Locomotion of free-swimming ghost knifefish: anal fin kinematics during four behaviors

The maneuverability demonstrated by the weakly electric ghost knifefish (Apteronotus albifrons) is a result of its highly flexible ribbon-like anal fin, which extends nearly three-quarters the length of its body and is composed of approximately 150 individual fin rays. To understand how movement of the anal fin controls locomotion we examined kinematics of the whole fin, as well as selected individual fin rays, during four locomotor behaviors executed by free-swimming ghost knifefish: forward swimming, backward swimming, heave (vertical) motion, and hovering. We used high-speed video (1000 fps) to examine the motion of the entire anal fin and we measured the three-dimensional curvature of four adjacent fin rays in the middle of the fin during each behavior to determine how individual fin rays bend along their length during swimming. Canonical discriminant analysis separated all four behaviors on anal fin kinematic variables and showed that forward and backward swimming behaviors contrasted the most: forward behaviors exhibited a large anterior wavelength and posterior amplitude while during backward locomotion the anal fin exhibited both a large posterior wavelength and anterior amplitude. Heave and hover behaviors were defined by similar kinematic variables; however, for each variable, the mean values for heave motions were generally greater than for hovering. Individual fin rays in the middle of the anal fin curved substantially along their length during swimming, and the magnitude of this curvature was nearly twice the previously measured maximum curvature for ray-finned fish fin rays during locomotion. Fin rays were often curved into the direction of motion, indicating active control of fin ray curvature, and not just passive bending in response to fluid loading.     

Disentangling the functional roles of morphology and motion in the swimming of fish

In fishes the shape of the body and the swimming mode generally are correlated. Slender-bodied fishes such as eels, lampreys, and many sharks tend to swim in the anguilliform mode, in which much of the body undulates at high amplitude. Fishes with broad tails and a narrow caudal peduncle, in contrast, tend to swim in the carangiform mode, in which the tail undulates at high amplitude. Such fishes also tend to have different wake structures. Carangiform swimmers generally produce two staggered vortices per tail beat and a strong downstream jet, while anguilliform swimmers produce a more complex wake, containing at least two pairs of vortices per tail beat and relatively little downstream flow. Are these differences a result of the different swimming modes or of the different body shapes, or both? Disentangling the functional roles requires a multipronged approach, using experiments on live fishes as well as computational simulations and physical models. We present experimental results from swimming eels (anguilliform), bluegill sunfish (carangiform), and rainbow trout (subcarangiform) that demonstrate differences in the wakes and in swimming performance. The swimming of mackerel and lamprey was also simulated computationally with realistic body shapes and both swimming modes: the normal carangiform mackerel and anguilliform lamprey, then an anguilliform mackerel and carangiform lamprey. The gross structure of simulated wakes (single versus double vortex row) depended strongly on Strouhal number, while body shape influenced the complexity of the vortex row, and the swimming mode had the weakest effect. Performance was affected even by small differences in the wakes: both experimental and computational results indicate that anguilliform swimmers are more efficient at lower swimming speeds, while carangiform swimmers are more efficient at high speed. At high Reynolds number, the lamprey-shaped swimmer produced a more complex wake than the mackerel-shaped swimmer, similar to the experimental results. Finally, we show results from a simple physical model of a flapping fin, using fins of different flexural stiffness. When actuated in the same way, fins of different stiffnesses propel themselves at different speeds with different kinematics. Future experimental and computational work will need to consider the mechanisms underlying production of the anguilliform and carangiform swimming modes, because anguilliform swimmers tend to be less stiff, in general, than are carangiform swimmers.     

Convergent evolution of locomotor morphology but not performance in gymnotiform swimmers

Convergent evolution of a novel locomotor strategy implies that a fitness benefit may be associated with the new gait. Opportunities to study this phenomenon are often constrained by a lack of transitional taxa, but teleost fishes offer examples of extant species across such evolutionary shifts in gait. For instance, one species from Osteoglossiformes and the entire order of Gymnotiformes independently evolved a novel gait, gymnotiform locomotion, where thrust is produced by the undulation of an elongate anal fin. Here, we investigate whether this convergence in gait is also associated with similarities in shape, burst swimming abilities, and/or steady‐swimming energetics. Specifically, we measured body and fin morphology of fish within Gymnotiformes and Osteoglossiformes, along with closely related Siluriformes and Cypriniformes, to examine the link between gymnotiform locomotion and morphology in a phylogenetic context. Second, we tested the burst swimming capabilities and oxygen consumption during endurance swimming of a subset of the same gymnotiform, osteoglossiform, and cypriniform species, including “transitional” Osteoglossiformes that exhibit intermediate gaits, to determine whether the evolution of this specialized gait is associated with a change in either of these performance metrics. Our results suggest that convergence on the gymnotiform gait is associated with morphological convergence, but does not constrain a fish's maximum sprinting speeds or their energetic demands during steady swimming.     

Bluegill Lepomis macrochirus synchronize pectoral fin motion and opercular pumping

The relative timing between operculum and pectoral fin motion was examined in swimming bluegill Lepomis macrochirus to determine if respiratory fluid flows from the operculum might have an effect on flow over the pectoral fin. Five bluegill were filmed swimming at speeds from 0·5 to 1·5 body (total) lengths s⁻¹. The timing of opercular pumping and pectoral fin beating was noted and analysed using circular statistics. Fish tended to ventilate their gills every second or third pectoral fin beat. While locomotion and ventilation had different frequencies, however, they were synchronized: fish maintained a consistent phase relationship between them. Thus, within pectoral fin beats when the operculum pumps, the jet consistently occurred during pectoral fin abduction, ending just after the fin was fully abducted and beginning adduction. Based on the distance between the opercular slit and the pectoral fin base, the jet was estimated to reach the fin during maximum abduction. Dye flow visualization confirmed this estimate, revealing that the opercular flow wraps around the base of the fin during peak abduction, when it is likely to have little hydrodynamic effect.     

Estimating fish swimming metrics and metabolic rates with accelerometers: the influence of sampling frequency

Accelerometry is growing in popularity for remotely measuring fish swimming metrics, but appropriate sampling frequencies for accurately measuring these metrics are not well studied. This research examined the influence of sampling frequency (1–25 Hz) with tri‐axial accelerometer biologgers on estimates of overall dynamic body acceleration (ODBA), tail‐beat frequency, swimming speed and metabolic rate of bonefish Albula vulpes in a swim‐tunnel respirometer and free‐swimming in a wetland mesocosm. In the swim tunnel, sampling frequencies of ≥ 5 Hz were sufficient to establish strong relationships between ODBA, swimming speed and metabolic rate. However, in free‐swimming bonefish, estimates of metabolic rate were more variable below 10 Hz. Sampling frequencies should be at least twice the maximum tail‐beat frequency to estimate this metric effectively, which is generally higher than those required to estimate ODBA, swimming speed and metabolic rate. While optimal sampling frequency probably varies among species due to tail‐beat frequency and swimming style, this study provides a reference point with a medium body‐sized sub‐carangiform teleost fish, enabling researchers to measure these metrics effectively and maximize study duration.     

Locomotor synergies in fish

The kinematic characteristics {f(v), A(v), w(v)} allow a first-approximation representation of locomotor synergies in the swimming of fish: f is the frequency of the transverse oscillations, A is the amplitude of the caudal fin sweep, w is the velocity of the locomotor wave, and v is the locomotion speed. The additional compared characteristics included the step length L(v) and the wavelength λ(v), where L ≡ vT is the distance covered by the fish during the period T ≡ 1/f, and λ ≡ wT. These kinematic characteristics were derived from video recordings of swimming in six fish species. Three of the species investigated belonged to the anguilliform type, while the three others belonged to the carangiform type. The constant value of the wavelength λ at all speeds v was the common feature of the two types. The anguilliform fish performed a oneparameter version of locomotion control: the locomotion speed v changed due to the change of the wave velocity w and the undulatory amplitude remained constant. The carangioid fish used a two-parameter version of control, with changes in both the wave velocity w and the amplitude of undulations of the body and tail fin.     

A Forced Damped Oscillation Framework for Undulatory Swimming Provides New Insights into How Propulsion Arises in Active and Passive Swimming

A fundamental issue in locomotion is to understand how muscle forcing produces apparently complex deformation kinematics leading to movement of animals like undulatory swimmers. The question of whether complicated muscle forcing is required to create the observed deformation kinematics is central to the understanding of how animals control movement. In this work, a forced damped oscillation framework is applied to a chain-link model for undulatory swimming to understand how forcing leads to deformation and movement. A unified understanding of swimming, caused by muscle contractions (“active” swimming) or by forces imparted by the surrounding fluid (“passive” swimming), is obtained. We show that the forcing triggers the first few deformation modes of the body, which in turn cause the translational motion. We show that relatively simple forcing patterns can trigger seemingly complex deformation kinematics that lead to movement. For given muscle activation, the forcing frequency relative to the natural frequency of the damped oscillator is important for the emergent deformation characteristics of the body. The proposed approach also leads to a qualitative understanding of optimal deformation kinematics for fast swimming. These results, based on a chain-link model of swimming, are confirmed by fully resolved computational fluid dynamics (CFD) simulations. Prior results from the literature on the optimal value of stiffness for maximum speed are explained.     

The locomotory function of the fins in the squid Loligo pealei

Kinematic data of high spatial and temporal resolution, acquired from image sequences of adult long-finned squid, Loligo pealei, during steady swimming in a flume, were used to examine the role of fins and the coordination between fin and jet propulsion in squid locomotion. Fin shape and body outlines were digitized and used to calculate fin wave speed, amplitude, frequency, angle of attack, body deformation, speed, and acceleration. L. pealei were observed to have two fin gait patterns with a transition at 1.4-1.8 mantle lengths per second (Lm s-1) marked by alternation between the two patterns. Fin motion in L. pealei exhibited characteristics of both traveling waves and flapping wings. At low speeds, fin motion was more wave-like; at high speeds, fin motion was more flap-like and was marked by regular periods during which the fins were wrapped tightly against the mantle. Fin cycle frequencies were dependent on swimming speed and gait, and obvious coordination between the fins and jet were observed. Fin wave speed, angle of attack, and body acceleration confirmed the role of fins in thrust production and revealed a role of fins at all swimming speeds by a transition from drag-based to lift-based thrust when fin wave speed dropped below swimming speed. Estimates of peak fin thrust were as high as 0.44-0.96 times peak jet thrust in steady swimming over the range of swimming speeds observed. Fin downstrokes generally contributed more to thrust than did upstrokes, especially at high speeds.     

Swimming Speed of Larval Snail Does Not Correlate with Size and Ciliary Beat Frequency

Many marine invertebrates have planktonic larvae with cilia used for both propulsion and capturing of food particles. Hence, changes in ciliary activity have implications for larval nutrition and ability to navigate the water column, which in turn affect survival and dispersal. Using high-speed high-resolution microvideography, we examined the relationship between swimming speed, velar arrangements, and ciliary beat frequency of freely swimming veliger larvae of the gastropod Crepidula fornicata over the course of larval development. Average swimming speed was greatest 6 days post hatching, suggesting a reduction in swimming speed towards settlement. At a given age, veliger larvae have highly variable speeds (0.8–4 body lengths s⁻¹) that are independent of shell size. Contrary to the hypothesis that an increase in ciliary beat frequency increases work done, and therefore speed, there was no significant correlation between swimming speed and ciliary beat frequency. Instead, there are significant correlations between swimming speed and visible area of the velar lobe, and distance between centroids of velum and larval shell. These observations suggest an alternative hypothesis that, instead of modifying ciliary beat frequency, larval C. fornicata modify swimming through adjustment of velum extension or orientation. The ability to adjust velum position could influence particle capture efficiency and fluid disturbance and help promote survival in the plankton.     

Kinematics of different types of locomotor movements in the deafferented rat

The kinematics of rat hindlimb movements were assessed and compared pre- and post-deafferentation during swimming, forelimb treadmill locomotion plus hindlimb swimming motion, and walking using all four limbs. All types of locomotion were characterized by an increase in the frequency of locomotor rhythm and reduced amplitude of motion at the hindlimb joints following deafferentation. The reduced change observed in the angle of the coxofemoral joint, indicative of a horizontal component in locomotor motion, was mainly brought about by less marked extension. This would confirm evidence indicating that increased load on the extremities, with its ensuing naturally-occurring afferent outflow, is accompanied by a reduced locomotor motion rate and a rise in the amplitude of the latter due to intensified extension of the limb. The increased forward carriage of the hind limb seen during the transition to four-legged locomotion persisted after deafferentation; this may be considered a sign of coordination amongst the limbs. Deafferentation led to a reduction in the MEG of muscle activity, which was found to be lowest in swimming and highest during walking. The role of the afferent inflow in shaping different types of locomotor motion is evaluated.A. A. Bogomolets Institute of Physiology, Academy of Sciences of the Ukrainian SSR, Kiev. Translated from Neirofiziologiya, Vol. 19, No. 4, pp. 520–525, July–August, 1987.     

The locomotory function of the fins in the squid Loligo pealei

Kinematic data of high spatial and temporal resolution, acquired from image sequences of adult long-finned squid, Loligo pealei, during steady swimming in a flume, were used to examine the role of fins and the coordination between fin and jet propulsion in squid locomotion. Fin shape and body outlines were digitized and used to calculate fin wave speed, amplitude, frequency, angle of attack, body deformation, speed, and acceleration. L. pealei were observed to have two fin gait patterns with a transition at 1.4-1.8 mantle lengths per second (L_m s^-1) marked by alternation between the two patterns. Fin motion in L. pealei exhibited characteristics of both traveling waves and flapping wings. At low speeds, fin motion was more wave-like; at high speeds, fin motion was more flap-like and was marked by regular periods during which the fins were wrapped tightly against the mantle. Fin cycle frequencies were dependent on swimming speed and gait, and obvious coordination between the fins and jet were observed. Fin wave speed, angle of attack, and body acceleration confirmed the role of fins in thrust production and revealed a role of fins at all swimming speeds by a transition from drag-based to lift-based thrust when fin wave speed dropped below swimming speed. Estimates of peak fin thrust were as high as 0.44-0.96 times peak jet thrust in steady swimming over the range of swimming speeds observed. Fin downstrokes generally contributed more to thrust than did upstrokes, especially at high speeds.     

Resolving Shifting Patterns of Muscle Energy Use in Swimming Fish

Muscle metabolism dominates the energy costs of locomotion. Although in vivo measures of muscle strain, activity and force can indicate mechanical function, similar muscle-level measures of energy use are challenging to obtain. Without this information locomotor systems are essentially a black box in terms of the distribution of metabolic energy. Although in situ measurements of muscle metabolism are not practical in multiple muscles, the rate of blood flow to skeletal muscle tissue can be used as a proxy for aerobic metabolism, allowing the cost of particular muscle functions to be estimated. Axial, undulatory swimming is one of the most common modes of vertebrate locomotion. In fish, segmented myotomal muscles are the primary power source, driving undulations of the body axis that transfer momentum to the water. Multiple fins and the associated fin muscles also contribute to thrust production, and stabilization and control of the swimming trajectory. We have used blood flow tracers in swimming rainbow trout (Oncorhynchus mykiss) to estimate the regional distribution of energy use across the myotomal and fin muscle groups to reveal the functional distribution of metabolic energy use within a swimming animal for the first time. Energy use by the myotomal muscle increased with speed to meet thrust requirements, particularly in posterior myotomes where muscle power outputs are greatest. At low speeds, there was high fin muscle energy use, consistent with active stability control. As speed increased, and fins were adducted, overall fin muscle energy use declined, except in the caudal fin muscles where active fin stiffening is required to maintain power transfer to the wake. The present data were obtained under steady-state conditions which rarely apply in natural, physical environments. This approach also has potential to reveal the mechanical factors that underlie changes in locomotor cost associated with movement through unsteady flow regimes.     

Is tilting behaviour at low swimming speeds unique to negatively buoyant fish? Observations on steelhead trout,Oncorhynchus mykiss,and bluegill,Lepomis macrochirus

When swimming at low speeds, steelhead trout and bluegill sunfish tilted the body at an angle to the mean swimming direction. Trout swam using continuous body/caudal fin undulation, with a positive (head-up) tilt angle ( 0 , degrees) that decreased with swimming speed ( u , cm s⁻¹) according to: 0 =(164±96).u^{(−1.14±0.41)} (regression coefficients; mean±2 s.e. ). Bluegill swimming gaits were more diverse and negative (head down) tilt angles were usual. Tilt angle was −3·0 ± 0.9° in pectoral fin swimming at speeds of approximately 0.2–1.7 body length s⁻¹ (Ls⁻¹; 3–24 cm s⁻¹), −4.5 ±2.6° during pectoral fin plus body/caudal fin swimming at 1·2–1·7 L s⁻¹ (17–24cm s⁻¹), and −5.0± 1.0° during continuous body/caudal fin swimming at 1.6 and 2.5 L s⁻¹ (22 and 35cm s⁻¹). At higher speeds, bluegill used burst-and-coast swimming for which the tilt angle was 0.1±0.6°. These observations suggest that tilting is a general phenomenon of low speed swimming at which stabilizers lose their effectiveness. Tilting is interpreted as an active compensatory mechanism associated with increased drag and concomitant increased propulsor velocities to provide better stabilizing forces. Increased drag associated with trimming also explains the well-known observation that the relationship between tail-beat frequency and swimming speed does not pass through the origin. Energy dissipated because of the drag increases at low swimming speeds is presumably smaller than that which would occur with unstable swimming.     

How small puffers (Teleostei: Tetraodontidae) swim

 The tetraodontiform swimming mode has recently attracted attention because puffers swim very steadily and, unlike most of the other median and paired fin (MPF) swimmers, use more than one pair of fins to propel themselves through the water. To date, only one study presenting data concerning the swimming kinematics of puffers has been published, and this study dealt only with two species of large body size. In the present study, the swimming kinematics of small puffers (<6 cm TL) Tetraodon schoutedeni is described and compared to the swimming kinematics of larger puffers and boxfish. The results show that, generally, the swimming kinematics of small puffers is similar to that of larger puffers. The main differences that were found are in the synchronization of dorsal and anal fin motion, and in the motion of the pectoral fins, which complete their adduction before the dorsal and anal fins do. Maximum fin beat frequency was 18.4 Hz, much faster than that of larger puffers. At slow and median swimming speeds, dorsal fin beat amplitude increases with swimming speed and then remains constant between median and fast swimming speeds. The results confirm previous findings that puffers swim extremely steadily. Most of the differences in swimming kinematics between large and small puffers can be attributed to the size differences, but the difference in fin synchronization should be further studied to be completely understood. Received: September 27, 2002 / Revised: January 7, 2003 / Accepted: February 6, 2003     

Coding conspecific identity and motion in the electric sense

Interactions among animals can result in complex sensory signals containing a variety of socially relevant information, including the number, identity, and relative motion of conspecifics. How the spatiotemporal properties of such evolving naturalistic signals are encoded is a key question in sensory neuroscience. Here, we present results from experiments and modeling that address this issue in the context of the electric sense, which combines the spatial aspects of vision and touch, with the temporal aspects of audition. Wave-type electric fish, such as the brown ghost knifefish, Apteronotus leptorhynchus, used in this study, are uniquely identified by the frequency of their electric organ discharge (EOD). Multiple beat frequencies arise from the superposition of the EODs of each fish. We record the natural electrical signals near the skin of a "receiving" fish that are produced by stationary and freely swimming conspecifics. Using spectral analysis, we find that the primary beats, and the secondary beats between them ("beats of beats"), can be greatly influenced by fish swimming; the resulting motion produces low-frequency envelopes that broaden all the beat peaks and reshape the "noise floor". We assess the consequences of this motion on sensory coding using a model electroreceptor. We show that the primary and secondary beats are encoded in the afferent spike train, but that motion acts to degrade this encoding. We also simulate the response of a realistic population of receptors, and find that it can encode the motion envelope well, primarily due to the receptors with lower firing rates. We discuss the implications of our results for the identification of conspecifics through specific beat frequencies and its possible hindrance by active swimming.     

Biological Inspiration: From Carangiform Fish to Multi-Joint Robotic Fish

This paper presents a novel approach to modelling carangiform fish-like swimming motion for multi-joint robotic fish so that they can obtain fish-like behaviours and mimic the body motion of carangiform fish. A given body motion function of fish swimming is firstly converted to a tail motion function which describes the tail motion relative to the head. Then, the tail motion function is discretized into a series of tail postures over time. Thirdly, a digital approximation method calculates the taming angles of joints in the tail to approximate each tail posture; and finally, these angles are grouped into a look-up table, or re-gressed to a time-dependent function, for practically controlling the tail motors in a multi-joint robotic fish. The paper made three contributions: tail motion relative to the head, an error function for digital approximation and regressing a look-up table for online optimization. To prove the feasibility of the proposed methodology, two basic swimming motion patterns, cruise straight and C-shape sharp turning, are modelled and implemented in our robotic fish. The experimental results show that the relative tail motion and the approximation error function are good choices and the proposed method is feasible.     

Age and serotonin effects on locomotion in marine trematode cercariae

The effect of serotonin solutions on the locomotor activity of cercariae with different swimming patterns, Cryptocotyle lingua and Himasthla elongate, was investigated during their lifespan using motion track analysis and a frame-by-frame count of behavioral elements. Serotonin caused a noticeable alteration of several locomotion parameters in both species studied, while the activity per se decreased significantly with age. In intermittently swimming C. lingua cercariae, serotonin induced an increase in the frequency of active swimming phases (spurts) without significant changes in the duration and velocity of the spurts themselves. In continuously swimming H. elongata cercariae, serotonin increased the number of stops during the first hour after the emission from the host mollusk under a constant average swimming velocity. Immunocytochemical visualization of serotonin revealed a decline in its level with age (time after emission) and different dynamics of this process in neurons located in the tail and body of C. lingua cercariae. The data are interpreted in the light of the modulatory role of serotonin known for other animals.     

Locomotion in hatchling leatherback turtles Dermochelys coriacea

Hatchling leatherback turtles can only swim forwards, and employ synchronized beating of the forelimbs whether swimming slowly or quickly. The hind limbs make no contribution to propulsion. Effectively, the hatchlings have two swimming speeds; subsurface and fast (30 cm s^-1) or surfaced and slow (8 cm s^-1). Intermediate velocities are transitory; the hatchlings were never seen to rest without movement, nor did they exhibit gliding of the type seen in green turtles. During fast ('vigorous') swimming, power is developed on both the upstroke and downstroke of the limb cycle. During slow swimming, power is only developed during the upstroke—a consequence of the orientation of the axis of limb beat which is opposite in direction to that of cheloniid sea turtles. Terrestrial locomotion is laboured and features an unstable gait which involves simultaneous movement of all four limbs and forward overbalancing during each limb cycle.     

Fish swimming stride by stride: speed limits and endurance

Summary Steadily swimming fish show a species-specific stride length and tail tip amplitude. These are constant over the entire speed range if expressed as a fraction of the body length. The speed of a fish equals the stride length times the tail beat frequency. We describe how maximum tail beat frequencies, and hence maximum swimming speeds, are related to temperature and body length.Maximum sustained swimming speeds, endurance during swimming at higher speeds, and maximum burst velocities of 27 species are compared. The rate of decline of endurance with increasing speed is either gradual or steep, with only a few cases in between Steady swimmers show the steepest decline.The published effects of temperature on endurance are not consistent.The effect of body size on the endurance curve could be investigated for two species. The maximum sustained speed decreases with increasing length, and the slope of the endurance curves steepens with increasing length with the same factor in both species. The maximum burst speed is 10 Ls^-1 on average.     

Mechanical properties of a bio-inspired robotic knifefish with an undulatory propulsor

South American electric knifefish are a leading model system within neurobiology. Recent efforts have focused on understanding their biomechanics and relating this to their neural processing strategies. Knifefish swim by means of an undulatory fin that runs most of the length of their body, affixed to the belly. Propelling themselves with this fin enables them to keep their body relatively straight while swimming, enabling straightforward robotic implementation with a rigid hull. In this study, we examined the basic properties of undulatory swimming through use of a robot that was similar in some key respects to the knifefish. As we varied critical fin kinematic variables such as frequency, amplitude, and wavelength of sinusoidal traveling waves, we measured the force generated by the robot when it swam against a stationary sensor, and its velocity while swimming freely within a flow tunnel system. Our results show that there is an optimal operational region in the fin's kinematic parameter space. The optimal actuation parameters found for the robotic knifefish are similar to previously observed parameters for the black ghost knifefish, Apteronotus albifrons. Finally, we used our experimental results to show how the force generated by the robotic fin can be decomposed into thrust and drag terms. Our findings are useful for future bio-inspired underwater vehicles as well as for understanding the mechanics of knifefish swimming.