CAREER: Towards Harnessing the Motility of Microorganisms: Fast Algorithms, Data-Driven Models, and 3D Interactive Visual Computing

Due to their small size, microorganisms perceive a fluid as much “stickier” than do fish or humans. Such small creatures must adopt a different strategy for efficient swimming. Many of them propel themselves in the fluid by wiggling micro-structures such as cilia and flagella. The remarkable efficiency of microorganisms at moving and navigating through a surrounding fluid has inspired recent construction of microfluidic devices for mixing and transport, and micro-machines for drug delivery and manipulation of cells. Since theoretical analyses and experimentation are challenging in this setting, mathematical modeling and numerical simulation have become indispensable in these developments. This project aims to create improved computational and visualization tools for advancing understanding of the motility of microorganisms and our capability to harness this process. The project will develop an interactive three-dimensional visual computing system to serve as (1) a research tool for studying the hydrodynamics of swimming microorganisms, (2) an engineering tool for testing and improving the design of artificial, bio-inspired micro-swimmers, and (3) an educational tool for introducing students of all levels to this field. The project will also provide direct training and research opportunities for undergraduate and graduate students, postdoctoral researchers, and high school teachers. The project includes plans to develop virtual reality games based on microswimmers to be exhibited at the Museum of Science & Technology as well as public libraries. Research objectives in this project include the development of an efficient, multigrid-like method for manipulating the large, dense matrices arising from the simulation of interacting micro-swimmers, a data-driven, reduced order model for tracking fluid particles, an efficient numerical method for optimizing the design of bio-inspired swimmers given a task, and a three-dimensional interactive visual computing system for real-time fluid visualization and manipulation. Multigrid methods exploit the geometry of the swimmers and are therefore expected to be more efficient than current numerical approaches. An artificial neural network will be leveraged as a data-driven, reduced order model for the change in a fluid particle’s position. This approach is intended to simulate a fluid particle's trajectory very efficiently, since it does not require calculating fluid-structure interactions, an important aspect in real-time and/or multi-query scenarios. The planned numerical optimization method takes advantage of both the reliability of a genetic algorithm at finding global optima and the efficiency of a gradient-based method when a good initial guess is given. The interactive visual computing system is intended to serve as a virtual laboratory for analysis of the effects of parameter changes. This project is jointly funded by the Computational Mathematics and the Mathematical Biology Programs of the Division of Mathematical Science. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.