Evaluation of the Phase-Dependent Rhythm Control of Human Walking Using Phase Response Curves.

Humans and animals control their walking rhythms to maintain motion in a variable environment. The neural mechanism for controlling rhythm has been investigated in many studies using mechanical and electrical stimulation. However, quantitative evaluation of rhythm variation in response to perturbation at various timings has rarely been investigated. Such a characteristic of rhythm is described by the phase response curve (PRC). Dynamical simulations of human skeletal models with changing walking rhythms (phase reset) described a relation between the effective phase reset on stability and PRC, and phase reset around touch-down was shown to improve stability. A PRC of human walking was estimated by pulling the swing leg, but such perturbations hardly influenced the stance leg, so the relation between the PRC and walking events was difficult to discuss. This research thus examines human response to variations in floor velocity. Such perturbation yields another problem, in that the swing leg is indirectly (and weakly) perturbed, so the precision of PRC decreases. To solve this problem, this research adopts the weighted spike-triggered average (WSTA) method. In the WSTA method, a sequential pulsed perturbation is used for stimulation. This is in contrast with the conventional impulse method, which applies an intermittent impulsive perturbation. The WSTA method can be used to analyze responses to a large number of perturbations for each sequence. In the experiment, perturbations are applied to walking subjects by rapidly accelerating and decelerating a treadmill belt, and measured data are analyzed by the WSTA and impulse methods. The PRC obtained by the WSTA method had clear and stable waveforms with a higher temporal resolution than those obtained by the impulse method. By investigation of the rhythm transition for each phase of walking using the obtained PRC, a rhythm change that extends the touch-down and mid-single support phases is found to occur.

Validating the feedback control of intersegmental coordination by fluctuation analysis of disturbed walking.

A walking motion is established by feedforward control for rhythmic locomotion and feedback control for adapting to environmental variations. To identify the control variables that underlie feedback control, uncontrolled manifold (UCM) analysis has been proposed and adopted for analyzing various movements. UCM analysis searches the controlled variables by comparing the fluctuation size of segmental groups related and unrelated to the movement of candidate variables, based on the assumption that a small fluctuation size indicates a relationship with the feedback control. The present study was based on UCM analysis and evaluated fluctuation size to determine the control mechanism for walking. While walking, the subjects were subjected to floor disturbances at two different frequencies, and the fluctuation sizes of the segmental groups related to characteristic variables were calculated and compared. The characteristic variables evaluated were the motion of the center of mass, limb axis, and head, and the intersegmental coordination of segmental groups with simultaneous coupled movements. Results showed that the fluctuations in intersegmental coordination were almost equally small for any segment, while fluctuations in the other variables were large in certain segments. Moreover, a comparison of the fluctuation sizes among the evaluated variables showed that the fluctuation size for intersegmental coordination was the smallest. These results indicate a possible relationship between intersegmental coordination and the control of walking.

Interlimb coordination is not strictly controlled during walking.

In human walking, the left and right legs move alternately, half a stride out of phase with each other. Although various parameters, such as stride frequency and length, vary with walking speed, the antiphase relationship remains unchanged. In contrast, during walking in left-right asymmetric situations, the relative phase shifts from the antiphase condition to compensate for the asymmetry. Interlimb coordination is important for adaptive walking and we expect that interlimb coordination is strictly controlled during walking. However, the control mechanism remains unclear. In the present study, we derived a quantity that models the control of interlimb coordination during walking using two coupled oscillators based on the phase reduction theory and Bayesian inference method. The results were not what we expected. Specifically, we found that the relative phase is not actively controlled until the deviation from the antiphase condition exceeds a certain threshold. In other words, the control of interlimb coordination has a dead zone like that in the case of the steering wheel of an automobile. It is conjectured that such forgoing of control enhances energy efficiency and maneuverability. Our discovery of the dead zone in the control of interlimb coordination provides useful insight for understanding gait control in humans.

Roles of the cerebellar vermis in predictive postural controls against external disturbances.

The central nervous system predictively controls posture against external disturbances; however, the detailed mechanisms remain unclear. We tested the hypothesis that the cerebellar vermis plays a substantial role in acquiring predictive postural control by using a standing task with floor disturbances in rats. The intact, lesioned, and sham groups of rats sequentially underwent 70 conditioned floor-tilting trials, and kinematics were recorded. Six days before these recordings, only the lesion group underwent focal suction surgery targeting vermal lobules IV-VIII. In the naïve stage of the sequential trials, the upright postures and fluctuations due to the disturbance were mostly consistent among the groups. Although the pattern of decrease in postural fluctuation due to learning corresponded among the groups, the learning rate estimated from the lumbar displacement was significantly lower in the lesion group than in the intact and sham groups. These results suggest that the cerebellar vermis contributes to predictive postural controls.

Contributions of phase resetting and interlimb coordination to the adaptive control of hindlimb obstacle avoidance during locomotion in rats: a simulation study.

Obstacle avoidance during locomotion is essential for safe, smooth locomotion. Physiological studies regarding muscle synergy have shown that the combination of a small number of basic patterns produces the large part of muscle activities during locomotion and the addition of another pattern explains muscle activities for obstacle avoidance. Furthermore, central pattern generators in the spinal cord are thought to manage the timing to produce such basic patterns. In the present study, we investigated sensory-motor coordination for obstacle avoidance by the hindlimbs of the rat using a neuromusculoskeletal model. We constructed the musculoskeletal part of the model based on empirical anatomical data of the rat and the nervous system model based on the aforementioned physiological findings of central pattern generators and muscle synergy. To verify the dynamic simulation by the constructed model, we compared the simulation results with kinematic and electromyographic data measured during actual locomotion in rats. In addition, we incorporated sensory regulation models based on physiological evidence of phase resetting and interlimb coordination and examined their functional roles in stepping over an obstacle during locomotion. Our results show that the phase regulation based on interlimb coordination contributes to stepping over a higher obstacle and that based on phase resetting contributes to quick recovery after stepping over the obstacle. These results suggest the importance of sensory regulation in generating successful obstacle avoidance during locomotion.

Computational prediction of muscle synergy using a finite element framework for a musculoskeletal model on lower limb.

Previous studies have demonstrated that the central nervous system activates muscles in module patterns to reduce the complexity needed to control each muscle while producing a movement, which is referred to as muscle synergy. In previous musculoskeletal modeling-based muscle synergy analysis studies, as a result of simplification of the joints, a conventional rigid-body link musculoskeletal model failed to represent the physiological interactions of muscle activation and joint kinematics. However, the interaction between the muscle level and joint level that exists in vivo is an important relationship that influences the biomechanics and neurophysiology of the musculoskeletal system. In the present, a lower limb musculoskeletal model coupling a detailed representation of a joint including complex contact behavior and material representations was used for muscle synergy analysis using a decomposition method of non-negative matrix factorization (NMF). The complexity of the representation of a joint in a musculoskeletal system allows for the investigation of the physiological interactions in vivo on the musculoskeletal system, thereby facilitating the decomposition of the muscle synergy. Results indicated that, the activities of the 20 muscles on the lower limb during the stance phase of gait could be controlled by three muscle synergies, and total variance accounted for by synergies was 86.42%. The characterization of muscle synergy and musculoskeletal biomechanics is consistent with the results, thus explaining the formational mechanism of lower limb motions during gait through the reduction of the dimensions of control issues by muscle synergy and the central nervous system.

Muscle synergy analysis yields an efficient and physiologically relevant method of assessing stroke.

The Fugl-Meyer Assessment is widely used to test motor function in stroke survivors. In the Fugl-Meyer Assessment, stroke survivors perform several movement tasks and clinicians subjectively rate the performance of each task item. The individual task items in the Fugl-Meyer Assessment are selected on the basis of clinical experience, and their physiological relevance has not yet been evaluated. In the present study, we aimed to objectively rate the performance of task items by measuring the muscle activity of 41 muscles from the upper body while stroke survivors and healthy participants performed 37 Fugl-Meyer Assessment upper extremity task items. We used muscle synergy analysis to compare muscle activity between subjects and found that 13 muscle synergies in the healthy participants (which we defined as standard synergies) were able to reconstruct all of the muscle activity in the Fugl-Meyer Assessment. Among the standard synergies, synergies involving the upper arms, forearms and fingers were activated to varying degrees during different task items. In contrast, synergies involving posterior trunk muscles were activated during all tasks, which suggests the importance of posterior trunk muscle synergies throughout all sequences. Furthermore, we noted the inactivation of posterior trunk muscle synergies in stroke survivors with severe but not mild impairments, suggesting that lower trunk stability and the underlying activity of posterior trunk muscle synergies may have a strong influence on stroke severity and recovery. By comparing the synergies of stroke survivors with standard synergies, we also revealed that some synergies in stroke survivors corresponded to merged standard synergies; the merging rate increased with the impairment of stroke survivors. Moreover, the degrees of severity-dependent changes in the merging rate (the merging rate-severity relationship) were different among different task items. This relationship was significant for 26 task items only and not for the other 11 task items. Because muscle synergy analysis evaluates coordinated muscle activities, this different dependency suggests that these 26 task items are appropriate for evaluating muscle coordination and the extent of its impairment in stroke survivors. Overall, we conclude that the Fugl-Meyer Assessment reflects physiological function and muscle coordination impairment and suggest that it could be performed using a subset of the 37 task items.

A model for group-size-dependent behaviour decisions in insects using an oscillator network.

Aggressive behaviour within pairs of male crickets leads to the establishment of a dominance hierarchy. Defeated males avoid their victorious adversaries for several hours before regaining aggressiveness. However, the defeated male does not regain aggressiveness if repeated fighting occurs. Loss of individual aggressiveness is limited by group size, which constrains the number of crickets fighting at any given time. Thus, group aggressive behaviour is modulated by an environmental factor, group size, which is ultimately determined by individual actions, i.e. fighting between two individuals. We developed a robot model to elucidate the mechanism of group-size-dependent behaviour alternation in crickets. The behaviour of individual robots was evaluated experimentally with mobile robots and the group behaviour of the robots was evaluated by computer simulation. We demonstrated that the group-size-dependent strategy in crickets could be generated by local interactions between robots, where the behaviour was governed by an oscillator and memory of the outcome of previous fights.

Quantitative evaluation of posture control in rats with inferior olive lesions.

Impairment of inferior olivary neurons (IONs) affects whole-body movements and results in abnormal gait and posture. Because IONs are activated by unpredicted motion rather than regular body movements, the postural dysfunction caused by ION lesions is expected to involve factors other than simple loss of feedback control. In this study, we measured the postural movements of rats with pharmacological ION lesions (IO rats) trained to stand on their hindlimbs. The coordination of body segments as well as the distribution and frequency characteristics of center of mass (COM) motion were analyzed. We determined that the lesion altered the peak properties of the power spectrum density of the COM, whereas changes in coordination and COM distribution were minor. To investigate how the observed properties reflected changes in the control system, we constructed a mathematical model of the standing rats and quantitatively identified the control system. We found an increase in linear proportional control and a decrease in differential and nonlinear control in IO rats compared with intact rats. The dystonia-like changes in body stiffness explain the nature of the linear proportional and differential control, and a disorder in the internal model is one possible cause of the decrease in nonlinear control.

A Model of Predictive Postural Control Against Floor Tilting in Rats.

Humans and animals learn the internal model of bodies and environments from their experience and stabilize posture against disturbances based on the predicted future states according to the internal model. We evaluated the mechanism of predictive control during standing, by using rats to construct a novel experimental system and comparing their behaviors with a mathematical model. In the experiments, rats (n = 6) that were standing upright using their hindlimbs were given a sensory input of light, after a certain period, the floor under them tilted backward. Initially, this disturbance induced a large postural response, including backward rotation of the center-of-mass angle and hindlimb segments. However, the rats gradually adjusted to the disturbance after experiencing 70 sequential trials, and a reduction in the amplitude of postural response was noted. We simulated the postural control of the rats under disturbance using an inverted pendulum model and model predictive control (MPC). MPC is a control method for predicting the future state using an internal model of the control target. It provides control inputs that optimize the predicted future states. Identification of the predictive and physiological parameters so that the simulation corresponds to the experiment, resulted in a value of predictive horizon (0.96 s) close to the interval time in the experiment (0.9-1.15 s). These results suggest that the rats predict posture dynamics under disturbance based on the timing of the sensory input and that the central nervous system provides plasticity mechanisms to acquire the internal model for MPC.

Variant and invariant patterns embedded in human locomotion through whole body kinematic coordination.

Step length, cadence and joint flexion all increase in response to increases in gradient and walking speed. However, the tuning strategy leading to these changes has not been elucidated. One characteristic of joint variation that occurs during walking is the close relationship among the joints. This property reduces the number of degrees of freedom and seems to be a key issue in discussing the tuning strategy. This correlation has been analyzed for the lower limbs, but the relation between the trunk and lower body is generally ignored. Two questions about posture during walking are discussed in this paper: (1) whether there is a low-dimensional restriction that determines walking posture, which depends not just on the lower limbs but on the whole body, including the trunk and (2) whether some simple rules appear in different walking conditions. To investigate the correlation, singular value decomposition was applied to a measured walking pattern. This showed that the whole movement can be described by a closed loop on a two-dimensional plane in joint space. Furthermore, by investigating the effect of the walking condition on the decomposed patterns, the position and the tilt of the constraint plane was found to change significantly, while the loop pattern on the constraint plane was shown to be robust. This result indicates that humans select only certain kinematic characteristics for adapting to various walking conditions.

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.

Contribution of Phase Resetting to Adaptive Rhythm Control in Human Walking Based on the Phase Response Curves of a Neuromusculoskeletal Model.

Humans walk adaptively in varying environments by manipulating their complicated and redundant musculoskeletal system. Although the central pattern generators in the spinal cord are largely responsible for adaptive walking through sensory-motor coordination, it remains unclear what neural mechanisms determine walking adaptability. It has been reported that locomotor rhythm and phase are regulated by the production of phase shift and rhythm resetting (phase resetting) for periodic motor commands in response to sensory feedback and perturbation. While the phase resetting has been suggested to make a large contribution to adaptive walking, it has only been investigated based on fictive locomotion in decerebrate cats, and thus it remains unclear if human motor control has such a rhythm regulation mechanism during walking. In our previous work, we incorporated a phase resetting mechanism into a motor control model and demonstrated that it improves the stability and robustness of walking through forward dynamic simulations of a human musculoskeletal model. However, this did not necessarily verify that phase resetting plays a role in human motor control. In our other previous work, we used kinematic measurements of human walking to identify the phase response curve (PRC), which explains phase-dependent responses of a limit cycle oscillator to a perturbation. This revealed how human walking rhythm is regulated by perturbations. In this study, we integrated these two approaches using a physical model and identification of the PRC to examine the hypothesis that phase resetting plays a role in the control of walking rhythm in humans. More specifically, we calculated the PRC using our neuromusculoskeletal model in the same way as our previous human experiment. In particular, we compared the PRCs calculated from two different models with and without phase resetting while referring to the PRC for humans. As a result, although the PRC for the model without phase resetting did not show any characteristic shape, the PRC for the model with phase resetting showed a characteristic phase-dependent shape with trends similar to those of the PRC for humans. These results support our hypothesis and will improve our understanding of adaptive rhythm control in human walking.

Variant and Invariant Spatiotemporal Structures in Kinematic Coordination to Regulate Speed During Walking and Running.

Humans walk, run, and change their speed in accordance with circumstances. These gaits are rhythmic motions generated by multi-articulated movements, which have specific spatiotemporal patterns. The kinematic characteristics depend on the gait and speed. In this study, we focused on the kinematic coordination of locomotor behavior to clarify the underlying mechanism for the effect of speed on the spatiotemporal kinematic patterns for each gait. In particular, we used seven elevation angles for the whole-body motion and separated the measured data into different phases depending on the foot-contact condition, that is, single-stance phase, double-stance phase, and flight phase, which have different physical constraints during locomotion. We extracted the spatiotemporal kinematic coordination patterns with singular value decomposition and investigated the effect of speed on the coordination patterns. Our results showed that most of the whole-body motion could be explained by only two sets of temporal and spatial coordination patterns in each phase. Furthermore, the temporal coordination patterns were invariant for different speeds, while the spatial coordination patterns varied. These findings will improve our understanding of human adaptation mechanisms to tune locomotor behavior for changing speed.

Gait Generation and Its Energy Efficiency Based on Rat Neuromusculoskeletal Model.

Changing gait is crucial for adaptive and smooth animal locomotion. Although it remains unclear what makes animals decide on a specific gait, energy efficiency is an important factor. It has been reported that the relationship of oxygen consumption with speed is U-shaped for each horse gait and that different gaits have different speeds at which oxygen consumption is minimized. This allows the horse to produce energy-efficient locomotion in a wide speed range by changing gait. However, the underlying mechanisms causing oxygen consumption to be U-shaped and the speeds for the minimum consumption to be different between different gaits are unclear. In the present study, we used a neuromusculoskeletal model of the rat to examine the mechanism from a dynamic viewpoint. Specifically, we constructed the musculoskeletal part of the model based on empirical anatomical data on rats and the motor control model based on the physiological concepts of the spinal central pattern generator and muscle synergy. We also incorporated the posture and speed regulation models at the levels of the brainstem and cerebellum. Our model achieved walking through forward dynamic simulation, and the simulated joint kinematics and muscle activities were compared with animal data. Our model also achieved trotting by changing only the phase difference of the muscle-synergy-based motor commands between the forelimb and hindlimb. Furthermore, the speed of each gait varied by changing only the extension phase duration and amplitude of the muscle synergy-based motor commands and the reference values for the regulation models. The relationship between cost of transport (CoT) and speed was U-shaped for both the generated walking and trotting, and the speeds for the minimum CoT were different for the two gaits, as observed in the oxygen consumption of horses. We found that the resonance property and the posture and speed regulations contributed to the CoT shape and difference in speeds for the minimum CoT. We further discussed the energy efficiency of gait based on the simulation results.

Neuromusculoskeletal model that walks and runs across a speed range with a few motor control parameter changes based on the muscle synergy hypothesis.

Humans walk and run, as well as change their gait speed, through the control of their complicated and redundant musculoskeletal system. These gaits exhibit different locomotor behaviors, such as a double-stance phase in walking and flight phase in running. The complex and redundant nature of the musculoskeletal system and the wide variation in locomotion characteristics lead us to imagine that the motor control strategies for these gaits, which remain unclear, are extremely complex and differ from one another. It has been previously proposed that muscle activations may be generated by linearly combining a small set of basic pulses produced by central pattern generators (muscle synergy hypothesis). This control scheme is simple and thought to be shared between walking and running at different speeds. Demonstrating that this control scheme can generate walking and running and change the speed is critical, as bipedal locomotion is dynamically challenging. Here, we provide such a demonstration by using a motor control model with 69 parameters developed based on the muscle synergy hypothesis. Specifically, we show that it produces both walking and running of a human musculoskeletal model by changing only seven key motor control parameters. Furthermore, we show that the model can walk and run at different speeds by changing only the same seven parameters based on the desired speed. These findings will improve our understanding of human motor control in locomotion and provide guiding principles for the control design of wearable exoskeletons and prostheses.

Network structure for control of coupled multiple nonlinear oscillators.

In recent research, the morphological effect is widely discussed from walking to the Internet, and its mechanism for generating the functionality has been discovered. In this paper, a module that employs the structural effect for controlling behavior is constructed using coupled nonuniform van der Pol oscillators. We first examine the synchrony of two types of oscillators focusing on number; then, an oscillator module that changes its synchrony from structural disposition is constructed. Oscillators are mutually arranged on a ring-shaped network, and an additional connection is used for transformation. The stability of this system is also discussed, and finally, the procedure for designing this structure-sensitive module using more than three types of oscillators is described.

Switching mechanism of sensor-motor coordination through an oscillator network model.

Insects have small brains, but their behavior is highly adaptive; this leads us to conclude that their brains possess a simple adaptation mechanism. This paper focuses on the pheromone processing of crickets, varying their aggression depending on their global neural connection, and proposes a behavior selection mechanism that can be controlled by network transformation. The controller is composed of an oscillator network, and its behavior is decided by the synchrony of organic oscillations. Furthermore, every network component corresponds to a certain brain module. A model is realized by using an analog circuit, and it is applied to a simple robot that displays the behavior of a real insect.

Adaptive hindlimb split-belt treadmill walking in rats by controlling basic muscle activation patterns via phase resetting.

To investigate the adaptive locomotion mechanism in animals, a split-belt treadmill has been used, which has two parallel belts to produce left-right symmetric and asymmetric environments for walking. Spinal cats walking on the treadmill have suggested the contribution of the spinal cord and associated peripheral nervous system to the adaptive locomotion. Physiological studies have shown that phase resetting of locomotor commands involving a phase shift occurs depending on the types of sensory nerves and stimulation timing, and that muscle activation patterns during walking are represented by a linear combination of a few numbers of basic temporal patterns despite the complexity of the activation patterns. Our working hypothesis was that resetting the onset timings of basic temporal patterns based on the sensory information from the leg, especially extension of hip flexors, contributes to adaptive locomotion on the split-belt treadmill. Our hypothesis was examined by conducting forward dynamic simulations using a neuromusculoskeletal model of a rat walking on a split-belt treadmill with its hindlimbs and by comparing the simulated motions with the measured motions of rats.

Postural control during quiet bipedal standing in rats.

The control of bipedal posture in humans is subject to non-ideal conditions such as delayed sensation and heartbeat noise. However, the controller achieves a high level of functionality by utilizing body dynamics dexterously. In order to elucidate the neural mechanism responsible for postural control, the present study made use of an experimental setup involving rats because they have more accessible neural structures. The experimental design requires rats to stand bipedally in order to obtain a water reward placed in a water supplier above them. Their motions can be measured in detail using a motion capture system and a force plate. Rats have the ability to stand bipedally for long durations (over 200 s), allowing for the construction of an experimental environment in which the steady standing motion of rats could be measured. The characteristics of the measured motion were evaluated based on aspects of the rats' intersegmental coordination and power spectrum density (PSD). These characteristics were compared with those of the human bipedal posture. The intersegmental coordination of the standing rats included two components that were similar to that of standing humans: center of mass and trunk motion. The rats' PSD showed a peak at approximately 1.8 Hz and the pattern of the PSD under the peak frequency was similar to that of the human PSD. However, the frequencies were five times higher in rats than in humans. Based on the analysis of the rats' bipedal standing motion, there were some common characteristics between rat and human standing motions. Thus, using standing rats is expected to be a powerful tool to reveal the neural basis of postural control.