Modeling and Optimization Analysis of Single Flagellum Bacterial Motion

Bacteria such as Rhodobacter sphaeroides use a single flagellum for propulsion and change of orientation. Simple organisms such as this have inspired nanorobotic designs with potential applications in medicine which motivates the present work. In this article, an elastic model for a single flagellum bacterium is presented and followed by an analysis of the system based on optimization. The model is based on the method of Regularized Stokeslet which allows for a discretization of the system into particles which are connected by spring forces. An optimal elasticity distribution that maximizes the mean forward speed is obtained. These elasticity coefficients are obtained through the use of an adjoint-based optimization scheme. The results are illustrated through a simulation showing improvement on the swimming patter of the bacteria.