Mixed uncertainty analysis on pumping by peristaltic hearts using Dempster-Shafer theory.

In this paper, we introduce the numerical strategy for mixed uncertainty propagation based on probability and Dempster-Shafer theories, and apply it to the computational model of peristalsis in a heart-pumping system. Specifically, the stochastic uncertainty in the system is represented with random variables while epistemic uncertainty is represented using non-probabilistic uncertain variables with belief functions. The mixed uncertainty is propagated through the system, resulting in the uncertainty in the chosen quantities of interest (QoI, such as flow volume, cost of transport and work). With the introduced numerical method, the uncertainty in the statistics of QoIs will be represented using belief functions. With three representative probability distributions consistent with the belief structure, global sensitivity analysis has also been implemented to identify important uncertain factors and the results have been compared between different peristalsis models. To reduce the computational cost, physics constrained generalized polynomial chaos method is adopted to construct cheaper surrogates as approximations for the full simulation.

What Can Computational Modeling Tell Us about the Diversity of Odor-Capture Structures in the Pancrustacea?

A major transition in the history of the Pancrustacea was the invasion of several lineages of these animals onto land. We investigated the functional performance of odor-capture organs, antennae with olfactory sensilla arrays, through the use of a computational model of advection and diffusion of odorants to olfactory sensilla while varying three parameters thought to be important to odor capture (Reynolds number, gap-width-to-sensillum-diameter ratio, and angle of the sensilla array with respect to oncoming flow). We also performed a sensitivity analysis on these parameters using uncertainty quantification to analyze their relative contributions to odor-capture performance. The results of this analysis indicate that odor capture in water and in air are fundamentally different. Odor capture in water and leakiness of the array are highly sensitive to Reynolds number and moderately sensitive to angle, whereas odor capture in air is highly sensitive to gap widths between sensilla and moderately sensitive to angle. Leakiness is not a good predictor of odor capture in air, likely due to the relative importance of diffusion to odor transport in air compared to water. We also used the sensitivity analysis to make predictions about morphological and kinematic diversity in extant groups of aquatic and terrestrial crustaceans. Aquatic crustaceans will likely exhibit denser arrays and induce flow within the arrays, whereas terrestrial crustaceans will rely on more sparse arrays with wider gaps and little-to-no animal-induced currents.

The role of the pericardium in the valveless, tubular heart of the tunicate Ciona savignyi.

Tunicates, small invertebrates within the phylum Chordata, possess a robust tubular heart which pumps blood through their open circulatory systems without the use of valves. This heart consists of two major components: the tubular myocardium, a flexible layer of myocardial cells that actively contracts to drive fluid down the length of the tube; and the pericardium, a stiff, outer layer of cells that surrounds the myocardium and creates a fluid-filled space between the myocardium and the pericardium. We investigated the role of the pericardium through in vivo manipulations on tunicate hearts and computational simulations of the myocardium and pericardium using the immersed boundary method. Experimental manipulations reveal that damage to the pericardium results in aneurysm-like bulging of the myocardium and major reductions in the net blood flow and percentage closure of the heart's lumen during contraction. In addition, varying the pericardium-to-myocardium (PM) diameter ratio by increasing damage severity was positively correlated with peak dye flow in the heart. Computational simulations mirror the results of varying the PM ratio experimentally. Reducing the stiffness of the myocardium in the simulations reduced mean blood flow only for simulations without a pericardium. These results indicate that the pericardium has the ability to functionally increase the stiffness of the myocardium and limit myocardial aneurysms. The pericardium's function is likely to enhance flow through the highly resistive circulatory system by acting as a support structure in the absence of connective tissue within the myocardium.

Physical properties of odorants affect behavior of trained detection dogs during close-quarters searches.

Trained detection dogs have a unique ability to find the sources of target odors in complex fluid environments. How dogs derive information about the source of an odor from an odor plume comprised of odorants with different physical properties, such as diffusivity, is currently unknown. Two volatile chemicals associated with explosive detection, ammonia (NH3, derived from ammonium nitrate-based explosives) and 2-ethyl-1-hexanol (2E1H, associated with composition C4 plastic explosives) were used to ascertain the effects of the physical properties of odorants on the search behavior and motion of trained dogs. NH3 has a diffusivity 3.6 times that of 2E1H. Fourteen civilian detection dogs were recruited to train on each target odorant using controlled odor mimic permeation systems as training aids over 6 weeks and then tested in a controlled-environment search trial where behavior, motion, and search success were analyzed. Our results indicate the target-odorant influences search motion and time spent in the stages of searching, with dogs spending more time in larger areas while localizing NH3. This aligns with the greater diffusivity of NH3 driving diffusion-dominated odor transport when dogs are close to the odor source in contrast to the advection-driven transport of 2E1H at the same distances.

Ontogenetic scaling of the olfactory antennae and flicking behavior of the shore crab, Hemigrapsus oregonensis.

Malacostracan crustaceans such as crabs flick antennae with arrays of olfactory sensilla called aesthetascs through the water to sense odors. Flicking by crabs consists of a quick downstroke, in which aesthetascs are deflected laterally (splayed), and a slower, reversed return stroke, in which aesthetascs clump together. This motion causes water to be flushed within and then held in between aesthetascs to deliver odor molecules to olfactory receptors. Although this odor sampling method relies on a narrow range of speeds, sizes, and specific arrangements of aesthetascs, most crabs dramatically change these during ontogeny. In this study, the morphometrics of the aesthetascs, array, and antennae and the flicking kinematics of the Oregon shore crab, Hemigrapsus oregonensis (Decapoda: Brachyura), are examined to determine their scaling relationships during ontogeny. The morphometrics of the array and antennae increase more slowly than would be predicted by isometry. Juvenile crabs' aesthetascs splay relatively further apart than adults, likely due to changing material properties of aesthetasc cuticle during growth. These results suggest that disproportionate growth and altered aesthetasc splay during flicking will mediate the size changes due to growth that would otherwise lead to a loss of function.

Melding Modeling and Morphology: A Call for Collaboration to Address Difficult Questions about the Evolution of Form and Function.

The nascent field of evolutionary biomechanics seeks to understand how form begets function, and researchers have taken two tacks toward this goal: inferring form based on function (comparative biomechanics) or inferring function based on form (functional morphology). Each tack has strengths and weaknesses, which the other could improve. The symposium, "Melding modeling and morphology-integrating approaches to understand the evolution of form and function" sought to highlight research stitching together the two tacks. In this introduction to the symposium's issue, we highlight these works, discuss the challenges of interdisciplinary collaborations, and suggest possible avenues available to create new collaborations to create a unifying framework for evolutionary biomechanics.

Functional Morphology of Gliding Flight I: Modeling Reveals Distinct Performance Landscapes Based on Soaring Strategies.

The physics of flight influences the morphology of bird wings through natural selection on flight performance. The connection between wing morphology and performance is unclear due to the complex relationships between various parameters of flight. In order to better understand this connection, we present a holistic analysis of gliding flight that preserves complex relationships between parameters. We use a computational model of gliding flight, along with analysis by uncertainty quantification, to (1) create performance landscapes of gliding based on output metrics (maximum lift-to-drag ratio, minimum gliding angle, minimum sinking speed, and lift coefficient at minimum sinking speed) and (2) predict what parameters of flight (chordwise camber, wing aspect ratio [AR], and Reynolds number) would differ between gliding and nongliding species of birds. We also examine performance based on the soaring strategy for possible differences in morphology within gliding birds. Gliding birds likely have greater ARs than non-gliding birds, due to the high sensitivity of AR on most metrics of gliding performance. Furthermore, gliding birds can use two distinct soaring strategies based on performance landscapes. First, maximizing distance traveled (maximizing lift-to-drag ratio and minimizing gliding angle) should result in wings with high ARs and middling-to-low wing chordwise camber. Second, maximizing lift extracted from updrafts should result in wings with middling ARs and high wing chordwise camber. Following studies can test these hypotheses using morphological measurements.

Uncertainty quantification reveals the physical constraints on pumping by peristaltic hearts.

Most biological functional systems are complex, and this complexity is a fundamental driver of diversity. Because input parameters interact in complex ways, a holistic understanding of functional systems is key to understanding how natural selection produces diversity. We present uncertainty quantification (UQ) as a quantitative analysis tool on computational models to study the interplay of complex systems and diversity. We investigate peristaltic pumping in a racetrack circulatory system using a computational model and analyse the impact of three input parameters (Womersley number, compression frequency, compression ratio) on flow and the energetic costs of circulation. We employed two models of peristalsis (one that allows elastic interactions between the heart tube and fluid and one that does not), to investigate the role of elastic interactions on model output. A computationally cheaper surrogate of the input parameter space was created with generalized polynomial chaos expansion to save computational resources. Sobol indices were then calculated based on the generalized polynomial chaos expansion and model output. We found that all flow metrics were highly sensitive to changes in compression ratio and insensitive to Womersley number and compression frequency, consistent across models of peristalsis. Elastic interactions changed the patterns of parameter sensitivity for energetic costs between the two models, revealing that elastic interactions are probably a key physical metric of peristalsis. The UQ analysis created two hypotheses regarding diversity: favouring high flow rates (where compression ratio is large and highly conserved) and minimizing energetic costs (which avoids combinations of high compression ratios, high frequencies and low Womersley numbers).

Functional Morphology of Gliding Flight II. Morphology Follows Predictions of Gliding Performance.

The evolution of wing morphology among birds, and its functional consequences, remains an open question, despite much attention. This is in part because the connection between form and function is difficult to test directly. To address this deficit, in prior work, we used computational modeling and sensitivity analysis to interrogate the impact of altering wing aspect ratio (AR), camber, and Reynolds number on aerodynamic performance, revealing the performance landscapes that avian evolution has explored. In the present work, we used a dataset of three-dimensionally scanned bird wings coupled with the performance landscapes to test two hypotheses regarding the evolutionary diversification of wing morphology associated with gliding flight behavior: (1) gliding birds would exhibit higher wing AR and greater chordwise camber than their non-gliding counterparts; and (2) that two strategies for gliding flight exist, with divergent morphological conformations. In support of our first hypothesis, we found evidence of morphological divergence in both wing AR and camber between gliders and non-gliders, suggesting that wing morphology of birds that utilize gliding flight is under different selective pressures than the wings of non-gliding taxa. Furthermore, we found that these morphological differences also yielded differences in coefficient of lift measured both at the maximum lift to drag ratio and at minimum sinking speed, with gliding taxa exhibiting higher coefficient of lift in both cases. Minimum sinking speed was also lower in gliders than non-gliders. However, contrary to our hypothesis, we found that the maximum ratio of the coefficient of lift to the coefficient of drag differed between gliders and non-gliders. This may point to the need for gliders to maintain high lift capability for takeoff and landing independent of gliding performance or could be due to the divergence in flight styles among gliders, as not all gliders are predicted to optimize either quantity. However, direct evidence for the existence of two morphologically defined gliding flight strategies was equivocal, with only slightly stronger support for an evolutionary model positing separate morphological optima for these strategies than an alternative model positing a single peak. The absence of a clear result may be an artifact of low statistical power owing to a relatively small sample size of gliding flyers expected to follow the "aerial search" strategy.

A tale of two antennules: the performance of crab odour-capture organs in air and water.

Odour capture is an important part of olfaction, where dissolved chemical cues (odours) are brought into contact with chemosensory structures. Antennule flicking by marine crabs is an example of discrete odour capture (sniffing) where an array of chemosensory hairs is waved through the water to create a flow-no flow pattern based on a narrow range of speeds, diameters of and spacings between hairs. Changing the speed of movement and spacing of hairs at this scale to manipulate flow represents a complicated fluid dynamics problem. In this study, we use numerical simulation of the advection and diffusion of a chemical gradient to reveal how morphological differences of the hair arrays affect odour capture. Specifically, we simulate odour capture by a marine crab (Callinectes sapidus) and a terrestrial crab (Coenobita rugosus) in both air and water to compare performance. We find that the antennule morphologies of each species are adaptions to capturing odours in their native habitats. Sniffing is an important part of odour capture for marine crabs in water where the diffusivity of odorant molecules is low and flow through the array is necessary. On the other hand, flow within the hair array diminishes odour-capture performance in air where diffusivities are high. This study highlights some of the adaptations necessary to transition from water to air.

Do terrestrial hermit crabs sniff? Air flow and odorant capture by flicking antennules.

Capture of odorant molecules by olfactory organs from the surrounding fluid is the first step of smelling. Sniffing intermittently moves fluid across sensory surfaces, increasing delivery rates of molecules to chemosensory receptors and providing discrete odour samples. Aquatic malacostracan crustaceans sniff by flicking olfactory antennules bearing arrays of chemosensory hairs (aesthetascs), capturing water in the arrays during downstroke and holding the sample during return stroke. Terrestrial malacostracans also flick antennules, but how their flicking affects odour capture from air is not understood. The terrestrial hermit crab, Coenobita rugosus, uses antennules bearing shingle-shaped aesthetascs to capture odours. We used particle image velocimetry to measure fine-scale fluid flow relative to a dynamically scaled physical model of a flicking antennule, and computational simulations to calculate diffusion to aesthetascs by odorant molecules carried in that flow. Air does not flow into the aesthetasc array during flick downstrokes or recovery strokes. Odorants are captured from air flowing around the outside of the array during flick downstrokes, when aesthetascs face upstream and molecule capture rates are 21% higher than for stationary antennules. Bursts of flicking followed by pauses deliver discrete odour samples to olfactory sensors, causing intermittency in odour capture by a different mechanism than aquatic crustaceans use.

Covering Ground: Movement Patterns and Random Walk Behavior in Aquilonastra anomala Sea Stars.

The paths animals take while moving through their environments affect their likelihood of encountering food and other resources; thus, models of foraging behavior abound. To collect movement data appropriate for comparison with these models, we used time-lapse photography to track movements of a small, hardy, and easy-to-obtain organism, Aquilonastra anomala sea stars. We recorded the sea stars in a tank over many hours, with and without a food cue. With food present, they covered less distance, as predicted by theory; this strategy would allow them to remain near food. We then compared the paths of the sea stars to three common models of animal movement: Brownian motion, Lévy walks, and correlated random walks; we found that the sea stars' movements most closely resembled a correlated random walk. Additionally, we compared the search performance of models of Brownian motion, a Lévy walk, and a correlated random walk to that of a model based on the sea stars' movements. We found that the behavior of the modeled sea star walk was similar to that of the modeled correlated random walk and the Brownian motion model, but that the sea star walk was slightly more likely than the other walks to find targets at intermediate distances. While organisms are unlikely to follow an idealized random walk in all details, our data suggest that comparing the effectiveness of an organism's paths to those from theory can give insight into the organism's actual movement strategy. Finally, automated optical tracking of invertebrates proved feasible, and A. anomala was revealed to be a tractable, 2D-movement study system.

Introduction to the Symposium "Leading Students and Faculty to Quantitative Biology through Active Learning".

The broad aim of this symposium and set of associated papers is to motivate the use of inquiry-based, active-learning teaching techniques in undergraduate quantitative biology courses. Practical information, resources, and ready-to-use classroom exercises relevant to physicists, mathematicians, biologists, and engineers are presented. These resources can be used to address the lack of preparation of college students in STEM fields entering the workforce by providing experience working on interdisciplinary and multidisciplinary problems in mathematical biology in a group setting. Such approaches can also indirectly help attract and retain under-represented students who benefit the most from "non-traditional" learning styles and strategies, including inquiry-based, collaborative, and active learning.

Flexibility of crab chemosensory sensilla enables flicking antennules to sniff.

The first step in smelling is capture of odorant molecules from the surrounding fluid. We used lateral flagella of olfactory antennules of crabs Callinectes sapidus to study the physical process of odor capture by antennae bearing dense tufts of hair-like chemosensory sensilla (aesthetascs). Fluid flow around and through aesthetasc arrays on dynamically scaled models of lateral flagella of C. sapidus was measured by particle image velocimetry to determine how antennules sample the surrounding water when they flick. Models enabled separate evaluation of the effects of flicking speed, aesthetasc spacing, and antennule orientation. We found that crab antennules, like those of other malacostracan crustaceans, take a discrete water sample during each flick by having a rapid downstroke, during which water flows into the aesthetasc array, and a slow recovery stroke, when water is trapped in the array and odorants have time to diffuse to aesthetascs. However, unlike antennules of crustaceans with sparse aesthetasc arrays, crabs enhance sniffing via additional mechanisms: 1) Aesthetascs are flexible and splay as a result of the hydrodynamic drag during downstrokes, then clump together during return strokes; and 2) antennules flick with aesthetascs on the upstream side of the stalk during downstrokes, but are hidden downstream during return strokes. Aiming aesthetascs into ambient flow maintains sniffing. When gaps between aesthetascs are wide, changes in antennule speed are more effective at altering flow through the array than when gaps are narrow. Nonetheless, if crabs had fixed gap widths, their ability to take discrete samples of their odorant environment would be diminished.

Ontogenetic changes in the olfactory antennules of the shore crab, Hemigrapsus oregonensis, maintain sniffing function during growth.

Malacostracan crustaceans capture odours using arrays of chemosensory hairs (aesthetascs) on antennules. Lobsters and stomatopods have sparse aesthetascs on long antennules that flick with a rapid downstroke when water flows between the aesthetascs and a slow return stroke when water is trapped within the array (sniffing). Changes in velocity only cause big differences in flow through an array in a critical range of hair size, spacing and speed. Crabs have short antennules bearing dense arrays of flexible aesthetascs that splay apart during downstroke and clump together during return. Can crabs sniff, and when during ontogeny are they big enough to sniff? Antennules of Hemigrapsus oregonensis representing an ontogenetic series from small juveniles to adults were used to design dynamically scaled physical models. Particle image velocimetry quantified fluid flow through each array and showed that even very small crabs capture a new water sample in their arrays during the downstroke and retain that sample during return stroke. Comparison with isometrically scaled antennules suggests that reduction in aesthetasc flexural stiffness during ontogeny, in addition to increase in aesthetasc number and decrease in relative size, maintain sniffing as crabs grow. Sniffing performance of intermediate-sized juveniles was worse than for smaller and larger crabs.

Using Active Learning to Teach Concepts and Methods in Quantitative Biology.

This article provides a summary of the ideas discussed at the 2015 Annual Meeting of the Society for Integrative and Comparative Biology society-wide symposium on Leading Students and Faculty to Quantitative Biology through Active Learning. It also includes a brief review of the recent advancements in incorporating active learning approaches into quantitative biology classrooms. We begin with an overview of recent literature that shows that active learning can improve students' outcomes in Science, Technology, Engineering and Math Education disciplines. We then discuss how this approach can be particularly useful when teaching topics in quantitative biology. Next, we describe some of the recent initiatives to develop hands-on activities in quantitative biology at both the graduate and the undergraduate levels. Throughout the article we provide resources for educators who wish to integrate active learning and technology into their classrooms.

Scaling of olfactory antennae of the terrestrial hermit crabs Coenobita rugosus and Coenobita perlatus during ontogeny.

Although many lineages of terrestrial crustaceans have poor olfactory capabilities, crabs in the family Coenobitidae, including the terrestrial hermit crabs in the genus Coenobita, are able to locate food and water using olfactory antennae (antennules) to capture odors from the surrounding air. Terrestrial hermit crabs begin their lives as small marine larvae and must find a suitable place to undergo metamorphosis into a juvenile form, which initiates their transition to land. Juveniles increase in size by more than an order of magnitude to reach adult size. Since odor capture is a process heavily dependent on the size and speed of the antennules and physical properties of the fluid, both the transition from water to air and the large increase in size during ontogeny could impact odor capture. In this study, we examine two species of terrestrial hermit crabs, Coenobita perlatus H. Milne-Edwards and Coenobita rugosus H. Milne-Edwards, to determine how the antennule morphometrics and kinematics of flicking change in comparison to body size during ontogeny, and how this scaling relationship could impact odor capture by using a simple model of mass transport in flow. Many features of the antennules, including the chemosensory sensilla, scaled allometrically with carapace width and increased slower than expected by isometry, resulting in relatively larger antennules on juvenile animals. Flicking speed scaled as expected with isometry. Our mass-transport model showed that allometric scaling of antennule morphometrics and kinematics leads to thinner boundary layers of attached fluid around the antennule during flicking and higher odorant capture rates as compared to antennules which scaled isometrically. There were no significant differences in morphometric or kinematic measurements between the two species.