Phase reset and dynamic stability during human gait

The human walking movement shows transient changes in response to single short-lived external perturbations, termed "stumbling reactions." During the stumbling reactions, the walking phase is reset. It has been considered that the reactions contribute to stabilizing the motion, but less evidence bridging between the rhythm reset and the dynamic stability of the gait has been provided. The present study tries to establish the relationship between them. To this end, we construct a simple dynamical system model of the human musculo-skeletal system interacting with the ground, whose joint kinematics during walking is constrained by a given periodic joint-angles-profile. We show first that the model can exhibit a stable limit cycle corresponding to the steady walking with no perturbations. The responses of the limit cycle oscillation are examined by applying a type of perturbations at various timings with various intensities, elucidating the stability of the model's walking when no phase reset is performed. We then observe that modifications of the periodic joint-angles-profile within a short time interval in response to the perturbation can alter the responses of the limit cycle oscillation and induce phase reset of the model's walking. It is shown that appropriate amounts of the phase reset can prevent the model from falling, even for the perturbation that induces falling in the case without the phase reset. This suggests that those phase resets can improve the dynamic stability of the gait. Moreover, the appropriate phase resets predicted by the model are compared with the experimentally observed phase resets during human stumbling reaction to show they share similar characteristics.     

Possible functional roles of phase resetting during walking

The walking rhythm is known to show phase shift or "reset" in response to external impulsive perturbations. We tried to elucidate functional roles of the phase reset possibly used for the neural control of locomotion. To this end, a system with a double pendulum as a simplified model of the locomotor control and a model of bipedal locomotion were employed and analyzed in detail. In these models, a movement corresponding to the normal steady-state walking was realized as a stable limit cycle solution of the system. Unexpected external perturbations applied to the system can push the state point of the system away from its limit cycle, either outside or inside the basin of attraction of the limit cycle. Our mathematical analyses of the models suggested functional roles of the phase reset during walking as follows. Function 1: an appropriate amount of the phase reset for a given perturbation can contribute to relocating the system's state point outside the basin of attraction of the limit cycle back to the inside. Function 2: it can also be useful to reduce the convergence time (the time necessary for the state point to return to the limit cycle). In experimental studies during walking of animals and humans, the reset of walking rhythm induced by perturbations was investigated using the phase transition curve (PTC) or the phase resetting curve (PRC) representing phase-dependent responses of the walking. We showed, for the simple double-pendulum model, the existence of the optimal phase control and the corresponding PTC that could optimally realize the aforementioned functions in response to impulsive force perturbations. Moreover, possible forms of PRC that can avoid falling against the force perturbations were predicted by the biped model, and they were compared with the experimentally observed PRC during human walking. Finally, physiological implications of the results were discussed.     

How to measure responses of the knee to lateral perturbations during gait? A proof-of-principle for quantification of knee instability

Knee instability is a major problem in patients with anterior cruciate ligament injury or knee osteoarthritis. A valid and clinically meaningful measure for functional knee instability is lacking. The concept of the gait sensitivity norm, the normalized perturbation response of a walking system to external perturbations, could be a sensible way to quantify knee instability. The aim of this study is to explore the feasibility of this concept for measurement of knee responses, using controlled external perturbations during walking in healthy subjects.Nine young healthy participants walked on a treadmill, while three dimensional kinematics were measured. Sudden lateral translations of the treadmill were applied at five different intensities during stance. Right knee kinematic responses and spatio-temporal parameters were tracked for the perturbed stride and following four cycles, to calculate perturbation response and gait sensitivity norm values (i.e. response/perturbation) in various ways.The perturbation response values in terms of knee flexion and abduction increased with perturbation intensity and decreased with an increased number of steps after perturbation. For flexion and ab/adduction during midswing, the gait sensitivity norm values were shown to be constant over perturbation intensities, demonstrating the potential of the gait sensitivity norm as a robust measure of knee responses to perturbations.These results show the feasibility of using the gait sensitivity norm concept for certain gait indicators based on kinematics of the knee, as a measure of responses during perturbed gait. The current findings in healthy subjects could serve as reference-data to quantify pathological knee instability.     

A Simple State-Determined Model Reproduces Entrainment and Phase-Locking of Human Walking

Theoretical studies and robotic experiments have shown that asymptotically stable periodic walking may emerge from nonlinear limit-cycle oscillators in the neuro-mechanical periphery. We recently reported entrainment of human gait to periodic mechanical perturbations with two essential features: 1) entrainment occurred only when the perturbation period was close to the original (preferred) walking period, and 2) entrainment was always accompanied by phase locking so that the perturbation occurred at the end of the double-stance phase. In this study, we show that a highly-simplified state-determined walking model can reproduce several salient nonlinear limit-cycle behaviors of human walking: 1) periodic gait that is 2) asymptotically stable; 3) entrainment to periodic mechanical perturbations only when the perturbation period is close to the model''s unperturbed period; and 4) phase-locking to locate the perturbation at the end of double stance. Importantly, this model requires neither supra-spinal control nor an intrinsic self-sustaining neural oscillator such as a rhythmic central pattern generator. Our results suggest that several prominent limit-cycle features of human walking may stem from simple afferent feedback processes without significant involvement of supra-spinal control or a self-sustaining oscillatory neural network.     

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.     

Planning and Control for Passive Dynamics Based Walking of 3D Biped Robots

Efficient walking is one of the main goals of research on biped robots.Passive Dynamics Based Walking (PDBW) has been proven to be an efficient pattern in numerous previous approaches to 2D biped walking.The goal of this study is to develop a feasible method for the application of PDBW to 3D robots.First a hybrid control method is presented,where a previously proposed two-point-foot walking pattern is employed to generate a PDBW gait in the sagittal plane and,in the frontal plane,a systematic balance control algorithm is applied including online planning of the landing point of the swing leg and feedback control of the stance foot.Then a multi-space planning structure is proposed to implement the proposed method on a 13-link 3D robot.Related kinematics and planning details of the robot are presented.Furthermore,a simulation of the 13-link biped robot verifies that stable and highly efficient walking can be achieved by the proposed control method.In addition,a number of features of the biped walking,including the transient powers and torques of the joints are explored.     

Responses in knee joint muscle activation patterns to different perturbations during gait in healthy subjects

PurposeTo compare the responses in knee joint muscle activation patterns to different perturbations during gait in healthy subjects.ScopeNine healthy participants were subjected to perturbed walking on a split-belt treadmill. Four perturbation types were applied, each at five intensities. The activations of seven muscles surrounding the knee were measured using surface EMG. The responses in muscle activation were expressed by calculating mean, peak, co-contraction (CCI) and perturbation responses (PR) values. PR captures the responses relative to unperturbed gait. Statistical parametric mapping analysis was used to compare the muscle activation patterns between conditions.ResultsPerturbations evoked only small responses in muscle activation, though higher perturbation intensities yielded a higher mean activation in five muscles, as well as higher PR. Different types of perturbation led to different responses in the rectus femoris, medial gastrocnemius and lateral gastrocnemius. The participants had lower CCI just before perturbation compared to the same phase of unperturbed gait.ConclusionsHealthy participants respond to different perturbations during gait with small adaptations in their knee joint muscle activation patterns. This study provides insights in how the muscles are activated to stabilize the knee when challenged. Furthermore it could guide future studies in determining aberrant muscle activation in patients with knee disorders.     

A neurobiological model of the recovery strategies from perturbed walking

This paper proposes a human mimetic neuro-musculo-skeletal model to simulate the recovery reactions from perturbations during walking. The computational model incorporates nonlinear viscoelastic muscular mechanics, supraspinal control of the center-of-mass, spinal pattern generator including muscle synergy network, spinal reflexes, and long-loop reflexes. Especially the long-loop reflexes specify recovery strategies based on the experimental observations [Schillings, A.M., van Wezel, B.M.H., Mulder, T.H., Duysen, J., 2000. Muscular responses and movement strategies during stumbling over obstacles. J. Neurophysiol. 83, 2093–2102; Eng, J.J., Winter, D.A., Patla, A.E., 1994. Strategies for recovery from a trip in early and late swing during human walking. Exp. Brain Res. 102, 339–349]. The model demonstrates two typical recovery strategies, i.e., elevating and lowering strategies against pulling over a swing leg. Sensed perturbation triggers a simple tonic pulse from the cortex. Depending on the swing phase, the tonic pulse activates a different compound of muscles over lower limbs. The compound induces corresponding recovery strategies. The reproduction of principal recovery behaviors may support the model's proposed functional and/or anatomical correspondence.     

A neurobiological model of the recovery strategies from perturbed walking

This paper proposes a human mimetic neuro-musculo-skeletal model to simulate the recovery reactions from perturbations during walking. The computational model incorporates nonlinear viscoelastic muscular mechanics, supraspinal control of the center-of-mass, spinal pattern generator including muscle synergy network, spinal reflexes, and long-loop reflexes. Especially the long-loop reflexes specify recovery strategies based on the experimental observations [Schillings, A.M., van Wezel, B.M.H., Mulder, T.H., Duysen, J., 2000. Muscular responses and movement strategies during stumbling over obstacles. J. Neurophysiol. 83, 2093–2102; Eng, J.J., Winter, D.A., Patla, A.E., 1994. Strategies for recovery from a trip in early and late swing during human walking. Exp. Brain Res. 102, 339–349]. The model demonstrates two typical recovery strategies, i.e., elevating and lowering strategies against pulling over a swing leg. Sensed perturbation triggers a simple tonic pulse from the cortex. Depending on the swing phase, the tonic pulse activates a different compound of muscles over lower limbs. The compound induces corresponding recovery strategies. The reproduction of principal recovery behaviors may support the model's proposed functional and/or anatomical correspondence.     

Anthropomorphic Design of the Human-Like Walking Robot

In this paper, we present a new concept of the mechanical design of a humanoid robot. The goal is to build a humanoid robot utilizing a new structure which is more suitable for human-like walking with the characteristics of the knee stretch, heel-contact, and toe-off. Inspired by human skeleton, we made an anthropomorphic pelvis for the humanoid robot. In comparison with conventional humanoid robots, with such the anthropomorphic pelvis, our robot is capable of adjusting the center of gravity of the upper body by the motion of pelvic tilt, thus reducing the required torque at the ankle joint and the velocity variations in human-like walking. With more precise analysis of the foot mechanism, the fixed-length inverted pendulum can be used to describe the dynamics of biped walking, thus preventing redundant works and power consumption in length variable inverted pendulum system. As the result of the new structure we propose, a humanoid robot is able to walk with human-like gait.     

A Bio-Inspired Biped Water Running Robot Incorporating the Watt-I Planar Linkage Mechanism

In this paper, a biped water running robot is developed by mimicking the water-running pattern of basilisk lizards. The dynamic mechanism of the robot was studied based on Watt-I planar linkages, and the movement trajectory of the double bar Assur Group was deduced to simulate the water-running foot trajectories of the basilisk lizard. A Central Pattern Generator （CPG）-based fuzzy control method was proposed to control the robot for realizing balance control and gait adjustment. The effectiveness of the proposed control method was verified on the prototype of a water running robot （weight： 320 g）. When the biped robot is running on water, the average force generated by the propulsion mechanism is 1.3 N, and the robot body tilt angle is 5~. The experiment results show that the propulsion mechanism is effective in realizing the basilisk lizards-like water running patterns, and the CPG-based fuzzy control method is effective in keeping the balance of the robot.     

Walking variability during continuous pseudo-random oscillations of the support surface and visual field

Walking on uneven surfaces or while undergoing perturbations has been associated with increased gait variability in both modeling and human studies. Previous gait research involving continuous perturbations has focused on sinusoidal oscillations, which can result in individuals predicting the perturbation and/or entraining to it. Therefore, we examined the effects of continuous, pseudo-random support surface and visual field oscillations on 12 healthy, young participants. Participants walked in a virtual reality environment under no perturbation (NOP), anterior–posterior (AP) walking surface and visual oscillation and mediolateral (ML) walking surface and visual oscillation conditions. Participants exhibited shorter (p≤0.005), wider (p<0.001) and faster (p<0.001) steps relative to NOP during ML perturbations and shorter (p≤0.005) and wider (p<0.001) steps during AP perturbations. Step length variability and step width variability both increased relative to NOP during all perturbation conditions (p<0.001) but exhibited greater increases for the ML perturbations (p<0.001). Participants exhibited greater trunk position variability and trunk velocity variability in the ML direction than in the AP direction during ML perturbations relative to NOP (p<0.001). Significantly greater variability in the ML direction indicates that to maintain stability, participants needed to exert greater control in the ML direction. This observation is consistent with prior modeling predictions. The large and consistent responses observed during ML visual and walking surface perturbations suggest potential for application during gait training and patient assessment.     

Evaluating functional roles of phase resetting in generation of adaptive human bipedal walking with a physiologically based model of the spinal pattern generator

The central pattern generators (CPGs) in the spinal cord strongly contribute to locomotor behavior. To achieve adaptive locomotion, locomotor rhythm generated by the CPGs is suggested to be functionally modulated by phase resetting based on sensory afferent or perturbations. Although phase resetting has been investigated during fictive locomotion in cats, its functional roles in actual locomotion have not been clarified. Recently, simulation studies have been conducted to examine the roles of phase resetting during human bipedal walking, assuming that locomotion is generated based on prescribed kinematics and feedback control. However, such kinematically based modeling cannot be used to fully elucidate the mechanisms of adaptation. In this article we proposed a more physiologically based mathematical model of the neural system for locomotion and investigated the functional roles of phase resetting. We constructed a locomotor CPG model based on a two-layered hierarchical network model of the rhythm generator (RG) and pattern formation (PF) networks. The RG model produces rhythm information using phase oscillators and regulates it by phase resetting based on foot-contact information. The PF model creates feedforward command signals based on rhythm information, which consists of the combination of five rectangular pulses based on previous analyses of muscle synergy. Simulation results showed that our model establishes adaptive walking against perturbing forces and variations in the environment, with phase resetting playing important roles in increasing the robustness of responses, suggesting that this mechanism of regulation may contribute to the generation of adaptive human bipedal locomotion.     

Retention of improvement in gait stability over 14 weeks due to trip-perturbation training is dependent on perturbation dose

Perturbation training is an emerging approach to reduce fall risk in the elderly. This study examined potential differences in retention of improvements in reactive gait stability over 14 weeks resulting from unexpected trip-like gait perturbations. Twenty-four healthy middle-aged adults (41–62 years) were assigned randomly to either a single perturbation group (SINGLE, n = 9) or a group subjected to eight trip-like gait perturbations (MULTIPLE, n = 15). While participants walked on a treadmill a custom-built brake-and-release system was used to unexpectedly apply resistance during swing phase to the lower right limb via an ankle strap. The anteroposterior margin of stability (MoS) was calculated as the difference between the anterior boundary of the base of support and the extrapolated centre of mass at foot touchdown for the perturbed step and the first recovery step during the first and second (MULTIPLE group only) perturbation trials for the initial walking session and retention-test walking 14 weeks later. Group MULTIPLE retained the improvements in reactive gait stability to the perturbations (increased MoS at touchdown for perturbed and first recovery steps; p < 0.01). However, in group SINGLE no differences in MoS were detected after 14 weeks compared to the initial walking session. These findings provide evidence for the requirement of a threshold trip-perturbation dose if adaptive changes in the human neuromotor system over several months, aimed at the improvement in fall-resisting skills, are to occur.     

Amplitude effects of medio-lateral mechanical and visual perturbations on gait

Falls during walking are a major contributor to accidental deaths and injuries that can result in debilitating hospitalization costs, lost productivity, and diminished quality of life. To reduce these losses, we must develop a more profound understanding of the characteristic responses to perturbations similar to those encountered in daily life. This study addresses this issue by building on our earlier studies that examined mechanical and visual perturbations in the same environment by applying the same continuous pseudo-random perturbations at multiple (3 mechanical, 5 visual) amplitudes. Walking variability during mechanical perturbations increased significantly with amplitude for all subjects and differences as measured by variabilities of step width, COM position, and COM velocity. These parameters were the only ones sensitive to the presence of visual perturbations, but none of them changed significantly with perturbation amplitude. Additionally, visual perturbation effects were far less consistent across participants, with several who were essentially unaffected by visual perturbations at any level. The homogeneity of the mechanical perturbation effects demonstrates that human responses to mechanical perturbations are similar because they are driven by kinetics that require similar corrections that must be made in order to maintain balance. Conversely, responses to visual perturbations are driven by the perceived need to make corrections and this perception is not accurate enough to produce amplitude-related corrections, even for a single participant, nor is this perception consistent across individuals. This latter finding is likely to be relevant to future visual perturbation studies and the diagnosis and rehabilitation of gait and balance disorders.     

Walking is not like reaching: evidence from periodic mechanical perturbations

The control architecture underlying human reaching has been established, at least in broad outline. However, despite extensive research, the control architecture underlying human locomotion remains unclear. Some studies show evidence of high-level control focused on lower-limb trajectories; others suggest that nonlinear oscillators such as lower-level rhythmic central pattern generators (CPGs) play a significant role. To resolve this ambiguity, we reasoned that if a nonlinear oscillator contributes to locomotor control, human walking should exhibit dynamic entrainment to periodic mechanical perturbation; entrainment is a distinctive behavior of nonlinear oscillators. Here we present the first behavioral evidence that nonlinear neuro-mechanical oscillators contribute to the production of human walking, albeit weakly. As unimpaired human subjects walked at constant speed, we applied periodic torque pulses to the ankle at periods different from their preferred cadence. The gait period of 18 out of 19 subjects entrained to this mechanical perturbation, converging to match that of the perturbation. Significantly, entrainment occurred only if the perturbation period was close to subjects' preferred walking cadence: it exhibited a narrow basin of entrainment. Further, regardless of the phase within the walking cycle at which perturbation was initiated, subjects' gait synchronized or phase-locked with the mechanical perturbation at a phase of gait where it assisted propulsion. These results were affected neither by auditory feedback nor by a distractor task. However, the convergence to phase-locking was slow. These characteristics indicate that nonlinear neuro-mechanical oscillators make at most a modest contribution to human walking. Our results suggest that human locomotor control is not organized as in reaching to meet a predominantly kinematic specification, but is hierarchically organized with a semi-autonomous peripheral oscillator operating under episodic supervisory control.     

A shoe sole-based apparatus and method for randomly perturbing the stance phase of gait: test-retest reliability in young adults

Walking on an irregular surface is associated with an elevated risk for a fall at any age. Yet, relatively little is known about how a human responds to an unexpected underfoot perturbation during gait. This is partly due to the difficulty of generating an intermittent but repeatable, unexpected, underfoot perturbation whose size and location are precisely known. So we developed a shoe sole-embedded apparatus for randomly perturbing the stance phase of gait. Medial and lateral flaps were concealed in the soles of pairs of sandals, along with their actuators. Either flap could be deployed within 400ms in the parasagittal plane under a swing foot; this altered the resulting sagittal and frontal plane orientations of the foot during the next stance phase, whereafter the flap was retracted following toe-off for the rest of that gait trial. We tested six healthy young subjects by randomly presenting a single medial or lateral perturbation in 12 of 30 gait trials. Traditional step kinematic measures were used to evaluate the test-retest reliability of the response to the stimulus at two different walking speeds in 60 randomized trials conducted 1 week apart. The method was effective in systematically inducing an alteration in gait, reproducible across visits, as evidenced by acceptable intraclass correlation coefficients for step width, time and length. We conclude that the apparatus and method has potential for measuring the ability of humans to reject one or more unexpected underfoot perturbations during gait.     

An Experimental Analysis of Overcoming Obstacle in Human Walking

In this paper, an experimental analysis of overcoming obstacle in human walking is carried out by means of a motion capture system. In the experiment, the lower body of an adult human is divided into seven segments, and three markers are pasted to each segment with the aim to obtain moving trajectory and to calculate joint variation during walking. Moreover, kinematic data in terms of displacement, velocity and acceleration are acquired as well. In addition, ground reaction forces are measured using force sensors. Based on the experimental results, features of overcoming obstacle in human walking are ana- lyzed. Experimental results show that the reason which leads to smooth walking can be identified as that the human has slight movement in the vertical direction during walking; the reason that human locomotion uses gravity effectively can be identified as that feet rotate around the toe joints during toe-off phase aiming at using gravitational potential energy to provide propulsion for swing phase. Furthermore, both normal walking gait and obstacle overcoming gait are characterized in a form that can provide necessary knowledge and useful databases for the implementation of motion planning and gait planning towards overcoming obstacle for humanoid robots.     

Noisy Interlimb Coordination Can Be a Main Cause of Freezing of Gait in Patients with Little to No Parkinsonism

Freezing of gait in patients with Parkinson’s disease is associated with several factors, including interlimb incoordination and impaired gait cycle regulation. Gait analysis in patients with Parkinson’s disease is confounded by parkinsonian symptoms such as rigidity. To understand the mechanisms underlying freezing of gait, we compared gait patterns during straight walking between 9 patients with freezing of gait but little to no parkinsonism (freezing patients) and 11 patients with Parkinson’s disease (non-freezing patients). Wireless sensors were used to detect foot contact and toe-off events, and the step phase of each foot contact was calculated by defining one stride cycle of the other leg as 360°. Phase-resetting analysis was performed, whereby the relation between the step phase of one leg and the subsequent phase change in the following step of the other leg was quantified using regression analysis. A small slope of the regression line indicates a forceful correction (phase reset) at every step of the deviation of step phase from the equilibrium phase, usually at around 180°. The slope of this relation was smaller in freezing patients than in non-freezing patients, but the slope exhibited larger step-to-step variability. This indicates that freezing patients executed a forceful but noisy correction of the deviation of step phase, whereas non-freezing patients made a gradual correction of the deviation. Moreover, freezing patients tended to show more variable step phase and stride time than non-freezing patients. Dynamics of a model of two coupled oscillators interacting through a phase resetting mechanism were examined, and indicated that the deterioration of phase reset by noise provoked variability in step phase and stride time. That is, interlimb coordination can affect regulation of the gait cycle. These results suggest that noisy interlimb coordination, which probably caused forceful corrections of step phase deviation, can be a cause of freezing of gait.     

Null space in the Hodgkin-Huxley Equations. A critical test.

Voltage perturbation methods based upon topological concepts are used to elicit responses from the Hodgkin-Huxley (HH) nonlinear differential equations. These responses present a critical check upon the validity of the HH model for electrical activity across squid axon membrane. It is shown that when a constant current is applied such that a stable equilibrium and rhythmic firing are present, the following predictions are inherent in the HH system of equations: (a) Small instantaneous voltage perturbations to the axon given at points along its firing spike result in phase resetting curves (when new phase versus old phase is plotted) with an average slope of 1. (b) A larger voltage perturbation (from certain points along the firing spike) results in the permanent cessation of periodic firing, with membrane voltage rapidly approaching the equilibrium value. (c) A still larger perturbation yields phase resetting curves with an average slope equal to 0. These predictions, coupled with Tasaki's experimental demonstration that squid axons in excellent condition do give repetitive firing under constant current, provide a critical test of the validity of the HH model.