Tyson L. Hedrick

Software techniques for two- and three-dimensional kinematic measurements of biological and biomimetic systems

Researchers studying aspects of locomotion or movement in biological and biomimetic systems commonly use video or stereo video recordings to quantify the behaviour of the system in question, often with an emphasis on measures of position, velocity and acceleration. However, despite the apparent simplicity of video analysis, it can require substantial investment of time and effort, even when performed with adequate software tools. This paper reviews the underlying principles of video and stereo video analysis as well as its automation and is accompanied by fully functional and freely available software implementation.

X-ray reconstruction of moving morphology (XROMM): precision, accuracy and applications in comparative biomechanics research

X-Ray Reconstruction of Moving Morphology (XROMM) comprises a set of 3D X-ray motion analysis techniques that merge motion data from in vivo X-ray videos with skeletal morphology data from bone scans into precise and accurate animations of 3D bones moving in 3D space. XROMM methods include: (1) manual alignment (registration) of bone models to video sequences, i.e., Scientific Rotoscoping; (2) computer vision-based autoregistration of bone models to biplanar X-ray videos; and (3) marker-based registration of bone models to biplanar X-ray videos. Here, we describe a novel set of X-ray hardware, software, and workflows for marker-based XROMM. Refurbished C-arm fluoroscopes retrofitted with high-speed video cameras offer a relatively inexpensive X-ray hardware solution for comparative biomechanics research. Precision for our biplanar C-arm hardware and analysis software, measured as the standard deviation of pairwise distances between 1 mm tantalum markers embedded in rigid objects, was found to be +/-0.046 mm under optimal conditions and +/-0.084 mm under actual in vivo recording conditions. Mean error in measurement of a known distance between two beads was within the 0.01 mm fabrication tolerance of the test object, and mean absolute error was 0.037 mm. Animating 3D bone models from sets of marker positions (XROMM animation) makes it possible to study skeletal kinematics in the context of detailed bone morphology. The biplanar fluoroscopy hardware and computational methods described here should make XROMM an accessible and useful addition to the available technologies for studying the form, function, and evolution of vertebrate animals.

Wingbeat Time and the Scaling of Passive Rotational Damping in Flapping Flight

Flying animals exhibit remarkable capabilities for both generating maneuvers and stabilizing their course and orientation after perturbation. Here we show that flapping fliers ranging in size from fruit flies to large birds benefit from substantial damping of angular velocity through a passive mechanism termed flapping counter-torque (FCT). Our FCT model predicts that isometrically scaled animals experience similar damping on a per-wingbeat time scale, resulting in similar turning dynamics in wingbeat time regardless of body size. The model also shows how animals may simultaneously specialize in both maneuverability and stability (at the cost of efficiency) and provides a framework for linking morphology, wing kinematics, maneuverability, and flight dynamics across a wide range of flying animals spanning insects, bats, and birds.

Quantifying the complexity of bat wing kinematics

Body motions (kinematics) of animals can be dimensionally complex, especially when flexible parts of the body interact with a surrounding fluid. In these systems, tracking motion completely can be difficult, and result in a large number of correlated measurements, with unclear contributions of each parameter to performance. Workers typically get around this by deciding a priori which variables are important (wing camber, stroke amplitude, etc.), and focusing only on those variables, but this constrains the ability of a study to uncover variables of influence. Here, we describe an application of proper orthogonal decomposition (POD) for assigning importances to kinematic variables, using dimensional complexity as a metric. We apply this method to bat flight kinematics, addressing three questions: (1) Does dimensional complexity of motion change with speed? (2) What body markers are optimal for capturing dimensional complexity? (3) What variables should a simplified reconstruction of bat flight include in order to maximally reconstruct actual dimensional complexity? We measured the motions of 17 kinematic markers (20 joint angles) on a bat (Cynopterus brachyotis) flying in a wind tunnel at nine speeds. Dimensional complexity did not change with flight speed, despite changes in the kinematics themselves, suggesting that the relative efficacy of a given number of dimensions for reconstructing kinematics is conserved across speeds. By looking at subsets of the full 17-marker set, we found that using more markers improved resolution of kinematic dimensional complexity, but that the benefit of adding markers diminished as the total number of markers increased. Dimensional complexity was highest when the hindlimb and several points along digits III and IV were tracked. Also, we uncovered three groups of joints that move together during flight by using POD to quantify correlations of motion. These groups describe 14/20 joint angles, and provide a framework for models of bat flight for experimental and modeling purposes.

A protocol and calibration method for accurate multi-camera field videography

Stereo videography is a powerful technique for quantifying the kinematics and behavior of animals, but it can be challenging to use in an outdoor field setting. We here present a workflow and associated software for performing calibration of cameras placed in a field setting and estimating the accuracy of the resulting stereoscopic reconstructions. We demonstrate the workflow through example stereoscopic reconstructions of bat and bird flight. We provide software tools for planning experiments and processing the resulting calibrations that other researchers may use to calibrate their own cameras. Our field protocol can be deployed in a single afternoon, requiring only short video clips of light, portable calibration objects.

Time-varying wing-twist improves aerodynamic efficiency of forward flight in butterflies

Insect wings can undergo significant chordwise (camber) as well as spanwise (twist) deformation during flapping flight but the effect of these deformations is not well understood. The shape and size of butterfly wings leads to particularly large wing deformations, making them an ideal test case for investigation of these effects. Here we use computational models derived from experiments on free-flying butterflies to understand the effect of time-varying twist and camber on the aerodynamic performance of these insects. High-speed videogrammetry is used to capture the wing kinematics, including deformation, of a Painted Lady butterfly (Vanessa cardui) in untethered, forward flight. These experimental results are then analyzed computationally using a high-fidelity, three-dimensional, unsteady Navier-Stokes flow solver. For comparison to this case, a set of non-deforming, flat-plate wing (FPW) models of wing motion are synthesized and subjected to the same analysis along with a wing model that matches the time-varying wing-twist observed for the butterfly, but has no deformation in camber. The simulations show that the observed butterfly wing (OBW) outperforms all the flat-plate wings in terms of usable force production as well as the ratio of lift to power by at least 29% and 46%, respectively. This increase in efficiency of lift production is at least three-fold greater than reported for other insects. Interestingly, we also find that the twist-only-wing (TOW) model recovers much of the performance of the OBW, demonstrating that wing-twist, and not camber is key to forward flight in these insects. The implications of this on the design of flapping wing micro-aerial vehicles are discussed.

Three-dimensional flow and lift characteristics of a hovering ruby-throated hummingbird.

A three-dimensional computational fluid dynamics simulation is performed for a ruby-throated hummingbird (Archilochus colubris) in hovering flight. Realistic wing kinematics are adopted in the numerical model by reconstructing the wing motion from high-speed imaging data of the bird. Lift history and the three-dimensional flow pattern around the wing in full stroke cycles are captured in the simulation. Significant asymmetry is observed for lift production within a stroke cycle. In particular, the downstroke generates about 2.5 times as much vertical force as the upstroke, a result that confirms the estimate based on the measurement of the circulation in a previous experimental study. Associated with lift production is the similar power imbalance between the two half strokes. Further analysis shows that in addition to the angle of attack, wing velocity and surface area, drag-based force and wing–wake interaction also contribute significantly to the lift asymmetry. Though the wing–wake interaction could be beneficial for lift enhancement, the isolated stroke simulation shows that this benefit is buried by other opposing effects, e.g. presence of downwash. The leading-edge vortex is stable during the downstroke but may shed during the upstroke. Finally, the full-body simulation result shows that the effects of wing–wing interaction and wing–body interaction are small.

Morphological and kinematic basis of the hummingbird flight stroke: scaling of flight muscle transmission ratio

Hummingbirds (Trochilidae) are widely known for their insect-like flight strokes characterized by high wing beat frequency, small muscle strains and a highly supinated wing orientation during upstroke that allows for lift production in both halves of the stroke cycle. Here, we show that hummingbirds achieve these functional traits within the limits imposed by a vertebrate endoskeleton and muscle physiology by accentuating a wing inversion mechanism found in other birds and using long-axis rotational movement of the humerus. In hummingbirds, long-axis rotation of the humerus creates additional wing translational movement, supplementing that produced by the humeral elevation and depression movements of a typical avian flight stroke. This adaptation increases the wing-to-muscle-transmission ratio, and is emblematic of a widespread scaling trend among flying animals whereby wing-to-muscle-transmission ratio varies inversely with mass, allowing animals of vastly different sizes to accommodate aerodynamic, biomechanical and physiological constraints on muscle-powered flapping flight.

Hawkmoth flight stability in turbulent vortex streets

SUMMARY Shedding of vortices is a common phenomenon in the atmosphere over a wide range of spatial and temporal scales. However, it is unclear how these vortices of varying scales affect the flight performance of flying animals. In order to examine these interactions, we trained seven hawkmoths (Manduca sexta) (wingspan ~9 cm) to fly and feed in a wind tunnel under steady flow (controls) and in the von Kármán vortex street of vertically oriented cylinders (two different cylinders with diameters of 10 and 5 cm) at speeds of 0.5, 1 and 2 m s−1. Cylinders were placed at distances of 5, 25 and 100 cm upstream of the moths. Moths exhibited large amplitude yaw oscillations coupled with modest oscillations in roll and pitch, and slight increases in wingbeat frequency when flying in both the near (recirculating) and middle (vortex dominated) wake regions. Wingbeat amplitude did not vary among treatments, except at 1 m s−1 for the large cylinder. Yaw and roll oscillations were synchronized with the vortex shedding frequencies in moths flying in the wake of the large cylinder at all speeds. In contrast, yaw and pitch were synchronized with the shedding frequency of small vortices at speeds ≤1 m s−1. Oscillations in body orientation were also substantially smaller in the small cylinder treatment when compared with the large cylinder, regardless of temporal or non-dimensional spatial scale. Moths flying in steady conditions reached a higher air speed than those flying into cylinder wakes. In general, flight effects produced by the cylinder wakes were qualitatively similar among the recirculating and vortex-dominated wake regions; the magnitude of those effects, however, declined gradually with downstream distance.

Effects of flight speed upon muscle activity in hummingbirds

SUMMARY Hummingbirds have the smallest body size and highest wingbeat frequencies of all flying vertebrates, so they represent one endpoint for evaluating the effects of body size on sustained muscle function and flight performance. Other bird species vary neuromuscular recruitment and contractile behavior to accomplish flight over a wide range of speeds, typically exhibiting a U-shaped curve with maxima at the slowest and fastest flight speeds. To test whether the high wingbeat frequencies and aerodynamically active upstroke of hummingbirds lead to different patterns, we flew rufous hummingbirds (Selasphorus rufus, 3 g body mass, 42 Hz wingbeat frequency) in a variable-speed wind tunnel (0–10 m s−1). We measured neuromuscular activity in the pectoralis (PECT) and supracoracoideus (SUPRA) muscles using electromyography (EMG, N=4 birds), and we measured changes in PECT length using sonomicrometry (N=1). Differing markedly from the pattern in other birds, PECT deactivation occurred before the start of downstroke and the SUPRA was deactivated before the start of upstroke. The relative amplitude of EMG signal in the PECT and SUPRA varied according to a U-shaped curve with flight speed; additionally, the onset of SUPRA activity became relatively later in the wingbeat at intermediate flight speeds (4 and 6 m s−1). Variation in the relative amplitude of EMG was comparable with that observed in other birds but the timing of muscle activity was different. These data indicate the high wingbeat frequency of hummingbirds limits the time available for flight muscle relaxation before the next half stroke of a wingbeat. Unlike in a previous study that reported single-twitch EMG signals in the PECT of hovering hummingbirds, across all flight speeds we observed 2.9±0.8 spikes per contraction in the PECT and 3.8±0.8 spikes per contraction in the SUPRA. Muscle strain in the PECT was 10.8±0.5%, the lowest reported for a flying bird, and average strain rate was 7.4±0.2 muscle lengths s−1. Among species of birds, PECT strain scales proportional to body mass to the 0.2 power (∞Mb0.2) using species data and ∞Mb0.3 using independent contrasts. This positive scaling is probably a physiological response to an adverse scaling of mass-specific power available for flight.