Control of leg protraction in the stick insect: a targeted movement showing compensation for externally applied forces

Summary In stick insects, the swing of each rear leg is aimed at the ipsilateral middle leg. The control of this targeted movement was investigated by applying external force to aid or oppose protraction of one rear leg as stick insects walked on a treadwheel.In the first condition studied, the target middle leg was stationary during the protraction of the rear leg (Figs. 1a, 2). The opposing forces tested were 14 and 32 times greater than the peak force exerted during unobstructed protraction. Nevertheless, the rear leg continued to step to a constant position behind the middle leg (Fig. 3).In the second condition, the target middle leg also walked on the wheel. As the force opposing protraction increased, the endpoint of rear leg protraction shifted caudally, the speed of protraction decreased, and the total protraction duration increased (Fig. 5; Table 1). The middle leg's position at the end of rear leg protraction shifted caudally but its posterior extreme position remained virtually unchanged. When the onset of the external force was abrupt, compensation often occurred within 20 ms (Fig. 6a).External forces aiding protraction increased protraction speed only slightly (Table 2). When the force was suddenly removed, the leg continued moving forward but with reduced velocity (Fig. 6b).It is concluded that position information is used only to determine the swing endpoint and that velocity is controlled during the movement. The results are compared with movements to a target by vertebrates and with models of motor control in general.Abbreviations AEP anterior extreme position - PEP posterior extreme position     

Walking in Aretaon asperrimus

This article describes basic parameters characterizing walking of the stick insect Aretaon asperrimus to allow a comparative approach with other insects studied. As in many other animals, geometrical parameters such as step amplitude and leg extreme positions do not vary with walking velocity. However, the relation between swing duration and stance duration is quite constant, in contrast to most insects studied. Therefore, velocity profiles during swing vary with walking velocity whereas time course of leg trajectories and leg angle trajectories are independent of walking velocity. Nevertheless, A. asperrimus does not show a classical tripod gait, but performs a metachronal, or tetrapod, gait, showing phase values differing from 0.5 between ipsilateral neighbouring legs. As in Carausius morosus, the detailed shape of the swing trajectory may depend on the form of the substrate. Effects describing coordinating influences between legs have been found that prevent the start of a swing as long as the posterior leg performs a swing. Further, the treading on tarsus reflex can be observed in Aretaon. No hint to the existence of a targeting influence has been found. Control of rearward walking is easiest interpreted by maintaining the basic rules but an anterior-posterior reversal of the information flow.     

The control of walking movements in the leg of the rock lobster

1. Experiments with rock lobsters walking on a treadmill were undertaken to obtain information upon the system controlling the movement of the legs. Results show that the position of the leg is an important parameter affecting the cyclic movement of the walking leg. Stepping can be interrupted when the geometrical conditions for terminating either a return stroke or a power stroke are not fullfilled. 2. The mean value of anterior and posterior extreme positions (AEP and PEP respectively) of the walking legs do not depend on the walking speed (Fig. 1). 3. When one leg is isolated from the other walking legs by placing it on a platform the AEPs and PEPs of the other legs show a broader distribution compared to controls (Figs. 2 and 3). 4. Force measurements (Fig. 4) are in agreement with the hypothesis that the movement of the leg is controlled by a position servomechanism. 5. When one leg stands on a stationary force transducer this leg develops forces which oscillate with the step rhythm of the other legs (Fig. 5). 6. A posteriorly directed influence is found, by which the return stroke of a leg can be started when the anterior leg performs a backward directed movement. 7. Results are compared with those obtained from stick insects. The systems controlling the movement of the individual leg are similar in both, lobster and stick insect but the influences between the legs seem to be considerably different.     

System identification of muscle–joint interactions of the cat hind limb during locomotion

Neurophysiological experiments in walking cats have shown that a number of neural control mechanisms are involved in regulating the movements of the hind legs during locomotion. It is experimentally hard to isolate individual mechanisms without disrupting the natural walking pattern and we therefore introduce a different approach where we use a model to identify what control is necessary to maintain stability in the musculo-skeletal system. We developed a computer simulation model of the cat hind legs in which the movements of each leg are produced by eight limb muscles whose activations follow a centrally generated pattern with no proprioceptive feedback. All linear transfer functions, from each muscle activation to each joint angle, were identified using the response of the joint angle to an impulse in the muscle activation at 65 postures of the leg covering the entire step cycle. We analyzed the sensitivity and stability of each muscle action on the joint angles by studying the gain and pole plots of these transfer functions. We found that the actions of most of the hindlimb muscles display inherent stability during stepping, even without the involvement of any proprioceptive feedback mechanisms, and that those musculo-skeletal systems are acting in a critically damped manner, enabling them to react quickly without unnecessary oscillations. We also found that during the late swing, the activity of the posterior biceps/semitendinosus (PB/ST) muscles causes the joints to be unstable. In addition, vastus lateralis (VL), tibialis anterior (TA) and sartorius (SAT) muscle-joint systems were found to be unstable during the late stance phase, and we conclude that those muscles require neuronal feedback to maintain stable stepping, especially during late swing and late stance phases. Moreover, we could see a clear distinction in the pole distribution (along the step cycle) for the systems related to the ankle joint from that of the other two joints, hip or knee. A similar pattern, i.e., a pattern in which the poles were scattered over the s-plane with no clear clustering according to the phase of the leg position, could be seen in the systems related to soleus (SOL) and TA muscles which would indicate that these muscles depend on neural control mechanisms, which may involve supraspinal structures, over the whole step cycle.     

Mechanisms of stick insect locomotion in a gap-crossing paradigm

Locomotion of stick insects climbing over gaps of more than twice their step length has proved to be a useful paradigm to investigate how locomotor behaviour is adapted to external conditions. In this study, swing amplitudes and extreme positions of single steps from gap-crossing sequences have been analysed and compared to corresponding parameters of undisturbed walking. We show that adaptations of the basic mechanisms concern movements of single legs as well as the coordination between the legs. Slowing down of stance velocity, searching movements of legs in protraction and the generation of short steps are crucial prerequisites in the gap-crossing task. The rules of leg coordination described for stick insect walking seem to be modified, and load on the supporting legs is assumed to have a major effect on coordination especially in slow walking. Stepping into the gap with a front leg and antennal contact with the far edge of the gap provide information, as both events influence the following leg movements, whereas antennal non-contact seems not to contain information. Integration of these results into the model of the walking controller can improve our understanding of insect locomotion in highly irregular environments.Abbreviations AEP anterior extreme position - fAEP fictive anterior extreme position - PEP posterior extreme position - TOT treading-on-tarsus     

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

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

A model of leg coordination in the stick insect,Carausius morosus

A model of interleg coordination presented in a separate report is evaluated here by perturbing the step pattern in three ways. First, when the initial leg configuration is varied, the simulated leg movements assume a stable coordination from natural starting configurations in a natural way (Fig. 1a). They also rapidly re-establish the normal coordination when started from unnatural configurations (Fig. 1b-d). An explicit hierarchy of natural frequencies for the legs of the three thoracic segments is not required. Second, when the coordination is perturbed by assigning one or more legs a retraction velocity different from the rest, gliding coordination or various integer step ratios can be produced (Figs. 2–4). Third, when the swing of one leg is obstructed, characteristic changes in the stepping of other legs occur (Fig. 5). Overall differences between the step patterns of the model and those of the stick insect are related to the form of the coordinating mechanisms. Errors made by the model, such as overlapping swings by adjacent legs or discrepancies in step timing and step end-points, point out the limitations of a model restricted to kinematic parameters.     

Normal gait characteristics under temporal and distance constraints

Walking patterns of 53 males and 39 females, all in good health, were studied at slow, free, and fast speeds using a walkway system developed by the author. Three males and three females, also in good health, were then studied under constrained walking conditions such as rhythm constraint, speed coupled with constraint, walking up or down a slope, line stepping contraint, stepping onto a marked square, and starting/stopping of walking. In the first set of experiments, the following results were obtained. When increasing speed, the male had a tendency to increase step length and the female had a tendency to increase cadence. The relationships between the speed and the statistics of gait parameters, i.e. the coefficient of variation and the symmetry were examined. The data in this experiment were also applied to Grieve's gait equations which formulated the relationships between step frequency and speed, or between swing time and cycle time.In the second set of experiments the following results were obtained. Although rhythm constraint (induced by a metronome) resulted in no difference of gait between males and females, a difference did appear in the case of speed coupled with constraint. When walking up and down a slope, the ascent case showed a longer step length and a lower cadence compared with the descent. The idea of functional asymmetry, a supporting function of the left leg and a moving function of the right leg, is well accepted. However, in this study of the effect of line stepping constraints predominant right-left functional differences were found. The perturbation of gait when the subjects stepped onto a marked square resembling a force-plate was recorded quantitatively. With regard to the starting and stopping characteristics of walking, it was concluded that the two steps from starting and the three steps before stopping should be excluded from ordinary data due to their acceleration and deceleration properties.     

The two groups of sensilla in the ventral coxal hairplate of Carausius morosus have different roles during walking

Abstract. The ventral coxal hairplate (cxHPv) of the stick insect Carausius morosus Br. (Phasmida: Bacteriidae) contains two morphologically distinct groups of sensilla designated as group 1 and 2 (Gl, G2). The function of these sensilla during walking was tested by selectively ablating one or both groups on one middle leg in thirty-four animals. It has previously been shown that ablation of the entire hairplate leads to two kinds of errors: the operated leg swings farther forward and the adjacent caudal leg ends its swing more to the rear relative to the operated leg. Following selective ablation of cxHPv Gl on the middle leg, the first kind of error is more pronounced, indicating that this group contributes more to limiting forward protraction during the swing. Following ablation of cxHPv G2, the second kind of error is more evident, indicating that during stance this group contributes more to the target information influencing the swing end-point of the adjacent caudal leg. These results are interpreted to reflect the phasic and phasic-tonic response characteristics of Gl and G2 hairs, respectively.     

Biomimetic Design and Optimal Swing of a Hexapod Robot Leg

Biological inspiration has spawned a wealth of solutions to both mechanical design and control schemes in the efforts to develop agile legged machines. This paper presents a compliant leg mechanism for a small six-legged robot, HITCR-ll, based on abstracted anatomy from insect legs. Kinematic structure, relative proportion of leg segment lengths and actuation system were analyzed in consideration of anatomical structure as well as muscle system of insect legs and desired mobility. A spring based passive compliance mechanism inspired by musculoskeletal structures of biological systems was integrated into distal segment of the leg to soften foot impact on touchdown. In addition, an efficient locomotion planner capable of generating natural movements for the legs during swing phase was proposed. The problem of leg swing was formulated as an optimal control procedure that satisfies a series of locomotion task terms while minimizing a biologically-based objective function, which was solved by a Gauss Pseudospectral Method （GPM） based numerical technique. We applied this swing generation algorithm to both a simulation platform and a robot prototype. Results show that the proposed leg structure and swing planner are able to successfully perform effective swing movements on rugged terrains.     

Voluntary stepping behavior under single- and dual-task conditions in chronic stroke survivors: A comparison between the involved and uninvolved legs

ObjectiveIf balance is lost, quick step execution can prevent falls. Research has shown that speed of voluntary stepping was able to predict future falls in old adults. The aim of the study was to investigate voluntary stepping behavior, as well as to compare timing and leg push-off force–time relation parameters of involved and uninvolved legs in stroke survivors during single- and dual-task conditions. We also aimed to compare timing and leg push-off force–time relation parameters between stroke survivors and healthy individuals in both task conditions.MethodsTen stroke survivors performed a voluntary step execution test with their involved and uninvolved legs under two conditions: while focusing only on the stepping task and while a separate attention-demanding task was performed simultaneously. Temporal parameters related to the step time were measured including the duration of the step initiation phase, the preparatory phase, the swing phase, and the total step time. In addition, force–time parameters representing the push-off power during stepping were calculated from ground reaction data and compared with 10 healthy controls.ResultsThe involved legs of stroke survivors had a significantly slower stepping time than uninvolved legs due to increased swing phase duration during both single- and dual-task conditions. For dual compared to single task, the stepping time increased significantly due to a significant increase in the duration of step initiation. In general, the force time parameters were significantly different in both legs of stroke survivors as compared to healthy controls, with no significant effect of dual compared with single-task conditions in both groups.ConclusionsThe inability of stroke survivors to swing the involved leg quickly may be the most significant factor contributing to the large number of falls to the paretic side. The results suggest that stroke survivors were unable to rapidly produce muscle force in fast actions. This may be the mechanism of delayed execution of a fast step when balance is lost, thus increasing the likelihood of falls in stroke survivors.     

A Neuro-Mechanical Model Explaining the Physiological Role of Fast and Slow Muscle Fibres at Stop and Start of Stepping of an Insect Leg

Stop and start of stepping are two basic actions of the musculo-skeletal system of a leg. Although they are basic phenomena, they require the coordinated activities of the leg muscles. However, little is known of the details of how these activities are generated by the interactions between the local neuronal networks controlling the fast and slow muscle fibres at the individual leg joints. In the present work, we aim at uncovering some of those details using a suitable neuro-mechanical model. It is an extension of the model in the accompanying paper and now includes all three antagonistic muscle pairs of the main joints of an insect leg, together with their dedicated neuronal control, as well as common inhibitory motoneurons and the residual stiffness of the slow muscles. This model enabled us to study putative processes of intra-leg coordination during stop and start of stepping. We also made use of the effects of sensory signals encoding the position and velocity of the leg joints. Where experimental observations are available, the corresponding simulation results are in good agreement with them. Our model makes detailed predictions as to the coordination processes of the individual muscle systems both at stop and start of stepping. In particular, it reveals a possible role of the slow muscle fibres at stop in accelerating the convergence of the leg to its steady-state position. These findings lend our model physiological relevance and can therefore be used to elucidate details of the stop and start of stepping in insects, and perhaps in other animals, too.     

Rotational locomotion by the cockroach Blattella germanica

Locomotion on complex substrata can be expressed in a plane by two geometric components of body movement: linear locomotion and rotational locomotion. This study examined pure rotation by analysing the geometry of leg movements and stepping patterns during the courtship turns of male Blattella germanica. Strict rotation or translation by an insect requires that each side of the body cover equal distance with respect to the substrate. There are three mechanisms by which the legs can maintain this equality: frequency of stepping, magnitude of the leg arcs relative to the body and the degree to which legs flex and extend during locomotion. During the courtship behaviour of Blattella germanica selected males executed turns involving body rotation along with leg movements in which the legs on the outside of the turn swung through greater average arcs than those on the inside of the turn. This difference should have resulted in a translation component. However, legs on the inside of the turn compensated by flexion and extension movements which were greater than those of opposing legs. The net effect was that both sides of the body covered equal average ground. These cockroaches used a wide variety of stepping combinations to effect rotation. The frequency of these combinations was compared to an expected frequency distribution of stepping combinations and further to an expected frequency of these stepping combinations used for straight walking. These comparisons demonstrated a similarity between interleg coordination during straight walking and that during turning in place.     

Dynamic simulation of insect walking

Insect walking relies on a complex interaction between the environment, body segments, muscles and the nervous system. For the stick insect in particular, previous investigations have highlighted the role of specific sensory signals in the timing of activity of central neural networks driving the individual leg joints. The objective of the current study was to relate specific sensory and neuronal mechanisms, known from experiments on reduced preparations, to the generation of the natural sequence of events forming the step cycle in a single leg. We have done this by simulating a dynamic 3D-biomechanical model of the stick insect coupled to a reduced model of the neural control system, incorporating only the mechanisms under study. The neural system sends muscle activation levels to the biomechanical system, which in turn provides correctly timed propriosensory signals back to the neural model. The first simulations were designed to test if the currently known mechanisms would be sufficient to explain the coordinated activation of the different leg muscles in the middle leg. Two experimental situations were mimicked: restricted stepping where only the coxa-trochanteral joint and the femur-tibia joint were free to move, and the unrestricted single leg movements on a friction-free surface. The first of these experimental situations is in fact similar to the preparation used in gathering much of the detailed knowledge on sensory and neuronal mechanisms. The simulations show that the mechanisms included can indeed account for the entire step cycle in both situations. The second aim was to test to what extent the same sensory and neuronal mechanisms would be adequate also for controlling the front and hind legs, despite the large differences in both leg morphology and kinematic patterns. The simulations show that front leg stepping can be generated by basically the same mechanisms while the hind leg control requires some reorganization. The simulations suggest that the influence from the femoral chordotonal organs on the network controlling levation-depression may have a reversed effect in the hind legs as compared to the middle and front legs. This, and other predictions from the model will have to be confirmed by additional experiments.     

Body Position Influences Which Neural Structures Are Recruited by Lumbar Transcutaneous Spinal Cord Stimulation

Transcutaneous stimulation of the human lumbosacral spinal cord is used to evoke spinal reflexes and to neuromodulate altered sensorimotor function following spinal cord injury. Both applications require the reliable stimulation of afferent posterior root fibers. Yet under certain circumstances, efferent anterior root fibers can be co-activated. We hypothesized that body position influences the preferential stimulation of sensory or motor fibers. Stimulus-triggered responses to transcutaneous spinal cord stimulation were recorded using surface-electromyography from quadriceps, hamstrings, tibialis anterior, and triceps surae muscles in 10 individuals with intact nervous systems in the supine, standing and prone positions. Single and paired (30-ms inter-stimulus intervals) biphasic stimulation pulses were applied through surface electrodes placed on the skin between the T11 and T12 inter-spinous processes referenced to electrodes on the abdomen. The paired stimulation was applied to evaluate the origin of the evoked electromyographic response; trans-synaptic responses would be suppressed whereas direct efferent responses would almost retain their amplitude. We found that responses to the second stimulus were decreased to 14%±5% of the amplitude of the response to the initial pulse in the supine position across muscles, to 30%±5% in the standing, and to only 80%±5% in the prone position. Response thresholds were lowest during standing and highest in the prone position and response amplitudes were largest in the supine and smallest in the prone position. The responses obtained in the supine and standing positions likely resulted from selective stimulation of sensory fibers while concomitant motor-fiber stimulation occurred in the prone position. We assume that changes of root-fiber paths within the generated electric field when in the prone position increase the stimulation thresholds of posterior above those of anterior root fibers. Thus, we recommend conducting spinal reflex or neuromodulation studies with subjects lying supine or in an upright position, as in standing or stepping.     

The influence of vibration on spinal alpha-motoneurons excitability in static conditions and during evoked stepping in human

In healthy human the excitability of spinal alpha-motoneurons under application of vibrostimulation (20-60 Hz) to different leg muscles was investigated both in stationary condition and during stepping movements caused by vibration in the condition of suspended leg. In 15 subjects the amplitude of H-reflex were compared under vibration of rectus femoris (RF) and biceps femoris (BF) muscles of left leg as well during vibration of rectus femoris of contralateral, motionless leg in three spatial positions: upright, supine and on right side of body with suspended left leg. In dynamic conditions the amount of H-reflex was compared during evoked and voluntary stepping at 8 intervals of step cycle. In all body positions the vibration of each ipsilateral leg muscles caused significant suppression of H-reflex, this suppression was more prominent in the air-stepping conditions. The vibration of contralateral leg RF muscle had a weak influence on the amplitude of H-reflex. In 7 subjects the muscle vibration of ipsilateral and contralateral legs generated stepping movements. During evoked "air-stepping" H-reflex had different amplitudes in different phases of step cycle. At the same time the differences between responses under voluntary and non-voluntary stepping were revealed only in stance phase. Thus, different degree of H-reflex suppression by vibration under different body position in space depends on, it seems to be, from summary afferent inflows to spinal cord interneurons, which participate in regulation of posture and locomotion. Seemingly, the increasing of spinal cord neurons excitability occurs under involuntary air-stepping in swing phase, which is necessary for activation of locomotor automatism under unloading leg conditions.     

Dominance of local sensory signals over inter-segmental effects in a motor system: modeling studies

Recent experiments, reported in the accompanying paper, have supplied key data on the impact afferent excitation has on the activity of the levator?Cdepressor motor system of an extremity in the stick insect. The main finding was that, stimulation of the campaniform sensillae of the partially amputated middle leg in an animal where all other but one front leg had been removed, had a dominating effect over that of the stepping ipsilateral front leg. In fact, the latter effect was minute compared to the former. In this article, we propose a local network that involves the neuronal part of the levator?Cdepressor motor system and use it to elucidate the mechanisms that underlie the generation of neuronal activity in the experiments. In particular, we show that by appropriately modulating the activity in the neurons of the central pattern generator of the levator?Cdepressor motor system, we obtain activity patterns of the motoneurons in the model that closely resemble those found in extracellular recordings in the stick insect. In addition, our model predicts specific properties of these records which depend on the stimuli applied to the stick insect leg. We also discuss our results on the segmental mechanisms in the context of inter-segmental coordination.     

Organization of a complex movement: fixed and variable components of the cockroach escape behavior

The escape behavior of the cockroach Periplaneta americana was studied by means of high speed filming (250 frames/s) and a computer-graphical analysis of the body and leg movements. The results are as follows: 1. The behavior begins with pure rotation of the body about the posteriorly located cerci, followed by rotation plus forward translation, and finally pure translation (Figs. 1, 2). 2. A consistent inter-leg coordination is used for the entire duration of the turn (Fig. 3A). At the start of the movement, five or all six legs execute their first stance phase (i.e. leg on the ground during locomotion) simultaneously. By the end of the turn the pattern has changed to the alternate 'tripod' coordination characteristic of insect walking. The change-over from all legs working together, to working alternately, occurs by means of a consistent pattern of delays in the stepping of certain legs. 3. The movements made by each leg during its initial stance phase are carried out using consistent movement components in the anterior-posterior (A-P) and the medial-lateral (M-L) axes (Fig. 4A). The movement at a particular joint in each middle leg is found to be diagnostic for the direction of turn. 4. The size and direction of a given leg's M-L movement in its initial stance phase depends on the same leg's prior A-P position (Fig. 5). No such feedback effects were seen among different legs. 5. Animals that are fixed to a slick surface on which they make slipping leg movements show the same inter-leg coordination (Fig. 3B), direction of initial stance movement (Fig. 4B) and dependence of the leg's initial M-L movement on its prior A-P position (Fig. 6), as did free-ranging animals. 6. Cockroaches that are walking at the moment they begin their escape reverse those ongoing leg movements that are contrary to escape movements. 7. These results are discussed in terms of the overall coordination of the complex movements, and in terms of the known properties of the neural circuitry for escape. Possibilities for neurobiological follow-up of certain of the findings presented here are also addressed.     

Dominance of local sensory signals over inter-segmental effects in a motor system: experiments

Legged locomotion requires that information local to one leg, and inter-segmental signals coming from the other legs are processed appropriately to establish a coordinated walking pattern. However, very little is known about the relative importance of local and inter-segmental signals when they converge upon the central pattern generators (CPGs) of different leg joints. We investigated this question on the CPG of the middle leg coxa?Ctrochanter (CTr)-joint of the stick insect which is responsible for lifting and lowering the leg. We used a semi-intact preparation with an intact front leg stepping on a treadmill, and simultaneously stimulated load sensors of the middle leg. We found that middle leg load signals induce bursts in the middle leg depressor motoneurons (MNs). The same local load signals could also elicit rhythmic activity in the CPG of the middle leg CTr-joint when the stimulation of middle leg load sensors coincided with front leg stepping. However, the influence of front leg stepping was generally weak such that front leg stepping alone was only rarely accompanied by switching between middle leg levator and depressor MN activity. We therefore conclude that the impact of the local sensory signals on the levator?Cdepressor motor system is stronger than the inter-segmental influence through front leg stepping.