Session B32: Biological Fluid Dynamics: General II

Corner Formation in the Wombat's Cubic Feces

Wombat feces begins as a wet yogurt-like slurry in the stomach and ends as a soft solid with six flat sides and eight distinct corners. The formation of corners and other singularities are rare in the world of fluid mechanics, yet the wombat possesses adaptations to encourage their formation. Our preliminary work has found that the wombat has periodic circumferential stiffness in their colon, but tests with intestine mimics made of pantyhose were unable to generate distinct corners. In this study, we consider the role of gut contractions in generating fluid flows that can generate corners. We present fabric intestinal mimics with which we can generate circumferential stresses, and simulations that combine intestinal material properties, the shape memory of the feces, and the gut contractions. This understanding of the resulting feces geometry could provide a simple and non-invasive health metric for wombats in captivity.   

In Silico Modeling of Formation and Growth of Thrombus under Blood Flow.

Understanding the spatio-temporal evolution of various biochemical species is critical to simulate the initiation and propagation of pathways that lead to thrombus formation in blood vessels. A large number of species and their reactions are challenging to synthesize through the experimental means. Thus, in silico modeling of the blood clot formation serves as a useful tool. To this end, blood is assumed as a multi-constituent mixture comprising of fluid and thrombus phase, which transports various biochemical agonists and inhibitors contributing to the coagulation cascade. In this study, blood is modeled using mass and momentum conservation equations with source term to account for the resistance on the blood flow from the thrombus formed. The transport of biochemical species involved is represented with convection-diffusion-reaction equations. The injury site is subjected to a constant influx of chemical agonist. The model used in this study accounts for the embolization of clot due to shear stress. We present the CFD simulation of the growth of thrombus at the site of endothelial injury due to chemical and shear-induced activation of platelets in a straight and stenosed blood vessel. The study also highlights the influence of flow pulsatility on the growth of thrombus.   

On cell proliferation in a tissue engineering scaffold pore, effects of nutrient concentration and scaffold internal geometry

Cell proliferation within a porous tissue engineering scaffold perfused with nutrient solution depends sensitively on the choice of pore geometry, flow rates, and nutrient concentration. Regions of high pore curvature encourage cell proliferation, while a critical flow rate is required to promote growth. Moreover, the dynamics of the nutrient culture medium consumption influence the cell growth. In experiments, such factors should be chosen meticulously to match the characteristics of the underlying cells and the particular goal of incubation. However, determining these factors poses a significant challenge that cannot be addressed by experimentation alone. In this talk, we present a first-principle mathematical theory for the nutrient concentration coupled to the growth of cells seeded on the pore walls, which is driven by the fluid flow within a tissue engineering scaffold pore. In addition, using asymptotic analysis based on the pore small aspect ratio, we derive a reduced model that enables a comprehensive analysis of the system to be performed. This approach reduces the numerical burdens, captures the experimental observations and suggests improvements to the design of a tissue engineering scaffold and the appropriate operating regime.   

An Assessment of Thrust, Drag, and Momentum Exchange of Undulation-Based Propulsion

Studies have shown increases in efficiency for undulating propulsion through interactions with unsteady wakes. Specifically, performance gains are related to favorable interactions between an undulation-like swimmer and an oncoming, unsteady wake such as in the case of schooling fish. In this study, Computational Fluid Dynamics (CFD) is used to evaluate the unsteady fluid interactions associated with undulation-based propulsion. The numerical accuracy of the CFD model is established and also shown to correlate well with benchmark experiments. While a number of optimization methods have been used to successfully design an undulation-based swimmer taking advantage of these unsteady wakes, the fundamental physics of the fluid mechanics responsible for propulsion is not fully understood. The aim of the effort is to refine the understanding of the forces associated with the unsteady wakes on an undulating foil. It is proposed that through evaluating the total pressure changes, shear forcing, and control-volume momentum changes during these interactions, additional insight can be developed. Using this approach, we believe we can identify the key fluid criteria responsible for increasing the propulsive efficiency of undulating swimmers.   

Pumping at low Reynolds numbers - the leucon sponge pump

Leuconoid sponges are filter-feeders with a complex system of branching inhalant and exhalant canals leading to and from the close-packed choanocyte chambers. Each of these choanocyte chambers holds many choanocytes that act as pumping units delivering the relatively high pressure rise needed to overcome the system pressure losses in canals and constrictions. We study these pumping units by solving the Navier-Stokes equations using computational fluid dynamics simulations. We find that each choanocyte operates as a leaky, positive displacement-type pump owing to the interaction between its beating flagellar vane and the collar, open at the base for inflow but sealed above. The leaking backflow is caused by small gaps between the vaned flagellum and the collar. The choanocyte pumps act in parallel, each delivering the same high pressure, because low-pressure and high-pressure zones in the choanocyte chamber are separated by a seal -- secondary reticulum. The mechanical pump power expended by the beating flagellum is compared with the useful (reversible) pumping power received by the water flow to arrive at a typical mechanical pump efficiency of about 70\,\%.   

Fluid Dynamics of Ballistic Strategies in Nematocyst Firing

Nematocysts are stinging organelles used by members of the phylum Cnidaria (jellyfish, anemones, hydra) for capturing prey and other important functions. Nematocysts are some of the fastest-known accelerating structures in the animal world. As such their rapid accelerations and small scales complicate resolving some aspects of their firing mechanism. We present results from mathematical models implemented in an immersed boundary framework that capture some of the dynamics of a a barb-like structure accelerating a short distance across a range of Reynolds numbers towards a passive target. Results indicate that acceleration and then coasting is not sufficient for a nematocyst to reach its target. We discuss the implications of these results for mechanisms required for small-scale ballistics.   

Growth and adaptation in a fungal hydraulic network

Biological networks such as fungal hydraulic networks have evolved to solve many of the same problems as human-built transportation networks. However, they must also briskly adapt to changing environments and modify their architecture without centralized control. Working with the model filamentous fungus, \textit{Neurospora crassa}, we characterize the growth of the network and propose a mathematical model for the collaborative behavior of its cells at various scales. We compare our model with measurements of the complex distribution of flows and resources across the cellular network.