Dynamic stability of passive dynamic walking on an irregular surface

Falls that occur during walking are a significant health problem. One of the greatest impediments to solve this problem is that there is no single obviously "correct" way to quantify walking stability. While many people use variability as a proxy for stability, measures of variability do not quantify how the locomotor system responds to perturbations. The purpose of this study was to determine how changes in walking surface variability affect changes in both locomotor variability and stability. We modified an irreducibly simple model of walking to apply random perturbations that simulated walking over an irregular surface. Because the model's global basin of attraction remained fixed, increasing the amplitude of the applied perturbations directly increased the risk of falling in the model. We generated ten simulations of 300 consecutive strides of walking at each of six perturbation amplitudes ranging from zero (i.e., a smooth continuous surface) up to the maximum level the model could tolerate without falling over. Orbital stability defines how a system responds to small (i.e., "local") perturbations from one cycle to the next and was quantified by calculating the maximum Floquet multipliers for the model. Local stability defines how a system responds to similar perturbations in real time and was quantified by calculating short-term and long-term local exponential rates of divergence for the model. As perturbation amplitudes increased, no changes were seen in orbital stability (r(2)=2.43%; p=0.280) or long-term local instability (r(2)=1.0%; p=0.441). These measures essentially reflected the fact that the model never actually "fell" during any of our simulations. Conversely, the variability of the walker's kinematics increased exponentially (r(2)>or=99.6%; p<0.001) and short-term local instability increased linearly (r(2)=88.1%; p<0.001). These measures thus predicted the increased risk of falling exhibited by the model. For all simulated conditions, the walker remained orbitally stable, while exhibiting substantial local instability. This was because very small initial perturbations diverged away from the limit cycle, while larger initial perturbations converged toward the limit cycle. These results provide insight into how these different proposed measures of walking stability are related to each other and to risk of falling.     

An artificial neural network that utilizes hip joint actuations to control bifurcations and chaos in a passive dynamic bipedal walking model

Chaos is a central feature of human locomotion and has been suggested to be a window to the control mechanisms of locomotion. In this investigation, we explored how the principles of chaos can be used to control locomotion with a passive dynamic bipedal walking model that has a chaotic gait pattern. Our control scheme was based on the scientific evidence that slight perturbations to the unstable manifolds of points in a chaotic system will promote the transition to new stable behaviors embedded in the rich chaotic attractor. Here we demonstrate that hip joint actuations during the swing phase can provide such perturbations for the control of bifurcations and chaos in a locomotive pattern. Our simulations indicated that systematic alterations of the hip joint actuations resulted in rapid transitions to any stable locomotive pattern available in the chaotic locomotive attractor. Based on these insights, we further explored the benefits of having a chaotic gait with a biologically inspired artificial neural network (ANN) that employed this chaotic control scheme. Remarkably, the ANN was quite robust and capable of selecting a hip joint actuation that rapidly transitioned the passive dynamic bipedal model to a stable gait embedded in the chaotic attractor. Additionally, the ANN was capable of using hip joint actuations to accommodate unstable environments and to overcome unforeseen perturbations. Our simulations provide insight on the advantage of having a chaotic locomotive system and provide evidence as to how chaos can be used as an advantageous control scheme for the nervous system.     

Energy efficient walking with central pattern generators: from passive dynamic walking to biologically inspired control

Like human walking, passive dynamic walking—i.e. walking down a slope with no actuation except gravity—is energy efficient by exploiting the natural dynamics. In the animal world, neural oscillators termed central pattern generators (CPGs) provide the basic rhythm for muscular activity in locomotion. We present a CPG model, which automatically tunes into the resonance frequency of the passive dynamics of a bipedal walker, i.e. the CPG model exhibits resonance tuning behavior. Each leg is coupled to its own CPG, controlling the hip moment of force. Resonance tuning above the endogenous frequency of the CPG—i.e. the CPG’s eigenfrequency—is achieved by feedback of both limb angles to their corresponding CPG, while integration of the limb angles provides resonance tuning at and below the endogenous frequency of the CPG. Feedback of the angular velocity of both limbs to their corresponding CPG compensates for the time delay in the loop coupling each limb to its CPG. The resonance tuning behavior of the CPG model allows the gait velocity to be controlled by a single parameter, while retaining the energy efficiency of passive dynamic walking.     

An upper-body can improve the stability and efficiency of passive dynamic walking

The compass-gait walker proposed by McGeer can walk down a shallow slope with a self-stabilizing gait that requires no actuation or control. However, as the slope goes to zero so does the walking speed, and dynamic gait stability is only possible over a very narrow range of slopes. Gomes and Ruina have results demonstrating that by adding a torso to the compass-gait walker, it can walk passively on level-ground with a non-infinitesimal constant average speed. However, the gait involves exaggerated joint movements, and for energetic reasons horizontal passive dynamic walking cannot be stable. We show in this research that in addition to collision-free walking, adding a torso improves stability and walking speed when walking downhill. Furthermore, adding arms to the torso results in a collision-free periodic gait with natural-looking torso and limb movements. Overall, in contrast to the suggestions that active control may be needed to balance an upper-body on legs, it turns out that the upper and lower bodies can be integrated to improve the stability, efficiency and speed of a passive dynamic walker.     

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

We explored how hip joint actuation can be used to control locomotive bifurcations and chaos in a passive dynamic walking model that negotiated a slightly sloped surface (gamma<0.019 rad). With no hip actuation, our passive dynamic walking model was capable of producing a chaotic locomotive pattern when the ramp angle was 0.01839 rad相似文献   

Effect of body weight support variation on muscle activities during robot assisted gait: a dynamic simulation study

Background and Objectives: While body weight support (BWS) intonation is vital during conventional gait training of neurologically challenged subjects, it is important to evaluate its effect during robot assisted gait training. In the present research we have studied the effect of BWS intonation on muscle activities during robotic gait training using dynamic simulations. Methods: Two dimensional (2-D) musculoskeletal model of human gait was developed conjointly with another 2-D model of a robotic orthosis capable of actuating hip, knee and ankle joints simultaneously. The musculoskeletal model consists of eight major muscle groups namely; soleus (SOL), gastrocnemius (GAS), tibialis anterior (TA), hamstrings (HAM), vasti (VAS), gluteus maximus (GLU), uniarticular hip flexors (iliopsoas, IP), and Rectus Femoris (RF). BWS was provided at levels of 0, 20, 40 and 60% during the simulations. In order to obtain a feasible set of muscle activities during subsequent gait cycles, an inverse dynamics algorithm along with a quadratic minimization algorithm was implemented. Results: The dynamic parameters of the robot assisted human gait such as joint angle trajectories, ground contact force (GCF), human limb joint torques and robot induced torques at different levels of BWS were derived. The patterns of muscle activities at variable BWS were derived and analysed. For most part of the gait cycle (GC) the muscle activation patterns are quite similar for all levels of BWS as is apparent from the mean of muscle activities for the complete GC. Conclusions: Effect of BWS variation during robot assisted gait on muscle activities was studied by developing dynamic simulation. It is expected that the proposed dynamic simulation approach will provide important inferences and information about the muscle function variations consequent upon a change in BWS during robot assisted gait. This information shall be quite important while investigating the influence of BWS intonation on neuromuscular parameters of interest during robotic gait training.     

Development of a robotic walking simulator for gait rehabilitation]

Restoration of gait is a major concern of rehabilitation after stroke or spinal cord injury. Modern concepts of motor learning favour a task-specific repetitive approach, i.e. "whoever wants to learn to walk again must walk." However, the physical demands this places on the therapist, is a limiting factor in the clinical routine setting. This article describes a robotic walking simulator for gait training that enables wheelchair-bound subjects to freely carry out repetitive practicing of an individually adapted gait pattern under simulation of the manual guidance of an experienced therapist. The technical principle applied makes use of programmable footplates with permanent foot/machine contact in combination with compliance control. The solution chosen comprises a planar parallel-serial hybrid kinematic system with three degrees of freedom that moves the feet in the sagittal plane. Gait analysis while floor walking and stair climbing, clinical practicability and safety aspects were the basis for the design. A variable compliance control enables man-machine interaction, ranging from purely position controlled movement to full compliance during swing phase above a virtual ground profile. In full compliance mode the robotic walking simulator behaves like a haptic device. The concept presented offers new prospects for individualized gait rehabilitation.     

Determinants of gait stability while walking on a treadmill: A machine learning approach

Dynamic balance in human locomotion can be assessed through the local dynamic stability (LDS) method. Whereas gait LDS has been used successfully in many settings and applications, little is known about its sensitivity to individual characteristics of healthy adults. Therefore, we reanalyzed a large dataset of accelerometric data measured for 100 healthy adults from 20 to 70 years of age performing 10 min treadmill walking. We sought to assess the extent to which the variations of age, body mass and height, sex, and preferred walking speed (PWS) could influence gait LDS. The random forest (RF) and multiple adaptive regression splines (MARS) algorithms were selected for their good bias-variance tradeoff and their capabilities to handle nonlinear associations. First, through variable importance measure (VIM), we used RF to evaluate which individual characteristics had the highest influence on gait LDS. Second, we used MARS to detect potential interactions among individual characteristics that may influence LDS. The VIM and MARS results indicated that PWS and age correlated with LDS, whereas no associations were found for sex, body height, and body mass. Further, the MARS model detected an age by PWS interaction: on one hand, at high PWS, gait stability is constant across age while, on the other hand, at low PWS, gait instability increases substantially with age. We conclude that it is advisable to consider the participants’ age as well as their PWS to avoid potential biases in evaluating dynamic balance through LDS.     

A nonlinear model of passive muscle viscosity

The material properties of passive skeletal muscle are critical to proper function and are frequently a target for therapeutic and interventional strategies. Investigations into the passive viscoelasticity of muscle have primarily focused on characterizing the elastic behavior, largely neglecting the viscous component. However, viscosity is a sizeable contributor to muscle stress and extensibility during passive stretch and thus there is a need for characterization of the viscous as well as the elastic components of muscle viscoelasticity. Single mouse muscle fibers were subjected to incremental stress relaxation tests to characterize the dependence of passive muscle stress on time, strain and strain rate. A model was then developed to describe fiber viscoelasticity incorporating the observed nonlinearities. The results of this model were compared with two commonly used linear viscoelastic models in their ability to represent fiber stress relaxation and strain rate sensitivity. The viscous component of mouse muscle fiber stress was not linear as is typically assumed, but rather a more complex function of time, strain and strain rate. The model developed here, which incorporates these nonlinearities, was better able to represent the stress relaxation behavior of fibers under the conditions tested than commonly used models with linear viscosity. It presents a new tool to investigate the changes in muscle viscous stresses with age, injury and disuse.     

Paired nonlinear behavior of active and passive joint torques associated with preparation for walk-to-run gait transition

This study investigated the lower extremity torque's active and passive features during the walk-to-run gait transition with continuously increased walking speed. Fourteen volunteers participated in the experiment. Kinematic and kinetic data were collected synchronously. Five strides leading up the gait transition were examined. Peaks of the passive (e.g., contact) and active (e.g., generalized muscle torques), along with net joint torque, and time to peak torques exhibited significant differences at the last stride before gait transition, compared to the first four strides, at the ankle, knee, and hip joints, respectively. Selected peak joint active and passive torques showed significant and opposite trends at critical events within a stride cycle: such ankle joint right after heel-contact, knee joint during weight acceptance, and both hip and knee joints right before toe-off. The magnitude and the corresponding time to active and passive peak torque changed in a nonlinear pattern before the transition from walk to run. The lower extremity segment-interaction during gait transition appeared to be an active reorganization exemplified by the interaction between the lower extremity's active and passive torque components.     

Repetitive gait of passive bipedal mechanisms in a three-dimensional environment

The inherent dynamics of bipedal, kneed mechanisms are studied with emphasis on the existence and stability, of repetitive gait in a three-dimensional environment, in the absence of external, active control. The investigation is motivated by observations that sustained anthropomorphic locomotion is largely a consequence of geometric and inertial properties of the mechanism. While the modeling excludes active control, the energy dissipated in ground and knee collisions is continuously re-injected by considering gait down slight inclines. The paper describes the dependence of the resulting passive gait in vertically constrained and unconstrained mechanisms on model parameters, such as ground compliance and ground slope. We also show the possibility of achieving statically unstable gait with appropriate parameter choices.     

Characterization of a system for studying human gait during slope walking

Sloped walking surfaces provide a unique environment for examining the biomechanics and neural control of locomotion. While sloped surfaces have been used in a variety of studies in recent years, the current literature provides little if any discussion of the integrity, i.e., validity, of the systems used to collect data. The goal of this study was to develop and characterize a testing system capable of evaluating the kinetics of human locomotion on sloped surfaces. A ramped walkway system with an embedded force plate was constructed and stabilized. Center of pressure and reaction force data from the force plate were evaluated at 6 ramp grades (0, 5, 15, 25, 35, and 39 %). Ground reaction force data at 0 % grade were effectively the same as data from the same force plate when mounted in the ground and were well within the range of intrasubject variability. Collectively, data from all tests demonstrate the fidelity of this ramp system and suggest it can be used to evaluate human locomotion over a range of slope intensities.     

gamma-synuclein has a dynamic intracellular localization

gamma-Synuclein is a member of the synuclein family consisting of three proteins. Within the last several years increasing attention has focused on these proteins because of their role in human diseases. alpha-Synuclein relevance to Parkinson's disease is based on mutations found in familial cases of the disease and its presence in filaments and inclusion bodies in sporadic cases. gamma-Synuclein is implicated in some forms of cancer and ocular diseases, while beta-synuclein may antagonize their pathological functions. In this paper we present data on the localization and properties of gamma-synuclein in several neuronal and nonneuronal cell cultures. We show that contrary to the current opinion, gamma-synuclein is not an exclusively cytoplasmic protein, but has a dynamic localization and can associate with subcellular structures. It is present in the perinuclear area and may be associated to centrosomes. On late steps of mitosis gamma-synuclein is not found in the centrosomes, and redistributes to the midbody in telophase. Under stress conditions a translocation of gamma-synuclein from the perinuclear area to the nucleus occurs exhibiting nucleocytoplasmic shuttling. gamma-Synuclein overexpression reduces neurite outgrowth in a greater extent then alpha-synuclein overexpression. These data support the view that gamma-synuclein may change its intracellular localization and associate with subcellular structures in response to intracellular signaling or stress.     

Hemiplegic gait: a kinematic analysis using walking speed as a basis.

The kinematics of treadmill ambulation of stroke patients (N = 9) and healthy subjects (N = 4) was studied at a wide range of different velocities (i.e. 0.25-1.5 m s-1), with a focus on the transverse rotations of the trunk. Video recordings revealed, for both stroke patients and healthy subjects, similar relations between walking speed and stride length as well as stride frequency. The phase difference between pelvic and thoracic rotations (i.e. trunk rotation) and the total range of trunk rotation were almost linearly related to the walking speed. Healthy subjects showed a marked increase in pelvic rotation from 1 to 1.5 m s-1. Using dimensional analysis in a comparison between stroke patients and healthy subjects, invariances in the coordination of gait were found for stride length, stride frequency, pelvic rotation, and trunk rotation. Constant relations were obtained between, on the one hand, dimensionless velocity and, on the other, dimensionless stride length as well as stride frequency. Transitions were found between the velocities 0.75 and 1 m s-1 for dimensionless pelvic rotation and trunk rotation, indicating that, from this velocity range onwards, pelvic swing lengthens the stride: rotations of pelvis, thorax and trunk become tightly coordinated. On the basis of the dimensionless stride length, stride frequency, pelvic rotation and trunk rotation, deficits in the gait of stroke patients could be quantified. It is concluded that walking speed is an important control parameter, which should be used as a basic variable in the evaluation of the gait of stroke patients.     

A novel gait platform to measure isolated plantar metatarsal forces during walking

A new gait platform described in this report allows an isolated measurement of the vertical and shear forces under an individual metatarsal head during barefoot walking. The apparatus incorporated a customized tactile force sensor and a high-speed camera system, which enabled easy identification of a single anatomical landmark at the forefoot’s plantar surface that is in contact with the sensor throughout stance. After calibration, the measured peak forces under the 2nd MTH showed variability of 3.7%, 9.2%, and 8.9% in vertical, anterior–posterior, and medial–lateral directions, respectively. The device therefore provides information about the magnitude and timing of such local metatarsal forces, and has been shown to be of significant research and clinical interest. Its ability to achieve this with a high degree of accuracy ensures its potential as a valuable research tool.     

Stability-normalised walking speed: A new approach for human gait perturbation research

In gait stability research, neither self-selected walking speeds, nor the same prescribed walking speed for all participants, guarantee equivalent gait stability among participants. Furthermore, these options may differentially affect the response to different gait perturbations, which is problematic when comparing groups with different capacities. We present a method for decreasing inter-individual differences in gait stability by adjusting walking speed to equivalent margins of stability (MoS). Eighteen healthy adults walked on a split-belt treadmill for two-minute bouts at 0.4 m/s up to 1.8 m/s in 0.2 m/s intervals. The stability-normalised walking speed (MoS = 0.05 m) was calculated using the mean MoS at touchdown of the final 10 steps of each speed. Participants then walked for three minutes at this speed and were subsequently exposed to a treadmill belt acceleration perturbation. A further 12 healthy adults were exposed to the same perturbation while walking at 1.3 m/s: the average of the previous group. Large ranges in MoS were observed during the prescribed speeds (6–10 cm across speeds) and walking speed significantly (P < 0.001) affected MoS. The stability-normalised walking speeds resulted in MoS equal or very close to the desired 0.05 m and reduced between-participant variability in MoS. The second group of participants walking at 1.3 m/s had greater inter-individual variation in MoS during both unperturbed and perturbed walking compared to 12 sex, height and leg length-matched participants from the stability-normalised walking speed group. The current method decreases inter-individual differences in gait stability which may benefit gait perturbation and stability research, in particular studies on populations with different locomotor capacities. [Preprint: https://doi.org/10.1101/314757]     

Coupled oscillators utilised as gait rhythm generators of a two-legged walking machine

The gait of current two-legged walking machines differs from that of humans, although the kinematic structures of these machines' legs frequently imitate human limbs. This paper presents a method of generating the trajectories of hip and knee joint angles resulting in a gait pattern similar to that of a human. For this purpose the solutions of coupled van der Pol oscillator equations are utilised. There is much evidence that these equations can be treated as a good model of the central pattern generator generating functional (also locomotional) rhythms in living creatures. The oscillator equations are solved by numerical integration. The method of changing the type of gait by changing appropriate parameter values in the oscillator equations is presented (change of velocity and trajectory of leg-ends). The results obtained enable enhanced control of twolegged walking systems by including gait pattern generators which will assume a similar role to that of biological generators.     

A bipedal compliant walking model generates periodic gait cycles with realistic swing dynamics

A simple spring mechanics model can capture the dynamics of the center of mass (CoM) during human walking, which is coordinated by multiple joints. This simple spring model, however, only describes the CoM during the stance phase, and the mechanics involved in the bipedality of the human gait are limited. In this study, a bipedal spring walking model was proposed to demonstrate the dynamics of bipedal walking, including swing dynamics followed by the step-to-step transition. The model consists of two springs with different stiffnesses and rest lengths representing the stance leg and swing leg. One end of each spring has a foot mass, and the other end is attached to the body mass. To induce a forward swing that matches the gait phase, a torsional hip joint spring was introduced at each leg. To reflect the active knee flexion for foot clearance, the rest length of the swing leg was set shorter than that of the stance leg, generating a discrete elastic restoring force. The number of model parameters was reduced by introducing dependencies among stiffness parameters. The proposed model generates periodic gaits with dynamics-driven step-to-step transitions and realistic swing dynamics. While preserving the mimicry of the CoM and ground reaction force (GRF) data at various gait speeds, the proposed model emulated the kinematics of the swing leg. This result implies that the dynamics of human walking generated by the actuations of multiple body segments is describable by a simple spring mechanics.