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

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 by comparison to experimental results. With this extension of the Immersed Boundary Method (IBM), we use the techniques originally developed in Part I ([19]) to treat biofilms as viscoelastic fluids possessing variable rheological properties anchored to a set of moving locations (i.e., the bacteria locations). In particular, we incorporate spatially continuous variable viscosity and density fields into our model. Although in [14,15], variable viscosity is used in an IBM context to model discrete viscosity changes across interfaces, to our knowledge this work and Part I are the first to apply the IBM to model a continuously variable viscosity field.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 [26] in which biofilms are grown and tested in a parallel plate rheometer. In order to initialize the positions of bacteria in the biofilm, experimentally obtained three dimensional coordinate data was used. One of the major conclusions of this effort is that treating the spring-like connections between bacteria as Maxwell or Zener elements provides good agreement with the mechanical characterization data. We also found that initializing the simulations with different coordinate data sets only led to small changes in the mechanical characterization results. Matlab code used to produce results in this paper will be available at https://github.com/MathBioCU/BiofilmSim.