered controlled perturbations at the level of the pelvis in eight directions: anterio-posterior (AP), medio-lateral (ML), and four combinations of these principal directions. Perturbations were repeated five times in each direction for six conditions (i.e., three different perturbation strengths and three different feet orientations). The comparison of the averaged ankle sum NJT (AP) responses showed that the time courses of the responses elicited by a perturbation acting only in the AP direction were identical to those elicited by a combination of two corresponding AP and ML perturbations. In contrast the observed averaged ankle NJT (ML) responses did not follow the same similarity. The comparison of the averaged ankle and hip sum NJT (ML) responses revealed that the time courses of the responses elicited by a perturbation acting only in the ML direction were identical to those elicited by a combination of two corresponding AP and ML perturbations. These findings were invariable of the experimental conditions and were consistent among all the eight subjects. Thereby, we conclude that the ankle sum NJT (AP) and the ankle and hip sum NJT (ML) are the global variables being controlled. This shows that CNS controls the recovery from the multiple direction perturbations of moderate strength by decoupling the AP-ML postural space into two orthogonal directions (AP and ML).     

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.     

Are age-related impairments in change-in-support balance reactions dependent on the method of balance perturbation?

Rapid “change-in-support” (stepping or grasping) balance-recovery reactions play a critical role in preventing falls. Studies investigating age-related impairments in these reactions using differing perturbation methods have shown contradictory results. The discrepancies could be due to the different mechanical and sensory stimuli provided by the different perturbation methods, but could also be due to other confounding factors (e.g. differences in perturbation predictability). This study compared two commonly used perturbation methods: weight-drop cable-pulls (CPs) and motor-driven surface-translations (STs). For each perturbation method, effects of aging on the change-in-support reactions were established by comparing 10 young (22–28 years) and 30 older (64–79 years) adults, using large unpredictable multi-directional perturbations similar to those used in previous studies showing age-related differences. Age-related differences in the pattern and spatio-temporal features of the limb movements were examined for stepping and grasping reactions evoked by antero-posterior perturbation of stance, as well as stepping reactions evoked by lateral perturbations delivered while subjects walked “in-place”. Although age-group effects were almost always more pronounced for ST perturbations, the direction of the effect was always the same for both perturbation methods; hence, the perturbation-dependent differences in mechanical and sensory stimuli did not seem to be a critical factor. Perturbation waveform appeared to be a more important factor. For the perturbation methods used here, the ST perturbations were more destabilising than the CP perturbations (leading to a more rapid rise in perturbatory ankle-torque and greater centre-of-mass motion prior to the onset of the postural reaction), and were consequently more effective in revealing age-related deficiencies.     

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.     

Mechanisms of Motor Adaptation in Reactive Balance Control

Balance control must be rapidly modified to provide stability in the face of environmental challenges. Although changes in reactive balance over repeated perturbations have been observed previously, only anticipatory postural adjustments preceding voluntary movements have been studied in the framework of motor adaptation and learning theory. Here, we hypothesized that adaptation occurs in task-level balance control during responses to perturbations due to central changes in the control of both anticipatory and reactive components of balance. Our adaptation paradigm consisted of a Training set of forward support-surface perturbations, a Reversal set of novel countermanding perturbations that reversed direction, and a Washout set identical to the Training set. Adaptation was characterized by a change in a motor variable from the beginning to the end of each set, the presence of aftereffects at the beginning of the Washout set when the novel perturbations were removed, and a return of the variable at the end of the Washout to a level comparable to the end of the Training set. Task-level balance performance was characterized by peak center of mass (CoM) excursion and velocity, which showed adaptive changes with repetitive trials. Only small changes in anticipatory postural control, characterized by body lean and background muscle activity were observed. Adaptation was found in the evoked long-latency muscular response, and also in the sensorimotor transformation mediating that response. Finally, in each set, temporal patterns of muscle activity converged towards an optimum predicted by a trade-off between maximizing motor performance and minimizing muscle activity. Our results suggest that adaptation in balance, as well as other motor tasks, is mediated by altering central sensitivity to perturbations and may be driven by energetic considerations.     

Chronotherapy of cancer: periodic perturbations in vascular growth and metastasis

A non-autonomous model was developed for vascular tumor growth and cancer metastasis under periodic perturbations that simulate chronotherapy. It was found that for a critical amplitude and a perturbation frequency of twice the autonomous frequency in vascular growth, less complex and therefore less robust states are reached and the tumor population decreases. In metastasis, similar results were found for a perturbation frequency equal to the autonomous frequency. In metastasis, similar behaviors occur, for a perturbation’s frequency equal to the fundamental frequency of system.     

Theoretical study of Beloussov’s hyper-restoration hypothesis for mechanical regulation of morphogenesis

Computational models were used to explore the idea that morphogenesis is regulated, in part, by feedback from mechanical stress according to Beloussov’s hyper-restoration (HR) hypothesis. According to this hypothesis, active tissue responses to stress perturbations tend to restore, but overshoot, the original (target) stress. To capture this behavior, the rate of growth or contraction is assumed to depend on the difference between the current and target stresses. Stress overshoot is obtained by letting the target stress change at a rate proportional to the same stress difference. The feasibility of the HR hypothesis is illustrated by models for stretching of epithelia, cylindrical bending of plates, invagination of cylindrical and spherical shells, and early amphibian development. In each case, an initial perturbation leads to an active mechanical response that changes the form of the tissue. The results show that some morphogenetic processes can be entirely self-driven by HR responses once they are initiated (possibly by genetic activity). Other processes, however, may require secondary mechanisms or perturbations to proceed to completion.     

Age-related changes in posture response under a continuous and unexpected perturbation

Aging is a critical factor to influence the functional performance during daily life. Without an appropriate posture control response when experiencing an unexpected external perturbation, fall may occur. A novel six-degree-of freedom platform with motion control protocol was designed to provide a real-life simulation of unexpected disturbance in order to discriminate the age-related changes of the balance control and the recovery ability. Twenty older adults and 20 healthy young adults participated in the study. The subjects stood barefoot on the novel movable platform, data of the center of mass (COM) excursion, joint rotation angle and electromyography (EMG) were recorded and compared. The results showed that the older adults had similar patterns of joint movement and COM excursion as the young adults during the balance reactive-recovery. However, larger proximal joint rotation in elderly group induced larger COM sway envelop and therefore loss of the compensatory strategy of posture recovery. The old adults also presented a lower muscle power. In order to keep an adequate joint stability preventing from falling, the EMG activity was increased, but the asymmetric pattern might be the key reason of unstable postural response. This novel design of moveable platform and test protocol comprised the computerized dynamic posturography (CDP) demonstrate its value to assess the possible sensory, motor, and central adaptive impairments to balance control and could be the training tool for posture inability person.     

Explosive voluntary torque is related to whole-body response to unexpected perturbations

Explosive torque has been demonstrated to relate to static balance. However, sports injuries occur dynamically and unpredictably, yet the relationship between explosive torque and balance response to dynamic perturbations is unknown. This study investigated the relationship between explosive torque of the plantar flexors and knee extensors and the centre of mass (COM) response to unexpected perturbations. Thirty-three healthy subjects (17 females, 16 males) were assessed for maximal and explosive isometric knee extension (KE) and plantar flexion (PF) torque and COM response (velocity (COMV), displacement (COMD)) to unexpected platform translations. Relationships between explosive torque and balance measures were investigated using Pearson’s correlation and multiple regression. A negative relationship between PF explosive torque at 50, 100, and 150 ms and COMV at 300, 400, and 500 ms (r = −0.363 to −0.508, p ≤ 0.049), and COMD at 400 and 500 ms (r = −0.349 to −0.416, p ≤ 0.046) was revealed. A negative relationship between KE explosive torque at 50, 100, and 150 ms and COMV at 400 ms (r = −0.381 to −0.411, p ≤ 0.029) but not COMD was also revealed. Multiple regression found PF 100 ms predicted 17.3% of variability in COMD at 500 ms and 25.8% of variability in COMV at 400 ms. These results suggest that producing torque rapidly may improve COM response to unexpected perturbation.     

Reflex muscle contractions can be elicited by valgus positional perturbations of the human knee

Experimental evidence on the reflex responses of thigh muscles to valgus mechanical perturbations at the human knee are presented. Random step positional deflections, ranging from 5 degrees to 12 degrees at 60 degrees /s, were applied to the fully extended knees of seven healthy subjects. Subjects were instructed to maintain a constant background co-activation ( approximately 2-11% MVC) of the quadriceps and hamstring muscles prior to and during the mechanical stimulus. We found that the reflex response to sustained valgus joint deflection in the vasti muscles had longer onset latencies (range: 83-92ms) than did the stretch reflex in the same muscles (latencies: 29-31ms). This reflex EMG response consisted typically of a peak followed by sustained muscle activity throughout the step perturbation. The sustained EMG activity was dependent on the amplitude of the perturbing stimulus, but in a nonlinear manner. The long latency of the valgus response suggests that the reflex originates in nonmuscular sensory pathways, potentially from mechanoreceptors lying in periarticular tissues such as joint ligaments and capsule. Analysis of the spatial distribution of reflex responses showed an asymmetrical pattern with preferential activation of medial vs. lateral muscles of the knee. We assess whether these asymmetric reflex contractions could promote joint stability, either by inducing generalized joint stiffening, or by preferential activation of those muscles that are best suited to resist induced ligament strain.     

Increasing neural network robustness improves match to macaque V1 eigenspectrum,spatial frequency preference and predictivity

Task-optimized convolutional neural networks (CNNs) show striking similarities to the ventral visual stream. However, human-imperceptible image perturbations can cause a CNN to make incorrect predictions. Here we provide insight into this brittleness by investigating the representations of models that are either robust or not robust to image perturbations. Theory suggests that the robustness of a system to these perturbations could be related to the power law exponent of the eigenspectrum of its set of neural responses, where power law exponents closer to and larger than one would indicate a system that is less susceptible to input perturbations. We show that neural responses in mouse and macaque primary visual cortex (V1) obey the predictions of this theory, where their eigenspectra have power law exponents of at least one. We also find that the eigenspectra of model representations decay slowly relative to those observed in neurophysiology and that robust models have eigenspectra that decay slightly faster and have higher power law exponents than those of non-robust models. The slow decay of the eigenspectra suggests that substantial variance in the model responses is related to the encoding of fine stimulus features. We therefore investigated the spatial frequency tuning of artificial neurons and found that a large proportion of them preferred high spatial frequencies and that robust models had preferred spatial frequency distributions more aligned with the measured spatial frequency distribution of macaque V1 cells. Furthermore, robust models were quantitatively better models of V1 than non-robust models. Our results are consistent with other findings that there is a misalignment between human and machine perception. They also suggest that it may be useful to penalize slow-decaying eigenspectra or to bias models to extract features of lower spatial frequencies during task-optimization in order to improve robustness and V1 neural response predictivity.