The effects of sensory loss and walking speed on the orbital dynamic stability of human walking

Peripheral sensory feedback is believed to contribute significantly to maintaining walking stability. Patients with diabetic peripheral neuropathy have a greatly increased risk of falling. Previously, we demonstrated that slower walking speeds in neuropathic patients lead to improved local dynamic stability. However, all subjects exhibited significant local instability during walking, even though no subject fell or stumbled during testing. The present study was conducted to determine if and how significant changes in peripheral sensation and walking speed affect orbital stability during walking. Trunk and lower extremity kinematics were examined from two prior experiments that compared patients with significant neuropathy to healthy controls and walking at multiple different speeds in young healthy subjects. Maximum Floquet multipliers were computed for each time series to quantify the orbital stability of these movements. All subjects exhibited orbitally stable walking kinematics, even though these same kinematics were previously shown to be locally unstable. Differences in orbital stability between neuropathic and control subjects were small and, with the exception of knee joint movements (p=0.001), not statistically significant (0.380p0.946). Differences in knee orbital stability were not mediated by differences in walking speed. This was supported by our finding that although orbital stability improved slightly with slower walking speeds, the correlations between walking speed and orbital stability were generally weak (r(2)16.7%). Thus, neuropathic patients do not gain improved orbital stability as a result of slowing down and do not experience any loss of orbital stability because of their sensory deficits.     

Real-time gait assessment utilizing a new way of accelerometry

Real-time registration of body segment angles is essential in artificial body position control. A new method is presented for the real-time calculation of the lower extremity angles using data obtained from pairs of two one-dimensional accelerometers. It is shown that, assuming rigid-body dynamics and simple hinge joints, relative angles (i.e. angles between segments) can be calculated without integration, thereby solving the problem of integration drift normally associated with accelerometry. During the stance phase of walking, the relative angles can be transformed to absolute angles (i.e. relative to the gravitational field direction) for the different leg segments. The feasibility of relative angle calculation is demonstrated by calculation of the knee angle of a healthy subject. Stability and resolution were demonstrated with measurements during standing. Measurements during standing up, sitting down and walking showed that shock (heel-strike) and skin movements, due to movements of the underlying muscle tissue, are the main error sources. Additional signal processing, e.g. low-pass filtering, can be used to diminish this error. The accuracy of the knee angle found is shown to be high enough to be used in a feedback controller for functional electrostimulation of the lower extremities.     

Electromyographic characterization of walking behavior initiated spontaneously in crayfish

Crayfish initiate walking behavior not only reflexively in response to external stimuli but also spontaneously in the absence of any specific stimulus. In order to analyze the initiation mechanism underlying these different types of walking, we made simultaneous electromyographic (EMG) recordings from thoracic legs when animals initiated walking, either reflexively or spontaneously, and video recorded their movements synchronously with the EMG recording. Two different stimuli, mechanical and chemical, were used to reflexively induce walking. A non-rhythmic, sustained activation of leg muscles was found to precede the behavioral initiation of either type of walking. The duration of this non-rhythmic muscle activation was significantly longer in the spontaneously initiated walking than in the mechanical stimulus-evoked walking, although no difference was observed between the spontaneous and chemical stimulus-evoked walking. EMG recordings from all eight legs revealed that their non-rhythmic muscle activation occurred almost simultaneously prior to initiation of rhythmical stepping movements. When an animal was suspended without a leg substratum, the timing of muscle activation was more variable among the legs than in the free condition on the substratum. When the circumesophageal commissures were both severed to eliminate signals descending from the brain to the thoracic ganglia, the bilaterally coordinated rhythmic burst activity was not observed in the walking legs. These findings suggest that the spontaneous initiation of walking behavior requires sensory feedback signals from leg proprioceptors, subserved by a different descending activation mechanism from that for stimulus-driven initiation of walking.     

Kinematics and ontogeny of locomotion in monkeys and human babies

Early ontogenetic stages are often assumed to reflect or to be similar to past phylogenetic stages within the evolution of man. Therefore, as a first step, the quadrupedal crawling locomotion of human children was analysed and compared to the quadrupedal walk of Macaca fascicularis. The movements of the human child were not only more irregular, they differed from the walk of the monkey mainly through extraordinarily short swing phases, and also through strong scoliotic movements of the spine. There is a compulsory synchronisation in the hip and knee joint movements of the human crawling baby. We conclude that human crawling may be a behavioural recapitulation of a quadrupedal evolutionary stage. However, with reference to kinematics, man is not only characterised by his unique, habitually bipedal, upright gait but also by a second, equally unique locomotion, namely crawling, which he assumes for a short phase during his first year of life.--The walking movements of the limbs in toddling infants were mainly characterised by i) rather stiff, abducted arms, which were moved mostly by spine torsions (similar to those of bipedally walking Gorilla) and not as a suspensory pendulum. However, they rather work as levers for the elastic torsion pendulum of the spine. ii) They are also characterised by frequently lacking the minor knee flexion, which occurs at about the heel strike within each stride of the adult human. Besides many other details of the results, foot movements differed from adult ones mainly in that the whole plantar surface was placed flat on the ground within a few milliseconds.     

The Complexity of Human Walking: A Knee Osteoarthritis Study

This study proposes a framework for deconstructing complex walking patterns to create a simple principal component space before checking whether the projection to this space is suitable for identifying changes from the normality. We focus on knee osteoarthritis, the most common knee joint disease and the second leading cause of disability. Knee osteoarthritis affects over 250 million people worldwide. The motivation for projecting the highly dimensional movements to a lower dimensional and simpler space is our belief that motor behaviour can be understood by identifying a simplicity via projection to a low principal component space, which may reflect upon the underlying mechanism. To study this, we recruited 180 subjects, 47 of which reported that they had knee osteoarthritis. They were asked to walk several times along a walkway equipped with two force plates that capture their ground reaction forces along 3 axes, namely vertical, anterior-posterior, and medio-lateral, at 1000 Hz. Data when the subject does not clearly strike the force plate were excluded, leaving 1–3 gait cycles per subject. To examine the complexity of human walking, we applied dimensionality reduction via Probabilistic Principal Component Analysis. The first principal component explains 34% of the variance in the data, whereas over 80% of the variance is explained by 8 principal components or more. This proves the complexity of the underlying structure of the ground reaction forces. To examine if our musculoskeletal system generates movements that are distinguishable between normal and pathological subjects in a low dimensional principal component space, we applied a Bayes classifier. For the tested cross-validated, subject-independent experimental protocol, the classification accuracy equals 82.62%. Also, a novel complexity measure is proposed, which can be used as an objective index to facilitate clinical decision making. This measure proves that knee osteoarthritis subjects exhibit more variability in the two-dimensional principal component space.     

Coordination of wing motion and walking suggests common control of zigzag motor program in a male silkworm moth

The male silkworm moth, Bombyx mori, exhibits a zigzagging pattern as it walks upwind to pheromones. This species usually does not fly, but obvious wing-beating accompanies the pheromone-mediated walking. Males supported by a `sled', after having their legs removed, also moved upwind in a pheromone plume along zigzagging tracks, indicating that wing-generated thrust and torque result in locomotory paths similar to those observed from walking moths. Using a high-speed video system we investigated the correlation between the wing movements and zigzag walking. The wing ipsilateral to the direction of the turn showed a greater degree of retraction with respect to the contralateral wing. The timing of the wing retraction pattern was synchronized with changes of direction in the walking track. Coordination of wing movements and walking pattern was not dependent on visual feedback or sensory feedback generated from neck movements associated with turning. The results presented here, taken together with our previous studies of descending interneurons suggest that the coordination of wing movements with the walking pattern may result from the activity of a set of identified interneurons descending from the brain to the thoracic ganglia and/or may be coordinated by coupling of oscillating circuits for walking and wing beating. Accepted: 15 May 1997     

Evolving experience-dependent robust behaviour in embodied agents

In this work, based on behavioural and dynamical evidence, a study of simulated agents with the capacity to change feedback from their bodies to accomplish a one-legged walking task is proposed to understand the emergence of coupled dynamics for robust behaviour. Agents evolve with evolutionary-defined biases that modify incoming body signals (sensory offsets). Analyses on whether these agents show further dependence to their environmental coupled dynamics than others with no feedback control is described in this article. The ability to sustain behaviours is tested during lifetime experiments with mutational and sensory perturbations after evolution. Using dynamical systems analysis, this work identifies conditions for the emergence of dynamical mechanisms that remain functional despite sensory perturbations. Results indicate that evolved agents with evolvable sensory offset depends not only on where in neural space the state of the neural system operates, but also on the transients to which the inner-system was being driven by sensory signals from its interactions with the environment, controller, and agent body. Experimental evidence here leads discussions on a dynamical systems perspective on behavioural robustness that goes beyond attractors of controller phase space.     

Individual muscle contributions to the axial knee joint contact force during normal walking

Muscles are significant contributors to the high joint forces developed in the knee during human walking. Not only do muscles contribute to the knee joint forces by acting to compress the joint, but they also develop joint forces indirectly through their contributions to the ground reaction forces via dynamic coupling. Thus, muscles can have significant contributions to forces at joints they do not span. However, few studies have investigated how the major lower-limb muscles contribute to the knee joint contact forces during walking. The goal of this study was to use a muscle-actuated forward dynamics simulation of walking to identify how individual muscles contribute to the axial tibio-femoral joint force. The simulation results showed that the vastii muscles are the primary contributors to the axial joint force in early stance while the gastrocnemius is the primary contributor in late stance. The tibio-femoral joint force generated by these muscles was at times greater than the muscle forces themselves. Muscles that do not cross the knee joint (e.g., the gluteus maximus and soleus) also have significant contributions to the tibio-femoral joint force through their contributions to the ground reaction forces. Further, small changes in walking kinematics (e.g., knee flexion angle) can have a significant effect on the magnitude of the knee joint forces. Thus, altering walking mechanics and muscle coordination patterns to utilize muscle groups that perform the same biomechanical function, yet contribute less to the knee joint forces may be an effective way to reduce knee joint loading during walking.     

Activation of walking by electrical stimulation in humans under the conditions of muscle unloading and its variations under the effect of afferent influences

The possibility of initiating an involuntary walking rhythm in a suspended human leg by electrical stimulation was studied. The subjects lay on the side with one leg suspended in an exoskeleton allowing horizontal rotation in three joints: the hip, knee, and ankle ones. To evoke involuntary walking of the suspended leg, two methods were used: continuous vibration of the quadriceps muscle of the hip and electrical stimulation of the cutaneous nerves innervating the foot of the immobile leg. The hip and ankle were involved in the involuntary movements, with reciprocal bursts of electromyographic activity being also observed in the antagonistic muscles of the hip. The application of an external load (4 N or 8 N) to the foot caused a perceptible intensification of its movements. An additional weight (0.5 kg) or a rubber band wrapped around the foot caused no substantial change in the pattern of stimulated walking. Electrical stimulation is an effective means of activating walking movements, and their characteristics confirm the assumption that the walking rhythm is of central origin. Additional afferentation from the sole’s receptors plays an important role in the modulation of the induced movements and the modification of the general walking pattern under the conditions of muscle unloading.     

Passive bipedal walking with phasic muscle contraction

The existence of self-organizing walking patterns is often considered the result of a mechanical system interacting with the environment and a (neural) oscillating unit. The pattern generators might be thought of as an indispensable component for the existence of limit cycle behavior. This paper shows that this is not a necessity for the existence of a self-organizing bipedal walking pattern. Stable walking cycles emerge from a simple passive bipedal structure, with an energy source inevitably present to sustain the oscillation. In this work the energy source is chosen to be phasic muscle contraction. A two-dimensional model is composed of two legs and a hip mass, symbolizing the trunk. The stance leg stiffness is generated by two muscles. The hip stiffness is generated by four muscles. Muscle activation is caused by two reflex-like trigger signals, without feedback control. Human equivalent model parameters such as geometry and mass distribution were assumed. With return map analysis, the model is analyzed on periodic behavior. Stable walking cycles were found and could be manipulated during walking by varying the muscle or reflex parameters, forcing the oscillation to converge to a new attractor. Received: 5 November 1998 / Accepted in revised form: 26 March 1999     

Contributions of muscles and passive dynamics to swing initiation over a range of walking speeds

Stiff-knee gait is a common walking problem in cerebral palsy characterized by insufficient knee flexion during swing. To identify factors that may limit knee flexion in swing, it is necessary to understand how unimpaired subjects successfully coordinate muscles and passive dynamics (gravity and velocity-related forces) to accelerate the knee into flexion during double support, a critical phase just prior to swing that establishes the conditions for achieving sufficient knee flexion during swing. It is also necessary to understand how contributions to swing initiation change with walking speed, since patients with stiff-knee gait often walk slowly. We analyzed muscle-driven dynamic simulations of eight unimpaired subjects walking at four speeds to quantify the contributions of muscles, gravity, and velocity-related forces (i.e. Coriolis and centrifugal forces) to preswing knee flexion acceleration during double support at each speed. Analysis of the simulations revealed contributions from muscles and passive dynamics varied systematically with walking speed. Preswing knee flexion acceleration was achieved primarily by hip flexor muscles on the preswing leg with assistance from biceps femoris short head. Hip flexors on the preswing leg were primarily responsible for the increase in preswing knee flexion acceleration during double support with faster walking speed. The hip extensors and abductors on the contralateral leg and velocity-related forces opposed preswing knee flexion acceleration during double support.     

Reconstructing muscle activation during normal walking: a comparison of symbolic and connectionist machine learning techniques

One symbolic (rule-based inductive learning) and one connectionist (neural network) machine learning technique were used to reconstruct muscle activation patterns from kinematic data measured during normal human walking at several speeds. The activation patterns (or desired outputs) consisted of surface electromyographic (EMG) signals from the semitendinosus and vastus medialis muscles. The inputs consisted of flexion and extension angles measured at the hip and knee of the ipsilateral leg, their first and second derivatives, and bilateral foot contact information. The training set consisted of data from six trials, at two different speeds. The testing set consisted of data from two additional trials (one at each speed), which were not in the training set. It was possible to reconstruct the muscular activation at both speeds using both techniques. Timing of the reconstructed signals was accurate. The integrated value of the activation bursts was less accurate. The neural network gave a continuous output, whereas the rule-based inductive learning rule tree gave a quantised activation level. The advantage of rule-based inductive learning was that the rules used were both explicit and comprehensible, whilst the rules used by the neural network were implicit within its structure and not easily comprehended. The neural network was able to reconstruct the activation patterns of both muscles from one network, whereas two separate rule sets were needed for the rule-based technique. It is concluded that machine learning techniques, in comparison to explicit inverse muscular skeletal models, show good promise in modelling nearly cyclic movements such as locomotion at varying walking speeds. However, they do not provide insight into the biomechanics of the system, because they are not based on the biomechanical structure of the system.     

A mathematical modeling study of inter-segmental coordination during stick insect walking

The biomechanical conditions for walking in the stick insect require a modeling approach that is based on the control of pairs of antagonistic motoneuron (MN) pools for each leg joint by independent central pattern generators (CPGs). Each CPG controls a pair of antagonistic MN pools. Furthermore, specific sensory feedback signals play an important role in the control of single leg movement and in the generation of inter-leg coordination or the interplay between both tasks. Currently, however, no mathematical model exists that provides a theoretical approach to understanding the generation of coordinated locomotion in such a multi-legged locomotor system. In the present study, I created such a theoretical model for the stick insect walking system, which describes the MN activity of a single forward stepping middle leg and helps to explain the neuronal mechanisms underlying coordinating information transfer between ipsilateral legs. In this model, CPGs that belong to the same leg, as well as those belonging to different legs, are connected by specific sensory feedback pathways that convey information about movements and forces generated during locomotion. The model emphasizes the importance of sensory feedback, which is used by the central nervous system to enhance weak excitatory and inhibitory synaptic connections from front to rear between the three thorax-coxa-joint CPGs. Thereby the sensory feedback activates caudal pattern generation networks and helps to coordinate leg movements by generating in-phase and out-of-phase thoracic MN activity.     

The three-dimensional determination of internal loads in the lower extremity

A three-dimensional model of the lower limb containing 47 muscles was developed to study the differences between a two- and three-dimensional approach for determining internal loads, the role of the dynamic joint representation, and the behavior of different load-bearing criteria in walking and running. The problem of redundancy of the musculo-skeletal system was resolved by applying inverse dynamics and static optimization methods. Different hypothetical load-bearing capabilities of hinge, spherical and intermediate joint types for the knee and the ankle joints were tested. It was found that even almost planar movements such as walking and running are associated with significant three-dimensional intersegment moments, especially in the frontal plane. Thus, a two-dimensional approach may underestimate internal loads up to 60%. It is shown that pure hinge joints are inappropriate for modeling the dynamical joint function of the knee and ankle joints. A more flexible joint representation in combination with a squared muscle stress minimization criterion predicted a lot of synergistic as well as antagonistic muscle activation which was also found in the EMG patterns. The results indicate the importance of muscular joint stabilization in natural human movements. Compared to in vivo measurements it is speculated that the predicted force magnitudes are considerably overestimated due to error propagation and still insufficient anatomical models. Thus, increased efforts to improve further the reliability of internal load calculations should be made in the future.     

A model of cerebrocerebello-spinomuscular interaction in the sagittal control of human walking

A computationally developed model of human upright balance control (Jo and Massaquoi on Biol cybern 91:188–202, 2004) has been enhanced to describe biped walking in the sagittal plane. The model incorporates (a) non-linear muscle mechanics having activation level -dependent impedance, (b) scheduled cerebrocerebellar interaction for control of center of mass position and trunk pitch angle, (c) rectangular pulse-like feedforward commands from a brainstem/ spinal pattern generator, and (d) segmental reflex modulation of muscular synergies to refine inter-joint coordination. The model can stand when muscles around the ankle are coactivated. When trigger signals activate, the model transitions from standing still to walking at 1.5 m/s. Simulated natural walking displays none of seven pathological gait features. The model can simulate different walking speeds by tuning the amplitude and frequency in spinal pattern generator. The walking is stable against forward and backward pushes of up to 70 and 75 N, respectively, and with sudden changes in trunk mass of up to 18%. The sensitivity of the model to changes in neural parameters and the predicted behavioral results of simulated neural system lesions are examined. The deficit gait simulations may be useful to support the functional and anatomical correspondences of the model. The model demonstrates that basic human-like walking can be achieved by a hierarchical structure of stabilized-long loop feedback and synergy-mediated feedforward controls. In particular, internal models of body dynamics are not required.     

Speed adaptation in a powered transtibial prosthesis controlled with a neuromuscular model

Control schemes for powered ankle-foot prostheses would benefit greatly from a means to make them inherently adaptive to different walking speeds. Towards this goal, one may attempt to emulate the intact human ankle, as it is capable of seamless adaptation. Human locomotion is governed by the interplay among legged dynamics, morphology and neural control including spinal reflexes. It has been suggested that reflexes contribute to the changes in ankle joint dynamics that correspond to walking at different speeds. Here, we use a data-driven muscle-tendon model that produces estimates of the activation, force, length and velocity of the major muscles spanning the ankle to derive local feedback loops that may be critical in the control of those muscles during walking. This purely reflexive approach ignores sources of non-reflexive neural drive and does not necessarily reflect the biological control scheme, yet can still closely reproduce the muscle dynamics estimated from biological data. The resulting neuromuscular model was applied to control a powered ankle-foot prosthesis and tested by an amputee walking at three speeds. The controller produced speed-adaptive behaviour; net ankle work increased with walking speed, highlighting the benefits of applying neuromuscular principles in the control of adaptive prosthetic limbs.     

Stability and motor adaptation in human arm movements

In control, stability captures the reproducibility of motions and the robustness to environmental and internal perturbations. This paper examines how stability can be evaluated in human movements, and possible mechanisms by which humans ensure stability. First, a measure of stability is introduced, which is simple to apply to human movements and corresponds to Lyapunov exponents. Its application to real data shows that it is able to distinguish effectively between stable and unstable dynamics. A computational model is then used to investigate stability in human arm movements, which takes into account motor output variability and computes the force to perform a task according to an inverse dynamics model. Simulation results suggest that even a large time delay does not affect movement stability as long as the reflex feedback is small relative to muscle elasticity. Simulations are also used to demonstrate that existing learning schemes, using a monotonic antisymmetric update law, cannot compensate for unstable dynamics. An impedance compensation algorithm is introduced to learn unstable dynamics, which produces similar adaptation responses to those found in experiments.     

Identifying Stride-To-Stride Control Strategies in Human Treadmill Walking

Variability is ubiquitous in human movement, arising from internal and external noise, inherent biological redundancy, and from the neurophysiological control actions that help regulate movement fluctuations. Increased walking variability can lead to increased energetic cost and/or increased fall risk. Conversely, biological noise may be beneficial, even necessary, to enhance motor performance. Indeed, encouraging more variability actually facilitates greater improvements in some forms of locomotor rehabilitation. Thus, it is critical to identify the fundamental principles humans use to regulate stride-to-stride fluctuations in walking. This study sought to determine how humans regulate stride-to-stride fluctuations in stepping movements during treadmill walking. We developed computational models based on pre-defined goal functions to compare if subjects, from each stride to the next, tried to maintain the same speed as the treadmill, or instead stay in the same position on the treadmill. Both strategies predicted average behaviors empirically indistinguishable from each other and from that of humans. These strategies, however, predicted very different stride-to-stride fluctuation dynamics. Comparisons to experimental data showed that human stepping movements were generally well-predicted by the speed-control model, but not by the position-control model. Human subjects also exhibited no indications they corrected deviations in absolute position only intermittently: i.e., closer to the boundaries of the treadmill. Thus, humans clearly do not adopt a control strategy whose primary goal is to maintain some constant absolute position on the treadmill. Instead, humans appear to regulate their stepping movements in a way most consistent with a strategy whose primary goal is to try to maintain the same speed as the treadmill at each consecutive stride. These findings have important implications both for understanding how biological systems regulate walking in general and for being able to harness these mechanisms to develop more effective rehabilitation interventions to improve locomotor performance.     

The effects of sloped surfaces on locomotion: a kinematic and kinetic analysis

Previous findings from studies of demanding tasks in humans and slope walking in quadrupeds suggest that human slope walking may require specialized neural control strategies. The goal of this investigation was to gain insight into these strategies by quantifying lower limb kinematics and kinetics during up- and downslope walking. Nine healthy volunteers walked at a self-selected speed on an instrumented ramp at each of five grades (-39%, -15%, 0%, +15%, +39%; or -21 degrees, -8.5 degrees, 0 degrees, +8.5 degrees, +21 degrees, respectively). For each subject, the selected speed was maintained at all grades to minimize the effect of speed on gait dynamics. Points of interest were identified in the kinematic and kinetic outcome measures and compared across grades; a significant grade effect was found for all points except the magnitude of the peak hip extensor moment during late stance. Kinematic postural changes were consistent with the need to raise the limb for toe clearance and heel strike and to lift the body during upslope walking, and to control the descent of the body during downslope walking. The support moment increased significantly during both upslope and downslope walking compared to level: the increases were predominantly due to the increasing hip extensor moment during upslope walking, and to the increasing knee extensor moment during downslope walking. In addition, the hip and knee joint moment patterns showed significant differences from the patterns observed during level walking. This non-uniform distribution of joint moment increases during up- and downslope walking compared to level walking suggests that these three tasks are not governed by the same control strategy.