Biomimetic and live medusae reveal the mechanistic advantages of a flexible bell margin

Jelly-Z: swimming performance and analysis of twisted and coiled polymer (TCP) actuated jellyfish soft robot

Monitoring, sensing, and exploration of over 70% of the Earth's surface that is covered with water is permitted through the deployment of underwater bioinspired robots without affecting the natural habitat. To create a soft robot actuated with soft polymeric actuators, this paper describes the development of a lightweight jellyfish-inspired swimming robot, which achieves a maximum vertical swimming speed of 7.3 mm/s (0.05 body length/s) and is characterized by a simple design. The robot, named Jelly-Z, utilizes a contraction-expansion mechanism for swimming similar to the motion of a Moon jellyfish. The objective of this paper is to understand the behavior of soft silicone structure actuated by novel self-coiled polymer muscles in an underwater environment by varying stimuli and investigate the associated vortex for swimming like a jellyfish. To better understand the characteristics of this motion, simplified Fluid-structure simulation, and particle image velocimetry (PIV) tests were conducted to study the wake structure from the robot's bell margin. The thrust generated by the robot was also characterized with a force sensor to ascertain the force and cost of transport (COT) at different input currents. Jelly-Z is the first robot that utilized twisted and coiled polymer fishing line (TCPFL) actuators for articulation of the bell and showed successful swimming operations. Here, a thorough investigation on swimming characteristics in an underwater setting is presented theoretically and experimentally. We found swimming metrics of the robot are comparable with other jellyfish-inspired robots that have utilized different actuation mechanisms, but the actuators used here are scalable and can be made in-house relatively easily, hence paving way for further advancements into the use of these actuators.

Hopscotching jellyfish: combining different duty cycle kinematics can lead to enhanced swimming performance

Jellyfish (Medusozoa) have been deemed the most energy-efficient animals in the world. Their bell morphology and relatively simple nervous systems make them attractive to robotocists. Although, the science community has devoted much attention to understanding their swimming performance, there is still much to be learned about the jet propulsive locomotive gait displayed by prolate jellyfish. Traditionally, computational scientists have assumed uniform duty cycle kinematics when computationally modeling jellyfish locomotion. In this study we used fluid-structure interaction modeling to determine possible enhancements in performance from shuffling different duty cycles together across multiple Reynolds numbers and contraction frequencies. Increases in speed and reductions in cost of transport were observed as high as 80% and 50%, respectively. Generally, the net effects were greater for cases involving lower contraction frequencies. Overall, robust duty cycle combinations were determined that led to enhanced or impeded performance.

Cool your jets: biological jet propulsion in marine invertebrates

Pulsatile jet propulsion is a common swimming mode used by a diverse array of aquatic taxa from chordates to cnidarians. This mode of locomotion has interested both biologists and engineers for over a century. A central issue to understanding the important features of jet-propelling animals is to determine how the animal interacts with the surrounding fluid. Much of our knowledge of aquatic jet propulsion has come from simple theoretical approximations of both propulsive and resistive forces. Although these models and basic kinematic measurements have contributed greatly, they alone cannot provide the detailed information needed for a comprehensive, mechanistic overview of how jet propulsion functions across multiple taxa, size scales and through development. However, more recently, novel experimental tools such as high-speed 2D and 3D particle image velocimetry have permitted detailed quantification of the fluid dynamics of aquatic jet propulsion. Here, we provide a comparative analysis of a variety of parameters such as efficiency, kinematics and jet parameters, and review how they can aid our understanding of the principles of aquatic jet propulsion. Research on disparate taxa allows comparison of the similarities and differences between them and contributes to a more robust understanding of aquatic jet propulsion.

Metachronal motion across scales: current challenges and future directions

Metachronal motion is used across a wide range of organisms for a diverse set of functions. However, despite its ubiquity, analysis of this behavior has been difficult to generalize across systems. Here we provide an overview of known commonalities and differences between systems that use metachrony to generate fluid flow. We also discuss strategies for standardizing terminology and defining future investigative directions that are analogous to other established subfields of biomechanics. Lastly, we outline key challenges that are common to many metachronal systems, opportunities that have arisen due to the advent of new technology (both experimental and computational), and next steps for community development and collaboration across the nascent network of metachronal researchers.

Neuromechanical wave resonance in jellyfish swimming

For organisms to have robust locomotion, their neuromuscular organization must adapt to constantly changing environments. In jellyfish, swimming robustness emerges when marginal pacemakers fire action potentials throughout the bell's motor nerve net, which signals the musculature to contract. The speed of the muscle activation wave is dictated by the passage times of the action potentials. However, passive elastic material properties also influence the emergent kinematics, with time scales independent of neuromuscular organization. In this multimodal study, we examine the interplay between these two time scales during turning. A three-dimensional computational fluid-structure interaction model of a jellyfish was developed to determine the resulting emergent kinematics, using bidirectional muscular activation waves to actuate the bell rim. Activation wave speeds near the material wave speed yielded successful turns, with a 76-fold difference in turning rate between the best and worst performers. Hyperextension of the margin occurred only at activation wave speeds near the material wave speed, suggesting resonance. This hyperextension resulted in a 34-fold asymmetry in the circulation of the vortex ring between the inside and outside of the turn. Experimental recording of the activation speed confirmed that jellyfish actuate within this range, and flow visualization using particle image velocimetry validated the corresponding fluid dynamics of the numerical model. This suggests that neuromechanical wave resonance plays an important role in the robustness of an organism's locomotory system and presents an undiscovered constraint on the evolution of flexible organisms. Understanding these dynamics is essential for developing actuators in soft body robotics and bioengineered pumps.

The most efficient metazoan swimmer creates a 'virtual wall' to enhance performance

It has been well documented that animals (and machines) swimming or flying near a solid boundary get a boost in performance. This ground effect is often modelled as an interaction between a mirrored pair of vortices represented by a true vortex and an opposite sign 'virtual vortex' on the other side of the wall. However, most animals do not swim near solid surfaces and thus near body vortex-vortex interactions in open-water swimmers have been poorly investigated. In this study, we examine the most energetically efficient metazoan swimmer known to date, the jellyfish Aurelia aurita, to elucidate the role that vortex interactions can play in animals that swim away from solid boundaries. We used high-speed video tracking, laser-based digital particle image velocimetry (dPIV) and an algorithm for extracting pressure fields from flow velocity vectors to quantify swimming performance and the effect of near body vortex-vortex interactions. Here, we show that a vortex ring (stopping vortex), created underneath the animal during the previous swim cycle, is critical for increasing propulsive performance. This well-positioned stopping vortex acts in the same way as a virtual vortex during wall-effect performance enhancement, by helping converge fluid at the underside of the propulsive surface and generating significantly higher pressures which result in greater thrust. These findings advocate that jellyfish can generate a wall-effect boost in open water by creating what amounts to a 'virtual wall' between two real, opposite sign vortex rings. This explains the significant propulsive advantage jellyfish possess over other metazoans and represents important implications for bio-engineered propulsion systems.

The Hydrodynamics of Jellyfish Swimming

Jellyfish have provided insight into important components of animal propulsion, such as suction thrust, passive energy recapture, vortex wall effects, and the rotational mechanics of turning. These traits are critically important to jellyfish because they must propel themselves despite severe limitations on force production imposed by rudimentary cnidarian muscular structures. Consequently, jellyfish swimming can occur only by careful orchestration of fluid interactions. Yet these mechanics may be more broadly instructive because they also characterize processes shared with other animal swimmers, whose structural and neurological complexity can obscure these interactions. In comparison with other animal models, the structural simplicity, comparative energetic efficiency, and ease of use in laboratory experimentation allow jellyfish to serve as favorable test subjects for exploration of the hydrodynamic bases of animal propulsion. These same attributes also make jellyfish valuable models for insight into biomimetic or bioinspired engineeringof swimming vehicles. Here, we review advances in understanding of propulsive mechanics derived from jellyfish models as a pathway toward the application of animal mechanics to vehicle designs.

The role of suction thrust in the metachronal paddles of swimming invertebrates

An abundance of swimming animals have converged upon a common swimming strategy using multiple propulsors coordinated as metachronal waves. The shared kinematics suggest that even morphologically and systematically diverse animals use similar fluid dynamic relationships to generate swimming thrust. We quantified the kinematics and hydrodynamics of a diverse group of small swimming animals who use multiple propulsors, e.g. limbs or ctenes, which move with antiplectic metachronal waves to generate thrust. Here we show that even at these relatively small scales the bending movements of limbs and ctenes conform to the patterns observed for much larger swimming animals. We show that, like other swimming animals, the propulsors of these metachronal swimmers rely on generating negative pressure along their surfaces to generate forward thrust (i.e., suction thrust). Relying on negative pressure, as opposed to high pushing pressure, facilitates metachronal waves and enables these swimmers to exploit readily produced hydrodynamic structures. Understanding the role of negative pressure fields in metachronal swimmers may provide clues about the hydrodynamic traits shared by swimming and flying animals.

A novel cylindrical overlap-and-fling mechanism used by sea butterflies

The clap-and-fling mechanism is a well-studied, unsteady lift generation mechanism widely used by flying insects and is considered obligatory for tiny insects flying at low to intermediate Reynolds numbers, Re However, some aquatic zooplankters including some pteropod (i.e. sea butterfly) and heteropod species swimming at low to intermediate Re also use the clap-and-fling mechanism. These marine snails have extremely flexible, actively deformed, muscular wings which they flap reciprocally to create propulsive force, and these wings may enable novel lift generation mechanisms not available to insects, which have less flexible, passively deformed wings. Using high-speed stereophotogrammetry and micro-particle image velocimetry, we describe a novel cylindrical overlap-and-fling mechanism used by the pteropod species Cuvierina atlantica In this maneuver, the pteropod's wingtips overlap at the end of each half-stroke to sequentially form a downward-opening cone, a cylinder and an upward-opening cone. The transition from downward-opening cone to cylinder produces a downward-directed jet at the trailing edges. Similarly, the transition from cylinder to upward-opening cone produces downward flow into the gap between the wings, a leading edge vortex ring and a corresponding sharp increase in swimming speed. The ability of this pteropod species to perform the cylindrical overlap-and-fling maneuver twice during each stroke is enabled by its slender body and highly flexible wings. The cylindrical overlap-and-fling mechanism observed here may inspire the design of new soft robotic aquatic vehicles incorporating highly flexible propulsors to take advantage of this novel lift generation technique.

Enhanced flight performance in non-uniformly flexible wings

The flexibility of biological propulsors such as wings and fins is believed to contribute to the higher performance of flying and swimming animals compared with their engineered peers. Flexibility seems to follow a universal design rule that induces bending patterns at about one-third from the distal tip of the propulsor’s span. However, the aerodynamic mechanisms that shaped this convergent design and the potential improvement in performance are not well understood. Here, we analyse the effect of heterogeneous flexibility on the flight performance (range and descent angle) of passively tumbling wings. Using experiments, numerical simulations, and scaling analysis, we demonstrate that spanwise tip flexibility that follows this empirical rule leads to improved flight performance. Improvement in flight range seems to be related to flutter-induced drag reduction. This mechanism is independent of the wing’s auto-rotation and represents a more general trait of wings with non-uniform tip flexibility.

Fluid and Predator-Prey Interactions of Scyphomedusae Fed Calanoid Copepods

The feeding current of scyphomedusae entrains and transports surrounding fluids and prey through trailing tentacles to initiate encounters with prey. After contact, most prey are retained for ingestion. However, the probability that a contact will occur depends on several factors including capture surface morphology, prey size and behavior. We examined how hydrodynamics, capture surface morphology and prey behavior affect the capture probability of copepods. To do this, we documented medusa-copepod interactions of four species of scyphomedusae (two semeostomes and two rhizostomes) possessing different capture surface morphologies. We tracked the movement and behavior of entrained copepods throughout the feeding process to quantify prey behavior effects upon capture efficiency (# captures/# encounters). The feeding currents generated by all the medusan species generated fluid shear deformation rates well above the detection limits of copepods. Despite strong hydrodynamic signals, copepod behavior was highly variable and only 58% of the copepods reacted to entrainment within feeding currents. Furthermore, copepod behavior (categorized as no reaction, escape jump or adjustment jump) did not significantly affect the capture efficiency. The scale and complexity of the feeding current generated by scyphomedusae may help explain the poor ability of copepods to avoid capture.

From single neurons to behavior in the jellyfish Aurelia aurita

Jellyfish nerve nets provide insight into the origins of nervous systems, as both their taxonomic position and their evolutionary age imply that jellyfish resemble some of the earliest neuron-bearing, actively-swimming animals. Here, we develop the first neuronal network model for the nerve nets of jellyfish. Specifically, we focus on the moon jelly Aurelia aurita and the control of its energy-efficient swimming motion. The proposed single neuron model disentangles the contributions of different currents to a spike. The network model identifies factors ensuring non-pathological activity and suggests an optimization for the transmission of signals. After modeling the jellyfish's muscle system and its bell in a hydrodynamic environment, we explore the swimming elicited by neural activity. We find that different delays between nerve net activations lead to well-controlled, differently directed movements. Our model bridges the scales from single neurons to behavior, allowing for a comprehensive understanding of jellyfish neural control of locomotion.

Hydrodynamics of Vortex Generation during Bell Contraction by the Hydromedusa Eutonina indicans (Romanes, 1876)

Swimming bell kinematics and hydrodynamic wake structures were documented during multiple pulsation cycles of a Eutonina indicans (Romanes, 1876) medusa swimming in a predominantly linear path. Bell contractions produced pairs of vortex rings with opposite rotational sense. Analyses of the momentum flux in these wake structures demonstrated that vortex dynamics related directly to variations in the medusa swimming speed. Furthermore, a bulk of the momentum flux in the wake was concentrated spatially at the interfaces between oppositely rotating vortices rings. Similar thrust-producing wake structures have been described in models of fish swimming, which posit vortex rings as vehicles for energy transport from locations of body bending to regions where interacting pairs of opposite-sign vortex rings accelerate the flow into linear propulsive jets. These findings support efforts toward soft robotic biomimetic propulsion.

A ctenophore (comb jelly) employs vortex rebound dynamics and outperforms other gelatinous swimmers

Gelatinous zooplankton exhibit a wide range of propulsive swimming modes. One of the most energetically efficient is the rowing behaviour exhibited by many species of schyphomedusae, which employ vortex interactions to achieve this result. Ctenophores (comb jellies) typically use a slow swimming, cilia-based mode of propulsion. However, species within the genus Ocyropsis have developed an additional propulsive strategy of rowing the lobes, which are normally used for feeding, in order to rapidly escape from predators. In this study, we used high-speed digital particle image velocimetry to examine the kinematics and fluid dynamics of this rarely studied propulsive mechanism. This mechanism allows Ocyropsis to achieve size-adjusted speeds that are nearly double those of other large gelatinous swimmers. The investigation of the fluid dynamic basis of this escape mode reveals novel vortex interactions that have not previously been described for other biological propulsion systems. The arrangement of vortices during escape swimming produces a similar configuration and impact as that of the well-studied 'vortex rebound' phenomenon which occurs when a vortex ring approaches a solid wall. These results extend our understanding of how animals use vortex-vortex interactions and provide important insights that can inform the bioinspired engineering of propulsion systems.

Propulsive design principles in a multi-jet siphonophore

Coordination of multiple propulsors can provide performance benefits in swimming organisms. Siphonophores are marine colonial organisms that orchestrate the motion of multiple swimming zooids for effective swimming. However, the kinematics at the level of individual swimming zooids (nectophores) have not been examined in detail. We used high speed, high resolution microvideography and particle image velocimetry (PIV) of the physonect siphonophore, Nanomia bijuga, to study the motion of the nectophores and the associated fluid motion during jetting and refilling. The integration of nectophore and velum kinematics allow for a high-speed (maximum ∼1 m s−1), narrow (1-2 mm) jet and rapid refill as well as a 1:1 ratio of jetting to refill time. Scaled to the 3 mm nectophore length, jet speeds reach >300 lengths s−1. Overall swimming performance is enhanced by velocity gradients produced in the nectophore during refill, which lead to a high pressure region that produces forward thrust. Generating thrust during both the jet and refill phases augments the distance travelled by 17% over theoretical animals, which generate thrust only during the jet phase. The details of velum kinematics and associated fluid mechanics elucidate how siphonophores effectively navigate three-dimensional space and could be applied to exit flow parameters in multijet underwater vehicles.

How the bending kinematics of swimming lampreys build negative pressure fields for suction thrust

Swimming animals commonly bend their bodies to generate thrust. For undulating animals such as eels and lampreys, their bodies bend in the form of waves that travel from head to tail. These kinematics accelerate the flow of adjacent fluids, which alters the pressure field in a manner that generates thrust. We used a comparative approach to evaluate the cause-and-effect relationships in this process by quantifying the hydrodynamic effects of body kinematics at the body-fluid interface of the lamprey, Petromyzon marinus, during steady-state swimming. We compared the kinematics and hydrodynamics of healthy control lampreys to lampreys whose spinal cord had been transected mid-body, resulting in passive kinematics along the posterior half of their body. Using high-speed particle image velocimetry (PIV) and a method for quantifying pressure fields, we detail how the active bending kinematics of the control lampreys were crucial for setting up strong negative pressure fields (relative to ambient fields) that generated high-thrust regions at the bends as they traveled all along the body. The passive kinematics of the transected lamprey were only able to generate significant thrust at the tail, relying on positive pressure fields. These different pressure and thrust scenarios are due to differences in how active versus passive body waves generated and controlled vorticity. This demonstrates why it is more effective for undulating lampreys to pull, rather than push, themselves through the fluid.

Diversity of Cnidarian Muscles: Function, Anatomy, Development and Regeneration

The ability to perform muscle contractions is one of the most important and distinctive features of eumetazoans. As the sister group to bilaterians, cnidarians (sea anemones, corals, jellyfish, and hydroids) hold an informative phylogenetic position for understanding muscle evolution. Here, we review current knowledge on muscle function, diversity, development, regeneration and evolution in cnidarians. Cnidarian muscles are involved in various activities, such as feeding, escape, locomotion and defense, in close association with the nervous system. This variety is reflected in the large diversity of muscle organizations found in Cnidaria. Smooth epithelial muscle is thought to be the most common type, and is inferred to be the ancestral muscle type for Cnidaria, while striated muscle fibers and non-epithelial myocytes would have been convergently acquired within Cnidaria. Current knowledge of cnidarian muscle development and its regeneration is limited. While orthologs of myogenic regulatory factors such as MyoD have yet to be found in cnidarian genomes, striated muscle formation potentially involves well-conserved myogenic genes, such as twist and mef2. Although satellite cells have yet to be identified in cnidarians, muscle plasticity (e.g., de- and re-differentiation, fiber repolarization) in a regenerative context and its potential role during regeneration has started to be addressed in a few cnidarian systems. The development of novel tools to study those organisms has created new opportunities to investigate in depth the development and regeneration of cnidarian muscle cells and how they contribute to the regenerative process.

Can gelatinous zooplankton influence the fate of crude oil in marine environments?

Gelatinous zooplankton are known for their capacity to excrete copious amounts of mucus that can be utilized by other organisms. The release of mucus is exacerbated by stressful conditions. Despite the recognized importance of cnidarian mucus to production and material flux in marine ecosystems, the role of gelatinous zooplankton in influencing the fate of oil spills is unknown. In this study we used laboratory experiments to observe the influence of mucus from the moon jellyfish (Aurelia aurita) on the aggregation and degradation of crude oil. The results show that jellyfish swimming in a dispersed solution of oil droplets produced copious amounts of mucus and the mucus aggregates that were shed by the animals contained 26 times more oil than the surrounding water. Incubation experiments showed that hydrocarbon degrading bacteria cell densities more than doubled in the presence of mucus and after 14days, resulted in a significant increase in oil degradation. These results suggest that jellyfish can aggregate dispersed oil droplets and embed them within a matrix that favors hydrocarbon degrading bacteria. While this study lends support to the hypothesis that the presence of gelatinous zooplankton can impact oil spills large scale mesocosm studies will be needed to fully quantify the influence on a natural system.

Control of vortex rings for manoeuvrability

Manoeuvrability is critical to the success of many species. Selective forces acting over millions of years have resulted in a range of capabilities currently unmatched by machines. Thus, understanding animal control of fluids for manoeuvring has both biological and engineering applications. Within inertial fluid regimes, propulsion involves the formation and interaction of vortices to generate thrust. We use both volumetric and planar imaging techniques to quantify how jellyfish (Aurelia aurita) modulate vortex rings during turning behaviour. Our results show that these animals distort individual vortex rings during turns to alter the force balance across the animal, primarily through kinematic modulation of the bell margin. We find that only a portion of the vortex ring separates from the body during turns, which may increase torque. Using a fluorescent actin staining method, we demonstrate the presence of radial muscle fibres lining the bell along the margin. The presence of radial muscles provides a mechanistic explanation for the ability of scyphomedusae to alter their bell kinematics to generate non-symmetric thrust for manoeuvring. These results illustrate the advantage of combining imaging methods and provide new insights into the modulation and control of vorticity for low-speed animal manoeuvring.

Effects of non-uniform stiffness on the swimming performance of a passively-flexing, fish-like foil model

Simple mechanical models emulating fish have been used recently to enable targeted study of individual factors contributing to swimming locomotion without the confounding complexity of the whole fish body. Yet, unlike these uniform models, the fish body is notable for its non-uniform material properties. In particular, flexural stiffness decreases along the fish's anterior-posterior axis. To identify the role of non-uniform bending stiffness during fish-like propulsion, we studied four foil model configurations made by adhering layers of plastic sheets to produce discrete regions of high (5.5 × 10(-5) Nm(2)) and low (1.9 × 10(-5) Nm(2)) flexural stiffness of biologically-relevant magnitudes. This resulted in two uniform control foils and two foils with anterior regions of high stiffness and posterior regions of low stiffness. With a mechanical flapping foil controller, we measured forces and torques in three directions and quantified swimming performance under both heaving (no pitch) and constant 0° angle of attack programs. Foils self-propelled at Reynolds number 21 000-115 000 and Strouhal number ∼0.20-0.25, values characteristic of fish locomotion. Although previous models have emphasized uniform distributions and heaving motions, the combination of non-uniform stiffness distributions and 0° angle of attack pitching program was better able to reproduce the kinematics of freely-swimming fish. This combination was likewise crucial in maximizing swimming performance and resulted in high self-propelled speeds at low costs of transport and large thrust coefficients at relatively high efficiency. Because these metrics were not all maximized together, selection of the 'best' stiffness distribution will depend on actuation constraints and performance goals. These improved models enable more detailed, accurate analyses of fish-like swimming.

Exploring vortex enhancement and manipulation mechanisms in jellyfish that contributes to energetically efficient propulsion

The ability of animals to propel themselves efficiently through a fluid medium is ecologically advantageous. Flexible components that influence vortex interactions are widespread among animal propulsors. However the mechanisms by which vortices are enhanced and appropriately positioned for thrust generation are still poorly understood. Here, we describe how kinematic propulsor movements of a jellyfish can enhance and reposition a vortex ring that allows the recapture of wake energy for secondary thrust generation and efficient locomotion. We use high-speed video and digital particle image velocimetry (DPIV) to resolve kinematics simultaneously with fluid structures. These results provide new insight into how animals can manipulate fluid structures to reduce metabolic energy demands of swimming muscles and may have implications in bio-inspired design.

Passive energy recapture in jellyfish contributes to propulsive advantage over other metazoans

Gelatinous zooplankton populations are well known for their ability to take over perturbed ecosystems. The ability of these animals to outcompete and functionally replace fish that exhibit an effective visual predatory mode is counterintuitive because jellyfish are described as inefficient swimmers that must rely on direct contact with prey to feed. We show that jellyfish exhibit a unique mechanism of passive energy recapture, which is exploited to allow them to travel 30% further each swimming cycle, thereby reducing metabolic energy demand by swimming muscles. By accounting for large interspecific differences in net metabolic rates, we demonstrate, contrary to prevailing views, that the jellyfish (Aurelia aurita) is one of the most energetically efficient propulsors on the planet, exhibiting a cost of transport (joules per kilogram per meter) lower than other metazoans. We estimate that reduced metabolic demand by passive energy recapture improves the cost of transport by 48%, allowing jellyfish to achieve the large sizes required for sufficient prey encounters. Pressure calculations, using both computational fluid dynamics and a newly developed method from empirical velocity field measurements, demonstrate that this extra thrust results from positive pressure created by a vortex ring underneath the bell during the refilling phase of swimming. These results demonstrate a physical basis for the ecological success of medusan swimmers despite their simple body plan. Results from this study also have implications for bioinspired design, where low-energy propulsion is required.

An algorithm to estimate unsteady and quasi-steady pressure fields from velocity field measurements

We describe and characterize a method for estimating the pressure field corresponding to velocity field measurements, such as those obtained by using particle image velocimetry. The pressure gradient is estimated from a time series of velocity fields for unsteady calculations or from a single velocity field for quasi-steady calculations. The corresponding pressure field is determined based on median polling of several integration paths through the pressure gradient field in order to reduce the effect of measurement errors that accumulate along individual integration paths. Integration paths are restricted to the nodes of the measured velocity field, thereby eliminating the need for measurement interpolation during this step and significantly reducing the computational cost of the algorithm relative to previous approaches. The method is validated by using numerically-simulated flow past a stationary, two-dimensional bluff body and a computational model of a three-dimensional, self-propelled anguilliform swimmer to study the effects of spatial and temporal resolution, domain size, signal-to-noise ratio, and out of plane effects. Particle image velocimetry measurements of a freely-swimming jellyfish medusa and a freely-swimming lamprey are analyzed using the method to demonstrate the efficacy of the approach when applied to empirical data.