Proprioceptive feedback amplification restores effective locomotion in a neuromechanical model of lampreys with spinal injuries.

Spinal injuries in many vertebrates can result in partial or complete loss of locomotor ability. While mammals often experience permanent loss, some nonmammals, such as lampreys, can regain swimming function, though the exact mechanism is not well understood. One hypothesis is that amplified proprioceptive (body-sensing) feedback can allow an injured lamprey to regain functional swimming even if the descending signal is lost. This study employs a multiscale, integrative, computational model of an anguilliform swimmer fully coupled to a viscous, incompressible fluid and examines the effects of amplified feedback on swimming behavior. This represents a model that analyzes spinal injury recovery by combining a closed-loop neuromechanical model with sensory feedback coupled to a full Navier-Stokes model. Our results show that in some cases, feedback amplification below a spinal lesion is sufficient to partially or entirely restore effective swimming behavior.

The role of vision and lateral line sensing for schooling in giant danios (Devario aequipinnatus).

Schooling is a collective behavior that relies on a fish's ability to sense and respond to the other fish around it. Previous work has identified 'rules' of schooling - attraction to neighbors that are far away, repulsion from neighbors that are too close and alignment with neighbors at the correct distance - but we do not understand well how these rules emerge from the sensory physiology and behavior of individual fish. In particular, fish use both vision and their lateral lines to sense each other, but it is unclear how much they rely on information from these sensory modalities to coordinate schooling behavior. To address this question, we studied how the schooling of giant danios (Devario aequipinnatus) changes when they are unable to see or use their lateral lines. We found that giant danios were able to school without their lateral lines but did not school in darkness. Surprisingly, giant danios in darkness had the same attraction properties as fish in light when they were in close proximity, indicating that they could sense nearby fish with their lateral lines. However, they were not attracted to more distant fish, suggesting that long-distance attraction through vision is important for maintaining a cohesive school. These results help us expand our understanding of the roles that vision and the lateral line play in the schooling of some fish species.

Kinematics and behaviour in fish escape responses: guidelines for conducting, analysing and reporting experiments.

Work carried out since the late 1970s has provided key insights into the comparative biomechanics, kinematics, behaviour and neurobiology of fish escape responses. An escape response is an ecologically important behaviour used by fishes to evade predation and aggression via rapid swimming movements. With environmental change expected to affect the physiology and biomechanics of aquatic ectotherms, there is a growing interest in understanding how environmental stressors affect the swimming performance and behaviour of fishes during escape responses, particularly in the context of predator-prey interactions. As the study of fish swimming continues to expand, there have been repeated calls to standardise experiments and reporting practices to facilitate integrative and comparative studies. Here, we provide a set of practical guidelines for conducting, analysing and reporting experiments on escape responses in fish, including a reporting checklist to assist authors undertaking these experiments. These resources will facilitate executing and reporting escape response experiments in a rigorous and transparent fashion, helping to advance the study of fish swimming in an era of rapid environmental change.

Regulation of the swimming kinematics of lampreys Petromyzon marinus across changes in viscosity.

The bodies of most swimming fishes are very flexible and deform as result of both external fluid dynamic forces and internal musculoskeletal forces. If fluid forces change, the body motion will also change unless the fish senses the change and alters its muscle activity to compensate. Lampreys and other fishes have mechanosensory cells in their spinal cords that allow them to sense how their body is bending. We hypothesized that lampreys (Petromyzon marinus) actively regulate body curvature to maintain a fairly constant swimming waveform even as swimming speed and fluid dynamic forces change. To test this hypothesis, we measured the steady swimming kinematics of lampreys swimming in normal water, and water in which the viscosity was increased by 10 or 20 times by adding methylcellulose. Increasing the viscosity over this range increases the drag coefficient, potentially increasing fluid forces up to 40%. Previous computational results suggested that if lampreys did not compensate for these forces, the swimming speed would drop by about 52%, the amplitude would drop by 39%, and posterior body curvature would increase by about 31%, while tail beat frequency would remain the same. Five juvenile sea lampreys were filmed swimming through still water, and midlines were digitized using standard techniques. Although swimming speed dropped by 44% from 1× to 10× viscosity, amplitude only decreased by 4%, and curvature increased by 7%, a much smaller change than the amount we estimated if there was no compensation. To examine the waveform overall, we performed a complex orthogonal decomposition and found that the first mode of the swimming waveform (the primary swimming pattern) did not change substantially, even at 20× viscosity. Thus, it appears that lampreys are compensating, at least partially, for the changes in viscosity, which in turn suggests that sensory feedback is involved in regulating the body waveform.

Flexibility is a hidden axis of biomechanical diversity in fishes.

Nearly all fish have flexible bodies that bend as a result of internal muscular forces and external fluid forces that are dynamically coupled with the mechanical properties of the body. Swimming is therefore strongly influenced by the body's flexibility, yet we do not know how fish species vary in their flexibility and in their ability to modulate flexibility with muscle activity. A more fundamental problem is our lack of knowledge about how any of these differences in flexibility translate into swimming performance. Thus, flexibility represents a hidden axis of diversity among fishes that may have substantial impacts on swimming performance. Although engineers have made substantial progress in understanding these fluid-structure interactions using physical and computational models, the last biological review of these interactions and how they give rise to fish swimming was carried out more than 20 years ago. In this Review, we summarize work on passive and active body mechanics in fish, physical models of fish and bioinspired robots. We also revisit some of the first studies to explore flexural stiffness and discuss their relevance in the context of more recent work. Finally, we pose questions and suggest future directions that may help reveal important links between flexibility and swimming performance.

Airfoil-like mechanics generate thrust on the anterior body of swimming fishes.

The anterior body of many fishes is shaped like an airfoil turned on its side. With an oscillating angle to the swimming direction, such an airfoil experiences negative pressure due to both its shape and pitching movements. This negative pressure acts as thrust forces on the anterior body. Here, we apply a high-resolution, pressure-based approach to describe how two fishes, bluegill sunfish (Lepomis macrochirus Rafinesque) and brook trout (Salvelinus fontinalis Mitchill), swimming in the carangiform mode, the most common fish swimming mode, generate thrust on their anterior bodies using leading-edge suction mechanics, much like an airfoil. These mechanics contrast with those previously reported in lampreys-anguilliform swimmers-which produce thrust with negative pressure but do so through undulatory mechanics. The thrust produced on the anterior bodies of these carangiform swimmers through negative pressure comprises 28% of the total thrust produced over the body and caudal fin, substantially decreasing the net drag on the anterior body. On the posterior region, subtle differences in body shape and kinematics allow trout to produce more thrust than bluegill, suggesting that they may swim more effectively. Despite the large phylogenetic distance between these species, and differences near the tail, the pressure profiles around the anterior body are similar. We suggest that such airfoil-like mechanics are highly efficient, because they require very little movement and therefore relatively little active muscular energy, and may be used by a wide range of fishes since many species have appropriately shaped bodies.

Resilience of neural networks for locomotion.

Locomotion is an essential behaviour for the survival of all animals. The neural circuitry underlying locomotion is therefore highly robust to a wide variety of perturbations, including injury and abrupt changes in the environment. In the short term, fault tolerance in neural networks allows locomotion to persist immediately after mild to moderate injury. In the longer term, in many invertebrates and vertebrates, neural reorganization including anatomical regeneration can restore locomotion after severe perturbations that initially caused paralysis. Despite decades of research, very little is known about the mechanisms underlying locomotor resilience at the level of the underlying neural circuits and coordination of central pattern generators (CPGs). Undulatory locomotion is an ideal behaviour for exploring principles of circuit organization, neural control and resilience of locomotion, offering a number of unique advantages including experimental accessibility and modelling tractability. In comparing three well-characterized undulatory swimmers, lampreys, larval zebrafish and Caenorhabditis elegans, we find similarities in the manifestation of locomotor resilience. To advance our understanding, we propose a comparative approach, integrating experimental and modelling studies, that will allow the field to begin identifying shared and distinct solutions for overcoming perturbations to persist in orchestrating this essential behaviour.

Swimming kinematics and performance of spinal transected lampreys with different levels of axon regeneration.

Axon regeneration is critical for restoring neural function after spinal cord injury. This has prompted a series of studies on the neural and functional recovery of lampreys after spinal cord transection. Despite this, there are still many basic questions remaining about how much functional recovery depends on axon regeneration. Our goal was to examine how swimming performance is related to degree of axon regeneration in lampreys recovering from spinal cord transection by quantifying the relationship between swimming performance and percent axon regeneration of transected lampreys after 11 weeks of recovery. We found that while swimming speeds varied, they did not relate to percent axon regeneration. In fact, swimming speeds were highly variable within individuals, meaning that most individuals could swim at both moderate and slow speeds, regardless of percent axon regeneration. However, none of the transected individuals were able to swim as fast as the control lampreys. To swim fast, control lampreys generated high amplitude body waves with long wavelengths. Transected lampreys generated body waves with lower amplitude and shorter wavelengths than controls, and to compensate, transected lampreys increased their wave frequencies to swim faster. As a result, transected lampreys had significantly higher frequencies than control lampreys at comparable swimming velocities. These data suggest that the control lampreys swam more efficiently than transected lampreys. In conclusion, there appears to be a minimal recovery threshold in terms of percent axon regeneration required for lampreys to be capable of swimming; however, there also seems to be a limit to how much they can behaviorally recover.

The role of curvature feedback in the energetics and dynamics of lamprey swimming: A closed-loop model.

Like other animals, lampreys have a central pattern generator (CPG) circuit that activates muscles for locomotion and also adjusts the activity to respond to sensory inputs from the environment. Such a feedback system is crucial for responding appropriately to unexpected perturbations, but it is also active during normal unperturbed steady swimming and influences the baseline swimming pattern. In this study, we investigate different functional forms of body curvature-based sensory feedback and evaluate their effects on steady swimming energetics and kinematics, since little is known experimentally about the functional form of curvature feedback. The distributed CPG is modeled as chains of coupled oscillators. Pairs of phase oscillators represent the left and right sides of segments along the lamprey body. These activate muscles that flex the body and move the lamprey through a fluid environment, which is simulated using a full Navier-Stokes model. The emergent curvature of the body then serves as an input to the CPG oscillators, closing the loop. We consider two forms of feedback, each consistent with experimental results on lamprey proprioceptive sensory receptors. The first, referred to as directional feedback, excites or inhibits the oscillators on the same side, depending on the sign of a chosen gain parameter, and has the opposite effect on oscillators on the opposite side. We find that directional feedback does not affect beat frequency, but does change the duration of muscle activity. The second feedback model, referred to as magnitude feedback, provides a symmetric excitatory or inhibitory effect to oscillators on both sides. This model tends to increase beat frequency and reduces the energetic cost to the lamprey when the gain is high and positive. With both types of feedback, the body curvature has a similar magnitude. Thus, these results indicate that the same magnitude of curvature-based feedback on the CPG with different functional forms can cause distinct differences in swimming performance.

Hydrodynamics of linear acceleration in bluegill sunfish, Lepomis macrochirus.

In their natural habitat, fish rarely swim steadily. Instead they frequently accelerate and decelerate. Relatively little is known about how fish produce extra force for acceleration in routine swimming behavior. In this study, we examined the flow around bluegill sunfish Lepomis macrochirus during steady swimming and during forward acceleration, starting at a range of initial swimming speeds. We found that bluegill produce vortices with higher circulation during acceleration, indicating a higher force per tail beat, but they do not substantially redirect the force. We quantified the flow patterns using high speed video and particle image velocimetry and measured acceleration with small inertial measurement units attached to each fish. Even in steady tail beats, the fish accelerates slightly during each tail beat, and the magnitude of the acceleration varies. In steady tail beats, however, a high acceleration is followed by a lower acceleration or a deceleration, so that the swimming speed is maintained; in unsteady tail beats, the fish maintains the acceleration over several tail beats, so that the swimming speed increases. We can thus compare the wake and kinematics during single steady and unsteady tail beats that have the same peak acceleration. During unsteady tail beats when the fish accelerates forward for several tail beats, the wake vortex forces are much higher than those at the same acceleration during single tail beats in steady swimming. The fish also undulates its body at higher amplitude and frequency during unsteady tail beats. These kinematic changes likely increase the fluid dynamic added mass of the body, increasing the forces required to sustain acceleration over several tail beats. The high amplitude and high frequency movements are also likely required to generate the higher forces needed for acceleration. Thus, it appears that bluegill sunfish face a trade-off during acceleration: the body movements required for acceleration also make it harder to accelerate.

The effects of lateral line ablation and regeneration in schooling giant danios.

Fish use multiple sensory systems, including vision and their lateral line system, to maintain position and speed within a school. Although previous studies have shown that ablating the lateral line alters schooling behavior, no one has examined how the behavior recovers as the sensory system regenerates. We studied how schooling behavior changes in giant danios, Devario aequipinnatus, when their lateral line system is chemically ablated and after the sensory hair cells regenerate. We found that fish could school normally immediately after chemical ablation, but that they had trouble schooling 1-2 weeks after the chemical treatment, when the hair cells had fully regenerated. We filmed groups of giant danios with two high-speed cameras and reconstructed the three-dimensional positions of each fish within a group. One fish in the school was treated with gentamycin to ablate all hair cells. Both types of neuromasts (canal and superficial) were completely ablated after treatment, but fully regenerated after 1 week. We quantified the structure of the school using nearest neighbor distance, bearing, elevation, and the cross-correlation of velocity between each pair of fish. Treated fish maintained a normal position within the school immediately after the lateral line ablation, but could not school normally 1 or 2 weeks after treatment, even though the neuromasts had fully regenerated. By 4-8 weeks post-treatment, the treated fish could again school normally. These results demonstrate that the behavioral recovery after lateral line ablation is a longer process than the regeneration of the hair cells themselves.

Characterization of the encoding properties of intraspinal mechanosensory neurons in the lamprey.

Proprioceptive sensory inputs are an integral part of the closed-loop system of locomotion. In the lamprey, a model organism for vertebrate locomotion, such sensory inputs come from intraspinal mechanosensory cells called "edge cells". These edge cells synapse directly onto interneurons in the spinal central pattern generator (CPG) circuit and allow the CPG to adjust the motor output according to how the body is bending. However, the encoding properties of the edge cells have never been fully characterized. To identify these properties and better understand edge cells' role in locomotion, we isolated spinal cords of silver lampreys (Ichthyomyzon unicuspis) and recorded extracellularly from the lateral tracts where edge cell axons are located. We identified cells that responded to mechanical stimuli and used standard spike sorting algorithms to identify separate units, then examined how the cells respond to bending rate and bending angle. Although some cells respond to the bending angle, as was previously known, the strongest and most common responses were to bending velocity. These encoding properties will help us better understand how lampreys and other basal vertebrates adapt their locomotor rhythms to different water flow patterns, perturbations, or other unexpected changes in their environments.

Long-axis twisting during locomotion of elongate fishes.

Fish live in a complex world and must actively adapt their swimming behavior to a range of environments. Most studies of swimming kinematics focus on two-dimensional properties related to the bending wave that passes from head to tail. However, fish also twist their bodies three dimensionally around their longitudinal axis as the bending wave passes down the body. We measured and characterized this movement, which we call 'wobble', in six species of elongate fishes (Anoplarchus insignis, Xiphister mucosus, Lumpenus sagitta, Pholis laeta, Apodichthys flavidus and Ronquilus jordani) from three different habitats (intertidal, nearshore and subtidal) using custom video analysis software. Wobble and bending are synchronized, with a phase shift between the wobble wave and bending wave. We found that species from the same habitats swim in similar ways, even if they are more closely related to species from different habitats. In nearshore species, the tail wobbles the most but, in subtidal and intertidal species, the head wobbles more than or the same as the tail. We also wanted to understand the relationship between wobble and the passive mechanics of the fish bodies. Therefore, we measured torsional stiffness and modulus along the body and found that modulus increases from head to tail in all six species. As wobble does not correlate with the passive properties of the body, it may play a different role in swimming behavior of fishes from different habitats.

Streamwise vortices destabilize swimming bluegill sunfish (Lepomis macrochirus).

In their natural environment, fish must swim stably through unsteady flows and vortices, including vertical vortices, typically shed by posts in a flow, horizontal cross-flow vortices, often produced by a step or a waterfall in a stream, and streamwise vortices, where the axis of rotation is aligned with the direction of the flow. Streamwise vortices are commonly shed by bluff bodies in streams and by ships' propellers and axial turbines, but we know little about their effects on fish. Here, we describe how bluegill sunfish use more energy and are destabilized more often in flow with strong streamwise vorticity. The vortices were created inside a sealed flow tank by an array of four turbines with similar diameter to the experimental fish. We measured oxygen consumption for seven sunfish swimming at 1.5 body lengths (BL) s(-1) with the turbines rotating at 2 Hz and with the turbines off (control). Simultaneously, we filmed the fish ventrally and recorded the fraction of time spent maneuvering side-to-side and accelerating forward. Separately, we also recorded lateral and ventral video for a combination of swimming speeds (0.5, 1.5 and 2.5 BL s(-1)) and turbine speeds (0, 1, 2 and 3 Hz), immediately after turning the turbines on and 10 min later to test for accommodation. Bluegill sunfish are negatively affected by streamwise vorticity. Spills (loss of heading), maneuvers and accelerations were more frequent when the turbines were on than in the control treatment. These unsteady behaviors, particularly acceleration, correlated with an increase in oxygen consumption in the vortex flow. Bluegill sunfish are generally fast to recover from roll perturbations and do so by moving their pectoral fins. The frequency of spills decreased after the turbines had run for 10 min, but was still markedly higher than in the control, showing that fish partially adapt to streamwise vorticity, but not completely. Coping with streamwise vorticity may be an important energetic cost for stream fishes or migratory fishes.

The effect of intrinsic muscular nonlinearities on the energetics of locomotion in a computational model of an anguilliform swimmer.

Animals move through their environments using muscles to produce force. When an animal׳s nervous system activates a muscle, the muscle produces different amounts of force depending on its length, its shortening velocity, and its time history of force production. These muscle forces interact with forces from passive tissue properties and forces from the external environment. Using an integrative computational model that couples an elastic, actuated model of an anguilliform, lamprey-like swimmer with a surrounding Navier-Stokes fluid, we study the effects of this coupling between the muscle force and the body motion. Swimmers with different forms of this coupling can achieve similar motions, but use different amounts of energy. The velocity dependence is the most important property of the ones we considered for reducing energy costs and helping us to stabilize oscillations. These effects are strongly influenced by how rapidly the muscle deactivates; if force decays too slowly, muscles on opposite sides of the body end up fighting each other, increasing energy cost. Work-dependent deactivation, an effect that causes a muscle to deactivate more rapidly if it has recently produced mechanical work, works together with the velocity dependence to reduce the energy cost of swimming.

Interactions between internal forces, body stiffness, and fluid environment in a neuromechanical model of lamprey swimming.

Animal movements result from a complex balance of many different forces. Muscles produce force to move the body; the body has inertial, elastic, and damping properties that may aid or oppose the muscle force; and the environment produces reaction forces back on the body. The actual motion is an emergent property of these interactions. To examine the roles of body stiffness, muscle activation, and fluid environment for swimming animals, a computational model of a lamprey was developed. The model uses an immersed boundary framework that fully couples the Navier-Stokes equations of fluid dynamics with an actuated, elastic body model. This is the first model at a Reynolds number appropriate for a swimming fish that captures the complete fluid-structure interaction, in which the body deforms according to both internal muscular forces and external fluid forces. Results indicate that identical muscle activation patterns can produce different kinematics depending on body stiffness, and the optimal value of stiffness for maximum acceleration is different from that for maximum steady swimming speed. Additionally, negative muscle work, observed in many fishes, emerges at higher tail beat frequencies without sensory input and may contribute to energy efficiency. Swimming fishes that can tune their body stiffness by appropriately timed muscle contractions may therefore be able to optimize the passive dynamics of their bodies to maximize peak acceleration or swimming speed.

Identification of the trade-off between speed and efficiency in undulatory swimming using a bio-inspired robot.

Anguilliform swimmers, like eels or lampreys, are highly efficient swimmers. Key to understanding their performances is the relationship between the body's kinematics and resulting swimming speed and efficiency. But, we cannot prescribe kinematics to living fish, and it is challenging to measure their power consumption. Here, we characterise the swimming speed and cost of transport of a free-swimming undulatory bio-inspired robot as we vary its kinematic parameters, including joint amplitude, body wavelength, and frequency. We identify a trade-off between speed and efficiency. Speed, in terms of stride length, increases for increasing maximum tail angle, described by the newly proposed specific tail amplitude and reaches a maximum value around the specific tail amplitude of unity. Efficiency, in terms of the cost of transport, is affected by the whole-body motion. Cost of transport decreases for increasing travelling wave-like kinematics, and lower specific tail amplitudes. Our results suggest that live eels tend to choose efficiency over speed and provide insights into the key characteristics affecting undulatory swimming performance.

Hydrodynamics of the bluegill sunfish C-start escape response: three-dimensional simulations and comparison with experimental data.

In this work we study the hydrodynamics of a bluegill sunfish performing a C-start maneuver in unprecedented detail using 3-D numerical simulations guided by previous laboratory experiments with live fish. The 3-D fish body geometry and kinematics are reconstructed from the experiments using high-speed video and prescribed as input to the numerical simulation. The calculated instantaneous flow fields at various stages of the C-start maneuver are compared with the two-dimensional particle image velocimetry measurements, and are shown to capture essentially all flow features observed in the measurements with good quantitative accuracy; the simulations reveal the experimentally observed three primary jet flow patterns whose momentum time series are in very good agreement with the measured flow field. The simulations elucidate for the first time the complex 3-D structure of the wake during C-starts, revealing an intricate vortical structure consisting of multiple connected vortex loops at the end of the C-start. We also find that the force calculated based on the 3-D flow field has higher magnitudes than that implied by the jet momentum on the midplane, and it exhibits large and rapid fluctuations during the two stages of the C-start. These fluctuations are physical and are related to the change in the direction of the acceleration of the fish body, which changes the location of the high and low pressure pockets around the fish.

Wake structures behind a swimming robotic lamprey with a passively flexible tail.

A robotic lamprey, based on the silver lamprey, Ichthyomyzon unicuspis, was used to investigate the influence of passive tail flexibility on the wake structure and thrust production during anguilliform swimming. A programmable microcomputer actuated 11 servomotors that produce a traveling wave along the length of the lamprey body. The waveform was based on kinematic studies of living lamprey, and the shape of the tail was taken from a computer tomography scan of the silver lamprey. The tail was constructed of flexible PVC gel, and nylon inserts were used to change its degree of flexibility. Particle image velocimetry measurements using three different levels of passive flexibility show that the large-scale structure of the wake is dominated by the formation of two pairs of vortices per shedding cycle, as seen in the case of a tail that flexed actively according to a pre-defined kinematic pattern, and did not bend in response to fluid forces. When the tail is passively flexible, however, the large structures are composed of a number of smaller vortices, and the wake loses coherence as the degree of flexibility increases. Momentum balance calculations indicate that, at a given tailbeat frequency, increasing the tail flexibility yields less net force, but changing the cycle frequency to match the resonant frequency of the tail increases the force production.