The dynamic pulsation of xeniid corals is one of the most fascinating phenomena observed in coral reefs. We quantified for the first time the flow near the tentacles of these soft corals. The flows generated are characterized by continual flow towards the polyp, slow mixing within the tentacles, and the subsequent ejection of this fluid volume into an upward jet that ensures the polyp continually samples new water with sufficient time for exchange to occur. These coral polyps typically grow in large colonies, where collective pulsing could enhance net flow rates and mixing. We tested whether patterns of collective pulsing emerge in coral colonies by searching for possible interactions between polyps within a colony using an information-theoretic approach (transfer entropy). Perhaps surprisingly, we did not detect any patterns of collective pulsing behavior in the colonies. Moreover, the lack of a pattern is consistent with previous work on many cnidarians where coordination between actively pulsing polyps and medusa has not been observed. We also showed that there is little to no fluid dynamic benefit of coordinated pulsing. The lack of coordination coupled with no obvious fluid dynamic benefit to grouping suggests that there may be non-fluid mechanical advantages to forming colonies such as predator avoidance and defense.

This work combined computational, mathematical, and experimental tools to ultimately answer some of questions posed in one of the five grand challenges in organismal biology: Integrating living and physical systems. Recent advancements in computational fluid dynamics have enabled researchers to efficiently explore problems that involve moving elastic boundaries immersed in fluids for problems such as cardiac fluid dynamics, insect flight, and fish swimming. Due to the inherent complexities of these systems, modeling choices must be made such as greatly simplifying the morphology, biophysics, or biochemistry or considering only one isolated component of the system. By considering a relatively simple system such as a pulsating coral polyp, we are able to answer biophysical questions using high fidelity computational models that make relatively few simplifications. In particular, we quantified the coordination (or lack thereof) between each polyp and determined the fluid dynamic consequences. In terms of bio-inspired design, Cnidarians represent one of the simplest examples of muscle driven movement in a multicellular animal. By understanding the purpose and mechanics of soft coral pulsing, we may better understand how macroscale movements in animals evolved. Furthermore, mathematical models of the simple movements of organisms have been applied to the design of robots and autonomous underwater vehicles. One potential application of the work is to inform the design efficient mesoscale mixers. 

The methods and tools that we developed for this project, all of which are freely available online, should find immediate use in a variety of applications in biological fluid dynamics. We developed 2D MATLAB and Python codes for solving fluid-structure interaction problems that can be used in undergraduate research projects and courses. Functionality is provided for including phenomena such as muscle contraction, neural activation, and porous media. We created a software library for obtaining 2D finite difference discretizations of complex boundaries. This tool enables the user to extract boundaries as discrete mesh points from digital images. These finite difference meshes can then be imported directly into existing immersed boundary software libraries including ib2d and IBAMR.  Given the versatility of immersed boundary methods, the potential impact of this work is quite broad. The results could inform studies which aim to address basic scientific questions such as the fluid-structure interactions which drive the formation of the developing heart to studies that consider the function of the lymphatic system. Immersed boundary methods have already been used to develop and test artificial heart valves, and the tools that we have provided should enable more cardiovascular scientists and engineers to answer fluid-structure interaction questions computationally.

A key focus of the educational effort of this grant was to create a unified training program for physicists, engineers, mathematicians and biologists centered on mathematical modeling in biology. In each of the four years of the grant, Miller taught graduate courses focused on numerical studies of biological fluid-structure interaction problems, and each student developed their own semester long research project. Miller also taught a first year seminar in which students used CAD and 3D scanning to describe organs and organisms that interact with fluids. As part of the semester long course projects, students 3D printed their models for use in flow tanks and simulated the flow around these objects using commercial software. To enhance students? research related skills, entrepreneurial mindsets, and making abilities, Miller participated in three faculty learning communities at UNC. Three graduate students and five undergraduates from backgrounds in biology, mathematics, physics, engineering, and computer science participated in this research.

Last Modified: 03/12/2020
Modified by: Laura A Miller