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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.

 

ABSTRACT 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. 

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 bodies of most swimming fishes are very flexible and deform due to 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 maintaina 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.

 

MONOLITh is a bioinspired, untethered crawling soft robot. The body is made from a lightweight reticulated foam that provides passive shape restoration and supports the internally embedded components (motors, battery, wireless controller). DC motors pull tendons attached to an external fabric that distributes forces, and novel differential friction elements enable forward locomotion. This robot is capable of traveling at a maximum speed of 0.1 body lengths/sec, lifting 100% its body weight, while remaining 95% soft materials by volume. We expect that the design principles and materials used to make this low cost and scalable robot will lead to the development of useful, and commercially viable, terrestrial or extraterrestrial vehicles. 

Fishes have repeatedly evolved characteristic body shapes depending on how close they live to the substrate. Pelagic fishes live in open water and typically have narrow, streamlined body shapes; benthic and demersal fishes live close to the substrate; and demersal fishes often have deeper bodies. These shape differences are often associated with behavioral differences: pelagic fishes swim nearly constantly, demersal fishes tend to maneuver near the substrate, and benthic fishes often lie in wait on the substrate. We hypothesized that these morphological and behavioral differences would be reflected in the mechanical properties of the body, and specifically in vertebral column stiffness, because it is an attachment point for the locomotor musculature and a central axis for body bending. The vertebrae of bony fishes are composed of two cones connected by a foramen, which is filled by the notochord. Since the notochord is more flexible than bony vertebral centra, we predicted that pelagic fishes would have narrower foramina or shallower cones, leading to less notochordal material and a stiffer vertebral column which might support continuous swimming. In contrast, we predicted that benthic and demersal fishes would have more notochordal material, making the vertebral column more flexible for diverse behaviors in these species. We therefore examined vertebral morphology in 79 species using micro‐computed tomography scans. Six vertebral features were measured including notochordal foramen diameter, centrum body length, and the cone angles and diameters for the anterior and posterior vertebral cones, along with body fineness. Using phylogenetic generalized least squares analyses, we found that benthic and pelagic species differed significantly, with larger foramina, shorter centra, and larger cones in benthic species. Thus, morphological differences in the internal shape of the vertebrae of fishes are consistent with a stiffer vertebral column in pelagic fishes and with a more flexible vertebral column in benthic species.

 

Abstract Swimming in schools has long been hypothesized to allow fish to save energy. Fish must exploit the energy from the wakes of their neighbors for maximum energy savings, a feat that requires them to both synchronize their tail movements and stay in certain positions relative to their neighbors. To maintain position in a school, we know that fish use multiple sensory systems, mainly their visual and flow sensing lateral line system. However, how fish synchronize their swimming movements in a school is still not well understood. Here we test the hypothesis that this synchronization may depend on functional differences in the two branches of the lateral line sensory system that detects water movements close to the fish’s body. The anterior branch, located on the head, encounters largely undisturbed free-stream flow, while the posterior branch, located on the trunk and tail, encounters flow that has been affected strongly by the tail movement. Thus, we hypothesize that the anterior branch may be more important for regulating position within the school, while the posterior branch may be more important for synchronizing tail movements. Our study examines functional differences in the anterior and posterior lateral line in the structure and tail synchronization of fish schools. We used a widely available aquarium fish that schools, the giant danio, Devario equipinnatus. Fish swam in a large circular tank where stereoscopic videos recordings were used to reconstruct the 3 D position of each individual within the school and to track tail kinematics to quantify synchronization. For one fish in each school, we ablated using cobalt chloride either the anterior region only, the posterior region only, or the entire lateral line system. We observed that ablating any region of the lateral line system causes fish to swim in a “box” or parallel swimming formation, which was different from the diamond formation observed in normal fish. Ablating only the anterior region did not substantially reduce tail beat synchronization but ablating only the posterior region caused fish to stop synchronizing their tail beats, largely because the tail beat frequency increased dramatically. Thus, the anterior and posterior lateral line system appear to have different behavioral functions in fish. Most importantly, we showed that the posterior lateral line system played a major role in determining tail beat synchrony in schooling fish. Without synchronization, swimming efficiency decreases, which can have an impact on the fitness of the individual fish and group. 

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. 

Abstract One key evolutionary innovation that separates vertebrates from invertebrates is the notochord, a central element that provides the stiffness needed for powerful movements. Later, the notochord was further stiffened by the vertebrae, cartilaginous and bony elements, surrounding the notochord. The ancestral notochord is retained in modern vertebrates as intervertebral material, but we know little about its mechanical interactions with surrounding vertebrae. In this study, the internal shape of the vertebrae—where this material is found—was quantified in sixteen species of fishes with various body shapes, swimming modes, and habitats. We used micro-computed tomography to measure the internal shape. We then created and mechanically tested physical models of intervertebral joints. We also mechanically tested actual vertebrae of five species. Material testing shows that internal morphology of the centrum significantly affects bending and torsional stiffness. Finally, we performed swimming trials to gather kinematic data. Combining these data, we created a model that uses internal vertebral morphology to make predictions about swimming kinematics and mechanics. We used linear discriminant analysis (LDA) to assess the relationship between vertebral shape and our categorical traits. The analysis revealed that internal vertebral morphology is sufficient to predict habitat, body shape, and swimming mode in our fishes. This model can also be used to make predictions about swimming in fishes not easily studied in the lab, such as deep sea and extinct species, allowing the development of hypotheses about their natural behavior. 

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 macrochirusRafinesque) and brook trout (Salvelinus fontinalisMitchill), 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.