Predicting human walking gaits with a simple planar model

Models of human walking with moderate complexity have the potential to accurately capture both joint kinematics and whole body energetics, thereby offering more simultaneous information than very simple models and less computational cost than very complex models. This work examines four- and six-link planar biped models with knees and rigid circular feet. The two differ in that the six-link model includes ankle joints. Stable periodic walking gaits are generated for both models using a hybrid zero dynamics-based control approach. To establish a baseline of how well the models can approximate normal human walking, gaits were optimized to match experimental human walking data, ranging in speed from very slow to very fast. The six-link model well matched the experimental step length, speed, and mean absolute power, while the four-link model did not, indicating that ankle work is a critical element in human walking models of this type. Beyond simply matching human data, the six-link model can be used in an optimization framework to predict normal human walking using a torque-squared objective function. The model well predicted experimental step length, joint motions, and mean absolute power over the full range of speeds.     

A single protofilament is sufficient to support unidirectional walking of Dynein and Kinesin

Cytoplasmic dynein and kinesin are two-headed microtubule motor proteins that move in opposite directions on microtubules. It is known that kinesin steps by a 'hand-over-hand' mechanism, but it is unclear by which mechanism dynein steps. Because dynein has a completely different structure from that of kinesin and its head is massive, it is suspected that dynein uses multiple protofilaments of microtubules for walking. One way to test this is to ask whether dynein can step along a single protofilament. Here, we examined dynein and kinesin motility on zinc-induced tubulin sheets (zinc-sheets) which have only one protofilament available as a track for motor proteins. Single molecules of both dynein and kinesin moved at similar velocities on zinc-sheets compared to microtubules, clearly demonstrating that dynein and kinesin can walk on a single protofilament and multiple rows of parallel protofilaments are not essential for their motility. Considering the size and the motile properties of dynein, we suggest that dynein may step by an inchworm mechanism rather than a hand-over-hand mechanism.     

A model of human walking energetics with an elastically-suspended load

Elastically-suspended loads have been shown to reduce the peak forces acting on the body while walking with a load when the suspension stiffness and damping are minimized. However, it is not well understood how elastically-suspended loads can affect the energetic cost of walking. Prior work shows that elastically suspending a load can yield either an increase or decrease in the energetic cost of human walking, depending primarily on the suspension stiffness, load, and walking speed. It would be useful to have a simple explanation that reconciles apparent differences in existing data. The objective of this paper is to help explain different energetic outcomes found with experimental load suspension backpacks and to systematically investigate the effect of load suspension parameters on the energetic cost of human walking. A simple two-degree-of-freedom model is used to approximate the energetic cost of human walking with a suspended load. The energetic predictions of the model are consistent with existing experimental data and show how the suspension parameters, load mass, and walking speed can affect the energetic cost of walking. In general, the energetic cost of walking with a load is decreased compared to that of a stiffly-attached load when the natural frequency of a load suspension is tuned significantly below the resonant walking frequency. The model also shows that a compliant load suspension is more effective in reducing the energetic cost of walking with low suspension damping, high load mass, and fast walking speed. This simple model could improve our understanding of how elastic load-carrying devices affect the energetic cost of walking with a load.     

Analysis of human abnormal walking using a multi-body model: joint models for abnormal walking and walking aids to reduce compensatory action

This paper proposes new models of diseased joints and evaluates the effectiveness of walking aids such as a cane and a brace for compensating for lost functions due to joint disorders. The ZMJ concept described in the previous work (Yamashita and Tagawa, 1988. In: Radharaman (Ed.), Robotics and Factories of the Future'87. Springer, New York, pp. 670-677) is modified into three joint models as follows: a passive element joint (PEJ) which has a spring at the diseased joint; a constrained range joint (CRJ), the motion of which stays within some constrained relative angle; a partial moment joint (PMJ) which can produce a partial amount of the moment produced about the joint in normal walking. A cane can enlarge a supporting area and adjust the posture of the upper torso to be upright. An ischial weight-bearing brace is effective for conservative management of hip disorders by reducing a load to the joint (Shiba et al., 1998. Clinical Orthopaedics and Related Research 351, 149-157). Walking aids like a cane or brace have been conveniently used by the handicapped. Abnormal walking was simulated for each joint model. Dynamic effects of a cane and a brace on abnormal walking were examined by the multi-body walking model.     

A three-dimensional whole-body model to predict human walking on level ground

Predictive simulation of human walking has great potential in clinical motion analysis and rehabilitation engineering assessment, but large computational cost and reliance on measurement data to provide initial guess have limited its wide use. We developed a computationally efficient model combining optimization and inverse dynamics to predict three-dimensional whole-body motions and forces during human walking without relying on measurement data. Using the model, we explored two different optimization objectives, mechanical energy expenditure and the time integral of normalized joint torque. Of the two criteria, the sum of the time integrals of the normalized joint torques produced a more realistic walking gait. The reason for this difference is that most of the mechanical energy expenditure is in the sagittal plane (based on measurement data) and this leads to difficulty in prediction in the other two planes. We conclude that mechanical energy may only account for part of the complex performance criteria driving human walking in three dimensions.

     

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.     

Modular control of human walking: A simulation study

Recent evidence suggests that performance of complex locomotor tasks such as walking may be accomplished using a simple underlying organization of co-active muscles, or “modules”, which have been assumed to be structured to perform task-specific biomechanical functions. However, no study has explicitly tested whether the modules would actually produce the biomechanical functions associated with them or even produce a well-coordinated movement. In this study, we generated muscle-actuated forward dynamics simulations of normal walking using muscle activation modules (identified using non-negative matrix factorization) as the muscle control inputs to identify the contributions of each module to the biomechanical sub-tasks of walking (i.e., body support, forward propulsion, and leg swing). The simulation analysis showed that a simple neural control strategy involving five muscle activation modules was sufficient to perform the basic sub-tasks of walking. Module 1 (gluteus medius, vasti, and rectus femoris) primarily contributed to body support in early stance while Module 2 (soleus and gastrocnemius) contributed to both body support and propulsion in late stance. Module 3 (rectus femoris and tibialis anterior) acted to decelerate the leg in early and late swing while generating energy to the trunk throughout swing. Module 4 (hamstrings) acted to absorb leg energy (i.e., decelerate it) in late swing while increasing the leg energy in early stance. Post-hoc analysis revealed an additional module (Module 5: iliopsoas) acted to accelerate the leg forward in pre- and early swing. These results provide evidence that the identified modules can act as basic neural control elements that generate task-specific biomechanical functions to produce well-coordinated walking.     

A manipulability analysis of human walking

From the literature of biomechanics, it is now clear that humans use elevating, lowering and delayed-lowering strategies in order to maintain stability during perturbed walking. The main purpose of this study is to provide insights into the role of manipulability in selection of these strategies. A 37 degrees of freedom (DoFs) model of the human body is developed to evaluate the manipulability indices during walking. The model is considered as a tree-like structure and its forward kinematics equations and the Jacobian are derived based on the Denavit-Hartenberg (DH) convention. A hybrid genetic algorithm (HGA) is then employed to map the experimental kinematics of a human to the model. The kinematic and dynamic manipulability indices of the swing phase of walking are evaluated concentrating on early, mid and late swing phases. The results indicate that the manipulability indices can characterize well the selection of elevating, lowering and delayed-lowering strategies at different stages of the swing phase. The results kinematically describe the reason of selecting delayed-lowering strategy at mid-swing phase that was not obvious in previous studies. Moreover, the results show that at mid-swing phase of walking the kinematic maneuverability is lower than that of the early and late swing phases.     

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]     

Synthesis of natural arm swing motion in human bipedal walking

It has historically been believed that the role of arm motion during walking is related to balancing. Arm motion during natural walking is distinguished in that each arm swing is with the motion of the opposing leg. Although this arm swing motion is generated naturally during bipedal walking, it is interesting to note that the arm swing motion is not necessary for stable walking. This paper attempts to explain the contribution of out-of-phase arm swing in human bipedal walking. Consequently, a human motion control methodology that generates this arm swing motion during walking is proposed. The relationship between arm swing and reaction moment about the vertical axis of the foot is explained in the context of the dynamics of a multi-body articulated system. From this understanding, it is reasoned that arm swing is the result of an effort to reduce the reaction moment about the vertical axis of the foot while the torso and legs are being controlled. This idea is applied to the generation of walking motion. The arm swing motion can be generated, not by designing and tracking joint trajectories of the arms, but by limiting the allowable reaction moment at the foot and minimizing whole-body motion while controlling the lower limbs and torso to follow the designed trajectory. Simulation results, first with the constraint on the foot vertical axis moment and then without, verify the relationship between arm swing and foot reaction moment. These results also demonstrate the use of the dynamic control method in generating arm swing motion.     

A numerical method for simulating the dynamics of human walking

This paper presents a general method for simulating the movement of the lower extremity during human walking. It is based upon two separate algorithms: one for single support (an open kinematic chain), and the other for the double support phase (a closed-loop linkage). Central to each of these is the recursive Newton-Euler inverse dynamics algorithm, applicable, as given, to any serial, spatial linkage.

For the unconstrained single support model, the Newton-Euler scheme is applied directly to numerically generate the equations of motion. In the case of double support, however, the kinematic constraint equations are used to first eliminate the redundant degrees of freedom, and then solve for the unknown ground reactions under the constrained limb.

The attractiveness of the method is that it offers a compact alternative to manually deriving the equations defining a mathematical model for human gait.     

A self-organizing model of walking patterns of insects

Insects generate walking patterns which depend upon external conditions. For example, when an insect is exposed to an additional load parallel to the direction in which it is walking, the walking pattern changes according to the magnitude of the load. Furthermore, even after some of its legs have been amputated, an insect will produce walking patterns with its remaining legs. These adaptations in insect walking could not previously be explained by a mathematical model, since the mathemati cal models were based upon the hypothesis that the relationship between walking velocity and walking patterns is fixed under all conditions. We have produced a mathematical model which describes self-organizing insect walking patterns in real-time by using feedback information regarding muscle load (Kimura et al. 1993). As part of this model, we introduced a new rule to coordinate leg movement, in which the information is circulated to optimize the efficiency of the energy transduction of each effector orga n. We describe this mechanism as ‘the least dissatisfaction for the greatest number of elements’. In this paper, we introduce the following aspects of this model, which reflect adaptability to changing circumstances: (1) after one leg is exposed to a transient perturbation, the walking pattern recovers swiftly; (2) when the external load parallel to the walking direction is continuously increased or decreased, the pattern transition point is shifted according to the magnitude of the load increme nt or decrement. This model generates a walking pattern which optimizes energy consumption at a given walking velocity even under these conditions; and (3) when some of the legs are amputated, the model generates walking patterns which are consistent with experimental results. We also discuss the ability of a hierarchical self-organizing model to describe a swift and flexible information processing system. Received: 8 February 1993/Accepted in revised form: 12 November 1993     

A self-organizing model of walking patterns of insects

It is well known that the motor systems of animals are controlled by a hierarchy consisting of a brain, central pattern generator, and effector organs. An animal's walking patterns change depending on its walking velocities, even when it has been decerebrated, which indicates that the walking patterns may, in fact, be generated in the subregions of the neural systems of the central pattern generator and the effector organs. In order to explain the self-organization of the walking pattern in response to changing circumstances, our model incorporates the following ideas: (1) the brain sends only a few commands to the central pattern generator (CPG) which act as constraints to self-organize the walking patterns in the CPG; (2) the neural network of the CPG is composed of oscillating elements such as the KYS oscillator, which has been shown to simulate effectively the diversity of the neural activities; and (3) we have introduced a rule to coordinate leg movement, in which the excitatory and inhibitory interactions among the neurons act to optimize the efficiency of the energy transduction of the effector organs. We describe this mechanism as the least dissatisfaction for the greatest number of elements, which is a self-organization rule in the generation of walking patterns. By this rule, each leg tends to share the load as efficiently as possible under any circumstances. Using this self-organizing model, we discuss the control mechanism of walking patterns.     

A mathematical model of the stability control of human thorax and pelvis movements during walking

A mathematical model is developed to study the human thorax and pelvis movements in the frontal plane during normal walking. The model comprises of two-link base-excited inverted pendulums with one-degree of rotational freedom for each link. Since the linear motion of the pelvis has a significant effect on the upper body stability, this effect is included in the model by having a base point moving in the frontal plane in a general way. Furthermore, because the postural stability is the primary requirement of normal human walking, the control law is developed based on Lyapunov's stability theory, which guarantees the stability of the pendulum system around the up-right position. To evaluate the model, the simulation results, including the angular displacement of each link and the torque applied on each link, are compared with those from gait measurements. It is shown that the simulation results match those from gait measurements closely. These results suggest that the proposed model can provide a useful framework for analysis of postural control mechanisms.     

A fast inverse dynamics model of walking for use in optimisation studies

Computer simulation of human gait, based on measured motion data, is a well-established technique in biomechanics. However, optimisation studies requiring many iterative gait cycle simulations have not yet found widespread application because of their high computational cost. Therefore, a computationally efficient inverse dynamics model of 3D human gait has been designed and compared with an equivalent model, created using a commercial multi-body dynamics package. The fast inverse dynamics model described in this paper led to an eight fold increase in execution speed. Sufficient detail is provided to allow readers to implement the model themselves.     

From swimming to walking: a single basic network for two different behaviors

 In this paper we consider the hypothesis that the spinal locomotor network controlling trunk movements has remained essentially unchanged during the evolutionary transition from aquatic to terrestrial locomotion. The wider repertoire of axial motor patterns expressed by amphibians would then be explained by the influence from separate limb pattern generators, added during this evolution. This study is based on EMG data recorded in vivo from epaxial musculature in the newt Pleurodeles waltl during unrestrained swimming and walking, and on a simplified model of the lamprey spinal pattern generator for swimming. Using computer simulations, we have examined the output generated by the lamprey model network for different input drives. Two distinct inputs were identified which reproduced the main features of the swimming and walking motor patterns in the newt. The swimming pattern is generated when the network receives tonic excitation with local intensity gradients near the neck and girdle regions. To produce the walking pattern, the network must receive (in addition to a tonic excitation at the girdles) a phasic drive which is out of phase in the neck and tail regions in relation to the middle part of the body. To fit the symmetry of the walking pattern, however, the intersegmental connectivity of the network had to be modified by reversing the direction of the crossed inhibitory pathways in the rostral part of the spinal cord. This study suggests that the input drive required for the generation of the distinct walking pattern could, at least partly, be attributed to mechanosensory feedback received by the network directly from the intraspinal stretch-receptor system. Indeed, the input drive required resembles the pattern of activity of stretch receptors sensing the lateral bending of the trunk, as expressed during walking in urodeles. Moreover, our results indicate that a nonuniform distribution of these stretch receptors along the trunk can explain the discontinuities exhibited in the swimming pattern of the newt. Thus, separate limb pattern generators can influence the original network controlling axial movements not only through a direct coupling at the central level but also via a mechanical coupling between trunk and limbs, which in turn influences the sensory signals sent back to the network. Taken together, our findings support the hypothesis of a phylogenetic conservatism of the spinal locomotor networks generating axial motor patterns from agnathans to amphibians. Received: 12 October 2001 / Accepted in revised form: 16 May 2002 Correspondence to: T. Bem (e-mail: tiaza.bem@ibib.waw.pl)     

A model of pattern generation of cockroach walking reconsidered

Cockroaches that have been decapitated or that have cut thoracic connectives can show rhythmic bursting in motoneurons to intrinsic leg muscles. These preparations have been studied as models for walking and to evaluate the functions of leg proprioceptors. The present study demonstrates that headless cockroaches walk extremely poorly and slowly with considerable discoordination of motoneuronal activity, these preparations show rhythmic motoneuron bursting that is similar to righting responses (attempts to turn upright) of intact animals when placed on their backs, and bursting is inhibited when a headless animal is turned or turns itself upright. Thus, rhythmic motoneuron activity of these preparations is most probably attempted righting rather than walking. It is concluded that the headless cockroach is useful for understanding the motor mechanisms underlying righting and walking but is not of value in assessing the functions of proprioceptive feedback.     

Interaction of influenza virus proteins with planar lipid bilayers: A model for virion assembly

Changes in conductance of oxidized cholesterol planar lipid bilayers were measured following the incorporation of isolated surface glycoproteins; hemagglutinin and neuraminidase (HA+NA) or matrix protein (M-protein) of influenza virus. The conductance dependence of the lipid bilayers on the HA+NA or M-protein concentrations indicates different mechanisms of interaction of these viral proteins with the lipid bilayer. Adsorption of M-protein molecules on one side of the lipid bilayer affects the character of the HA+NA interaction with the opposite side. Planar lipid bilayers can be a useful model for investigation of the assembly of influenza virions and other enveloped viruses.     

Metabolic cost of walking: equation and model

Twenty years of published experience with the Workman-Armstrong equation for predicting walking VO2 is reviewed. The equation is reexpressed in currently accepted terminology, and it is shown that the equation serves well as a basic model of normal walking. Employing this model to analyze VO2/step leads to the elaboration of a three-compartment model of the metabolic cost of walking. This three-compartment model provides a rational estimate of the fraction of walking's metabolic cost that powers the actual walking movement. Doubt is expressed that "comfortable speed of walking" is definable in energy terms. It is suggested that the requirements of maintaining balance while walking may determine both the comfortable speed of walking and the curvilinearity of the relationship between ground-speed and freely chosen step frequency of walking.