Kinematics and motor activity during tethered walking and turning in the cockroach, <Emphasis Type="Italic">Blaberus discoidalis</Emphasis>

When insects turn from walking straight, their legs have to follow different motor patterns. In order to examine such pattern change precisely, we stimulated single antenna of an insect, thereby initiating its turning behavior, tethered over a lightly oiled glass plate. The resulting behavior included asymmetrical movements of prothoracic and mesothoracic legs. The mesothoracic leg on the inside of the turn (in the apparent direction of turning) extended the coxa-trochanter and femur-tibia joints during swing rather than during stance as in walking, while the outside mesothoracic leg kept a slow walking pattern. Electromyograms in mesothoracic legs revealed consistent changes in the motor neuron activity controlling extension of the coxa-trochanter and femur-tibia joints. In tethered walking, depressor trochanter activity consistently preceded slow extensor tibia activity. This pattern was reversed in the inside mesothoracic leg during turning. Also for turning, extensor and depressor motor neurons of the inside legs were activated in swing phase instead of stance. Turning was also examined in free ranging animals. Although more variable, some trials resembled the pattern generated by tethered animals. The distinct inter-joint and inter-leg coordination between tethered turning and walking, therefore, provides a good model to further study the neural control of changing locomotion patterns.     

Phase-Dependent Effects of Transcutaneous Spinal Cord Stimulation on Regulation of Kinematics of Human Stepping Motions

The effect of transcutaneous electrical spinal cord stimulation on the kinematic parameters of movement of the ipsilateral and contralateral legs in healthy subjects during treadmill walking at speeds of 1.5 to 1.7 km/h has been studied. The stimulation electrodes were placed 2.5 cm lateral from the right and left sides of the spinal midline at L1 and T11 levels. During the stance phase, stimulation was administered at L1 level at a frequency of 15 Hz; during the swing phase the stimuli was delivered to T11 at a frequency of 30 Hz, followed by alternating stimulation at L1 and T11. The stimulation during the swing phase (T11) was more effective than that during the stance phase (L1); the most impressive changes in kinematic parameters were observed when combined delivery of stimulations to L1 and T11 was performed. With unilateral spinal stimulation, the amplitude of the angles in the hip, knee and/or ankle joints, the length of the transfer, and the height of the leg elevation increased in the ipsilateral leg. Similar but less pronounced changes were observed in the contralateral leg. A 10% increase in the duration of stimulation in the swing phase caused a change in the kinematic stepping parameters both in ipsilateral and contralateral legs. The maximum effect was observed when bilateral alternating stimulation was used. These data show that phasic transcutaneous electrical spinal cord stimulation, using a wide range of natural walking speeds, can be applied to control kinematic movement parameters.

     

Leg coordination during turning on an extremely narrow substrate in a bug, Mesocerus marginatus (Heteroptera, Coreidae)

The turning movement of a bug, Mesocerus marginatus, is observed when it walks upside-down below a horizontal beam and, at the end of the beam, performs a sharp turn by 180 degrees . The turn at the end of the beam is accomplished in three to five steps, without strong temporal coordination among legs. During the stance, leg endpoints (tarsi) run through rounded trajectories, rotating to the same side in all legs. During certain phases of the turn, a leg is strongly depressed and the tarsus crosses the midline. Swing movements rotate to the same side as do leg endpoints in stance, in strong contrast to the typical swing movements found in turns or straight walk on a flat surface. Terminal location is found after the search through a trajectory that first moves away from the body and then loops back to find substrate. When a leg during stance has crossed the midline, in the following swing movement the leg may move even stronger on the contralateral side, i.e. is stronger depressed, in contrast to swing movements in normal walking, where the leg is elevated. These results suggest that the animals apply a different control strategy compared to walking and turning on a flat surface.     

Insect rope-walkers: kinematics of walking on thin rods in a bug, Graphosoma italicum (Heteroptera, Pentatomidae)

Leg positions during walking on a plane and on thin rods were recorded by photography, videorecording, and videokymography. Joint angles were reconstructed from the tibia-ending position, using a 3-D model of the body. Participation of leg joints in propulsion was analysed by calculating the partial derivatives of tibia end-point position on different joint angles. Adjustment to walking with a narrow ground base is achieved by additional femur depression and flexion of the tibia in the stance phase. In the swing phase, the leg is raised by the same amount as when walking on a plane, but not to the same superior position, as on a plane. The contribution of the subcoxal joint to body propulsion is 64-94% in fore-and middle legs and 22-49% in hind legs. The oblique alignment of the coxal pivot within the thorax helps maintain a long stride for variable ground bases. In Graphosoma , it is close to the optimal position: according to several criteria, the angle between the coxal axis and the body vertical shall be arctan π/2, or ∼ 57.5°.     

Effects of load inversion in cockroach walking

To examine how walking patterns are adapted to changes in load, we recorded leg movements and muscle activities when cockroaches (Periplaneta americana) walked upright and on an inverted surface. Animals were videotaped to measure the hindleg femoro-tibial joint angle while myograms were taken from the tibial extensor and flexor muscles. The joint is rapidly flexed during swing and extended in stance in upright and inverted walking. When inverted, however, swing is shorter in duration and the joint traverses a range of angles further in extension. In slow upright walking, slow flexor motoneurons fire during swing and the slow extensor in stance, although a period of co-contraction occurs early in stance. In inverted walking, patterns of muscle activities are altered. Fast flexor motoneurons fire both in the swing phase and early in stance to support the body by pulling the animal toward the substrate. Extensor firing occurs late in stance to propel the animal forward. These findings are discussed within the context of a model in which stance is divided into an early support and subsequent propulsion phase. We also discuss how these changes in use of the hindleg may represent adaptations to the reversal of the effects of gravity.     

Identified nonspiking interneurons in leg reflexes and during walking in the stick insect

In the stick insect Carausius morosus identified nonspiking interneurons (type E4) were investigated in the mesothoracic ganglion during intraand intersegmental reflexes and during searching and walking.In the standing and in the actively moving animal interneurons of type E4 drive the excitatory extensor tibiae motoneurons, up to four excitatory protractor coxae motoneurons, and the common inhibitor 1 motoneuron (Figs. 1–4).In the standing animal a depolarization of this type of interneuron is induced by tactile stimuli to the tarsi of the ipsilateral front, middle and hind legs (Fig. 5). This response precedes and accompanies the observed activation of the affected middle leg motoneurons. The same is true when compensatory leg placement reflexes are elicited by tactile stimuli given to the tarsi of the legs (Fig. 6).During forward walking the membrane potential of interneurons of type E4 is strongly modulated in the step-cycle (Figs.8–10). The peak depolarization occurs at the transition from stance to swing. The oscillations in membrane potential are correlated with the activity profile of the extensor motoneurons and the common inhibitor 1 (Fig. 9).The described properties of interneuron type E4 in the actively behaving animal show that these interneurons are involved in the organization and coordination of the motor output of the proximal leg joints during reflex movements and during walking.Abbreviations CLP reflex, compensatory leg placement reflex - CI1 common inhibitor I motoneuron - fCO femoral chordotonal organ - FETi fast extensor tibiae motoneuron - FT femur-tibia - SETi slow extensor tibiae motoneuron     

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

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

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.     

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.     

Behaviour-based modelling of hexapod locomotion: linking biology and technical application

Walking in insects and most six-legged robots requires simultaneous control of up to 18 joints. Moreover, the number of joints that are mechanically coupled via body and ground varies from one moment to the next, and external conditions such as friction, compliance and slope of the substrate are often unpredictable. Thus, walking behaviour requires adaptive, context-dependent control of many degrees of freedom. As a consequence, modelling legged locomotion addresses many aspects of any motor behaviour in general. Based on results from behavioural experiments on arthropods, we describe a kinematic model of hexapod walking: the distributed artificial neural network controller walknet. Conceptually, the model addresses three basic problems in legged locomotion. (I) First, coordination of several legs requires coupling between the step cycles of adjacent legs, optimising synergistic propulsion, but ensuring stability through flexible adjustment to external disturbances. A set of behaviourally derived leg coordination rules can account for decentralised generation of different gaits, and allows stable walking of the insect model as well as of a number of legged robots. (II) Second, a wide range of different leg movements must be possible, e.g. to search for foothold, grasp for objects or groom the body surface. We present a simple neural network controller that can simulate targeted swing trajectories, obstacle avoidance reflexes and cyclic searching-movements. (III) Third, control of mechanically coupled joints of the legs in stance is achieved by exploiting the physical interactions between body, legs and substrate. A local positive displacement feedback, acting on individual leg joints, transforms passive displacement of a joint into active movement, generating synergistic assistance reflexes in all mechanically coupled joints.     

Three-dimensional modular control of human walking

Recent studies have suggested that complex muscle activity during walking may be controlled using a reduced neural control strategy organized around the co-excitation of multiple muscles, or modules. Previous computer simulation studies have shown that five modules satisfy the sagittal-plane biomechanical sub-tasks of 2D walking. The present study shows that a sixth module, which contributes primarily to mediolateral balance control and contralateral leg swing, is needed to satisfy the additional non-sagittal plane demands of 3D walking. Body support was provided by Module 1 (hip and knee extensors, hip abductors) in early stance and Module 2 (plantarflexors) in late stance. In early stance, forward propulsion was provided by Module 4 (hamstrings), but net braking occurred due to Modules 1 and 2. Forward propulsion was provided by Module 2 in late stance. Module 1 accelerated the body medially throughout stance, dominating the lateral acceleration in early stance provided by Modules 4 and 6 (adductor magnus) and in late stance by Module 2, except near toe-off. Modules 3 (ankle dorsiflexors, rectus femoris) and 5 (hip flexors and adductors except adductor magnus) accelerated the ipsilateral leg forward in early swing whereas Module 4 decelerated the ipsilateral leg prior to heel-strike. Finally, Modules 1, 4 and 6 accelerated the contralateral leg forward prior to and during contralateral swing. Since the modules were based on experimentally measured muscle activity, these results provide further evidence that a simple neural control strategy involving muscle activation modules organized around task-specific biomechanical functions may be used to control complex human movements.     

Common motor mechanisms support body load in serially homologous legs of cockroaches in posture and walking

We studied the mechanisms underlying support of body load in posture and walking in serially homologous legs of cockroaches. Activities of the trochanteral extensor muscle in the front or middle legs were recorded neurographically while animals were videotaped. Body load was increased via magnets attached to the thorax and varied through a coil below the substrate. In posture, tonic firing of the slow trochanteral extensor motoneuron (Ds) in each leg was strongly modulated by changing body load. Rapid load increases produced decreases in body height and sharp increments in extensor firing. The peak of extensor activity more closely approximated the maximum velocity of body displacement than the body position. In walking, extensor bursts in front and middle legs were initiated during swing and continued into the stance phase. Moderate tonic increases in body load elicited similar, specific, phase dependent changes in both legs: extensor firing was not altered in swing but was higher after foot placement in stance. These motor adjustments to load are not anticipatory but apparently depend upon sensory feedback. These data are consistent with previous findings in the hind legs and support the idea that body load is countered by common motor mechanisms in serially homologous legs.     

Leg movements of stick insects walking with five legs on a treadwheel and with one leg on a motor-driven belt

Stick insects walking with five legs on a self-propelled treadwheel and with the left hindleg (L3) on a motor-driven belt may move the "belt" leg L3 and the "wheel" legs with different frequencies. When L3 made less steps than L2, that step of L2, which was performed during the swing phase of L3, is prolonged. The time interval between the end of swing phase of L3 and the onset of the following swing phase of L2 was remarkably constant. When L3 made more steps than L2, that step of L3, which was performed during the swing phase of L2, is prolonged. Again, the time interval between the end of swing phase of L3 preceding a L2 swing phase and the onset of the L2 swing phase was relatively constant. For both kinds of walking situations phase response curves were drawn. They show that two types of coordinating channels exist: An anteriorly directed type is more dependent on absolute time than on phase. A posteriorly directed type is phase-dependent. Both inhibit the transition from stance to swing for some time. The results are compared with the existing coordination models.     

Skeletal adaptations for forwards and sideways walking in three species of decapod crustaceans

Crustaceans have been successfully employed to study legged locomotion for decades. Most studies have focused on either forwards-walking macrurans, or sideways-walking brachyurans. Libinia emarginata is a Majoid crab (Brachyura) and as such belongs to the earliest group to have evolved the crab form from homoloid ancestors. Unlike most brachyurans, Libinia walks forwards 80% of the time. We employed standard anatomical techniques and motion analysis to compare the skeleton, stance, and the range of motion of the legs of Libinia to the sideways-walking green shore crab (Carcinus maenas), and to the forwards-walking crayfish (Procambarus clarkii). We found animals tended to have greater ranges of motion for joints articulating in the preferred direction of locomotion. Leg segments proximal to such joints were comparatively longer. Thorax elongation, leg length and placement at rest also reflected walking preference. Comparative studies of walking in Libinia and other brachyurans may shed light on the neuroethology of legged locomotion, and on the anatomical and physiological changes necessary for sideways-walking in crustaceans.     

Vibration signals from the FT joint can induce phase transitions in both directions in motoneuron pools of the stick insect walking system

The influence of vibratory signals from the femoral chordotonal organ fCO on the activities of muscles and motoneurons in the three main leg joints of the stick insect leg, i.e., the thoraco-coxal (TC) joint, the coxa-trochanteral (CT) joint, and the femur-tibia (FT) joint, was investigated when the animal was in the active behavioral state. Vibration stimuli induced a switch in motor activity (phase transition), for example, in the FT joint motor activity switched from flexor tibiae to extensor tibiae or vice versa. Similarly, fCO vibration induced phase transitions in both directions between the motoneuron pools of the TC joint and the CT joint. There was no correlation between the directions of phase transition in different joints. Vibration stimuli presented during simultaneous fCO elongation terminated the reflex reversal motor pattern in the FT joint prematurely by activating extensor and inactivating flexor tibiae motoneurons. In legs with freely moving tibia, fCO vibration promoted phase transitions in tibial movement. Furthermore, ground vibration promoted stance-swing transitions as long as the leg was not close to its anterior extreme position during stepping. Our results provide evidence that, in the active behavioral state of the stick insect, vibration signals can access the rhythm generating or bistable networks of the three main leg joints and can promote phase transitions in motor activity in both directions. The results substantiate earlier findings on the modular structure of the single-leg walking pattern generator and indicate a new mechanism of how sensory influence can contribute to the synchronization of phase transitions in adjacent leg joints independent of the walking direction.     

Responses of the lower limb to load carrying in walking man

Muscle activity patterns of several lower limb muscles were examined in the left leg of normal human subjects walking at comfortable speed on a treadmill. In addition knee angular changes and the durations of the swing and stance phases of the step cycle were recorded. Data were collected during a period of normal control walking and when the subject carried a load, either in his right or left hand or on his back. Load (up to 20% of body weight) carried in either hand caused minimal changes in the kinematic parameters investigated but evoked significant prolongation of the normal ongoing electromyographic activity in the contralateral Gluteus medius and in the ipsilateral Gastrocnemius, Vastus lateralis and Semimembranosus. Load (up to 50% of body weight) carried on the back significantly shortened the swing phase and prolonged the ongoing electromyographic activity of the Vastus lateralis. These findings would seem to indicate that the activity of the leg musculature during walking is so tightly controlled that deviation from the normal kinematic pattern of the legs is largely prevented even when body posture and balance are disturbed by carrying substantial additional load.     

A modular artificial neural net for controlling a six-legged walking system

 A system that controls the leg movement of an animal or a robot walking over irregular ground has to ensure stable support for the body and at the same time propel it forward. To do so, it has to react adaptively to unpredictable features of the environment. As part of our study of the underlying mechanisms, we present here a model for the control of the leg movement of a 6-legged walking system. The model is based on biological data obtained from the stick insect. It represents a combined treatment of realistic kinematics and biologically motivated, adaptive gait generation. The model extends a previous algorithmic model by substituting simple networks of artificial neurons for the algorithms previously used to control leg state and interleg coordination. Each system controlling an individual leg consists of three subnets. A hierarchically superior net contains two sensory and two ‘premotor’ units; it rhythmically suppresses the output of one or the other of the two subordinate nets. These are continuously active. They might be called the ‘swing module’ and the ‘stance module’ because they are responsible for controlling the swing (return stroke) and the stance (power stroke) movements, respectively. The swing module consists of three motor units and seven sensory units. It can produce appropriate return stroke movements for a broad range of initial and final positions, can cope with mechanical disturbances of the leg movement, and is able to react to an obstacle which hinders the normal performance of the swing movement. The complete model is able to walk at different speeds over irregular surfaces. The control system rapidly reestablishes a stable gait when the movement of the legs is disturbed. Received: 13 July 1994/Accepted in revised form: 15 November 1994     

Mechanical and metabolic determinants of the preferred step width in human walking

We studied the selection of preferred step width in human walking by measuring mechanical and metabolic costs as a function of experimentally manipulated step width (0.00-0.45L, as a fraction of leg length L). We estimated mechanical costs from individual limb external mechanical work and metabolic costs using open circuit respirometry. The mechanical and metabolic costs both increased substantially (54 and 45%, respectively) for widths greater than the preferred value (0.15-0.45L) and with step width squared (R(2) = 0.91 and 0.83, respectively). As predicted by a three-dimensional model of walking mechanics, the increases in these costs appear to be a result of the mechanical work required for redirecting the centre of mass velocity during the transition between single stance phases (step-to-step transition costs). The metabolic cost for steps narrower than preferred (0.10-0.00L) increased by 8%, which was probably as a result of the added cost of moving the swing leg laterally in order to avoid the stance leg (lateral limb swing cost). Trade-offs between the step-to-step transition and lateral limb swing costs resulted in a minimum metabolic cost at a step width of 0.12L, which is not significantly different from foot width (0.11L) or the preferred step width (0.13L). Humans appear to prefer a step width that minimizes metabolic cost.     

Control of body position of a stick insect standing on uneven surfaces

When a multi-legged animal walks over uneven surfaces, each leg has to span a different distance between body and ground. Thus the animal has to solve the problem of how to control the body height, i.e. to coordinate the movement of the legs in such a way that the vertical projections of leg lengths match these distances. For the standing animal, this is investigated here by testing twelve different substrate configurations and measuring body height and forces applied by the legs on the substrate. The results are consistent with the hypothesis that the legs can be considered to represent independent height controllers. They can be understood as proportional controllers with nonlinear characteristics. The mechanical coupling between the leg is sufficient to explain the experimental results. Thus, no neuronal coupling has to be assumed to exist between these controllers. This agrees with a hypothesis proposed earlier for walking animals (Cruse 1976).     

Three-dimensional knee joint contact forces during walking in unilateral transtibial amputees

Individuals with unilateral transtibial amputations have greater prevalence of osteoarthritis in the intact knee joint relative to the residual leg and non-amputees, but the cause of this greater prevalence is unclear. The purpose of this study was to compare knee joint contact forces and the muscles contributing to these forces between amputees and non-amputees during walking using forward dynamics simulations. We predicted that the intact knee contact forces would be higher than those of the residual leg and non-amputees. In the axial and mediolateral directions, the intact and non-amputee legs had greater peak tibio-femoral contact forces and impulses relative to the residual leg. The peak axial contact force was greater in the intact leg relative to the non-amputee leg, but the stance phase impulse was greater in the non-amputee leg. The vasti and hamstrings muscles in early stance and gastrocnemius in late stance were the largest contributors to the joint contact forces in the non-amputee and intact legs. Through dynamic coupling, the soleus and gluteus medius also had large contributions, even though they do not span the knee joint. In the residual leg, the prosthesis had large contributions to the joint forces, similar to the soleus in the intact and non-amputee legs. These results identify the muscles that contribute to knee joint contact forces during transtibial amputee walking and suggest that the peak knee contact forces may be more important than the knee contact impulses in explaining the high prevalence of intact leg osteoarthritis.