Automated Reconstruction of Three-Dimensional Fish Motion,Forces, and Torques

Fish can move freely through the water column and make complex three-dimensional motions to explore their environment, escape or feed. Nevertheless, the majority of swimming studies is currently limited to two-dimensional analyses. Accurate experimental quantification of changes in body shape, position and orientation (swimming kinematics) in three dimensions is therefore essential to advance biomechanical research of fish swimming. Here, we present a validated method that automatically tracks a swimming fish in three dimensions from multi-camera high-speed video. We use an optimisation procedure to fit a parameterised, morphology-based fish model to each set of video images. This results in a time sequence of position, orientation and body curvature. We post-process this data to derive additional kinematic parameters (e.g. velocities, accelerations) and propose an inverse-dynamics method to compute the resultant forces and torques during swimming. The presented method for quantifying 3D fish motion paves the way for future analyses of swimming biomechanics.     

Bipedal walking and running with spring-like biarticular muscles

Compliant elements in the leg musculoskeletal system appear to be important not only for running but also for walking in human locomotion as shown in the energetics and kinematics studies of spring-mass model. While the spring-mass model assumes a whole leg as a linear spring, it is still not clear how the compliant elements of muscle-tendon systems behave in a human-like segmented leg structure. This study presents a minimalistic model of compliant leg structure that exploits dynamics of biarticular tension springs. In the proposed bipedal model, each leg consists of three leg segments with passive knee and ankle joints that are constrained by four linear tension springs. We found that biarticular arrangements of the springs that correspond to rectus femoris, biceps femoris and gastrocnemius in human legs provide self-stabilizing characteristics for both walking and running gaits. Through the experiments in simulation and a real-world robotic platform, we show how behavioral characteristics of the proposed model agree with basic patterns of human locomotion including joint kinematics and ground reaction force, which could not be explained in the previous models.     

BACTERIA‐INDUCED MOTILITY REDUCTION IN LINGULODINIUM POLYEDRUM (DINOPHYCEAE)1

Biotic factors that affect phytoplankton physiology and behavior are not well characterized but probably play a crucial role in regulating their population dynamics in nature. We document evidence that some marine bacteria can decrease the swimming speed of motile phytoplankton through the release of putative protease(s). Using the dinoflagellate Lingulodinium polyedrum (F. Stein) J. D. Dodge as a model system, we showed that the motility‐reducing components of bacterial‐algal cocultures were mostly heat labile, were of high molecular weight (>50 kDa), and could be partially neutralized by incubations with protease inhibitors. We further showed that additions of the purified protease pronase E decreased dinoflagellate swimming speed in a concentration‐dependent manner. We propose that motility can be used as a marker for dinoflagellate stress or general unhealthy status due to proteolytic bacteria, among other factors.     

A model for insect locomotion in the horizontal plane: Feedforward activation of fast muscles, stability, and robustness

We develop a neuromechanical model for running insects that includes a simplified hexapedal leg geometry with agonist-antagonist muscle pairs actuating each leg joint. Restricting to dynamics in the horizontal plane and neglecting leg masses, we reduce the model to three degrees of freedom describing translational and yawing motions of the body. Muscles are driven by stylized action potentials characteristic of fast motoneurons, and modeled using an activation function and nonlinear length and shortening velocity dependence. Parameter values are based on measurements from depressor muscles and observations of kinematics and dynamics of the cockroach Blaberus discoidalis; in particular, motoneuronal inputs and muscle force levels are chosen to approximately achieve joint torques that are consistent with measured ground reaction forces. We show that the model has stable double-tripod gaits over the animal's speed range, that its dynamics at preferred speeds matches those observed, and that it maintains stable gaits, with low frequency yaw deviations, when subject to random perturbations in foot touchdown and lift-off timing and action potential input timing. We explain this in terms of the low-dimensional dynamics.     

A bipedal compliant walking model generates periodic gait cycles with realistic swing dynamics

A simple spring mechanics model can capture the dynamics of the center of mass (CoM) during human walking, which is coordinated by multiple joints. This simple spring model, however, only describes the CoM during the stance phase, and the mechanics involved in the bipedality of the human gait are limited. In this study, a bipedal spring walking model was proposed to demonstrate the dynamics of bipedal walking, including swing dynamics followed by the step-to-step transition. The model consists of two springs with different stiffnesses and rest lengths representing the stance leg and swing leg. One end of each spring has a foot mass, and the other end is attached to the body mass. To induce a forward swing that matches the gait phase, a torsional hip joint spring was introduced at each leg. To reflect the active knee flexion for foot clearance, the rest length of the swing leg was set shorter than that of the stance leg, generating a discrete elastic restoring force. The number of model parameters was reduced by introducing dependencies among stiffness parameters. The proposed model generates periodic gaits with dynamics-driven step-to-step transitions and realistic swing dynamics. While preserving the mimicry of the CoM and ground reaction force (GRF) data at various gait speeds, the proposed model emulated the kinematics of the swing leg. This result implies that the dynamics of human walking generated by the actuations of multiple body segments is describable by a simple spring mechanics.     

Stable walking with asymmetric legs

Asymmetric leg function is often an undesired side-effect in artificial legged systems and may reflect functional deficits or variations in the mechanical construction. It can also be found in legged locomotion in humans and animals such as after an accident or in specific gait patterns. So far, it is not clear to what extent differences in the leg function of contralateral limbs can be tolerated during walking or running. Here, we address this issue using a bipedal spring-mass model for simulating walking with compliant legs. With the help of the model, we show that considerable differences between contralateral legs can be tolerated and may even provide advantages to the robustness of the system dynamics. A better understanding of the mechanisms and potential benefits of asymmetric leg operation may help to guide the development of artificial limbs or the design novel therapeutic concepts and rehabilitation strategies.     

Muscle function in animal movement: passive mechanical properties of leech muscle

We investigated passive properties of leech body wall as part of a larger project to understand better mechanisms that control locomotion and to establish mathematical models that predict such dynamical behavior. In tests of length-tension relationships in 2-segment-long preparations of body wall through step-stretch manipulations (step size = 1 mm), we discovered that these relationships are nonlinear, with significant hysteresis, even for the relatively small changes in length that occur during swimming. We developed a mathematical model comprising three nonlinear springs, two in series with nonlinear dashpots that describe well the tension statics and dynamics for step-stretch experiments. This model suggested that body wall dynamics are slow enough to be neglected when predicting the tension generated by imposed sinusoidal length changes (about ±10% of nominal) at 1–3 Hz, mimicking swimming. We derived a static model, comprising one nonlinear spring, which predicts sinusoidal data accurately, even when preparations were exposed to serotonin (0.1–10 μM). Preparations bathed in saline-serotonin had significantly reduced steady-state and peak tensions, without alterations in tension dynamics. Anesthetizing preparations (8% ethanol) reduced body wall tension by 77%, indicating that passive tension in the obliquely striated longitudinal muscles of leeches results primarily from a resting tonus.     

Experimental Studies and Dynamics Modeling Analysis of the Swimming and Diving of Whirligig Beetles (Coleoptera: Gyrinidae)

Whirligig beetles (Coleoptera, Gyrinidae) can fly through the air, swiftly swim on the surface of water, and quickly dive across the air-water interface. The propulsive efficiency of the species is believed to be one of the highest measured for a thrust generating apparatus within the animal kingdom. The goals of this research were to understand the distinctive biological mechanisms that allow the beetles to swim and dive, while searching for potential bio-inspired robotics applications. Through static and dynamic measurements obtained using a combination of microscopy and high-speed imaging, parameters associated with the morphology and beating kinematics of the whirligig beetle''s legs in swimming and diving were obtained. Using data obtained from these experiments, dynamics models of both swimming and diving were developed. Through analysis of simulations conducted using these models it was possible to determine several key principles associated with the swimming and diving processes. First, we determined that curved swimming trajectories were more energy efficient than linear trajectories, which explains why they are more often observed in nature. Second, we concluded that the hind legs were able to propel the beetle farther than the middle legs, and also that the hind legs were able to generate a larger angular velocity than the middle legs. However, analysis of circular swimming trajectories showed that the middle legs were important in maintaining stable trajectories, and thus were necessary for steering. Finally, we discovered that in order for the beetle to transition from swimming to diving, the legs must change the plane in which they beat, which provides the force required to alter the tilt angle of the body necessary to break the surface tension of water. We have further examined how the principles learned from this study may be applied to the design of bio-inspired swimming/diving robots.     

Patterns of setal numbers conserved during early development of swimming legs of Copepoda (Crustacea)

During swimming leg development, the number of setae present on the exopod and endopod of the bilobed bud, the transformed swimming leg with 1-segmented rami and the swimming leg with 2-segmented rami of copepods is analysed. For swimming leg 1, the most frequent number of setae on the presumptive rami of the bilobed bud is found at a higher percentage among copepod species than the most frequent number of setae for either the transformed swimming leg with 1-segmented rami or the swimming leg with 2-segmented rami. However, for swimming legs 2–4 the most frequent number of setae for the the transformed swimming leg with 1-segmented rami is found at a higher percentage of species than that on either the bilobed bud or the swimming leg with 2-segmented rami. Thus, in the cases of swimming legs 2–4, species with different numbers of setae on the presumptive exopod and endopod of the bud bilobed bud develop the same number of setae on the rami of the transformed swimming leg with 1-segmented rami. Increasing the number of species analysed is expected to make more robust the hypothesis that the number of setae on the transformed swimming leg with 1-segmented rami is conserved relative to the number of setae on the bilobed bud.     

Effect of leg kick on active drag in front-crawl swimming: Comparison of whole stroke and arms-only stroke during front-crawl and the streamlined position

The purpose of this study was to examine the effect of leg kick on the resistance force in front-crawl swimming. The active drag in front-crawl swimming with and without leg motion was evaluated using measured values of residual thrust (MRT method) and compared with the passive drag of the streamlined position (SP) for the same swimmers. Seven male competitive swimmers participated in this study, and the testing was conducted in a swimming flume. Each swimmer performed front-crawl under two conditions: using arms and legs (whole stroke: WS) and using arms only (arms-only stroke: AS). Active drag and passive drag were measured at swimming velocities of 1.1 and 1.3 m s⁻¹ using load cells connected to the swimmer via wires. We calculated a drag coefficient to compare the resistances of the WS, AS and SP at each velocity. For both the WS and AS at both swimming velocities, active drag coefficient was found to be about 1.6–1.9 times larger than that in passive conditions. In contrast, although leg movement did not cause a difference in drag coefficient for front-crawl swimming, there was a large effect size (d = 1.43) at 1.3 m s⁻¹. Therefore, although upper and lower limb movements increase resistance compared to the passive condition, the effect of leg kick on drag may depend on swimming velocity.     

鲢幼鱼通过水流速度障碍的模拟

鱼类能否通过水流速度障碍直接影响过鱼设施的过鱼效果。利用计算机技术,综合水力因素、鱼类行为、地理特征及环境因子,展开鱼类通过水流速度障碍的模拟,有助于过鱼设施的优化设计。以国外涵洞式鱼道模拟软件Fish Xing为切入点,结合主要模块和关键因子,对我国特有鱼类鲢幼鱼进行模拟,得到鲢通过不同水流速度障碍的成功率;对比鲢在物理模型中的游泳表现,从模型主要模块和影响鱼类游泳表现的关键因子角度,分析影响鱼类通过水流速度障碍模拟的因素。结果表明,Fish Xing软件不能精确模拟鲢通过水流速度障碍的表现。分析表明,该软件在地理要素、管道特征和水力信息等参数方面具备独特的优势,但对我国鱼类有一定局限性,主要体现在鱼类的生物学信息如鱼类游泳特征等方面存在不足;进行鱼过障碍的模拟需要深入研究目标鱼类的生理特征、游泳能力及其与水力环境因子的响应关系。     

Leg rings impact the diving performance of a foot-propelled diver

Leg rings are frequently used to mark aquatic birds in order to identify individuals, and study population dynamics and migration patterns, with the proviso being that the rings should not affect the birds. The effects of tags and rings are of particular interest in diving birds because any change in body shape could impact swimming efficiency and costs, as water is almost a thousand times denser than air. We attached tri-axial accelerometers to both ringed and unringed breeding Imperial Shags Leucocarbo atriceps to assess dive performance based on descent angle, descent rate, power stroke rate, power stroke peak acceleration amplitude and Vectorial Dynamic Body Acceleration (VeDBA) as a proxy for energy expenditure. Ringed birds, especially females, had a higher foot-stroke amplitude than unringed animals. In addition, the overall efficiency of the ringed individuals, as expressed by the descent rate per unit VeDBA, was compromised (by 3.5% in females and 4.3% in males) compared with unringed birds. We conclude that leg rings change the diving performance of Imperial Shags, although the effect is small and may not affect reproductive success. However, given that birds are typically ringed for life, we urge researchers to be particularly careful about the potential cumulative effect of attaching leg rings to foot-propelled diving species.     

A simulation study of the dynamics of a driven filament in an Aristotelian fluid

We describe a method, based on techniques used in molecular dynamics, for simulating the inertialess dynamics of an elastic filament immersed in a fluid. The model is used to study the "one-armed swimmer". That is, a flexible appendage externally perturbed at one extremity. For small-amplitude motion our simulations confirm theoretical predictions that, for a filament of given length and stiffness, there is a driving frequency that is optimal for both speed and efficiency. However, we find that to calculate absolute values of the swimming speed we need to slightly modify existing theoretical approaches. For the more relevant case of large-amplitude motion we find that while the basic picture remains the same, the dependence of the swimming speed on both frequency and amplitude is substantially modified. For large-amplitudes we show that the one-armed swimmer is comparatively neither inefficient nor slow. This begs the question, why are there little or no one-armed swimmers in nature?     

Feedback control strategies for spatial navigation revealed by dynamic modelling of learning in the Morris water maze

The Morris water maze is an experimental procedure in which animals learn to escape swimming in a pool using environmental cues. Despite its success in neuroscience and psychology for studying spatial learning and memory, the exact mnemonic and navigational demands of the task are not well understood. Here, we provide a mathematical model of rat swimming dynamics on a behavioural level. The model consists of a random walk, a heading change and a feedback control component in which learning is reflected in parameter changes of the feedback mechanism. The simplicity of the model renders it accessible and useful for analysis of experiments in which swimming paths are recorded. Here, we used the model to analyse an experiment in which rats were trained to find the platform with either three or one extramaze cue. Results indicate that the 3-cues group employs stronger feedback relying only on the actual visual input, whereas the 1-cue group employs weaker feedback relying to some extent on memory. Because the model parameters are linked to neurological processes, identifying different parameter values suggests the activation of different neuronal pathways.     

Toward Fast and Efficient Mobility in Aquatic Environment: A Robot with Compliant Swimming Appendages Inspired by a Water Beetle

Water beetles are proficient drag-powered swimmers,with oar-like legs.Inspired by this mechamsm,here we propose a miniature robot,with mobility provided by a pair of legs with swimming appendages.The robot has optimized linkage structure to maximize the stroke angle,which is actuated by a single DC motor with a series of gears and a spring.A simplified swimming appendage model is proposed to calculate the deflection due to the applied drag force,and is compared with simulated data using COMSOL Multiphysics.Also,the swimming appendages are optimized by considering their locations on the legs using two fitness functions,and six different configurations are selected.We investigate the performance of the robot with various types of appendage using a high-speed camera,and motion capture cameras.The robot with the proposed configuration exhibits fast and efficient movement compared with other robots.In addition,the locomotion of the robot is analyzed by considering its dynamics,and compared with that of a water boatman (Corixidae).     

A Computational Model of the Fluid Dynamics of Undulatory and Flagellar Swimming

We present a mathematical model and numerical method designedto study the fluid dynamics of swimming organisms. The fullNavier— Stokes equations are solved in a domain of fluidwithin which an organism undergoing time—dependent motionsis immersed. Of interest are both the dynamics of a single organismand the relationship of its morphology to its motility properties,as well as the collective hydrodynamic interactions of groupsof swimmers with each other and their environment. Biologicalapplications include spermatozoa motility in the reproductivetract, swimming of non-smooth filaments, and collective swimmingof algal cells.     

Ants swimming in pitcher plants: kinematics of aquatic and terrestrial locomotion in Camponotus schmitzi

Camponotus schmitzi ants live in symbiosis with the Bornean pitcher plant Nepenthes bicalcarata. Unique among ants, the workers regularly dive and swim in the pitcher's digestive fluid to forage for food. High-speed motion analysis revealed that C.?schmitzi ants swim at the surface with all legs submerged, with an alternating tripod pattern. Compared to running, swimming involves lower stepping frequencies and larger phase delays within the legs of each tripod. Swimming ants move front and middle legs faster and keep them more extended during the power stroke than during the return stroke. Thrust estimates calculated from three-dimensional leg kinematics using a blade-element approach confirmed that forward propulsion is mainly achieved by the front and middle legs. The hind legs move much less, suggesting that they mainly serve for steering. Experiments with tethered C.?schmitzi ants showed that characteristic swimming movements can be triggered by submersion in water. This reaction was absent in another Camponotus species investigated. Our study demonstrates how insects can use the same locomotory system and similar gait patterns for moving on land and in water. We discuss insect adaptations for aquatic/amphibious lifestyles and the special adaptations of C.?schmitzi to living on an insect-trapping pitcher plant.     

Dynamics of filaments: modelling the dynamics of driven microfilaments

We describe a method for simulating the inertialess dynamics of a flexible filament immersed in a fluid. Typically, this regime is appropriate for filaments a few micrometres or less in size (flagella that propel micro-organisms for example). We apply the model to two systems; a filament that is wiggled at one end and planar swimming motion characteristic of simple spermatozoa. For the former we find qualitative agreement with theory. The shape is determined by a balance between bending and viscous forces and there is an optimal balance that maximizes the propulsion generated by this mechanism. Quantitatively we find less satisfactory agreement. For the spermatozoa, assuming a relatively naive bending mechanism in the form of a travelling force quadrupole wave, the model generates waveforms in very good agreement with experiment. This is only true, however, if the bending forces acting on the filament are large compared with the viscous forces. Experimental measurements of the tail stiffness imply this should not be the case. We discuss the implications of this observation in the context of the sperm's swimming mechanism.     

On the aperiodic locomotor behavior of Halobacterium salinarium under periodic light stimuli

Two long time series of swimming intervals of a bacterium inverting its motion under periodic light pulses are analysed. The associated next-period plots reveal, through their filiform structure, that the underlying dynamics are low-dimensional. Using recently described properties of such dynamics, a simple second-order black-box model for the swimming intervals is derived and validated. The model reinforces the conjecture that this bacterium is endowed with an oscillator controlling the switching of the flagellar motor.