Variable viscosity and density biofilm simulations using an immersed boundary method, part II: Experimental validation and the heterogeneous rheology-IBM

Abstract

Abstract. The goal of this work is to develop a numerical simulation that accurately captures the biomechanical response of bacterial biofilms and their associated extracellular matrix (ECM). In this, the second of a two-part effort, the primary focus is on formally presenting the heterogeneous rheology Immersed Boundary Method (hrIBM) and validating our model against experimental results. With this extension of the Immersed Bounadry Method (IBM), we use the techniques originally developed in Part I, (Hammond et al. [15]) to treat the biofilm as a viscoelastic fluid possessing variable rheological properties anchored to a set of moving locations (i.e., the bacteria locations). We validate our modeling approach from Part I by comparing dynamic moduli and compliance moduli computed from our model to data from mechanical characterization experiments on Staphylococcus epidermidis biofilms. The experimental setup is described in Pavlovsky et al. (2013) [22] in which biofilms are grown and tested in a parallel plate rheometer. Matlab code used to produce results in this paper will be available at https://github.com/MathBioCU/BiofilmSim.Key words. Navier-Stokes equation, biofilm, immersed boundary method, computational fluid dynamics, viscoelastic fluid 1. Introduction. The goal of this work is to develop a numerical simulation method that accurately captures the biomechanical response of bacterial biofilms and their associated extracellular matrix (ECM). In this second paper, we show that the model and simulation method developed in part I [15], can be used to predict material properties of a biofilm and that the simulated results mimic experimentally measured results. The underlying mathematical technique is an adaptation of the Immersed Boundary Method (IBM) that takes into account the finite volume of bacteria, and variable material parameters found in biofilms whose variation is anchored to the positions of bacteria in a biofilm. We call this method the heterogeneous rheology Immersed Boundary Method (hrIBM). A key feature of our results is that the simulations are initialized with experimentally measured position data providing the locations of bacteria in live S. epidermidis biofilms. This removes ambiguity about how to represent the biofilm computationally. When using this data, the bulk physical properties estimated through simulation match experimental results. We also verify that when using different position data sets that possess similar spatial statistics, the physical properties of the biofilm do not change significantly. We also provide quantitative results on the periodic rotation of suspended aggregates of bacteria in shear flow.In recent years, much work has been done to develop detailed mathematical models that capture the biomechanical response of bacterial biofilms to physical changes [1,2,9,15,16]. In general, the physical properties governing the growth, attachment, and detachment of a biofilm are dependent on the ECM, a viscous mixture of polysaccharides and other biological products excreted b...

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