Fishes regulate tail-beat kinematics to minimize speed-specific cost of transport

Energetic expenditure is an important factor in animal locomotion. Here we test the hypothesis that fishes control tail-beat kinematics to optimize energetic expenditure during undulatory swimming. We focus on two energetic indices used in swimming hydrodynamics, cost of transport and Froude efficiency. To rule out one index in favour of another, we use computational-fluid dynamics models to compare experimentally observed fish kinematics with predicted performance landscapes and identify energy-optimized kinematics for a carangiform swimmer, an anguilliform swimmer and larval fishes. By locating the areas in the predicted performance landscapes that are occupied by actual fishes, we found that fishes use combinations of tail-beat frequency and amplitude that minimize cost of transport. This energy-optimizing strategy also explains why fishes increase frequency rather than amplitude to swim faster, and why fishes swim within a narrow range of Strouhal numbers. By quantifying how undulatory-wave kinematics affect thrust, drag, and power, we explain why amplitude and frequency are not equivalent in speed control, and why Froude efficiency is not a reliable energetic indicator. These insights may inspire future research in aquatic organisms and bioinspired robotics using undulatory propulsion.

Voltage imaging identifies spinal circuits that modulate locomotor adaptation in zebrafish

Motor systems must continuously adapt their output to maintain a desired trajectory. While the spinal circuits underlying rhythmic locomotion are well described, little is known about how the network modulates its output strength. A major challenge has been the difficulty of recording from spinal neurons during behavior. Here, we use voltage imaging to map the membrane potential of glutamatergic neurons throughout the spinal cord of the larval zebrafish during fictive swimming in a virtual environment. We mapped the spiking, subthreshold dynamics, relative timing, and sub-cellular electrical propagation across large populations of simultaneously recorded cells. We validated the approach by confirming properties of known sub-types, and we characterized a yet undescribed sub-population of tonic-spiking ventral V3 neurons whose spike rate correlated with swimming strength and bout length. Optogenetic activation of V3 neurons led to stronger swimming and longer bouts but did not affect tail-beat frequency. Genetic ablation of V3 neurons led to reduced locomotor adaptation. The power of voltage imaging allowed us to identify V3 neurons as a critical driver of locomotor adaptation in zebrafish.

A Method for Estimating the Velocity at Which Anaerobic Metabolism Begins in Swimming Fish

Anaerobic metabolism begins before fish reach their critical swimming speed. Anaerobic metabolism affects the swimming ability of fish, which is not conducive to their upward tracking. The initiation of anaerobic metabolism therefore provides a better predictor of flow barriers than critical swimming speed. To estimate the anaerobic element of metabolism for swimming fish, the respiratory metabolism and swimming performance of adult crucian carp (Carassius auratus, mass = 260.10 ± 7.93, body length = 19.32 ± 0.24) were tested in a closed tank at 20 ± 1 °C. The swimming behavior and rate of oxygen consumption of these carp were recorded at various swimming speeds. Results indicate (1) The critical swimming speed of the crucian carp was 0.85 ± 0.032 m/s (4.40 ± 0.16 BL/s). (2) When a power function was fitted to the data, oxygen consumption, as a function of swimming speed, was determined to be AMR = 131.24 + 461.26Us1.27 (R2 = 0.948, p < 0.001) and the power value (1.27) of Us indicated high swimming efficiency. (3) Increased swimming speed led to increases in the tail beat frequency. (4) Swimming costs were calculated via rate of oxygen consumption and hydrodynamic modeling. Then, the drag coefficient of the crucian carp during swimming was calibrated (0.126–0.140), and the velocity at which anaerobic metabolism was initiated was estimated (0.52 m/s), via the new method described herein. This study adds to our understanding of the metabolic patterns of fish at different swimming speeds.

Locomotion of juvenile silver carp (Hypophthalmichthys molitrix) near the separation zone at the channel confluence

&lt;p&gt;Knowledge of locomotion of fish with significant rheotaxis at river confluences is critical for prediction of fish distribution at a river network. Recently, less silver carps observed in the Poyang Lake should be related to the hydrodynamic change at the confluence of the lake outlet and the Yangtze River. The operation of the Three Gorges Dam has largely changed the hydrodynamics at this confluence. Silver carp is one of the four major Chinese carps, and has significant rheotaxis. In this study, a series of laboratory experiments were conducted to figure out the behavioral responses of juvenile silver carps to hydrodynamics near the separation zone at the channel confluence. The separation zone at a river confluence is one of the main zones for carp habitat and feeding. The locomotion and trajectory of juvenile silver carps were recorded through infrared thermal imaging at the confluence flume. Flow velocity field near the separation zone was measured by a Particle Image Velocimetry (PIV) system. A total of 40 juvenile silver carps were released from the separation zone and swam to the upstream, among which 24 carps swam to the tributary and the other to the main channel. Almost all 24 carps moved along the beginning of the boundary of the separation zone near the corner where the flow shear was strong. It seems that instead of avoiding places with great vorticity, they preferentially chose the trajectory where the flow vorticity was large continuously. They increased the tail-beat frequency and decreased the tail-beat amplitude to maintain body stability when they encountered the flow with large vorticity. These results are beneficial for the regulation of upstream dams to adjust the hydrodynamics at the confluence and improve local ecology.&lt;/p&gt;

Nonlinear analysis of compliant robotic fish locomotion

Compliant robotic fish can achieve a better swimming performance than rigid-bodied robotic fish. Therefore, this article investigates the swimming behavior of the compliant robotic fish based on a new swimming model that combines the large-amplitude elongated-body theory with decoupled natural orthogonal complement matrices. The simulation reveals that the multi-order resonances are generated in tail-beat amplitude, forward speed, stride length, and transport efficiency when the compliant robotic fish is driven at the corresponding frequency. Moreover, the resonant effects demonstrate the nonlinear behaviors as the driving torque increases. A control strategy for resonance utilization is presented to improve the performance capabilities. The potential influence factors for resonant effects are also discussed, showing that the tail-generated hydrodynamic force significantly impacts the resonant effect. These nonlinear characteristics can provide important guidelines for the motion control of the compliant robotic fish.

Comprehensive Hydrodynamic Investigation of Zebrafish Tail Beats in a Microfluidic Device with a Shape Memory Alloy

The zebrafish is acknowledged as a reliable species of choices for biomechanical-related investigations. The definite quantification of the hydrodynamic flow physics caused by behavioral patterns, particularly in the zebrafish tail beat, is critical for a comprehensive understanding of food toxicity in this species, and it can be further interpreted for possible human responses. The zebrafish’s body size and swimming speed place it in the intermediate flow regime, where both viscous and inertial forces play significant roles in the fluid–structure interaction. This pilot work highlighted the design and development of a novel microfluidic device coupled with a shape memory alloy (SMA) actuator to immobilize the zebrafish within the observation region for hydrodynamic quantification of the tail-beating behavioral responses, which may be induced by the overdose of food additive exposure. This study significantly examined behavioral patterns of the zebrafish in early developmental stages, which, in turn, generated vortex circulation. The presented findings on the behavioral responses of the zebrafish through the hydrodynamic analysis provided a golden protocol to assess the zebrafish as an animal model for new drug discovery and development.

Effect of tail fin loss on swimming capability and tail beat frequency of juvenile black carp Mylopharyngodon piceus

Fin clipping is a common practice in fisheries management, and hatchery fish are often marked this way. In the wild, the tail (caudal) fin may be damaged or lost to predation or disease. Because the tail fin is important to fish swimming behavior and ability, this study was designed to examine the effects of partial and complete loss of the tail fin on the swimming ability of juvenile black carp Mylopharyngodon piceus. Swimming speed and tail beat frequency were measured for 3 groups (intact tail fin, partial tail fin, no tail fin) using a stepped velocity test conducted in a fish respirometer. We found that critical swimming speed (Ucrit) and burst speed (Uburst) decreased slightly in the partial fin group and significantly in the no fin group. In the group with no tail fin, Uburst decreased more than Ucrit, clearly reducing the ability to avoid predators. Moreover, mean tail beat frequency (TBFmean), Ucrit and Uburst all decreased slightly in the partial fin group and significantly in the no fin group. A decrease in tail beat force and TBF both reduce swimming capability. These findings contribute to developing our understanding of the relationship between fish tail fins and swimming.

Extreme temperature combined with hypoxia, affects swimming performance in brown trout (Salmo trutta)

Climate change is predicted to impact freshwater aquatic environments through changes to water temperature (Twater), river flow and eutrophication. Riverine habitats contain many economically and ecologically important fishes. One such group is the migratory salmonids, which are sensitive to warm Twater and low O2 (hypoxia). While several studies have investigated the independent effects of Twater and hypoxia on fish physiology, the combined effects of these stressors is less well known. Furthermore, no study has investigated the effects of Twater and O2 saturation levels within the range currently experienced by a salmonid species. Thus, the aim of this study was to investigate the simultaneous effects of Twater and O2 saturation level on the energetics and kinematics of steady-state swimming in brown trout, Salmo trutta. No effect of O2 saturation level (70 and 100% air saturation) on tail-beat kinematics was detected. Conversely, Twater (10, 14, 18 and 22°C) did affect tail-beat kinematics, but a trade-off between frequency (ftail) and amplitude (A, maximum tail excursion) maintained the Strouhal number (St = ftail• A/U, where U is swimming speed) within the theoretically most mechanically efficient range. Swimming oxygen consumption rate (${\dot{M}}_{{\mathsf{O}}_{\mathsf{2}}}$) and cost of transport increased with both U and Twater. The only effect of O2 saturation level was observed at the highest Twater (22°C) and fastest swimming speed (two speeds were used—0.6 and 0.8 m s−1). As the extremes of this study are consistent with current summer conditions in parts of UK waterways, our findings may indicate that S. trutta will be negatively impacted by the increased Twater and reduced O2 levels likely presented by anthropogenic climate change.

Tuna robotics: A high-frequency experimental platform exploring the performance space of swimming fishes

Tuna and related scombrid fishes are high-performance swimmers that often operate at high frequencies, especially during behaviors such as escaping from predators or catching prey. This contrasts with most fish-like robotic systems that typically operate at low frequencies (< 2 hertz). To explore the high-frequency fish swimming performance space, we designed and tested a new platform based on yellowfin tuna (Thunnus albacares) and Atlantic mackerel (Scomber scombrus). Body kinematics, speed, and power were measured at increasing tail beat frequencies to quantify swimming performance and to study flow fields generated by the tail. Experimental analyses of freely swimming tuna and mackerel allow comparison with the tuna-like robotic system. The Tunabot (255 millimeters long) can achieve a maximum tail beat frequency of 15 hertz, which corresponds to a swimming speed of 4.0 body lengths per second. Comparison of midline kinematics between scombrid fish and the Tunabot shows good agreement over a wide range of frequencies, with the biggest discrepancy occurring at the caudal fin, primarily due to the rigid propulsor used in the robotic model. As frequency increases, cost of transport (COT) follows a fish-like U-shaped response with a minimum at ~1.6 body lengths per second. The Tunabot has a range of ~9.1 kilometers if it swims at 0.4 meter per second or ~4.2 kilometers at 1.0 meter per second, assuming a 10–watt-hour battery pack. These results highlight the capabilities of high-frequency biological swimming and lay the foundation to explore a fish-like performance space for bio-inspired underwater vehicles.