Mechanisms underlying rhythmic locomotion: body-fluid interaction in undulatory swimming

Magnetically Actuated Soft Microrobot with Environmental Adaptative Multimodal Locomotion Towards Targeted Delivery

The development of environmentally adaptive solutions for magnetically actuated microrobots to enable targeted delivery in complex and confined fluid environments presents a significant challenge. Inspired by the natural locomotion of crucian carp, a barbell-shaped soft microrobot (MBS2M) is proposed. A mechano-electromagnetic hybrid actuation system is developed to generate oscillating magnetic fields to manipulate the microrobot. The MBS2M can seamlessly transition between three fundamental locomotion modes: fast navigation (FN), high-precision navigation (HPN), and fixed-point rotation (FPR). Moreover, the MBS2M can move in reverse without turning. The multimodal locomotion endows the MBS2M's adaptability in diverse environments. It can smoothly pass through confined channels, climb over obstacles, overcome gravity for vertical motion, track complex pathways, traverse viscous environments, overcome low fluid resistance, and navigate complex spaces mimicking in vivo environments. Additionally, the MBS2M is capable of drug loading and release in response to ultrasound excitation. In an ex vivo porcine liver vein, the microrobot demonstrated targeted navigation under ultrasound guidance, showcasing its potential for specialized in vivo tasks.

Form and function of anguilliform swimming

Anguilliform swimmers are long and narrow animals that propel themselves by undulating their bodies. Observations in nature and recent investigations suggest that anguilliform swimming is highly efficient. However, understanding the underlying reasons for the efficiency of this type of locomotion requires interdisciplinary studies spanning from biology to hydrodynamics. Regrettably, these different fields are rarely discussed together, which hinders our ability to understand the repeated evolution of this swimming mode in vertebrates. This review compiles the current knowledge of the anatomical features that drive anguilliform swimming, compares the resulting kinematics across a wide range of anguilliform swimmers, and describes the resulting hydrodynamic interactions using data from both in vivo experiments and computational studies.

Decoupling and Reprogramming the Wiggling Motion of Midge Larvae Using a Soft Robotic Platform

The efficient motility of invertebrates helps them survive under evolutionary pressures. Reconstructing the locomotion of invertebrates and decoupling the influence of individual basic motion are crucial for understanding their underlying mechanisms, which, however, generally remain a challenge due to the complexity of locomotion gaits. Herein, a magnetic soft robot to reproduce midge larva's key natural swimming gaits is developed, and the coupling effect between body curling and rotation on motility is investigated. Through the authors' systematically decoupling studies using programmed magnetic field inputs, the soft robot (named LarvaBot) experiences various coupled gaits, including biomimetic side-to-side flexures, and unveils that the optimal rotation amplitude and the synchronization of curling and rotation greatly enhance its motility. The LarvaBot achieves fast locomotion and upstream capability at the moderate Reynolds number regime. The soft robotics-based platform provides new insight to decouple complex biological locomotion, and design programmed swimming gaits for the fast locomotion of soft-bodied swimmers.

Phase response analyses support a relaxation oscillator model of locomotor rhythm generation in Caenorhabditis elegans

Neural circuits coordinate with muscles and sensory feedback to generate motor behaviors appropriate to an animal's environment. In C. elegans, the mechanisms by which the motor circuit generates undulations and modulates them based on the environment are largely unclear. We quantitatively analyzed C. elegans locomotion during free movement and during transient optogenetic muscle inhibition. Undulatory movements were highly asymmetrical with respect to the duration of bending and unbending during each cycle. Phase response curves induced by brief optogenetic inhibition of head muscles showed gradual increases and rapid decreases as a function of phase at which the perturbation was applied. A relaxation oscillator model based on proprioceptive thresholds that switch the active muscle moment was developed and is shown to quantitatively agree with data from free movement, phase responses, and previous results for gait adaptation to mechanical loadings. Our results suggest a neuromuscular mechanism underlying C. elegans motor pattern generation within a compact circuit.

Flexible tensegrity wing design and insights in principles of swimming kinematics of batoid rays

A novel tensegrity wing design is first proposed which can emulate the kinematic waves of the pectoral fin of batoid rays and has a simple structure for manufacture. The attitude control and the regulation of wing natural frequency are realized by wing morphing. Then analytical insights in batoid ray swimming are gained by analyzing the analytical wing (cable)-fluid interaction model, whose parameters are determined based on the biological data. The stride length (traveled distance per cycle normalized by the body length (BL)) is shown to be almost invariant among different-sized rays if the phase and amplitude of wing flexion angles remain unchanged. This result is supported by biological data, 1.5 and 1.47 respectively for the manta ray and cownose ray, though their flapping frequencies (0.15-0.45 Hz and 0.64-1.25 Hz respectively) and body sizes (1.25 m and 0.15 m respectively) are very different, and similar to the expression for the carangiform fish swimming. In other words, the swimming kinematics of two different swimming forms are described by a similar analytical equation when the body resonance is exploited. The fluid force and cable tension are both found to be proportional to the fourth power of the body size and the square of the wing flapping frequency, which may tell that the flapping frequency of the manta ray (BL = 1.25 m) is much smaller than that of the cownose ray (BL = 0.15 m) is to avoid both the large actuation tension and fluid force density due to the size increase.

Effect of body stiffness distribution on larval fish-like efficient undulatory swimming

Energy-efficient propulsion is a critical design target for robotic swimmers. Although previous studies have pointed out the importance of nonuniform body bending stiffness distribution (k) in improving the undulatory swimming efficiency of adult fish-like robots in the inertial flow regime, whether such an elastic mechanism is beneficial in the intermediate flow regime remains elusive. Hence, we develop a class of untethered soft milliswimmers consisting of a magnetic composite head and a passive elastic body with different k These robots realize larval zebrafish-like undulatory swimming at the same scale. Investigations reveal that uniform k and high swimming frequency (60 to 100 Hz) are favorable to improve their efficiency. A shape memory polymer-based milliswimmer with tunable k on the fly confirms such findings. Such acquired knowledge can guide the design of energy-efficient leading edge-driven soft undulatory milliswimmers for future environmental and biomedical applications in the same flow regime.

Effects of symmetry breaking in the viscous pumping of an oscillating plate in the intermediate Reynolds numbers

Pumping fluid is essential to numerous applications across a wide range of scales from viscous dominated to inertia driven flows. Most traditional applications occur within a range where inertia is the dominating factor influencing the pump performance, and hence many practical designs are based on mechanisms that rely on this assumption. As one explores smaller devices, however, the increasing effect of viscosity renders these traditional mechanisms ineffective. In the current work, a bio-inspired pump is constructed from a two-dimensional oscillating solid and flexible plate to study the effect of diminishing inertia within a narrow channel. The goal is to quantify and better understand the role played by a shift from symmetric to asymmetric kinematics of an oscillating rigid or flexible plate in the transition regime between viscous and inertia dominated flows. This is done through both a temporal asymmetry using a rigid plate (e.g. scallop) and a geometric asymmetry using a passive one-way hinged articulation (e.g. jellyfish). One-way flexibility results in a rigid plate during the effective stroke while permitting a simple hinged articulation during the recovery stroke. The waveform used for the temporally asymmetric case consists of a basic triangle waveform which could generate faster effective strokes than recovery strokes. The results of the single-plate tests indicate that increased asymmetry introduced in the triangular wave actuation leads to increased pumping performance and energy consumption. In the case of flexible plates, the results show that a mass-specific pumping efficiency was higher for a higher actuation frequency at the same Reynolds numbers.

Thrust generation during steady swimming and acceleration from rest in anguilliform swimmers

Escape swimming is a crucial behavior by which undulatory swimmers evade potential threats. The hydrodynamics of escape swimming have not been well studied, particularly for anguilliform swimmers, such as the sea lamprey Petromyzon marinus. For this study, we compared the kinematics and hydrodynamics of larval sea lampreys with those of lampreys accelerating from rest during escape swimming. We used experimentally derived velocity fields to calculate pressure fields and distributions of thrust and drag along the body. Lampreys initiated acceleration from rest with the formation of a high-amplitude body bend at approximately one-quarter body length posterior to the head. This deep body bend produced two high-pressure regions from which the majority of thrust for acceleration was derived. In contrast, steady swimming was characterized by shallower body bends and negative-pressure-derived thrust, which was strongest near the tail. The distinct mechanisms used for steady swimming and acceleration from rest may reflect the differing demands of the two behaviors. High-pressure-based mechanisms, such as the one used for acceleration from rest, could also be important for low-speed maneuvering during which drag-based turning mechanisms are less effective. The design of swimming robots may benefit from the incorporation of such insights from unsteady swimming.

3D computational models explain muscle activation patterns and energetic functions of internal structures in fish swimming

How muscles are used is a key to understanding the internal driving of fish swimming. However, the underlying mechanisms of some features of the muscle activation patterns and their differential appearance in different species are still obscure. In this study, we explain the muscle activation patterns by using 3D computational fluid dynamics models coupled to the motion of fish with prescribed deformation and examining the torque and power required along the fish body with two primary swimming modes. We find that the torque required by the hydrodynamic forces and body inertia exhibits a wave pattern that travels faster than the curvature wave in both anguilliform and carangiform swimmers, which can explain the traveling wave speeds of the muscle activations. Notably, intermittent negative power (i.e., power delivered by the fluid to the body) on the posterior part, along with a timely transfer of torque and energy by tendons, explains the decrease in the duration of muscle activation towards the tail. The torque contribution from the body elasticity further clarifies the wave speed increase or the reverse of the wave direction of the muscle activation on the posterior part of a carangiform swimmer. For anguilliform swimmers, the absence of the aforementioned changes in the muscle activation on the posterior part is consistent with our torque prediction and the absence of long tendons from experimental observations. These results provide novel insights into the functions of muscles and tendons as an integral part of the internal driving system, especially from an energy perspective, and they highlight the differences in the internal driving systems between the two primary swimming modes.

For undulatory swimming, fish form posteriorly traveling waves of body bending by activating their muscles sequentially along the body. However, experimental observations have shown that the muscle activation wave does not simply match the bending wave. Researchers have previously computed the torque required for muscles along the body based on classic hydrodynamic theories and explained the higher wave speed of the muscle activation compared to the curvature wave. However, the origins of other features of the muscle activation pattern and their variation among different species are still obscure after decades of research. In this study, we use 3D computational fluid dynamics models to compute the spatiotemporal distributions of both the torque and power required for eel-like and mackerel-like swimming. By examining both the torque and power patterns and considering the energy transfer, storage, and release by tendons and body viscoelasticity, we can explain not only the features and variations in the muscle activation patterns as observed from fish experiments but also how tendons and body elasticity save energy. We provide a mechanical picture in which the body shape, body movement, muscles, tendons, and body elasticity of a mackerel (or similar) orchestrate to make swimming efficient.

Biomechanics of swimming in developing larval fish

Most larvae of bony fish are able to swim almost immediately after hatching. Their locomotory system supports several vital functions: fish larvae make fast manoeuvres to escape from predators, aim accurately during suction feeding and may migrate towards suitable future habitats. Owing to their small size and low swimming speed, larval fish operate in the intermediate hydrodynamic regime, which connects the viscous and inertial flow regimes. They experience relatively strong viscous effects at low swimming speeds, and relatively strong inertial effects at their highest speeds. As the larvae grow and increase swimming speed, a shift occurs towards the inertial flow regime. To compensate for size-related limitations on swimming speed, fish larvae exploit high tail beat frequencies at their highest speeds, made possible by their low body inertia and fast neuromuscular system. The shifts in flow regime and body inertia lead to changing functional demands on the locomotory system during larval growth. To reach the reproductive adult stage, the developing larvae need to adjust to and perform the functions necessary for survival. Just after hatching, many fish larvae rely on yolk and need to develop their feeding systems before the yolk is exhausted. Furthermore, the larvae need to develop and continuously adjust their sensory, neural and muscular systems to catch prey and avoid predation. This Review discusses the hydrodynamics of swimming in the intermediate flow regime, the changing functional demands on the locomotory system of the growing and developing larval fish, and the solutions that have evolved to accommodate these demands.

How the bending kinematics of swimming lampreys build negative pressure fields for suction thrust

Swimming animals commonly bend their bodies to generate thrust. For undulating animals such as eels and lampreys, their bodies bend in the form of waves that travel from head to tail. These kinematics accelerate the flow of adjacent fluids, which alters the pressure field in a manner that generates thrust. We used a comparative approach to evaluate the cause-and-effect relationships in this process by quantifying the hydrodynamic effects of body kinematics at the body-fluid interface of the lamprey, Petromyzon marinus, during steady-state swimming. We compared the kinematics and hydrodynamics of healthy control lampreys to lampreys whose spinal cord had been transected mid-body, resulting in passive kinematics along the posterior half of their body. Using high-speed particle image velocimetry (PIV) and a method for quantifying pressure fields, we detail how the active bending kinematics of the control lampreys were crucial for setting up strong negative pressure fields (relative to ambient fields) that generated high-thrust regions at the bends as they traveled all along the body. The passive kinematics of the transected lamprey were only able to generate significant thrust at the tail, relying on positive pressure fields. These different pressure and thrust scenarios are due to differences in how active versus passive body waves generated and controlled vorticity. This demonstrates why it is more effective for undulating lampreys to pull, rather than push, themselves through the fluid.

Development and Training of a Neural Controller for Hind Leg Walking in a Dog Robot

Animals dynamically adapt to varying terrain and small perturbations with remarkable ease. These adaptations arise from complex interactions between the environment and biomechanical and neural components of the animal's body and nervous system. Research into mammalian locomotion has resulted in several neural and neuro-mechanical models, some of which have been tested in simulation, but few “synthetic nervous systems” have been implemented in physical hardware models of animal systems. One reason is that the implementation into a physical system is not straightforward. For example, it is difficult to make robotic actuators and sensors that model those in the animal. Therefore, even if the sensorimotor circuits were known in great detail, those parameters would not be applicable and new parameter values must be found for the network in the robotic model of the animal. This manuscript demonstrates an automatic method for setting parameter values in a synthetic nervous system composed of non-spiking leaky integrator neuron models. This method works by first using a model of the system to determine required motor neuron activations to produce stable walking. Parameters in the neural system are then tuned systematically such that it produces similar activations to the desired pattern determined using expected sensory feedback. We demonstrate that the developed method successfully produces adaptive locomotion in the rear legs of a dog-like robot actuated by artificial muscles. Furthermore, the results support the validity of current models of mammalian locomotion. This research will serve as a basis for testing more complex locomotion controllers and for testing specific sensory pathways and biomechanical designs. Additionally, the developed method can be used to automatically adapt the neural controller for different mechanical designs such that it could be used to control different robotic systems.

A classic model animal in the 21st century: recent lessons from the leech nervous system

The medicinal leech (genus Hirudo) is a classic model animal in systems neuroscience. The leech has been central to many integrative studies that establish how properties of neurons and their interconnections give rise to the functioning of the animal at the behavioral level. Leeches exhibit several discrete behaviors (such as crawling, swimming and feeding) that are each relatively simple. Importantly, these behaviors can all be studied - at least at a basal level - in the isolated nervous system. The leech nervous system is particularly amenable to such studies because of its distributed nature; sensory processing and generation of behavior occur to a large degree in iterated segmental ganglia that each contain only ∼400 neurons. Furthermore, the neurons are relatively large and are arranged with stereotyped topography on the surface of the ganglion, which greatly facilitates their identification and accessibility. This Commentary provides an overview of recent work on the leech nervous system, with particular focus on circuits that underlie leech behavior. Studies that combine the unique features of the leech with modern optical and genetic techniques are also discussed. Thus, this Commentary aims to explain the continued appeal of the leech as an experimental animal in the 21st century.

A review on locomotion robophysics: the study of movement at the intersection of robotics, soft matter and dynamical systems

Discovery of fundamental principles which govern and limit effective locomotion (self-propulsion) is of intellectual interest and practical importance. Human technology has created robotic moving systems that excel in movement on and within environments of societal interest: paved roads, open air and water. However, such devices cannot yet robustly and efficiently navigate (as animals do) the enormous diversity of natural environments which might be of future interest for autonomous robots; examples include vertical surfaces like trees and cliffs, heterogeneous ground like desert rubble and brush, turbulent flows found near seashores, and deformable/flowable substrates like sand, mud and soil. In this review we argue for the creation of a physics of moving systems-a 'locomotion robophysics'-which we define as the pursuit of principles of self-generated motion. Robophysics can provide an important intellectual complement to the discipline of robotics, largely the domain of researchers from engineering and computer science. The essential idea is that we must complement the study of complex robots in complex situations with systematic study of simplified robotic devices in controlled laboratory settings and in simplified theoretical models. We must thus use the methods of physics to examine both locomotor successes and failures using parameter space exploration, systematic control, and techniques from dynamical systems. Using examples from our and others' research, we will discuss how such robophysical studies have begun to aid engineers in the creation of devices that have begun to achieve life-like locomotor abilities on and within complex environments, have inspired interesting physics questions in low dimensional dynamical systems, geometric mechanics and soft matter physics, and have been useful to develop models for biological locomotion in complex terrain. The rapidly decreasing cost of constructing robot models with easy access to significant computational power bodes well for scientists and engineers to engage in a discipline which can readily integrate experiment, theory and computation.

Experimental investigation of efficient locomotion of underwater snake robots for lateral undulation and eel-like motion patterns

Underwater snake robots offer many interesting capabilities for underwater operations. The long and slender structure of such robots provide superior capabilities for access through narrow openings and within confined areas. This is interesting for inspection and monitoring operations, for instance within the subsea oil and gas industry and within marine archeology. In addition, underwater snake robots can provide both inspection and intervention capabilities and are thus interesting candidates for the next generation inspection and intervention AUVs. Furthermore, bioinspired locomotion through oscillatory gaits, like lateral undulation and eel-like motion, is interesting from an energy efficiency point of view. Increasing the motion efficiency in terms of the achieved forward speed by improving the method of propulsion is a key issue for underwater robots. Moreover, energy efficiency is one of the main challenges for long-term autonomy of these systems. In this study, we will consider both these two aspects of efficiency. This paper considers the energy efficiency of swimming snake robots by presenting and experimentally investigating fundamental properties of the velocity and the power consumption of an underwater snake robot for both lateral undulation and eel-like motion patterns. In particular, we investigate the relationship between the parameters of the gait patterns, the forward velocity and the energy consumption for different motion patterns. The simulation and experimental results are seen to support the theoretical findings.

Diverse anguilliform swimming kinematics in Pacific hagfish (Eptatretus stoutii) and Atlantic hagfish (Myxine glutinosa)

Anguilliform mode swimmers pass waves of lateral bending down their elongate bodies to propel forward. Hagfishes (Myxinidae) are classified as anguilliform swimmers, but their unique habits and reduced morphology—including a flexible body lacking a vertebral column—have the potential to translate into unique swimming behaviour within this broad classification. Their roles as active scavengers and hunters can require considerable bouts of swimming, yet quantitative data on hagfish locomotion are limited. Here, we aim to provide a more complete mechanistic understanding of hagfish swimming by quantifying whole-body kinematics of steady swimming in Pacific hagfish (Eptatretus stoutii (Lockington, 1878)) and Atlantic hagfish (Myxine glutinosa L., 1758), species from the two main lineages of Myxinidae. We analyzed high-speed video of hagfishes swimming at voluntary swim speeds and found that both species swim using high-amplitude undulatory waves. Swim speed is generally frequency-modulated, but patterns in wave speed, wavelength, and amplitude along the body and across swim speeds are variable, implying versatile mechanisms for the control of swim speed in these highly flexible fishes. We propose mechanistic explanations for this kinematic variability and compare hagfish with other elongate swimmers, demonstrating that the hagfish’s rich locomotory repertoire adds variety to the already diverse set of locomotory kinematics found in anguilliform swimmers.

Multiplexed modulation of behavioral choice

Stimuli in the environment, as well as internal states, influence behavioral choice. Of course, animals are often exposed to multiple external and internal factors simultaneously, which makes the ultimate determinants of behavior quite complex. We observed the behavioral responses of European leeches, Hirudo verbana, as we varied one external factor (surrounding water depth) with either another external factor (location of tactile stimulation along the body) or an internal factor (body distention following feeding). Stimulus location proved to be the primary indicator of behavioral response. In general, anterior stimulation produced shortening behavior, midbody stimulation produced local bending, and posterior stimulation usually produced either swimming or crawling but sometimes a hybrid of the two. By producing a systematically measured map of behavioral responses to body stimulation, we found wide areas of overlap between behaviors. When we varied the surrounding water depth, this map changed significantly, and a new feature - rotation of the body along its long axis prior to swimming - appeared. We found additional interactions between water depth and time since last feeding. A large blood meal initially made the animals crawl more and swim less, an effect that was attenuated as water depth increased. The behavioral map returned to its pre-feeding form after approximately 3 weeks as the leeches digested their blood meal. In summary, we found multiplexed impacts on behavioral choice, with the map of responses to tactile stimulation modified by water depth, which itself modulated the impact that feeding had on the decision to swim or crawl.

Motor coordination: a local hub for coordination

A local interneuron of a crayfish central pattern generator serves as a hub that integrates ascending and descending coordinating information and passes it on to a local oscillatory microcircuit to coordinate a series of segmental appendages known as swimmerets.

Discontinuous locomotion and prey sensing in the leech

The medicinal leech, Hirudo verbana, is an aquatic predator that utilizes water waves to locate its prey. However, to reach their prey, the leeches must move within the same water that they are using to sense prey. This requires that they either move ballistically towards a pre-determined prey location or that they account for their self-movement and continually track prey. We found that leeches do not localize prey ballistically. Instead, they require continual sensory information to track their prey. Indeed, in the event that the prey moves, leeches will approach the prey's new location. While leeches need to continually sense water disturbances to update their percept of prey location, their own behavior is discontinuous--prey involves switching between swimming, crawling and non-locomoting. Each of these behaviors may allow for different sensory capabilities and may require different sensory filters. Here, we examined the sensory capabilities of leeches during each of these behaviors. We found that while one could expect the non-locomoting phases to direct subsequent behaviors, crawling phases were more effective than non-locomotor phases for providing direction. During crawling bouts, leeches adjusted their heading so as to become more directed towards the stimulus. This was not observed during swimming. Furthermore, in the presence of prey-like stimuli, leeches crawled more often and for longer periods of time.

Analytical insights into optimality and resonance in fish swimming

This paper provides analytical insights into the hypothesis that fish exploit resonance to reduce the mechanical cost of swimming. A simple body-fluid fish model, representing carangiform locomotion, is developed. Steady swimming at various speeds is analysed using optimal gait theory by minimizing bending moment over tail movements and stiffness, and the results are shown to match with data from observed swimming. Our analysis indicates the following: thrust-drag balance leads to the Strouhal number being predetermined based on the drag coefficient and the ratio of wetted body area to cross-sectional area of accelerated fluid. Muscle tension is reduced when undulation frequency matches resonance frequency, which maximizes the ratio of tail-tip velocity to bending moment. Finally, hydrodynamic resonance determines tail-beat frequency, whereas muscle stiffness is actively adjusted, so that overall body-fluid resonance is exploited.

Biological clockwork underlying adaptive rhythmic movements

Owing to the complexity of neuronal circuits, precise mathematical descriptions of brain functions remain an elusive ambition. A more modest focus of many neuroscientists, central pattern generators, are more tractable neuronal circuits specialized to generate rhythmic movements, including locomotion. The relative simplicity and well-defined motor functions of these circuits provide an opportunity for uncovering fundamental principles of neuronal information processing. Here we present the culmination of mathematical analysis that captures the adaptive behaviors emerging from interactions between a central pattern generator, the body, and the physical environment during locomotion. The biologically realistic model describes the undulatory motions of swimming leeches with quantitative accuracy and, without further parameter tuning, predicts the sweeping changes in oscillation patterns of leeches undulating in air or swimming in high-viscosity fluid. The study demonstrates that central pattern generators are capable of adapting oscillations to the environment through sensory feedback, but without guidance from the brain.

Modeling and analysis of propulsion in the multiflagellated micoorganism Giardia lamblia

The goal of this work was to analyze the propulsion of multiflagellated microorganisms, and to draw insight to the underlying physics and biology of the movement. Giardia lamblia was chosen as the model organism due to its unique ability to mechanically attach to various surfaces, its rapid movement, and its fine control over steering and navigation. In this work, a mechanics model was utilized to study the mechanics and propulsive contribution of the ventral and anterior flagella in Giardia. It was discovered that energy is supplied mainly at the proximal portion of these flagella, supporting the hypothesis that a decreasing adenosine triphosphate (ATP) gradient along the length of the flagella would not affect the motion observed. Similarly, the elasticity of the flagella allows the energy input at the proximal portion to be transferred to the distal portion, where the majority of thrust is generated. Specifically, we found that the ventral flagella are the driving force for planar propulsion and turning, while the anterior flagella are used for steering and control.

Emergence of the advancing neuromechanical phase in a resistive force dominated medium

Undulatory locomotion, a gait in which thrust is produced in the opposite direction of a traveling wave of body bending, is a common mode of propulsion used by animals in fluids, on land, and even within sand. As such, it has been an excellent system for discovery of neuromechanical principles of movement. In nearly all animals studied, the wave of muscle activation progresses faster than the wave of body bending, leading to an advancing phase of activation relative to the curvature toward the tail. This is referred to as "neuromechanical phase lags" (NPL). Several multiparameter neuromechanical models have reproduced this phenomenon, but due to model complexity, the origin of the NPL has proved difficult to identify. Here, we use perhaps the simplest model of undulatory swimming to predict the NPL accurately during sand-swimming by the sandfish lizard, with no fitting parameters. The sinusoidal wave used in sandfish locomotion, the friction-dominated and noninertial granular resistive force environment, and the simplicity of the model allow detailed analysis, and reveal the fundamental mechanism responsible for the phenomenon: the combination of synchronized torques from distant points on the body and local traveling torques. This general mechanism should help explain the NPL in organisms in other environments; we therefore propose that sand-swimming could be an excellent system with which to generate and test other neuromechanical models of movement quantitatively. Such a system can also provide guidance for the design and control of robotic undulatory locomotors in complex environments.

Mechanics of undulatory swimming in a frictional fluid

The sandfish lizard (Scincus scincus) swims within granular media (sand) using axial body undulations to propel itself without the use of limbs. In previous work we predicted average swimming speed by developing a numerical simulation that incorporated experimentally measured biological kinematics into a multibody sandfish model. The model was coupled to an experimentally validated soft sphere discrete element method simulation of the granular medium. In this paper, we use the simulation to study the detailed mechanics of undulatory swimming in a "granular frictional fluid" and compare the predictions to our previously developed resistive force theory (RFT) which models sand-swimming using empirically determined granular drag laws. The simulation reveals that the forward speed of the center of mass (CoM) oscillates about its average speed in antiphase with head drag. The coupling between overall body motion and body deformation results in a non-trivial pattern in the magnitude of lateral displacement of the segments along the body. The actuator torque and segment power are maximal near the center of the body and decrease to zero toward the head and the tail. Approximately 30% of the net swimming power is dissipated in head drag. The power consumption is proportional to the frequency in the biologically relevant range, which confirms that frictional forces dominate during sand-swimming by the sandfish. Comparison of the segmental forces measured in simulation with the force on a laterally oscillating rod reveals that a granular hysteresis effect causes the overestimation of the body thrust forces in the RFT. Our models provide detailed testable predictions for biological locomotion in a granular environment.

Using computational and mechanical models to study animal locomotion

Recent advances in computational methods have made realistic large-scale simulations of animal locomotion possible. This has resulted in numerous mathematical and computational studies of animal movement through fluids and over substrates with the purpose of better understanding organisms' performance and improving the design of vehicles moving through air and water and on land. This work has also motivated the development of improved numerical methods and modeling techniques for animal locomotion that is characterized by the interactions of fluids, substrates, and structures. Despite the large body of recent work in this area, the application of mathematical and numerical methods to improve our understanding of organisms in the context of their environment and physiology has remained relatively unexplored. Nature has evolved a wide variety of fascinating mechanisms of locomotion that exploit the properties of complex materials and fluids, but only recently are the mathematical, computational, and robotic tools available to rigorously compare the relative advantages and disadvantages of different methods of locomotion in variable environments. Similarly, advances in computational physiology have only recently allowed investigators to explore how changes at the molecular, cellular, and tissue levels might lead to changes in performance at the organismal level. In this article, we highlight recent examples of how computational, mathematical, and experimental tools can be combined to ultimately answer the questions posed in one of the grand challenges in organismal biology: "Integrating living and physical systems."

Serotonin as an integrator of leech behavior and muscle mechanical performance

The obliquely striated muscle in the leech body wall has a broad functional repertoire; it provides power for both locomotion and suction feeding. It also operates over an unusually high strain range, undergoing up to threefold changes in length. Serotonin (5-HT) may support this functional flexibility, integrating behavior and biomechanics. It can act centrally, promoting motor outputs that drive body wall movements, and peripherally, modulating the mechanical properties of body wall muscle. During isometric contractions 5-HT enhances active force production and reduces resting muscle tone. We therefore hypothesized that 5-HT would increase net work output during the cyclical contractions associated with locomotion and feeding. Longitudinal strains measured during swimming, crawling and feeding were applied to body wall muscle in vitro with the timing and duration of stimulation selected to maximize net work output. The net work output during all simulated behaviors significantly increased in the presence of 100μM 5-HT relative to the 5-HT-free control condition. Without 5-HT the muscle strips could not achieve a net positive work output during simulated swimming. The decrease in passive tension associated with 5-HT may also be important in reducing muscle antagonist work during longitudinal muscle lengthening. The behavioral and mechanical effects of 5-HT during locomotion are clearly complementary, promoting particular behaviors and enhancing muscle performance during those behaviors. Although 5-HT can enhance muscle mechanical performance during simulated feeding, low in vivo activity in serotonergic neurons during feeding may mean that its mechanical role during this behavior is less important than during locomotion.

Mechanisms underlying rhythmic locomotion: interactions between activation, tension and body curvature waves

Undulatory animal locomotion arises from three closely related propagating waves that sweep rostrocaudally along the body: activation of segmental muscles by motoneurons (MNs), strain of the body wall, and muscle tension induced by activation and strain. Neuromechanical models that predict the relative propagation speeds of neural/muscle activation, muscle tension and body curvature can reveal crucial underlying control features of the central nervous system and the power-generating mechanisms of the muscle. We provide an analytical explanation of the relative speeds of these three waves based on a model of neuromuscular activation and a model of the body-fluid interactions for leech anguilliform-like swimming. First, we deduced the motoneuron spike frequencies that activate the muscle and the resulting muscle tension during swimming in intact leeches from muscle bending moments. Muscle bending moments were derived from our video-recorded kinematic motion data by our body-fluid interaction model. The phase relationships of neural activation and muscle tension in the strain cycle were then calculated. Our study predicts that the MN activation and body curvature waves have roughly the same speed (the ratio of curvature to MN activation speed ≈0.84), whereas the tension wave travels about twice as fast. The high speed of the tension wave resulting from slow MN activation is explained by the multiplicative effects of MN activation and muscle strain on tension development. That is, the product of two slower waves (activation and strain) with appropriate amplitude, bias and phase can generate a tension wave with twice the propagation speed of the factors. Our study predicts that (1) the bending moment required for swimming is achieved by minimal MN spike frequency, rather than by minimal muscle tension; (2) MN activity is greater in the mid-body than in the head and tail regions; (3) inhibitory MNs not only accelerate the muscle relaxation but also reduce the intrinsic tonus tension during one sector of the swim cycle; and (4) movements of the caudal end are passive during swimming. These predictions await verification or rejection through further experiments on swimming animals.

Spikes alone do not behavior make: why neuroscience needs biomechanics

Neural circuits do not function in isolation; they interact with the physical world, accepting sensory inputs and producing outputs via muscles. Since both these pathways are constrained by physics, the activity of neural circuits can only be understood by considering biomechanics of muscles, bodies, and the exterior world. We discuss how animal bodies have natural stable motions that require relatively little activation or control from the nervous system. The nervous system can substantially alter these motions, by subtly changing mechanical properties such as body or leg stiffness. Mechanics can also provide robustness to perturbations without sensory reflexes. By considering a complete neuromechanical system, neuroscientists and biomechanicians together can provide a more integrated view of neural circuitry and behavior.

Neural circuits controlling behavior and autonomic functions in medicinal leeches

In the study of the neural circuits underlying behavior and autonomic functions, the stereotyped and accessible nervous system of medicinal leeches, Hirudo sp., has been particularly informative. These leeches express well-defined behaviors and autonomic movements which are amenable to investigation at the circuit and neuronal levels. In this review, we discuss some of the best understood of these movements and the circuits which underlie them, focusing on swimming, crawling and heartbeat. We also discuss the rudiments of decision-making: the selection between generally mutually exclusive behaviors at the neuronal level.

Mechanisms underlying rhythmic locomotion: dynamics of muscle activation

We have studied the dynamical properties of tension development in leech longitudinal muscle during swimming. A new method is proposed for modeling muscle properties under functionally relevant conditions where the muscle is subjected to both periodic activation and rhythmic length changes. The 'dual-sinusoid' experiments were conducted on preparations of leech nerve cord and body wall. The longitudinal muscle was activated periodically by injection of sinusoidal currents into an identified motoneuron. Simultaneously, sinusoidal length changes were imposed on the body wall with prescribed phase differences (12 values equally spaced over 2π radians) with respect to the current injection. Through the singular value decomposition of appropriately constructed tension data matrices, the leech muscle was found to have a multiplicative structure in which the tension was expressed as the product of activation and length factors. The time courses of activation and length factors were determined from the tension data and were used to develop component models. The proposed modeling method is a general one and is applicable to contractile elements for which the effects of series elasticity are negligible.