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

Mechanical modeling of mechanosensitive insect strain sensors as a tool to investigate exoskeletal interfaces

During walking, sensory information is measured and monitored by sensory organs that can be found on and within various limb segments. Strain can be monitored by insect load sensors, campaniform sensilla (CS), which have components embedded within the exoskeleton. CS vary in eccentricity, size, and orientation, which can affect their sensitivity to specific strains. Directly investigating the mechanical interfaces that these sensors utilize to encode changes in load bears various obstacles, such as modeling of viscoelastic properties. To circumvent the difficulties of modeling and performing biological experiments in small insects, we developed 3-dimensional printed resin models based on high-resolution imaging of CS. Through the utilization of strain gauges and a motorized tensile tester, physiologically plausible strain can be mimicked while investigating the compression and tension forces that CS experience; here, this was performed for a field of femoral CS inDrosophila melanogaster. Different loading scenarios differentially affected CS compression and the likely neuronal activity of these sensors and elucidate population coding of stresses acting on the cuticle.

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.