Mechanosensory encoding of forces in walking uphill and downhill: force feedback can stabilize leg movements in stick insects.

Force feedback could be valuable in adapting walking to diverse terrains, but the effects of changes in substrate inclination on discharges of sensory receptors that encode forces have rarely been examined. In insects, force feedback is provided by campaniform sensilla, mechanoreceptors that monitor forces as cuticular strains. We neurographically recorded responses of stick insect tibial campaniform sensilla to "naturalistic" forces (joint torques) that occur at the hind leg femur-tibia (FT) joint in uphill, downhill, and level walking. The FT joint torques, obtained in a previous study that used inverse dynamics to analyze data from freely moving stick insects, are quite variable during level walking (including changes in sign) but are larger in magnitude and more consistent when traversing sloped surfaces. Similar to vertebrates, insects used predominantly extension torque in propulsion on uphill slopes and flexion torques to brake forward motion when going downhill. Sensory discharges to joint torques reflected the torque direction but, unexpectedly, often occurred as multiple bursts that encoded the rate of change of positive forces (dF/dt) even when force levels were high. All discharges also showed hysteresis (history dependence), as firing substantially decreased or ceased during transient force decrements. These findings have been tested in simulation in a mathematical model of the sensilla (Szczecinski NS, Dallmann CJ, Quinn RD, Zill SN. Bioinspir Biomim 16: 065001, 2021) that accurately reproduced the biological data. Our results suggest the hypothesis that sensory feedback from the femoro-tibial joint indicating force dynamics (dF/dt) can be used to counter the instability in traversing sloped surfaces in animals and, potentially, in walking machines.NEW & NOTEWORTHY Discharges of sensory receptors (campaniform sensilla) in the hind legs of stick insects can differentially signal forces that occur in walking uphill versus walking downhill. Unexpectedly, sensory firing most closely reflects the rate of change of force (dF/dt) even when the force levels are high. These signals have been replicated in a mathematical model of the receptors and could be used to stabilize leg movements both in the animal and in a walking robot.

Adaptive load feedback robustly signals force dynamics in robotic model of Carausius morosus stepping.

Animals utilize a number of neuronal systems to produce locomotion. One type of sensory organ that contributes in insects is the campaniform sensillum (CS) that measures the load on their legs. Groups of the receptors are found on high stress regions of the leg exoskeleton and they have significant effects in adapting walking behavior. Recording from these sensors in freely moving animals is limited by technical constraints. To better understand the load feedback signaled by CS to the nervous system, we have constructed a dynamically scaled robotic model of the Carausius morosus stick insect middle leg. The leg steps on a treadmill and supports weight during stance to simulate body weight. Strain gauges were mounted in the same positions and orientations as four key CS groups (Groups 3, 4, 6B, and 6A). Continuous data from the strain gauges were processed through a previously published dynamic computational model of CS discharge. Our experiments suggest that under different stepping conditions (e.g., changing "body" weight, phasic load stimuli, slipping foot), the CS sensory discharge robustly signals increases in force, such as at the beginning of stance, and decreases in force, such as at the end of stance or when the foot slips. Such signals would be crucial for an insect or robot to maintain intra- and inter-leg coordination while walking over extreme terrain.

Sensory signals of unloading in insects are tuned to distinguish leg slipping from load variations in gait: experimental and modeling studies.

In control of walking, sensory signals of decreasing forces are used to regulate leg lifting in initiation of swing and to detect loss of substrate grip (leg slipping). We used extracellular recordings in two insect species to characterize and model responses to force decrements of tibial campaniform sensilla, receptors that detect forces as cuticular strains. Discharges to decreasing forces did not occur upon direct stimulation of the sites of mechanotransduction (cuticular caps) but were readily elicited by bending forces applied to the leg. Responses to bending force decreases were phasic but had rate sensitivities similar to discharges elicited by force increases in the opposite direction. Application of stimuli of equivalent amplitude at different offset levels showed that discharges were strongly dependent upon the tonic level of loading: firing was maximal to complete unloading of the leg but substantially decreased or eliminated by sustained loads. The contribution of cuticle properties to sensory responses was also evaluated: discharges to force increases showed decreased adaptation when mechanical stress relaxation was minimized; firing to force decreases could be related to viscoelastic "creep" in the cuticle. Discharges to force decrements apparently occur due to cuticle viscoelasticity that generates transient strains similar to bending in the opposite direction. Tuning of sensory responses through cuticular and membrane properties effectively distinguishes loss of substrate grip/complete unloading from force variations due to gait in walking. We have successfully reproduced these properties in a mathematical model of the receptors. Sensors with similar tuning could fulfil these functions in legs of walking machines.NEW & NOTEWORTHY Decreases in loading of legs are important in the regulation of posture and walking in both vertebrates and invertebrates. Recordings of activities of tibial campaniform sensilla, which encode forces in insects, showed that their responses are specifically tuned to detect force decreases at the end of the stance phase of walking or when a leg slips. These results have been reproduced in a mathematical model of the receptors and also have potential applications in robotics.

A computational model of insect campaniform sensilla predicts encoding of forces during walking.

Control of forces is essential in both animals and walking machines. Insects measure forces as strains in their exoskeletons via campaniform sensilla (CS). Deformations of cuticular caps embedded in the exoskeleton excite afferents that project to the central nervous system. CS afferent firing frequency (i.e. 'discharge') is highly dynamic, correlating with the rate of change of the force. Discharges adapt over time to tonic forces and exhibit hysteresis during cyclic loading.In this study we characterized a phenomenological model that predicts CS discharge, in which discharge is proportional to the instantaneous stimulus force relative to an adaptive variable. In contrast to previous studies of sensory adaptation, our model (1) is nonlinear and (2) reproduces the characteristic power-law adaptation with first order dynamics only (i.e. no 'fractional derivatives' are required to explain dynamics). We solve the response of the system analytically in multiple cases and use these solutions to derive the dynamics of the adaptive variable. We show that the model can reproduce responses of insect CS to many different force stimuli after being tuned to reproduce only one response, suggesting that the model captures the underlying dynamics of the system. We show that adaptation to tonic forces, rate-sensitivity, and hysteresis are different manifestations of the same underlying mechanism: the adaptive variable. We tune the model to replicate the dynamics of three different CS groups from two insects (cockroach and stick insect), demonstrating that it is generalizable. We also invert the model to estimate the stimulus force given the discharge recording from the animal. We discuss the adaptive neural and mechanical processes that the model may mimic and the model's use for understanding the role of load feedback in insect motor control. A preliminary model and results were previously published in the proceedings of the Conference on Biohybrid and Biomimetic Systems.

Evaluation of force feedback in walking using joint torques as "naturalistic" stimuli.

Control of adaptive walking requires the integration of sensory signals of muscle force and load. We have studied how mechanoreceptors (tibial campaniform sensilla) encode "naturalistic" stimuli derived from joint torques of stick insects walking on a horizontal substrate. Previous studies showed that forces applied to the legs using the mean torque profiles of a proximal joint were highly effective in eliciting motor activities. However, substantial variations in torque direction and magnitude occurred at the more distal femorotibial joint, which can generate braking or propulsive forces and provide lateral stability. To determine how these forces are encoded, we used torque waveforms of individual steps that had maximum values in stance in the directions of flexion or extension. Analysis of kinematic data showed that the torques in different directions tended to occur in different ranges of joint angles. Variations within stance were not accompanied by comparable changes in joint angle but often reflected vertical ground reaction forces and leg support of body load. Application of torque waveforms elicited sensory discharges with variations in firing frequency similar to those seen in freely walking insects. All sensilla directionally encoded the dynamics of force increases and showed hysteresis to transient force decreases. Smaller receptors exhibited more tonic firing. Our findings suggest that dynamic sensitivity in force feedback can modulate ongoing muscle activities to stabilize distal joints when large forces are generated at proximal joints. Furthermore, use of "naturalistic" stimuli can reproduce characteristics seen in freely moving animals that are absent in conventional restrained preparations.NEW & NOTEWORTHY Sensory encoding of forces during walking by campaniform sensilla was characterized in stick insects using waveforms of joint torques calculated by inverse dynamics as mechanical stimuli. Tests using the mean joint torque and torques of individual steps showed the system is highly sensitive to force dynamics (dF/dt). Use of "naturalistic" stimuli can reproduce characteristics of sensory discharges seen in freely walking insects, such as load transfer among legs.

Rethinking gross anatomy in a compressed time frame: Clinical symptoms, not case studies, as the basis for introductory instruction.

The goal of this observational study was to develop effective approaches to introduce first year medical students to gross anatomy/embryology in a compressed time frame. Pedagogical reorganization of anatomy instruction in the regions of Lower Extremity and Head and Neck was based upon core clinical conditions taught in second-year and USMLE Step 1 board review courses. These conditions were not presented as clinical problems, as many students had limited prior training in medical terminology, but focused upon clinical symptoms, allowing for direct correlation of structure and function. Instruction stressed vocabulary acquisition and was extended to prepare for laboratory dissections. Overall methodology was multimodal, including "flipped" and traditional lectures, study of prosections/radiographs and small group laboratory review sessions. Content was significantly reduced: knowledge of muscle actions and innervations was required, not muscle origins and insertions. Performance was evaluated by criterion-based written examinations that included a set of questions (34) asked repetitively over an 8 year period (n = 606 students) and by regional practical exams. Mean scores in all areas were sustained or numerically improved, despite the compression of instruction duration. Analysis showed no significant differences based upon question format or instructional modality. Despite the high performance levels, students needing assistance in learning could be identified by score distributions. A survey of students indicated that these changes effectively decreased stress and facilitated review for the USMLE Step 1 Board examination. These results suggest that training in gross anatomy can be modified to a compressed duration by instruction in the context of clinical symptomatology.

Gradients in mechanotransduction of force and body weight in insects.

Posture and walking require support of the body weight, which is thought to be detected by sensory receptors in the legs. Specificity in sensory encoding occurs through the numerical distribution, size and response range of sense organs. We have studied campaniform sensilla, receptors that detect forces as strains in the insect exoskeleton. The sites of mechanotransduction (cuticular caps) were imaged by light and confocal microscopy in four species (stick insects, cockroaches, blow flies and Drosophila). The numbers of receptors and cap diameters were determined in projection images. Similar groups of receptors are present in the legs of each species (flies lack Group 2 on the anterior trochanter). The number of receptors is generally related to the body weight but similar numbers are found in blow flies and Drosophila, despite a 30 fold difference in their weight. Imaging data indicate that the gradient (range) of cap sizes may more closely correlate with the body weight: the range of cap sizes is larger in blow flies than in Drosophila but similar to that found in juvenile cockroaches. These studies support the idea that morphological properties of force-detecting sensory receptors in the legs may be tuned to reflect the body weight.

Identification of the origin of force-feedback signals influencing motor neurons of the thoraco-coxal joint in an insect.

Force feedback from Campaniform sensilla (CS) on insect limbs helps to adapt motor outputs to environmental conditions, but we are only beginning to reveal the neural control mechanisms that mediate these influences. We studied CS groups that affect control of the thoraco-coxal joint in the stick insect Carausius morosus by applying horizontal and vertical forces to the leg stump. Motor effects of ablation of CS groups were evaluated by recording extracellularly from protractor (ProCx) and retractor (RetCx) nerves. Extracellular recordings showed that the effects of stimulating the sensilla were consistent with their broad ranges of directional sensitivity: for example, RetCx firing in response to posterior bending could be reduced by ablating several groups of trochanteral CS, whereas ablation of tibial and femoral sensilla had little effect. In contrast, ProCx motor neuron activity upon anteriorly directed stimuli was affected mainly by ablating a single CS group (G2). Dye fills of trochanteral, femoral and tibial CS groups with fluorescent dyes revealed a common projection pattern with little group specificity. These findings support the idea that the influences of CS feedback are determined by the activities of pre-motor interneurons, facilitating fast and task-dependent adaptation to changing environmental conditions.

Force dynamics and synergist muscle activation in stick insects: the effects of using joint torques as mechanical stimuli.

Many sensory systems are tuned to specific parameters of behaviors and have effects that are task-specific. We have studied how force feedback contributes to activation of synergist muscles in serially homologous legs of stick insects. Forces were applied using conventional half-sine or ramp and hold functions. We also utilized waveforms of joint torques calculated from experiments in freely walking animals. In all legs, forces applied to either the tarsus (foot) or proximal leg segment (trochanter) activated synergist muscles that generate substrate grip and support, but coupling of the depressor muscle to tarsal forces was weak in the front legs. Activation of trochanteral receptors using ramp and hold functions generated positive feedback to the depressor muscle in all legs when animals were induced to seek substrate grip. However, discharges of the synergist flexor muscle showed adaptation at moderate force levels. In contrast, application of forces using torque waveforms, which do not have a static hold phase, produced sustained discharges in muscle synergies with little adaptation. Firing frequencies reflected the magnitude of ground reaction forces, were graded to changes in force amplitude, and could also be modulated by transient force perturbations added to the waveforms. Comparison of synergist activation by torques and ramp and hold functions revealed a strong influence of force dynamics (dF/d t). These studies support the idea that force receptors can act to tune muscle synergies synchronously to the range of force magnitudes and dynamics that occur in each leg according to their specific use in behavior. NEW & NOTEWORTHY The effects of force receptors (campaniform sensilla) on leg muscles and synergies were characterized in stick insects using both ramp and hold functions and waveforms of joint torques calculated by inverse dynamics. Motor responses were sustained and showed reduced adaptation to the more "natural" and nonlinear torque stimuli. Calculation of the first derivative (dF/d t) of the torque waveforms demonstrated that this difference was correlated with the dynamic sensitivities of the system.

Effects of force detecting sense organs on muscle synergies are correlated with their response properties.

Sense organs that monitor forces in legs can contribute to activation of muscles as synergist groups. Previous studies in cockroaches and stick insects showed that campaniform sensilla, receptors that encode forces via exoskeletal strains, enhance muscle synergies in substrate grip. However synergist activation was mediated by different groups of receptors in cockroaches (trochanteral sensilla) and stick insects (femoral sensilla). The factors underlying the differential effects are unclear as the responses of femoral campaniform sensilla have not previously been characterized. The present study characterized the structure and response properties (via extracellular recording) of the femoral sensilla in both insects. The cockroach trochantero-femoral (TrF) joint is mobile and the joint membrane acts as an elastic antagonist to the reductor muscle. Cockroach femoral campaniform sensilla show weak discharges to forces in the coxo-trochanteral (CTr) joint plane (in which forces are generated by coxal muscles) but instead encode forces directed posteriorly (TrF joint plane). In stick insects, the TrF joint is fused and femoral campaniform sensilla discharge both to forces directed posteriorly and forces in the CTr joint plane. These findings support the idea that receptors that enhance synergies encode forces in the plane of action of leg muscles used in support and propulsion.

Speed-dependent interplay between local pattern-generating activity and sensory signals during walking in Drosophila.

In insects, the coordinated motor output required for walking is based on the interaction between local pattern-generating networks providing basic rhythmicity and leg sensory signals, which modulate this output on a cycle-to-cycle basis. How this interplay changes speed-dependently and thereby gives rise to the different coordination patterns observed at different speeds is not sufficiently understood. Here, we used amputation to reduce sensory signals in single legs and decouple them mechanically during walking in Drosophila. This allowed for the dissociation between locally generated motor output in the stump and coordinating influences from intact legs. Leg stumps were still rhythmically active during walking. Although the oscillatory frequency in intact legs was dependent on walking speed, stumps showed a high and relatively constant oscillation frequency at all walking speeds. At low walking speeds we found no strict cycle-to-cycle coupling between stumps and intact legs. In contrast, at high walking speeds stump oscillations were strongly coupled to the movement of intact legs on a one-to-one basis. Although during slow walking there was no preferred phase between stumps and intact legs, we nevertheless found a preferred time interval between touch-down or lift-off events in intact legs and levation or depression of stumps. Based on these findings, we hypothesize that, as in other insects, walking speed in Drosophila is predominantly controlled by indirect mechanisms and that direct modulation of basic pattern-generating circuits plays a subsidiary role. Furthermore, inter-leg coordination strength seems to be speed-dependent and greater coordination is evident at higher walking speeds.

Force feedback reinforces muscle synergies in insect legs.

The nervous system solves complex biomechanical problems by activating muscles in modular, synergist groups. We have studied how force feedback in substrate grip is integrated with effects of sense organs that monitor support and propulsion in insects. Campaniform sensilla are mechanoreceptors that encode forces as cuticular strains. We tested the hypothesis that integration of force feedback from receptors of different leg segments during grip occurs through activation of specific muscle synergies. We characterized the effects of campaniform sensilla of the feet (tarsi) and proximal segments (trochanter and femur) on activities of leg muscles in stick insects and cockroaches. In both species, mechanical stimulation of tarsal sensilla activated the leg muscle that generates substrate grip (retractor unguis), as well as proximal leg muscles that produce inward pull (tibial flexor) and support/propulsion (trochanteral depressor). Stimulation of campaniform sensilla on proximal leg segments activated the same synergistic group of muscles. In stick insects, the effects of proximal receptors on distal leg muscles changed and were greatly enhanced when animals made active searching movements. In insects, the task-specific reinforcement of muscle synergies can ensure that substrate adhesion is rapidly established after substrate contact to provide a stable point for force generation.

WITHDRAWN: Positive force feedback in development of substrate grip in the stick insect tarsus.

The Publisher regrets that this article is an accidental duplication of an article that has already been published, http://dx.doi.org/10.1016/j.asd.2014.06.002. The duplicate article has therefore been withdrawn.

Positive force feedback in development of substrate grip in the stick insect tarsus.

The mechanics of substrate adhesion has recently been intensively studied in insects but less is known about the sensorimotor control of substrate engagement. We characterized the responses and motor effects of tarsal campaniform sensilla in stick insects to understand how sensory signals of force could contribute to substrate grip. The tarsi consist of a chain of segments linked by highly flexible articulations. Morphological studies showed that one to four campaniform sensilla are located on the distal end of each segment. Activities of the receptors were recorded neurographically and sensilla were identified by stimulation and ablation of their cuticular caps. Responses were characterized to bending forces and axial loads, muscle contractions and to forces applied to the retractor apodeme (tendon). The tarsal sensilla effectively encoded both the rate and amplitude of loads and muscle forces, but only when movement was resisted. Mechanical stimulation of the receptors produced activation of motor neurons in the retractor unguis and tibial flexor muscles. These findings indicate that campaniform sensilla can provide information about the effectiveness of the leg muscles in generating substrate adherence. They can also produce positive force feedback that could contribute to the development of substrate grip and stabilization of the tarsal chain.

Directional specificity and encoding of muscle forces and loads by stick insect tibial campaniform sensilla, including receptors with round cuticular caps.

In many systems, loads are detected as the resistance to muscle contractions. We studied responses to loads and muscle forces in stick insect tibial campaniform sensilla, including a subgroup of receptors (Group 6B) with unusual round cuticular caps in oval-shaped collars. Loads were applied in different directions and muscle contractions were emulated by applying forces to the tibial flexor muscle tendon (apodeme). All sensilla 1) were maximally sensitive to loads applied in the plane of joint movement and 2) encoded muscle forces but did not discharge to unresisted movements. Identification of 6B sensilla by stimulation of cuticular caps demonstrated that receptor responses were correlated with their morphology. Sensilla with small cuticular collars produced small extracellular potentials, had low thresholds and strong tonic sensitivities that saturated at moderate levels. These receptors could effectively signal sustained loads. The largest spikes, derived from sensilla with large cuticular collars, had strong dynamic sensitivities and signaled a wide range of muscle forces and loads. Tibial sensilla are apparently tuned to produce no responses to inertial forces, as occur in the swing phase of walking. This conclusion is supported by tests in which animals 'stepped' on a compliant surface and sensory discharges only occurred in stance.

Force encoding in stick insect legs delineates a reference frame for motor control.

The regulation of forces is integral to motor control. However, it is unclear how information from sense organs that detect forces at individual muscles or joints is incorporated into a frame of reference for motor control. Campaniform sensilla are receptors that monitor forces by cuticular strains. We studied how loads and muscle forces are encoded by trochanteral campaniform sensilla in stick insects. Forces were applied to the middle leg to emulate loading and/or muscle contractions. Selective sensory ablations limited activities recorded in the main leg nerve to specific receptor groups. The trochanteral campaniform sensilla consist of four discrete groups. We found that the dorsal groups (Groups 3 and 4) encoded force increases and decreases in the plane of movement of the coxo-trochanteral joint. Group 3 receptors discharged to increases in dorsal loading and decreases in ventral load. Group 4 showed the reverse directional sensitivities. Vigorous, directional responses also occurred to contractions of the trochanteral depressor muscle and to forces applied at the muscle insertion. All sensory discharges encoded the amplitude and rate of loading or muscle force. Stimulation of the receptors produced reflex effects in the depressor motoneurons that could reverse in sign during active movements. These data, in conjunction with findings of previous studies, support a model in which the trochanteral receptors function as an array that can detect forces in all directions relative to the intrinsic plane of leg movement. The array could provide requisite information about forces and simplify the control and adaptation of posture and walking.

Encoding of force increases and decreases by tibial campaniform sensilla in the stick insect, Carausius morosus.

Detection of force increases and decreases is important in motor control. Experiments were performed to characterize the structure and responses of tibial campaniform sensilla, receptors that encode forces through cuticular strains, in the middle leg of the stick insect (Carausius morosus). The sensilla consist of distinct subgroups. Group 6A sensilla are located 0.3 mm distal to the femoro-tibial joint and have oval shaped cuticular caps. Group 6B receptors are 1 mm distal to the joint and have round caps. All sensilla show directional, phasico-tonic responses to forces applied to the tibia in the plane of joint movement. Group 6B sensilla respond to force increases in the direction of joint extension while Group 6A receptors discharge when those forces decrease. Forces applied in the direction of joint flexion produce the reverse pattern of sensory discharge. All receptors accurately encode the rate of change of force increments and decrements. Contractions of tibial muscles also produce selective, directional sensory discharges. The subgroups differ in their reflex effects: Group 6B receptors excite and Group 6A sensilla inhibit tibial extensor and trochanteral depressor motoneurons. The tibial campaniform sensilla can, therefore, encode force increases or decreases and aid in adapting motor outputs to changes in load.

Detecting substrate engagement: responses of tarsal campaniform sensilla in cockroaches.

Sensory signals of contact and engagement with the substrate are important in the control and adaptation of posture and locomotion. We characterized responses of campaniform sensilla, receptors that encode forces as cuticular strains, in the tarsi (feet) of cockroaches using neurophysiological techniques and digital imaging. A campaniform sensillum on the fourth tarsal segment was readily identified by its large action potential in nerve recordings. The receptor discharged to contractions of the retractor unguis muscle, which engages the pretarsus (claws and arolium) with the substrate. We mimicked the effects of muscle contractions by applying displacements to the retractor apodeme (tendon). Sensillum firing did not occur to unopposed movements, but followed engagement of the claws with an object. Vector analysis of forces suggested that resisted muscle contractions produce counterforces that axially compress the tarsal segments. Close joint packing of tarsal segments was clearly observed following claw engagement. Physiological experiments showed that the sensillum responded vigorously to axial forces applied directly to the distal tarsus. Discharges of tarsal campaniform sensilla could effectively signal active substrate engagement when the pretarsal claws and arolium are used to grip the substrate in climbing, traversing irregular terrains or walking on inverted surfaces.

Neurobiology: reconstructing the neural control of leg coordination.

Walking is adaptable because the timing of movements of individual legs can be varied while maintaining leg coordination. Recent work in stick insects shows that leg coordination set by interactions of pattern generating circuits can be overridden by sensory feedback.

Sensory signals of unloading in one leg follow stance onset in another leg: transfer of load and emergent coordination in cockroach walking.

The transfer of load from one leg to another is an essential component in walking, but sense organs that signal this process have rarely been identified. We used high-speed digital imaging and neurophysiological recordings to characterize activities of tibial campaniform sensilla, receptors that detect forces via cuticular strains, in the middle legs of cockroaches during walking. Previous studies demonstrated that the distal tibial sensilla discharge when body load is suddenly decreased in freely standing animals. Sensory recordings during walking showed that distal receptors in the middle leg fired an intense burst near the end of the stance phase. We tested the hypothesis that initiation of distal firing resulted from the action of other legs entering stance. Analysis of leg movements in slow walking showed that sensory bursts in the middle leg closely followed stance onset of the ipsilateral hind leg while the ipsilateral front leg entered stance earlier in phase. Similar phases of leg movement were found in slow walking in experiments in which animals had no implanted recording wires. Those studies also demonstrated that the opposite middle leg entered stance earlier in phase. Measurements of leg positions in walking showed that the hind leg tarsus was placed closest to the middle leg, in keeping with a "targeting" strategy. Triggering of distal bursts in the middle leg by mechanical action of the hind leg could facilitate the onset of swing in the middle leg through local reflex effects and contribute to emergent coordination of leg movements in metachronal gaits.