Reliability and minimal detectable change of stiffness and other mechanical properties of the ankle joint in standing and walking.

BACKGROUND: Ankle joint stiffness and viscosity are fundamental mechanical descriptions that govern the movement of the body and impact an individual's walking ability. Hence, these internal properties of a joint have been increasingly used to evaluate the effects of pathology (e.g., stroke) and in the design and control of robotic and prosthetic devices. However, the reliability of these measurements is currently unclear, which is important for translation to clinical use. RESEARCH QUESTION: Can we reliably measure the mechanical impedance parameters of the ankle while standing and walking? METHODS: Eighteen able-bodied individuals volunteered to be tested on two different days separated by at least 24 h. Participants received several small random ankle dorsiflexion perturbations while standing and during the stance phase of walking using a custom-designed robotic platform. Three-dimensional motion capture cameras and a 6-component force plate were used to quantify ankle joint motions and torque responses during normal and perturbed conditions. Ankle mechanical impedance was quantified by computing participant-specific ensemble averages of changes in ankle angle and torque due to perturbation and fitting a second-order parametric model consisting of stiffness, viscosity, and inertia. The test-retest reliability of each parameter was assessed using intraclass correlation coefficients (ICCs). We also computed the minimal detectable change (MDC) for each impedance parameter to establish the smallest amount of change that falls outside the measurement error of the instrument. RESULTS: In standing, the reliability of stiffness, viscosity, and inertia was good to excellent (ICCs=0.67-0.91). During walking, the reliability of stiffness and viscosity was good to excellent (ICCs=0.74-0.84) while that of inertia was fair to good (ICCs=0.47-0.68). The MDC for a single subject ranged from 20%- 65% of the measurement mean but was higher (>100%) for inertia during walking. SIGNIFICANCE: Results indicate that dynamic measures of ankle joint impedance were generally reliable and could serve as an adjunct clinical tool for evaluating gait impairments.

A comparative study of Sumudu HPM and Elzaki HPM for coupled Burgers' equation.

The two hybrid algorithms Sumudu HPM and Elzaki HPM are used in the current study to tackle coupled Burgers' equations and produce accurate results. To demonstrate the validity of the given approaches, three instances are used. Applying Sumudu HPM and Elzaki HPM yields the same approximate and exact answers in all of the examples taken into consideration, which is proved with the help of the accompanying figures. It attests to the entire acceptance and accuracy of the solutions produced by these methods. The proposed regimes also have error and convergence analyses available. The current analytical regimes offer a more effective method of handling partial differential equations than the intricate numerical systems. It is also asserted that exact and approximation solutions are compatible. Also announced is the planned regime's numerical convergence.

Alignment with neighbours enables escape from dead ends in flocking models.

Coordinated movement in animal groups (flocks, schools, herds, etc.) is a classic and well-studied form of collective behaviour. Most theoretical studies consider agents in unobstructed spaces; however, many animals move in often complicated environments and must navigate around and through obstacles. Here we consider simulated agents behaving according to typical flocking rules, with the addition of repulsion from obstacles, and study their collective behaviour in environments with concave obstacles (dead ends). We find that groups of such agents heading for a goal can spontaneously escape dead ends without wall-following or other specialized behaviours, in what we term 'flocking escapes'. The mechanism arises when agents align with one another while heading away from the goal, forming a self-stable cluster that persists long enough to exit the obstacle and avoids becoming trapped again when turning back towards the goal. Solitary agents under the same conditions are never observed to escape. We show that alignment with neighbours reduces the effective turning speed of the group while letting individuals maintain high manoeuvrability when needed. The relative robustness of flocking escapes in our studies suggests that this emergent behaviour may be relevant for a variety of animal species.

How Does Ankle Mechanical Stiffness Change as a Function of Muscle Activation in Standing and During the Late Stance of Walking?

OBJECTIVE: Ankle joint stiffness is known to be modulated by co-contraction of the ankle muscles; however, it is unclear to what extent changes in agonist muscle activation alone affect ankle joint stiffness. This study tested the effects of varying levels of ankle muscle activation on ankle joint mechanical stiffness in standing and during the late stance phase of walking. METHODS: Dorsiflexion perturbations were applied at various levels of ankle muscle activation via a robotic platform in standing and walking conditions. In standing, muscle activation was modulated by having participants perform an EMG target matching task that required varying levels of plantarflexor activation. In walking, muscle activation was modulated by changing walking speeds through metronome-based auditory feedback. Ankle stiffness was evaluated by performing a Least-squares system identification using a parametric model consisting of stiffness, damping, and inertia. The association between ankle muscle activation and joint stiffness was evaluated using correlation analyses. Linear regression models were used to determine the extent to which muscle activation contributed to ankle stiffness. An inclusive statistical approach (both classical and Bayesian analyses) was adopted to measure the statistical significance (p-value) and Bayes Factor (BF10). RESULTS: Results indicate that plantarflexor activity was positively correlated with ankle stiffness in both standing and walking (p<0.001, BF10>900), whereas dorsiflexor activity was negatively correlated with ankle stiffness in walking (p = 0.014, BF10 = 3.9) but not in standing (p = 0.725). Regression analyses indicated that ankle muscle activation predicted about 84% of the variation in ankle stiffness in standing and 45% in walking (p<0.001, BF10>100). CONCLUSION: Ankle muscle activation significantly contributes to ankle stiffness during standing and walking. SIGNIFICANCE: The results highlight the role of muscle activation on maintaining joint stiffness and underscore the importance of accounting for muscle activation when measuring ankle stiffness in healthy as well as patient populations.

Characterization and clinical implications of ankle impedance during walking in chronic stroke.

Individuals post-stroke experience persisting gait deficits due to altered joint mechanics, known clinically as spasticity, hypertonia, and paresis. In engineering, these concepts are described as stiffness and damping, or collectively as joint mechanical impedance, when considered with limb inertia. Typical clinical assessments of these properties are obtained while the patient is at rest using qualitative measures, and the link between the assessments and functional outcomes and mobility is unclear. In this study we quantify ankle mechanical impedance dynamically during walking in individuals post-stroke and in age-speed matched control subjects, and examine the relationships between mechanical impedance and clinical measures of mobility and impairment. Perturbations were applied to the ankle joint during the stance phase of walking, and least-squares system identification techniques were used to estimate mechanical impedance. Stiffness of the paretic ankle was decreased during mid-stance when compared to the non-paretic side; a change independent of muscle activity. Inter-limb differences in ankle joint damping, but not joint stiffness or passive clinical assessments, strongly predicted walking speed and distance. This work provides the first insights into how stroke alters joint mechanical impedance during walking, as well as how these changes relate to existing outcome measures. Our results inform clinical care, suggesting a focus on correcting stance phase mechanics could potentially improve mobility of chronic stroke survivors.

Riverine landscape dynamics of the Upper Ganga River (Haridwar-Narora), India.

Earth observation data provides an exceptional opportunity to study the temporal dynamics of large rivers. The availability of spatially continuous, synoptic and temporally repetitive satellite data allows the reconstruction of historical dynamics of large rivers along with the identification of the causal factors. An absolute paucity of information on the effect of hydrogeomorphic processes on the dynamics of the Upper Ganga River (UGR), especially upon its entry in the plains, motivated this research. This study aims to analyse morphological changes in the river channel, map temporal changes in the land use/land cover (LULC) within the riverscape and thereby understand the landscape dynamics in the UGR (Haridwar to Narora) during 1993-2017 by means of earth observation data. The analysis showed that the river remains straight with a sinuosity index of < 1; however, the braiding increased considerably (from 3.79 to 4.53). Erosion being more prominent on the left bank in comparison to the right bank with 85.89 km2 eroded on the left bank in comparison to 59.21 km2 eroded along the right bank. Riverine landscape has been observed to have a higher rate of accretion in comparison to erosion (8.09 km2 yr-1 and 6.04 km2 yr-1, respectively). Morphological change has brought a transition in the land use patterns with marked variation in vegetation and agriculture along with built-up. Significant changes in the composition of the LULC are largely due to the manifold increase in the agriculture extent (≈ 12 times), built-up (5 times) and the decrease in vegetation cover from 43.9% in 1993 to just 10.94% in 2017.

Heavy metal pollution in surface water of the Upper Ganga River, India: human health risk assessment.

To assess the risk on human health, heavy metal contamination was analysed from surface water in the Upper Ganga river, India. Spatial and seasonal distribution of Fe, Mn, Zn, Cr and Pb was evaluated at eight sites during pre-monsoon and post-monsoon season of 2017. Average concentration of heavy metals was high, often exceeding the limits prescribed for surface water by Bureau of Indian Standard (BIS) and the World Health Organization (WHO). Based on heavy metal pollution index (HPI), 87% of the river stretch was classified as medium to highly polluted. Simultaneous assessment of the health risk employing chronic daily intake (CDI) and hazard quotient (HQ) indicates that exposure through ingestion and dermal pathways currently poses no serious threat to human health (CDI < 1, HQ < 1). For the two population groups analysed, HQIngestion values for Cr (adults 0.51, child 0.55) and Pb (adult 0.31, child 0.34) were significantly higher as compared with other heavy metals. HIIngestion varied from 0.85 to 1.64 for adult and 0.92 to 1.77 for child group, indicating health risk to both groups with child group being more risk prone from either of the exposure pathways. In addition, HI values revealed an increased risk to health for both groups during the post-monsoon season. Higher hazard index (HI) values (> 1) in the Upper Ganga river indicate an ever-increasing non-carcinogenic risk to the exposed population within the riverine landscape. The study highlights the impact of heavy metals in degrading the water quality of the Upper Ganga river and also advocates immediate attention towards reducing human health risk.

A controller for walking derived from how humans recover from perturbations.

Humans can walk without falling despite some external perturbations, but the control mechanisms by which this stability is achieved have not been fully characterized. While numerous walking simulations and robots have been constructed, no full-state walking controller for even a simple model of walking has been derived from human walking data. Here, to construct such a feedback controller, we applied thousands of unforeseen perturbations to subjects walking on a treadmill and collected data describing their recovery to normal walking. Using these data, we derived a linear controller to make the classical inverted pendulum model of walking respond to perturbations like a human. The walking model consists of a point-mass with two massless legs and can be controlled only through the appropriate placement of the foot and the push-off impulse applied along the trailing leg. We derived how this foot placement and push-off impulse are modulated in response to upper-body perturbations in various directions. This feedback-controlled biped recovers from perturbations in a manner qualitatively similar to human recovery. The biped can recover from perturbations over twenty times larger than deviations experienced during normal walking and the biped's stability is robust to uncertainties, specifically, large changes in body and feedback parameters.

Walking crowds on a shaky surface: stable walkers discover Millennium Bridge oscillations with and without pedestrian synchrony.

Why did the London Millennium Bridge shake when there was a big enough crowd walking on it? What features of human walking dynamics when coupled to a shaky surface produce such shaking? Here, we use a simple biped model capable of walking stably in three dimensions to examine these questions. We simulate multiple such stable bipeds walking simultaneously on a bridge, showing that they naturally synchronize under certain conditions, but that synchronization is not required to shake the bridge. Under such shaking conditions, the simulated walkers increase their step widths and expend more metabolic energy than when the bridge does not shake. We also find that such bipeds can walk stably on externally shaken treadmills, synchronizing with the treadmill motion for a range of oscillation amplitudes and frequencies. Our simulations illustrate how interactions between (idealized) bipeds through the walking surface can produce emergent collective behaviour that may not be exhibited by just a single biped.

Walking on a moving surface: energy-optimal walking motions on a shaky bridge and a shaking treadmill can reduce energy costs below normal.

Understanding how humans walk on a surface that can move might provide insights into, for instance, whether walking humans prioritize energy use or stability. Here, motivated by the famous human-driven oscillations observed in the London Millennium Bridge, we introduce a minimal mathematical model of a biped, walking on a platform (bridge or treadmill) capable of lateral movement. This biped model consists of a point-mass upper body with legs that can exert force and perform mechanical work on the upper body. Using numerical optimization, we obtain energy-optimal walking motions for this biped, deriving the periodic body and platform motions that minimize a simple metabolic energy cost. When the platform has an externally imposed sinusoidal displacement of appropriate frequency and amplitude, we predict that body motion entrained to platform motion consumes less energy than walking on a fixed surface. When the platform has finite inertia, a mass- spring-damper with similar parameters to the Millennium Bridge, we show that the optimal biped walking motion sustains a large lateral platform oscillation when sufficiently many people walk on the bridge. Here, the biped model reduces walking metabolic cost by storing and recovering energy from the platform, demonstrating energy benefits for two features observed for walking on the Millennium Bridge: crowd synchrony and large lateral oscillations.

Climate variability, vulnerability, and coping mechanism in Alaknanda catchment, Central Himalaya, India.

A study was carried out to discover trends in the rainfall and temperature pattern of the Alaknanda catchment in the Central Himalaya. Data on the annual rainfall, monsoon rainfall for the last decade, and average annual temperatures over the last few decades were analyzed. Nonparametric methods (Mann-Kendall and Sen's method) were employed to identify trends. The Mann-Kendall test shows a decline in rainfall and rise in temperature, and these trends were found to be statistically significant at the 95% confidence level for both transects. Sen's method also confirms this trend. This aspect has to be considered seriously for the simple reason that if the same trend continues in the future, more chances of drought are expected. The impact of climate change has been well perceived by the people of the catchment, and a coping mechanism has been developed at the local level.