Mathematical and Computational Studies of the Biomechanics of Bacterial Biofilms
Bacterial biofilms are communities of bacteria growing on a surface, typically in anaqueous environment. Interest in understanding biofilm behavior arises from a variety of applications; strategies to mitigate corrosion in industrial machinery, the treatment of bacterial infections, and process control in bioreactors are a few examples. I will discuss the validation of a mathematical model of fluid-structure interaction in biofilms by comparison with experimental data. The model is based on the Immersed Boundary Method, but requires several crucial modifications specific to biofilm modeling.
I will then discuss a statistical model of the positions of bacteria within a biofilm. Using a Metropolis-Hastings algorithm, I generate ‘artificial’ biofilms and demonstrate through simulation, that statistical properties of the statistical model closely match experimental data. The influence which the choice of statistical model has on mechanical properties of the resulting biofilm is shown through numerical simulation.
For the last section of the talk, the focus is on error propagation in the Method of Regularized Stokeslets, a numerical method that can be used to simulate biofilm fluid-structure interaction at small Reynolds numbers. Through an a posteriori error analysis and numerical simulation, I will demonstrate how various types of numerical error propagate over time.
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