Muscle performance in a soft-bodied terrestrial crawler: constitutive modelling of strain-rate dependency

Conductive and elastic bottlebrush elastomers for ultrasoft electronics

Understanding biological systems and mimicking their functions require electronic tools that can interact with biological tissues with matched softness. These tools involve biointerfacing materials that should concurrently match the softness of biological tissue and exhibit suitable electrical conductivities for recording and reading bioelectronic signals. However, commonly employed intrinsically soft and stretchable materials usually contain solvents that limit stability for long-term use or possess low electronic conductivity. To date, an ultrasoft (i.e., Young's modulus <30 kPa), conductive, and solvent-free elastomer does not exist. Additionally, integrating such ultrasoft and conductive materials into electronic devices is poorly explored. This article reports a solvent-free, ultrasoft and conductive PDMS bottlebrush elastomer (BBE) composite with single-wall carbon nanotubes (SWCNTs) as conductive fillers. The conductive SWCNT/BBE with a filler concentration of 0.4 - 0.6 wt% reveals an ultralow Young's modulus (<11 kPa) and satisfactory conductivity (>2 S/m) as well as adhesion property. Furthermore, we fabricate ultrasoft electronics based on laser cutting and 3D printing of conductive and non-conductive BBEs and demonstrate their potential applications in wearable sensing, soft robotics, and electrophysiological recording.

A neuromechanical model for Drosophila larval crawling based on physical measurements

BACKGROUND

Animal locomotion requires dynamic interactions between neural circuits, the body (typically muscles), and surrounding environments. While the neural circuitry of movement has been intensively studied, how these outputs are integrated with body mechanics (neuromechanics) is less clear, in part due to the lack of understanding of the biomechanical properties of animal bodies. Here, we propose an integrated neuromechanical model of movement based on physical measurements by taking Drosophila larvae as a model of soft-bodied animals.

RESULTS

We first characterized the kinematics of forward crawling in Drosophila larvae at a segmental and whole-body level. We then characterized the biomechanical parameters of fly larvae, namely the contraction forces generated by neural activity, and passive elastic and viscosity of the larval body using a stress-relaxation test. We established a mathematical neuromechanical model based on the physical measurements described above, obtaining seven kinematic values characterizing crawling locomotion. By optimizing the parameters in the neural circuit, our neuromechanical model succeeded in quantitatively reproducing the kinematics of larval locomotion that were obtained experimentally. This model could reproduce the observation of optogenetic studies reported previously. The model predicted that peristaltic locomotion could be exhibited in a low-friction condition. Analysis of floating larvae provided results consistent with this prediction. Furthermore, the model predicted a significant contribution of intersegmental connections in the central nervous system, which contrasts with a previous study. This hypothesis allowed us to make a testable prediction for the variability in intersegmental connection in sister species of the genus Drosophila.

CONCLUSIONS

We generated a neurochemical model based on physical measurement to provide a new foundation to study locomotion in soft-bodied animals and soft robot engineering.

A pseudo-anelastic model for stress softening in liquid crystal elastomers

Liquid crystal elastomers exhibit stress softening with residual strain under cyclic loads. Here, we model this phenomenon by generalizing the classical pseudo-elastic formulation of the Mullins effect in rubber. Specifically, we modify the neoclassical strain-energy density of liquid crystal elastomers, depending on the deformation and the nematic director, by incorporating two continuous variables that account for stress softening and the associated set strain. As the material behaviour is governed by different forms of the strain-energy density on loading and unloading, the model is referred to as pseudo-anelastic. We then analyse qualitatively the mechanical responses of the material under cyclic uniaxial tension, which is easier to reproduce in practice, and further specialize the model in order to calibrate its parameters to recent experimental data at different temperatures. The excellent agreement between the numerical and experimental results confirms the suitability of our approach. Since the pseudo-energy function is controlled by the strain-energy density for the primary deformation, it is valid also for materials under multiaxial loads. Our study is relevant to mechanical damping applications and serves as a motivation for further experimental tests.

The control of nocifensive movements in the caterpillar Manduca sexta

In response to a noxious stimulus on the abdomen, caterpillars lunge their head towards the site of stimulation. This nocifensive 'strike' behavior is fast (∼0.5 s duration), targeted and usually unilateral. It is not clear how the fast strike movement is generated and controlled, because caterpillar muscle develops peak force relatively slowly (∼1 s) and the baseline hemolymph pressure is low (<2 kPa). Here, we show that strike movements are largely driven by ipsilateral muscle activation that propagates from anterior to posterior segments. There is no sustained pre-strike muscle activation that would be expected for movements powered by the rapid release of stored elastic energy. Although muscle activation on the ipsilateral side is correlated with segment shortening, activity on the contralateral side consists of two phases of muscle stimulation and a marked decline between them. This decrease in motor activity precedes rapid expansion of the segment on the contralateral side, presumably allowing the body wall to stretch more easily. The subsequent increase in contralateral motor activation may slow or stabilize movements as the head reaches its target. Strike behavior is therefore a controlled fast movement involving the coordination of muscle activity on each side and along the length of the body.

Caterpillar Climbing: Robust, Tension-Based Omni-Directional Locomotion

Animals that must transition from horizontal to inclined or vertical surfaces typically change their locomotion strategy to compensate for the relative shift in gravitational forces. The species that have been studied have stiff articulated skeletons that allow them to redistribute ground reaction forces (GRFs) to control traction. Most also change their stepping patterns to maintain stability as they climb. In contrast, caterpillars, most of which are highly scansorial, soft-bodied, and lack rigid support or joints, can move with the same general kinematics in all orientations. In this study, we measure the GRFs exerted by the abdominal prolegs of Manduca sexta (Linnaeus) during locomotion. We show that, despite the orthogonal shift in gravitational forces, caterpillars use the same tension-based environmental skeleton strategy to crawl horizontally and to climb vertically. Furthermore, the transition from horizontal to vertical surfaces does not seem to require a change in gait; instead gravitational loading is used to help maintain a stance-phase body tension against which the muscles can pull the body upwards.

Application of Acoustoelasticity to Evaluate Nonlinear Modulus in Ex Vivo Kidneys

Currently, dynamic elastography techniques estimate the linear elastic shear modulus of different body tissues. New methods that investigate other properties of soft tissues such as anisotropy, viscosity, and shear nonlinearity would provide more information about the structure and function of the tissue and might provide a better contrast than tissue stiffness and hence provide more effective diagnostic tools for some diseases. It has previously been shown that shear wave velocity in a medium changes due to an applied stress, a phenomenon called acoustoelasticity (AE). Applying a stress to compress a medium while measuring the shear wave velocity versus strain provides data with which the third-order nonlinear shear modulus can be estimated. To evaluate the feasibility of estimating , we evaluated ten ex vivo porcine kidneys embedded in 10% porcine gelatin to mimic the case of a transplanted kidney. Under assumptions of an elastic incompressible medium for AE measurements, the shear modulus was quantified at each compression level and the applied strain was assessed by measuring the change in the thickness of the kidney cortex. Finally, was calculated by applying the AE theory. Our results demonstrated that it is possible to estimate a nonlinear shear modulus by monitoring the changes in strain and due to kidney deformation. The magnitudes of are higher when the compression is performed progressively and when using a plate attached to the transducer. Nevertheless, the values obtained for are similar to those previously reported in the literature for breast tissue.

Dynamical analysis and development of a biologically inspired SMA caterpillar robot

With the goal of robustly designing and fabricating a soft robot based on a caterpillar featuring shape memory alloy (SMA) actuators, analytical and numerical models for a soft robot were created based on the forward crawling motion of the Manduca sexta caterpillar. The analytical model features a rod theory and the mechanics of undulation were analyzed using a motion pattern based on the 'Witch of Agnesi' curve. Complementing these models, experiments on a SMA actuator sample were performed in order to determine its flexural rigidity and curvature as a function of the actuation voltage. A series of these actuators can be modeled as a system of rigid bodies connected by torsional springs. As these bodies are actuated according to the motion pattern based on the individual caterpillar segments, ground contact forces are calculated and analyzed to determine the requirements of successful forward locomotion. The energetics of the analytical and numerical models are then compared and discussed.

Mechanical Behavior of a Bacillus subtilis Pellicle

Bacterial biofilms consist of a complex network of biopolymers embedded with microorganisms, and together these components form a physically robust structure that enables bacteria to grow in a protected environment. This structure can help unwanted biofilms persist in situations ranging from chronic infection to the biofouling of industrial equipment, but under certain circumstances it can allow the biofilm to disperse and colonize new niches. Mechanical properties are therefore a key aspect of biofilm life. In light of the recently discovered growth-induced compressive stress present within a biofilm, we studied the mechanical behavior of Bacillus subtilis pellicles, or biofilms at the air-liquid interface, and tracked simultaneously the force response and macroscopic structural changes during elongational deformations. We observed that pellicles behaved viscoelastically in response to small deformations, such that the growth-induced compressive stress was still present, and viscoplastically at large deformations, when the pellicles were under tension. In addition, by using particle imaging velocimetry we found that the pellicle deformations were nonaffine, indicating heterogeneous mechanical properties with the pellicle being more pliable near attachment surfaces. Overall, our results indicate that we must consider not only the viscoelastic but also the viscoplastic and mechanically heterogeneous nature of these structures to understand biofilm dispersal and removal.

Orientation-Dependent Changes in Single Motor Neuron Activity during Adaptive Soft-Bodied Locomotion

Recent major advances in understanding the organizational principles underlying motor control have focused on a small number of animal species with stiff articulated skeletons. These model systems have the advantage of easily quantifiable mechanics, but the neural codes underlying different movements are difficult to characterize because they typically involve a large population of neurons controlling each muscle. As a result, studying how neural codes drive adaptive changes in behavior is extremely challenging. This problem is highly simplified in the tobacco hawkmoth Manduca sexta, which, in its larval stage (caterpillar), is predominantly soft-bodied. Since each M. sexta muscle is innervated by one, occasionally two, excitatory motor neurons, the electrical activity generated by each muscle can be mapped to individual motor neurons. In the present study, muscle activation patterns were converted into motor neuron frequency patterns by identifying single excitatory junction potentials within recorded electromyographic traces. This conversion was carried out with single motor neuron resolution thanks to the high signal selectivity of newly developed flexible microelectrode arrays, which were specifically designed to record from M. sexta muscles. It was discovered that the timing of motor neuron activity and gait kinematics depend on the orientation of the plane of motion during locomotion. We report that, during climbing, the motor neurons monitored in the present study shift their activity to correlate with movements in the animal's more anterior segments. This orientation-dependent shift in motor activity is in agreement with the expected shift in the propulsive forces required for climbing. Our results suggest that, contrary to what has been previously hypothesized, M.sexta uses central command timing for adaptive load compensation.

Bone-free: soft mechanics for adaptive locomotion

Muscular hydrostats (such as mollusks), and fluid-filled animals (such as annelids), can exploit their constant-volume tissues to transfer forces and displacements in predictable ways, much as articulated animals use hinges and levers. Although larval insects contain pressurized fluids, they also have internal air tubes that are compressible and, as a result, they have more uncontrolled degrees of freedom. Therefore, the mechanisms by which larval insects control their movements are expected to reveal useful strategies for designing soft biomimetic robots. Using caterpillars as a tractable model system, it is now possible to identify the biomechanical and neural strategies for controlling movements in such highly deformable animals. For example, the tobacco hornworm, Manduca sexta, can stiffen its body by increasing muscular tension (and therefore body pressure) but the internal cavity (hemocoel) is not iso-barometric, nor is pressure used to directly control the movements of its limbs. Instead, fluid and tissues flow within the hemocoel and the body is soft and flexible to conform to the substrate. Even the gut contributes to the biomechanics of locomotion; it is decoupled from the movements of the body wall and slides forward within the body cavity at the start of each step. During crawling the body is kept in tension for part of the stride and compressive forces are exerted on the substrate along the axis of the caterpillar, thereby using the environment as a skeleton. The timing of muscular activity suggests that crawling is coordinated by proleg-retractor motoneurons and that the large segmental muscles produce anterograde waves of lifting that do not require precise timing. This strategy produces a robust form of locomotion in which the kinematics changes little with orientation. In different species of caterpillar, the presence of prolegs on particular body segments is related to alternative kinematics such as "inching." This suggests a mechanism for the evolution of different gaits through changes in the usage of prolegs, rather than, through extensive alterations in the motor program controlling the body wall. Some of these findings are being used to design and test novel control-strategies for highly deformable robots. These "softworm" devices are providing new insights into the challenges faced by any soft animal navigating in a terrestrial environment.

Modeling of caterpillar crawl using novel tensegrity structures

Caterpillars are soft-bodied animals. They have a relatively simple nervous system, and yet are capable of exhibiting complex movement. This paper presents a 2D caterpillar simulation which mimics caterpillar locomotion using Assur tensegrity structures. Tensegrity structures are structures composed of a set of elements always under compression and a set of elements always under tension. Assur tensegrities are a novel sub-group of tensegrity structures. In the model, each caterpillar segment is represented by a 2D Assur tensegrity structure called a triad. The mechanical structure and the control scheme of the model are inspired by the biological caterpillar. The unique engineering properties of Assur tensegrity structures, together with the suggested control scheme, provide the model with a controllable degree of softness-each segment can be either soft or rigid. The model exhibits several characteristics which are analogous to those of the biological caterpillar. One such characteristic is that the internal pressure of the caterpillar is not a function of its size. During growth, body mass is increased 10 000-fold, while internal pressure remains constant. In the same way, the model is able to maintain near constant internal forces regardless of size. The research also suggests that caterpillars do not invest considerably more energy while crawling than while resting.

Scaling of caterpillar body properties and its biomechanical implications for the use of a hydrostatic skeleton

Caterpillars can increase their body mass 10,000-fold in 2 weeks. It is therefore remarkable that most caterpillars appear to maintain the same locomotion kinematics throughout their entire larval stage. This study examined how the body properties of a caterpillar might change to accommodate such dramatic changes in body load. Using Manduca sexta as a model system, we measured changes in body volume, tissue density and baseline body pressure, and the dimensions of load-bearing tissues (the cuticle and muscles) over a body mass range from milligrams to several grams. All Manduca biometrics relevant to the hydrostatic skeleton scaled allometrically but close to the isometric predictions. Body density and pressure were almost constant. We next investigated the effects of scaling on the bending stiffness of the caterpillar hydrostatic skeleton. The anisotropic non-linear mechanical response of Manduca muscles and soft cuticle has previously been quantified and modeled with constitutive equations. Using biometric data and these material laws, we constructed finite element models to simulate a hydrostatic skeleton under different conditions. The results show that increasing the internal pressure leads to a non-linear increase in bending stiffness. Increasing the body size results in a decrease in the normalized bending stiffness. Muscle activation can double this stiffness in the physiological pressure range, but thickening the cuticle or increasing the muscle area reduces the structural stiffness. These non-linear effects may dictate the effectiveness of a hydrostatic skeleton at different sizes. Given the shared anatomy and size variation in Lepidoptera larvae, these mechanical scaling constraints may implicate the diverse locomotion strategies in different species.

Modeling locomotion of a soft-bodied arthropod using inverse dynamics

Most bio-inspired robots have been based on animals with jointed, stiff skeletons. There is now an increasing interest in mimicking the robust performance of animals in natural environments by incorporating compliant materials into the locomotory system. However, the mechanics of moving, highly conformable structures are particularly difficult to predict. This paper proposes a planar, extensible-link model for the soft-bodied tobacco hornworm caterpillar, Manduca sexta, to provide insight for biologists and engineers studying locomotion by highly deformable animals and caterpillar-like robots. Using inverse dynamics to process experimentally acquired point-tracking data, ground reaction forces and internal forces were determined for a crawling caterpillar. Computed ground reaction forces were compared to experimental data to validate the model. The results show that a system of linked extendable joints can faithfully describe the general form and magnitude of the contact forces produced by a crawling caterpillar. Furthermore, the model can be used to compute internal forces that cannot be measured experimentally. It is predicted that between different body segments in stance phase the body is mostly kept in tension and that compression only occurs during the swing phase when the prolegs release their grip. This finding supports a recently proposed mechanism for locomotion by soft animals in which the substrate transfers compressive forces from one part of the body to another (the environmental skeleton) thereby minimizing the need for hydrostatic stiffening. The model also provides a new means to characterize and test control strategies used in caterpillar crawling and soft robot locomotion.

Hysteresis in the production of force by larval Dipteran muscle

We describe neuromuscular hysteresis – the dependence of muscle force on recent motoneuron activity – in the body wall muscles of larval Sarcophaga bullata and Drosophila melanogaster. In semi-intact preparations, isometric force produced by a train of nerve impulses at a constant rate was significantly less than that produced by the same train of stimuli with a brief (200 ms) high-frequency burst of impulses interspersed. Elevated force did not decay back to predicted values after the burst but instead remained high throughout the duration of the stimulus train. The increased force was not due to a change in excitatory junction potentials (EJPs); EJP voltage and time course before and after the high-frequency burst were not statistically different. Single muscle and semi-intact preparations exhibited hysteresis similarly, suggesting that connective tissues of the origin or insertion are not crucial to the mechanism of hysteresis. Hysteresis was greatest at low motoneuron rates – yielding a ~100% increase over predicted values based on constant-rate stimulation alone – and decreased as impulse rate increased. We modulated motoneuron frequency rhythmically across rates and cycle periods similar to those observed during kinematic analysis of larval crawling. Positive force hysteresis was also evident within these more physiological activation parameters.

Motor patterns associated with crawling in a soft-bodied arthropod

Soft-bodied animals lack distinct joints and levers, and so their locomotion is expected to be controlled differently from that of animals with stiff skeletons. Some invertebrates, such as the annelids, use functionally antagonistic muscles (circumferential and longitudinal) acting on constant-volume hydrostatics to produce extension and contraction. These processes form the basis for most theoretical considerations of hydrostatic locomotion in organisms including larval insects. However, caterpillars do not move in this way, and their powerful appendages provide grip independent of their dimensional changes. Here, we show that the anterograde wave of movement seen in the crawling tobacco hornworm, Manduca sexta, is mediated by co-activation of dorsal and ventral muscles within a body segment, rather than by antiphasic activation, as previously believed. Furthermore, two or three abdominal segments are in swing phase simultaneously, and the activities of motor neurons controlling major longitudinal muscles overlap in more than four segments. Recordings of muscle activity during natural crawling show that some are activated during both their shortening and elongation. These results do not support the typical peristaltic model of crawling, but they do support a tension-based model of crawling, in which the substrate is utilized as an anchor to generate propulsion.

The substrate as a skeleton: ground reaction forces from a soft-bodied legged animal

The measurement of forces generated during locomotion is essential for the development of accurate mechanical models of animal movements. However, animals that lack a stiff skeleton tend to dissipate locomotor forces in large tissue deformation and most have complex or poorly defined substrate contacts. Under these conditions, measuring propulsive and supportive forces is very difficult. One group that is an exception to this problem is lepidopteran larvae which, despite lacking a rigid skeleton, have well-developed limbs (the prolegs) that can be used for climbing in complex branched structures and on a variety of surfaces. Caterpillars therefore are excellent for examining the relationship between soft body deformation and substrate reaction forces during locomotion. In this study, we devised a method to measure the ground reaction forces (GRFs) at multiple contact points during crawling by the tobacco hornworm (Manduca sexta). Most abdominal prolegs bear similar body weight during their stance phase. Interestingly, forward reaction forces did not come from pushing off the substrate. Instead, most positive reaction forces came from anterior abdominal prolegs loaded in tension while posterior legs produced drag in most instances. The counteracting GRFs effectively stretch the animal axially during the second stage of a crawl cycle. These findings help in understanding how a terrestrial soft-bodied animal can interact with its substrate to control deformation without hydraulic actuation. The results also provide insights into the behavioral and mechanistic constraints leading to the evolution of diverse proleg arrangements in different species of caterpillar.

Morphological communication: exploiting coupled dynamics in a complex mechanical structure to achieve locomotion

Traditional engineering approaches strive to avoid, or actively suppress, nonlinear dynamic coupling among components. Biological systems, in contrast, are often rife with these dynamics. Could there be, in some cases, a benefit to high degrees of dynamical coupling? Here we present a distributed robotic control scheme inspired by the biological phenomenon of tensegrity-based mechanotransduction. This emergence of morphology-as-information-conduit or ‘morphological communication’, enabled by time-sensitive spiking neural networks, presents a new paradigm for the decentralized control of large, coupled, modular systems. These results significantly bolster, both in magnitude and in form, the idea of morphological computation in robotic control. Furthermore, they lend further credence to ideas of embodied anatomical computation in biological systems, on scales ranging from cellular structures up to the tendinous networks of the human hand.

Kinematics of horizontal and vertical caterpillar crawling

Unlike horizontal crawling, vertical crawling involves two counteracting forces: torque rotating the body around its center of mass and gravity resisting forward movement. The influence of these forces on kinematics has been examined in the soft-bodied larval stage of Manduca sexta. We found that crawling and climbing are accomplished using the same movements, with both segment timing and proleg lift indistinguishable in horizontal and vertical locomotion. Minor differences were detected in stride length and in the delay between crawls, which led to a lower crawling speed in the vertical orientation. Although these differences were statistically significant, they were much smaller than the variation in kinematic parameters between animals. The ability of Manduca to crawl and climb using the same movements is best explained by Manduca's relatively small size, slow speed and strong, controlled, passive grip made possible by its proleg/crochets.

Soft-cuticle biomechanics: a constitutive model of anisotropy for caterpillar integument

The mechanical properties of soft tissues are important for the control of motion in many invertebrates. Pressurized cylindrical animals such as worms have circumferential reinforcement of the body wall; however, no experimental characterization of comparable anisotropy has been reported for climbing larvae such as caterpillars. Using uniaxial, real-time fluorescence extensometry on millimeter scale cuticle specimens we have quantified differences in the mechanical properties of cuticle to circumferentially and longitudinally applied forces. Based on these results and the composite matrix-fiber structure of cuticle, a pseudo-elastic transversely isotropic constitutive material model was constructed with circumferential reinforcement realized as a Horgan-Saccomandi strain energy function. This model was then used numerically to describe the anisotropic material properties of Manduca cuticle. The constitutive material model will be used in a detailed finite-element analysis to improve our understanding of the mechanics of caterpillar crawling.