To walk or to run - a question of movement attractor stability.

During locomotion, humans change gait mode between walking and running as locomotion speed is either increased or decreased. Dynamical systems theory predicts that the self-organization of coordinated motor behaviors dictates the transition from one distinct stable attractor behavior to another distinct attractor behavior (e.g. walk to run or vice versa) as the speed is changed. To evaluate this prediction, the present study investigated the attractor stability of walking and running across a range of speeds evoking both self-selected gait mode and non-self-selected gait mode. Eleven subjects completed treadmill walking for 3 min at 0.89, 1.12, 1.34, 1.56, 1.79, 2.01, 2.24 and 2.46 m s-1 and running for 3 min at 1.79, 2.01, 2.24, 2.46, 2.68, 2.91, 3.13 and 3.35 m s-1 in randomized order while lower limb joint angles and sacrum displacements was recorded. Attractor stability was quantified by continuous relative phase and deviation phase of lower limb segment angles, and the largest Lyapunov exponent, correlation dimension and movement variability of the sacrum marker displacement and the hip, knee and ankle joint angles. Lower limb attractor stability during walking was maximized at speeds close to the self-selected preferred walking speed and increased during running as speed was increased. Furthermore, lower limb attractor stability was highest at a particular gait mode closest to the corresponding preferred speed, in support of the prediction of dynamical systems theory. This was not the case for the sacrum displacement attractor, suggesting that lower limb attractor behavior provides a more appropriate order parameter compared with sacrum displacement.

Opioid-Induced Reductions in Gait Variability in Healthy Volunteers and Individuals with Knee Osteoarthritis.

OBJECTIVE: To investigate differences in gait variability induced by two different single-dose opioid formulations and an inert placebo in healthy volunteers and knee osteoarthritis patients. DESIGN: Experimental, randomized, double-blinded, crossover study of inert placebo (calcium tablets), 50 mg of tapentadol, and 100 mg of tramadol. SETTING: Laboratory setting. SUBJECTS: Healthy volunteers and knee osteoarthritis patients. METHODS: At three visits, separated by seven days, one tablet was administered per visit according to the randomization code. At each visit, a baseline measurement was done before tablet administration, after which hourly measurements were performed for six hours, yielding a total of seven measurements per visit. Gait variability was measured by three-dimensional gait analysis, recorded during six minutes of continuous treadmill walking at self-selected speed. One hundred seventy gait cycles were identified from detection of clear events of the knee joint angle trajectories. Gait variability was assessed as average standard deviations over a gait cycle of the sacrum displacements and accelerations; sagittal plane ankle, knee, and hip joint angles; step widths; and stride times. RESULTS: Twenty-four opioid-naïve and neurologically intact participants (12 healthy volunteers and 12 knee osteoarthritis patients) were included and completed the experiment. Tapentadol reduced the variability of sacrum displacements and accelerations compared with placebo and tramadol. There were no differences between experimental conditions regarding the variability in lower-extremity joint angle variability, step widths, or stride times. CONCLUSIONS: In opioid-naïve and neurologically intact individuals, tapentadol seems to reduce movement variability during treadmill walking, compared with placebo and tramadol. This can be interpreted as a loss of adaptability that might increase the risk of falling if the system is perturbed.

On the calculation of sample entropy using continuous and discrete human gait data.

Sample entropy (SE) has relative consistency using biologically-derived, discrete data >500 data points. For certain populations, collecting this quantity is not feasible and continuous data has been used. The effect of using continuous versus discrete data on SE is unknown, nor are the relative effects of sampling rate and input parameters m (comparison vector length) and r (tolerance). Eleven subjects walked for 10-minutes and continuous joint angles (480Hz) were calculated for each lower-extremity joint. Data were downsampled (240, 120, 60Hz) and discrete range-of-motion was calculated. SE was quantified for angles and range-of-motion at all sampling rates and multiple combinations of parameters. A differential relationship between joints was observed between range-of-motion and joint angles. Range-of-motion SE showed no difference; whereas, joint angle SE significantly decreased from ankle to knee to hip. To confirm findings from biological data, continuous signals with manipulations to frequency, amplitude, and both were generated and underwent similar analysis to the biological data. In general, changes to m, r, and sampling rate had a greater effect on continuous compared to discrete data. Discrete data was robust to sampling rate and m. It is recommended that different data types not be compared and discrete data be used for SE.

Changes in soleus H-reflex during walking in middle-aged, healthy subjects.

INTRODUCTION: To assess the effect of aging on stretch reflex modulation during walking, soleus H-reflexes obtained in 15 middle-aged (mean age 56.4±6.9 years) and 15 young (mean age 23.7±3.9 years) subjects were compared. METHODS: The H-reflex amplitude, muscle activity (EMG) of the soleus and tibialis anterior muscles, and EMG/H-reflex gain were measured during 4-km/h treadmill walking. RESULTS: The normalized H-reflex amplitude was lower in the swing phase for the middle-aged group, and there was no difference in muscle activity. EMG/H-reflex gain did not differ between groups. CONCLUSIONS: H-reflex amplitude during walking was affected by aging, and changes during the swing phase could be seen in the middle-aged subjects. Subdividing the 2 age groups into groups of facilitated or suppressed swing-phase H-reflex revealed that the H-reflex amplitude modulation pattern in the group with facilitated swing-phase H-reflex may be influenced by aging.

Isometric force complexity may not fully originate from the nervous system.

In humans and animals, spatial and temporal information from the nervous system are translated into muscle force enabling movements of body segments. To gain deeper understanding of this translation of information into movements, we investigated the motor control dynamics of isometric contractions in children, adolescents, young adults and older adults. Twelve children, thirteen adolescents, fourteen young adults, and fifteen older adults completed two minutes of submaximal isometric plantar- and dorsiflexion. Simultaneously, sensorimotor cortex EEG, tibialis anterior and soleus EMG and plantar- and dorsiflexion force was recorded. Surrogate analysis suggested that all signals were from a deterministic origin. Multiscale entropy analysis revealed an inverted U-shape relationship between age and complexity for the force but not for the EEG and EMG signals. This suggests that temporal information in from the nervous system is modulated by the musculoskeletal system during the transmission into force. The entropic half-life analyses indicated that this modulation increases the time scale of the temporal dependency in the force signal compared to the neural signals. Together this indicates that the information embedded in produced force does not exclusively reflect the information embedded in the underlying neural signal.

Stride-to-stride time intervals are independently affected by the temporal pattern and probability distribution of visual cues.

The temporal structure of the variability of the stride-to-stride time intervals during paced walking is affected by the underlying autocorrelation function (ACF) of the pacing signal. This effect could be accounted for by differences in the underlying probability distribution function (PDF) of the pacing signal. We investigated the isolated and combined effect of the ACF and PDF of the pacing signals on the temporal structure of the stride-to-stride time intervals during visually guided paced overground walking. Ten young, healthy participants completed four walking trials while synchronizing their footstep to a visual pacing signal with a temporal pattern of either pink or white noise (different ACF) and either a Gaussian or normal probability distribution (different PDF). The scaling exponent from the Detrended Fluctuation Analysis was used to quantify the temporal structure of the stride-to-stride time intervals. The ACF and PDF of the pacing signals had independent effects on the scaling exponent of the stride-to-stride time intervals. The scaling exponent was higher during the pink noise pacing trials compared to the white noise pacing trials and higher during the trials with the Gaussian probability distribution compared to the uniform distribution. The results suggest that the sensorimotor system in healthy young individuals has an affinity towards external cues with a pink noise pattern and a Gaussian probability distribution during paced walking.

Calculating sample entropy from isometric torque signals: methodological considerations and recommendations.

We investigated the effect of different sampling frequencies, input parameters and observation times for sample entropy (SaEn) calculated on torque data recorded from a submaximal isometric contraction. Forty-six participants performed sustained isometric knee flexion at 20% of their maximal contraction level and torque data was sampled at 1,000 Hz for 180 s. Power spectral analysis was used to determine the appropriate sampling frequency. The time series were downsampled to 750, 500, 250, 100, 50, and 25 Hz to investigate the effect of different sampling frequency. Relative parameter consistency was investigated using combinations of vector lengths of two and three and tolerance limits of 0.1, 0.15, 0.2, 0.25, 0.3, 0.35, and 0.4, and data lengths between 500 and 18,000 data points. The effect of different observations times was evaluated using Bland-Altman plot for observations times between 5 and 90 s. SaEn increased at sampling frequencies below 100 Hz and was unaltered above 250 Hz. In agreement with the power spectral analysis, this advocates for a sampling frequency between 100 and 250 Hz. Relative consistency was observed across the tested parameters and at least 30 s of observation time was required for a valid calculation of SaEn from torque data.

Reflex response and control of the human soleus and gastrocnemius muscles during walking and running at increasing velocity.

We measured the soleus and the gastrocnemius H-reflex modulation in seven subjects during walking at 4.5 km/h and during running at 8, 12 and 15 km/h. The recordings in the medial gastrocnemius were corrected for cross-talk from the soleus muscle. The gastrocnemius H-reflex was in general lower than the soleus H-reflex. In both muscles the H-reflex increased significantly from walking to running but also with increasing running speed. The peak of EMG activity increased in both muscles with increasing speed. The V-wave of both muscles was absent or rather low during walking, but it increased significantly from walking to running with increasing running speed in the soleus but not in the medial gastrocnemius. In both muscles the V-wave was highest just prior to heel strike. It is suggested that this was due to a high firing frequency of the motoneurones in this phase of the movement. It is concluded that a shift towards the faster gastrocnemius at higher running speeds on behalf of the soleus muscle did not occur. The fact that the physiological cross-sectional area of the soleus is much larger than that of the lumped gastrocnemii is most probably the reason why the soleus is important also at higher running velocities.

Electro-suit treatment of children with unilateral cerebral palsy alters nonlinear dynamics of walking.

BACKGROUND: Cerebral palsy (CP) is characterized by spasticity and muscle contracture development and associated with mild to severe motor impairments including reduced gait function. Treatment with the Exopulse® suit has been shown to reduce spasticity of the affected muscles and constitutes a non-invasive alternative to pharmaceutical agents and surgical denervation. The present study investigated the effect of systematic treatment with the Exopulse® suit on the nonlinear dynamics and variability of trunk accelerations during walking in children with unilateral CP. METHODS: Twelve patients (mean age: 12 years, range 7-17 years) with unilateral CP (GMFCS level 1 and 2) received 24 weeks Exopulse® suit treatment with patient-specific muscle stimulation. Before and after the treatment, the patients completed 4 min treadmill walking while trunk accelerometry was obtained. The nonlinear dynamics was quantified by the largest Lyapunov exponent and the complexity index from the multiscale entropy and movement variability was quantified by the root mean square ratio. Pre- vs post-treatment differences were evaluated by a paired Student's t-test. FINDINGS: The largest Lyapunov exponent (p-value = 0.041) and the complexity index (p-value = 0.030) of the acceleration in the anterior-posterior direction was significantly lower post-treatment. No other between-trial differences were observed. INTERPRETATION: The present study suggests that 24 weeks of Exopulse® suit treatment alters the nonlinear dynamics but not the variability of the trunk accelerations during walking in children with unilateral CP. The temporal structure of the trunk acceleration in the anterior-posterior direction was altered towards that of healthy individuals.

Inter-limb coupling in individuals with transtibial amputation during bilateral stance is direction dependent.

We investigated the control of upright standing in individuals with unilateral transtibial amputation (TTA) by assessing the inter-limb coupling and the coupling between the center of pressure beneath both limbs combined (COPNET) and the center of pressure (COP) beneath the prosthetic limb and the intact limb. Twenty-one adults with TTA and eighteen unimpaired adults completed 90 s of standing on two parallel force plates. The inter-limb coupling and the coupling between the COP beneath each limb and the COPNET were assessed by quantifying the synchronization of the COP signals. This included the number of epochs with synchronized signals, the total duration of signal synchronization and the relative phase and deviation phase between the signals. Additionally, magnitude and temporal characteristics of the COP displacements were quantified. Individuals with TTA exhibited looser inter-limb coupling in the anterior-posterior direction, characterized by more shifts between epochs with synchronized signals, shorter total duration of signal synchronization, less in-phase coordination patterns and a higher deviation phase between the two limbs, compared to unimpaired individuals. This coincided with a larger and more irregular postural sway in the TTA group. No group difference was observed in the mediolateral direction. The coupling between the COPNET and the COP beneath the individual limbs was similarly direction dependent, and tighter for the intact side, suggesting that an intact limb-driven strategy was utilized.

Entropy Analysis in Gait Research: Methodological Considerations and Recommendations.

The usage of entropy analysis in gait research has grown considerably the last two decades. The present paper reviews the application of different entropy analyses in gait research and provides recommendations for future studies. While single-scale entropy analysis such as approximate and sample entropy can be used to quantify regularity/predictability/probability, they do not capture the structural richness and component entanglement characterized by a complex system operating across multiple spatial and temporal scales. Thus, for quantification of complexity, either multiscale entropy or refined composite multiscale entropy is recommended. For both single- and multiscale-scale entropy analyses, care should be made when selecting the input parameters of tolerance window r, vector length m, time series length N and number of scales. This selection should be based on the proposed research question and the type of data collected and not copied from previous studies. Parameter consistency should be investigated and published along with the main results to ensure transparency and enable comparisons between studies. Furthermore, since the interpretation of the absolute size of both single- and multiscale entropy analyses outcomes is not straightforward, comparisons should always be made with a control condition or group.

The temporal pattern and the probability distribution of visual cueing can alter the structure of stride-to-stride variability.

The structure of the stride-to-stride time intervals during paced walking can be altered by the temporal pattern of the pacing cues, however, it is unknown if an altered probability distribution of these cues could also affect stride-to-stride time intervals. We investigated the effect of the temporal pattern and probability distribution of visual pacing cues on the temporal structure of the variability of the stride-to-stride time intervals during walking. Participants completed self-paced walking (SPW) and walking paced by visual cueing that had a temporal pattern of either pink noise presented with a normal distribution (PNND), shuffled pink noise presented with a normal distribution (SPNND), white noise presented with a normal distribution (WNND), and white noise presented with a uniform distribution (WNUD). The temporal structure of the stride-to-stride time intervals was quantified using the scaling exponent calculated from Detrended Fluctuation Analysis. The scaling exponent was higher during the SPW and PNND trials than during the SPNND, WNND and WNUD trials and it was lower during the WNUD trial compared to the SPNND trial. The results revealed that both the temporal pattern and the probability distribution of the visual pacing cues can affect the scaling exponent of the variability of the stride-to-stride time intervals. This information is fundamental in understanding how visual input is involved in the control of gait.

Dynamics of Postural Control in Elite Sport Rifle Shooters.

Thirteen shooters and eleven non-shooters completed two-legged and single-legged stance on a force platform. The dynamics of the center of pressure trajectory was assessed using sample entropy, correlation dimension and entropic half-life. Additionally, the body sway was quantified as the elliptical area of the trajectory. The shooters had lower sample entropy and tended to have longer entropic half-life during the single-legged stance. Across the two tasks, the correlation dimension in the anterior-posterior direction and the body sway in both directions were lower in the shooters. This suggests that extensive training in quiet stance is associated with altered postural control, especially during challenging single-legged stance and to a lesser extend during two-legged stance.

Filtering affects the calculation of the largest Lyapunov exponent.

The calculation of the largest Lyapunov exponent (LyE) requires the reconstruction of the time series in an N-dimensional state space. For this, the time delay (Tau) and embedding dimension (EmD) are estimated using the Average Mutual Information and False Nearest Neighbor algorithms. However, the estimation of these variables (LyE, Tau, EmD) could be compromised by prior filtering of the time series evaluated. Therefore, we investigated the effect of filtering kinematic marker data on the calculation of Tau, EmD and LyE using several different computational codes. Kinematic marker data were recorded from 37 subjects during treadmill walking and filtered using a low pass digital filter with a range of cut-off frequencies (23.5-2Hz). Subsequently, the Tau, EmD and LyE were calculated from all cut-off frequencies. Our results demonstrated that the level of filtering affected the outcome of the Tau, EmD and LyE calculations for all computational codes used. However, there was a more consistent outcome for cut-off frequencies above 10 Hz which corresponded to the optimal cut-off frequency that could be used with this data. This suggested that kinematic data should remain unfiltered or filtered conservatively before calculating Tau, EmD and LyE.

On the application of entropic half-life and statistical persistence decay for quantification of time dependency in human gait.

Entropic half-life (ENT½) and statistical persistence decay (SPD) was recently introduced as measures of time dependency in stride time intervals during walking. The present study investigated the effect of data length on ENT½ and SPD and additionally applied these measures to stride length and stride speed intervals. First, stride times were collected from subjects during one hour of treadmill walking. ENT½ and SPD were calculated from a range of stride numbers between 250 and 2500. Secondly, stride times, stride lengths and stride speeds were collected from subjects during 16 min of treadmill walking. ENT½ and SPD were calculated from the stride times, stride lengths and stride speeds. The ENT½ values reached a plateau between 1000 and 2500 strides whereas the SPD increased linearly with the number of included strides. This suggests that ENT½ can be compared if 1000 strides or more are included, but only SPD obtained from same number of strides should be compared. The ENT½ and SPD of the stride times were significantly longer compared to that of the stride lengths and stride speeds. This indicates that the time dependency is greater in the motor control of stride time compared to that of stride lengths and stride speeds.

Quantifying Asymmetry in Gait: The Weighted Universal Symmetry Index to Evaluate 3D Ground Reaction Forces.

Though gait asymmetry is used as a metric of functional recovery in clinical rehabilitation, there is no consensus on an ideal method for its evaluation. Various methods have been proposed to analyze single bilateral signals but are limited in scope, as they can often use only positive signals or discrete values extracted from time-scale data as input. By defining five symmetry axioms, a framework for benchmarking existing methods was established and a new method was described here for the first time: the weighted universal symmetry index (wUSI), which overcomes limitations of other methods. Both existing methods and the wUSI were mathematically compared to each other and in respect to their ability to fulfill the proposed symmetry axioms. Eligible methods that fulfilled these axioms were then applied using both discrete and continuous approaches to ground reaction force (GRF) data collected from healthy gait, both with and without artificially induced asymmetry using a single instrumented elbow crutch. The wUSI with a continuous approach was the only symmetry method capable of identifying GRF asymmetry differences in different walking conditions in all three planes of motion. When used with a continuous approach, the wUSI method was able to detect asymmetries while avoiding artificial inflation, a common problem reported in other methods. In conclusion, the wUSI is proposed as a universal method to quantify three-dimensional GRF asymmetries, which may also be expanded to other biomechanical signals.

Comparative analysis of power, work and muscle activation during weight-stack and iso-inertial flywheel resistance exercise in young adults with cerebral palsy.

INTRODUCTION: The development of efficient resistance exercise protocols to counteract muscle dysfunction in cerebral palsy is warranted. Whether individuals with cerebral palsy are able to perform iso-inertial resistance (flywheel) exercise in a comparable manner to typically developed subjects has never been experimentally tested. DESIGN: A comparative, controlled study. SUBJECTS: Eight young ambulatory adults with cerebral palsy (mean age 19 years; Gross Motor Function Classification System (GMFCS) I-III) and 8 typically developed control subjects (mean age 21 years). METHODS: Subjects performed acute bouts on the weight-stack and flywheel leg-press device, respectively. Range of motion, electromyography, power, work and muscle thickness (ultrasound) data were collected. RESULTS: Subjects with cerebral palsy were able to produce a greater eccentric/concentric peak power ratio on the flywheel (p < 0.05 vs ratio in weight-stack), however absolute values were lower (p < 0.05 vs weight-stack). Typically developed subjects produced more power per mm of thigh muscle than the cerebral palsy group, independent of leg, device and action. DISCUSSION: Subjects with cerebral palsy could not elicit the eccentric overload seen in typically developed subjects. Furthermore, peak power production per mm muscle was markedly reduced in both legs in subjects with cerebral palsy. In conclusion, this comparative study of weight-stack and flywheel exercise does not support the implementation of the current iso-inertial protocol for young adults with cerebral palsy.

The Effect of Ankle Bracing on Kinematics in Simulated Sprain and Drop Landings: A Double-Blind, Placebo-Controlled Study.

BACKGROUND: The efficacy of external ankle braces to protect against sudden inversion sprain has yet to be determined while taking into account the possible placebo effect of brace application. PURPOSE: To assess the protective effect of an external ankle brace on ankle kinematics during simulated inversion sprain and single-legged drop landings among individuals with a history of unilateral lateral ankle sprain. HYPOTHESIS: The primary hypothesis was that active and placebo external braces would reduce inversion angle during simulated inversion sprain. STUDY DESIGN: Controlled laboratory study. METHODS: Sixteen participants with ankle instability and previous sprain performed single-legged drop landings and sudden inversion tilt perturbations. Kinematics of the affected limb were assessed in 3 conditions (active bracing, passive placebo bracing, and unbraced) across 2 measurement days. Participators and investigators were blinded to the brace type tested. The effect of bracing on kinematics was assessed with repeated measures analysis of variance with statistical parametric mapping, with post hoc tests performed for significant interactions. RESULTS: Only active bracing reduced inversion angles during a sudden ankle inversion when compared with the unbraced condition. This reduction was apparent between 65 and 140 milliseconds after the initial fall. No significant differences in inversion angle were found between the passive placebo brace and unbraced conditions during sudden ankle inversion. Furthermore, no significant differences were found among all tested conditions in the sagittal plane kinematics at the knee and ankle. CONCLUSION: During an inversion sprain, only the actively protecting ankle brace limited inversion angles among participants. These results do not indicate a placebo effect of external bracing for patients with ankle instability and a history of unilateral ankle sprain. Furthermore, sagittal plane knee kinematics appear to remain unaffected by bracing during single-legged landing, owing to the limited effects of bracing on sagittal ankle kinematics. These results highlight the role of brace design on biomechanical function during sports-related and injury-prone movements. CLINICAL RELEVANCE: Athletes prone to reinjury after lateral ankle sprain may benefit from brace designs that allow for full sagittal range of motion but restrict only frontal plane motion.

Sampling frequency influences sample entropy of kinematics during walking.

Sample entropy (SaEn) has been used to assess the regularity of lower limb joint angles during walking. However, changing sampling frequency and the number of included strides can potentially affect the outcome. The present study investigated the effect of sample frequency and the number of included strides on the calculations of SaEn in joint angle signals recorded during treadmill walking. Eleven subjects walked at their preferred walking speed for 10 min, and SaEn was calculated on sagittal plane hip, knee, and ankle angle signals extracted from 50, 100, 200, 300, and 400 strides at sampling frequencies of 60, 120, 240, and 480 Hz. Increase in sampling frequency decreased the SaEn significantly for the three joints. The number of included strides had no effect on the SaEn calculated on the hip joint angle and only limited effect on the SaEn calculated on the knee and ankle joint signals. The present study suggests that the number of data points within each stride to a greater extent determines the size of the SaEn compared to the number of strides and emphasizes the use of a fixed number of data points within each stride when applying SaEn to lower limb joint angles during walking. Graphical abstract Sampling frequency influences sample entropy of kinematics during walking.