Hip actuations can be used to control bifurcations and chaos in a passive dynamic walking model

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.

Effect of simulated sensorimotor noise on kinematic variability and stability of a biped walking model

Whether higher variability in older adults' walking is an indication of increased instability has been challenged recently. We performed a computer simulation to investigate the effect of sensorimotor noise on the kinematic variability and stability in a biped walking model. Stochastic differential equations of the system with additive Gaussian white noise was constructed and solved. Sensorimotor noise mainly resulted in higher kinematic variability but its influence on gait stability is minimal. This implies that kinematic variability evident in walking gaits of older adults could be the result of internal sensorimotor noise and not an indication of instability.

Benefits of nonlinear analysis indices of walking stride interval in the evaluation of neurodegenerative diseases

Indices characterising the long-range temporal structure of walking stride interval (SI) variability such as Hurst exponent (H) and fractal dimension (D) may be used in addition to indices measuring the amount of variability like the coefficient of variation (CV). We assess the added value of the former indices in a clinical neurological context. Our aim is to demonstrate that they provide a clinical significance in aging and in frequent neurodegenerative diseases such as Parkinson's disease, Huntington, and amyotrophic lateral sclerosis. Indices assessing the temporal structure of variability are mainly dependent on SI time series length and algorithms used, making quantitative comparisons between different studies difficult or even impossible. Here, we recompute these indices from available SI time series, either from our lab or from online databases. More precisely, we recompute CV, H, and D in a unified way. The average SI is also added to the measured parameters. We confirm that variability indices are relevant indicators of aging process and neurodegenerative diseases. While CV is sensitive to aging process and pathology, it does not discriminate between specific neurodegenerative diseases. H, which measures predictability of SI, significantly decreases with age but increases in patients suffering from amyotrophic lateral sclerosis. D, catching complexity of SI, is correlated with total functional capacity in patients with Huntington's disease. We conclude that the computation of H complements the clinical diagnosis of walking in patients with neurodegenerative diseases and we recommend it as a relevant supplement to classical CV or averaged SI. Since H and D indices did not lead to the same observations, suggesting the multi-fractal nature of SI dynamics, we recommend to open clinical gait analysis to the evaluation of more parameters.

Multiple-Joint Pedestrian Tracking Using Periodic Models

Estimating accurate positions of multiple pedestrians is a critical task in robotics and autonomous cars. We propose a tracker based on typical human motion patterns to track multiple pedestrians. This paper assumes that the legs' reflection and extension angles are approximately changing periodically during human motion. A Fourier series is fitted in order to describe the moving, such as describing the position and velocity of the hip, knee, and ankle. Our tracker receives the position of the ankle, knee, and hip as measurements. As a proof of concept, we compare our tracker with state-of-the-art methods. The proposed models have been validated by experimental data, the Human Gait Database (HuGaDB), and the Karlsruhe Institute of Technology and Toyota Technological Institute (KITTI) tracking benchmark. The results indicate that our tracker is able to estimate the reflection and extension angles with a precision of 90.97%. Moreover, the comparison shows that the tracking precision increases up to 1.3% with the proposed tracker when compared to a constant velocity based tracker.

Non-linear dynamics in parkinsonism

Over the last 30 years, the functions (and dysfunctions) of the sensory-motor circuitry have been mostly conceptualized using linear modelizations which have resulted in two main models: the “rate hypothesis” and the “oscillatory hypothesis.” In these two models, the basal ganglia data stream is envisaged as a random temporal combination of independent simple patterns issued from its probability distribution of interval interspikes or its spectrum of frequencies respectively. More recently, non-linear analyses have been introduced in the modelization of motor circuitry activities, and they have provided evidences that complex temporal organizations exist in basal ganglia neuronal activities. Regarding movement disorders, these complex temporal organizations in the basal ganglia data stream differ between conditions (i.e., parkinsonism, dyskinesia, healthy control) and are responsive to treatments (i.e., l-DOPA, deep brain stimulation). A body of evidence has reported that basal ganglia neuronal entropy (a marker for complexity/irregularity in time series) is higher in hypokinetic state. In line with these findings, an entropy-based model has been recently formulated to introduce basal ganglia entropy as a marker for the alteration of motor processing and a factor of motor inhibition. Importantly, non-linear features have also been identified as a marker of condition and/or treatment effects in brain global signals (EEG), muscular activities (EMG), or kinetic of motor symptoms (tremor, gait) of patients with movement disorders. It is therefore warranted that the non-linear dynamics of motor circuitry will contribute to a better understanding of the neuronal dysfunctions underlying the spectrum of parkinsonian motor symptoms including tremor, rigidity, and hypokinesia.

Gait variability is altered in older adults when listening to auditory stimuli with differing temporal structures

Gait variability in the context of a deterministic dynamical system may be quantified using nonlinear time series analyses that characterize the complexity of the system. Pathological gait exhibits altered gait variability. It can be either too periodic and predictable, or too random and disordered, as is the case with aging. While gait therapies often focus on restoration of linear measures such as gait speed or stride length, we propose that the goal of gait therapy should be to restore optimal gait variability, which exhibits chaotic fluctuations and is the balance between predictability and complexity. In this context, our purpose was to investigate how listening to different auditory stimuli affects gait variability. Twenty-seven young and 27 elderly subjects walked on a treadmill for 5 min while listening to white noise, a chaotic rhythm, a metronome, and with no auditory stimulus. Stride length, step width, and stride intervals were calculated for all conditions. Detrended Fluctuation Analysis was then performed on these time series. A quadratic trend analysis determined that an idealized inverted-U shape described the relationship between gait variability and the structure of the auditory stimuli for the elderly group, but not for the young group. This proof-of-concept study shows that the gait of older adults may be manipulated using auditory stimuli. Future work will investigate which structures of auditory stimuli lead to improvements in functional status in older adults.

New insights into anterior cruciate ligament deficiency and reconstruction through the assessment of knee kinematic variability in terms of nonlinear dynamics

PURPOSE

Injuries to the anterior cruciate ligament (ACL) occur frequently, particularly in young adult athletes, and represent the majority of the lesions of knee ligaments. Recent investigations suggest that the assessment of kinematic variability using measures of nonlinear dynamics can provide with important insights with respect to physiological and pathological states. The purpose of the present article was to critically review and synthesize the literature addressing ACL deficiency and reconstruction from a nonlinear dynamics standpoint.

METHODS

A literature search was carried out in the main medical databases for studies published between 1990 and 2010.

RESULTS

Seven studies investigated knee kinematic variability in ACL patients. Results provided support for the theory of "optimal movement variability". Practically, loss below optimal variability is associated with a more rigid and very repeatable movement pattern, as observed in the ACL-deficient knee. This is a state of low complexity and high predictability. On the other hand, increase beyond optimal variability is associated with a noisy and irregular movement pattern, as found in the ACL-reconstructed knee, regardless of which type of graft is used. This is a state of low complexity and low predictability. In both cases, the loss of optimal variability and the associated high complexity lead to an incapacity to respond appropriately to the environmental demands, thus providing an explanation for vulnerability to pathological changes following injury.

CONCLUSION

Subtle fluctuations that appear in knee kinematic patterns provide invaluable insight into the health of the neuromuscular function after ACL rupture and reconstruction. It is thus critical to explore them in longitudinal studies and utilize nonlinear measures as an important component of post-reconstruction medical assessment.

LEVEL OF EVIDENCE

II.

Human movement variability, nonlinear dynamics, and pathology: is there a connection?

Fields studying movement generation, including robotics, psychology, cognitive science, and neuroscience utilize concepts and tools related to the pervasiveness of variability in biological systems. The concept of variability and the measures for nonlinear dynamics used to evaluate this concept open new vistas for research in movement dysfunction of many types. This review describes innovations in the exploration of variability and their potential importance in understanding human movement. Far from being a source of error, evidence supports the presence of an optimal state of variability for healthy and functional movement. This variability has a particular organization and is characterized by a chaotic structure. Deviations from this state can lead to biological systems that are either overly rigid and robotic or noisy and unstable. Both situations result in systems that are less adaptable to perturbations, such as those associated with unhealthy pathological states or absence of skillfulness.

Classification of periodic and chaotic passive limit cycles for a compass-gait biped with gait asymmetries

In this paper we study the problem of passive walking for a compass-gait biped with gait asymmetries. In particular, we identify and classify bifurcations leading to chaos caused by the gait asymmetries because of unequal leg masses. We present bifurcation diagrams showing step period versus the ratio of leg masses at various walking slopes. The cell mapping method is used to find stable limit cycles as the parameters are varied. It is found that a variety of bifurcation diagrams can be grouped into six stages that consist of three expanding and three contracting stages. The analysis of each stage shows that marginally stable limit cycles exhibit period-doubling, period-remerging, and saddle-node bifurcations. We also show qualitative changes regarding chaos, i.e., generation and extinction of chaos follow cyclic patterns in passive dynamic walking.

High resolution MEMS accelerometers to estimate VO2 and compare running mechanics between highly trained inter-collegiate and untrained runners

BACKGROUND

The purposes of this study were to determine the validity and reliability of high resolution accelerometers (HRA) relative to VO(2) and speed, and compare putative differences in HRA signal between trained (T) and untrained (UT) runners during treadmill locomotion.

METHODOLOGY

Runners performed 2 incremental VO(2max) trials while wearing HRA. RMS of high frequency signal from three axes (VT, ML, AP) and the Euclidean resultant (RES) were compared to VO(2) to determine validity and reliability. Additionally, axial rms relative to speed, and ratio of axial accelerations to RES were compared between T and UT to determine if differences in running mechanics could be identified between the two groups.

PRINCIPAL FINDINGS

Regression of RES was strongly related to VO(2), but T was different than UT (r = 0.96 vs 0.92; p<.001) for walking and running. During walking, only the ratio of ML and AP to RES were different between groups. For running, nearly all acceleration parameters were lower for T than UT, the exception being ratio of VT to RES, which was higher in T than UT. All of these differences during running were despite higher VO(2), O(2) cost, and lower RER in T vs UT, which resulted in no significant difference in energy expenditure between groups.

CONCLUSIONS/SIGNFICANCE

These results indicate that HRA can accurately and reliably estimate VO(2) during treadmill locomotion, but differences exist between T and UT that should be considered when estimating energy expenditure. Differences in running mechanics between T and UT were identified, yet the importance of these differences remains to be determined.

A passive dynamic walking robot that has a deterministic nonlinear gait

There is a growing body of evidence that the step-to-step variations present in human walking are related to the biomechanics of the locomotive system. However, we still have limited understanding of what biomechanical variables influence the observed nonlinear gait variations. It is necessary to develop reliable models that closely resemble the nonlinear gait dynamics in order to advance our knowledge in this scientific field. Previously, Goswami et al. [1998. A study of the passive gait of a compass-like biped robot: symmetry and chaos. International Journal of Robotic Research 17(12)] and Garcia et al. [1998. The simplest walking model: stability, complexity, and scaling. Journal of Biomechanical Engineering 120(2), 281-288] have demonstrated that passive dynamic walking computer models can exhibit a cascade of bifurcations in their gait pattern that lead to a deterministic nonlinear gait pattern. These computer models suggest that the intrinsic mechanical dynamics may be at least partially responsible for the deterministic nonlinear gait pattern; however, this has not been shown for a physical walking robot. Here we use the largest Laypunov exponent and a surrogation analysis method to confirm and extend Garcia et al.'s and Goswami et al.'s original results to a physical passive dynamic walking robot. Experimental outcomes from our walking robot further support the notion that the deterministic nonlinear step-to-step variations present in gait may be partly governed by the intrinsic mechanical dynamics of the locomotive system. Furthermore the nonlinear analysis techniques used in this investigation offer novel methods for quantifying the nature of the step-to-step variations found in human and robotic gait.

Do horizontal propulsive forces influence the nonlinear structure of locomotion?

Background

Several investigations have suggested that changes in the nonlinear gait dynamics are related to the neural control of locomotion. However, no investigations have provided insight on how neural control of the locomotive pattern may be directly reflected in changes in the nonlinear gait dynamics. Our simulations with a passive dynamic walking model predicted that toe-off impulses that assist the forward motion of the center of mass influence the nonlinear gait dynamics. Here we tested this prediction in humans as they walked on the treadmill while the forward progression of the center of mass was assisted by a custom built mechanical horizontal actuator.

Methods

Nineteen participants walked for two minutes on a motorized treadmill as a horizontal actuator assisted the forward translation of the center of mass during the stance phase. All subjects walked at a self-select speed that had a medium-high velocity. The actuator provided assistive forces equal to 0, 3, 6 and 9 percent of the participant's body weight. The largest Lyapunov exponent, which measures the nonlinear structure, was calculated for the hip, knee and ankle joint time series. A repeated measures one-way analysis of variance with a t-test post hoc was used to determine significant differences in the nonlinear gait dynamics.

Results

The magnitude of the largest Lyapunov exponent systematically increased as the percent assistance provided by the mechanical actuator was increased.

Conclusion

These results support our model's prediction that control of the forward progression of the center of mass influences the nonlinear gait dynamics. The inability to control the forward progression of the center of mass during the stance phase may be the reason the nonlinear gait dynamics are altered in pathological populations. However, these conclusions need to be further explored at a range of walking speeds.