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...

No abstract

This paper revisits the relativistic limiting current in planar, cylindrical, and spherical diodes, with alternative analytic and numerical treatments which are easy to implement. Convenient, approximate expressions for the limited current are presented for gap voltages up to 10 MV. They are accurate to within 1% for planar diode, and to within 4% for both cylindrical and spherical diode in the range 10 À5 < r c =r a < 500, where r a and r c are, respectively, the anode and cathode radius.

No abstract

In this work we consider how surface-adherent bacterial biofilm communities respond in flowing systems.We simulate the fluid-structure interaction and separation process using the immersed boundary method.In these simulations we model and simulate different density and viscosity values of the biofilm than that of the surrounding fluid. The simulation also includes breakable springs connecting the bacteria in the biofilm.This allows the inclusion of erosion and detachment into the simulation. We use the incompressible Navier-Stokes (N-S) equations to describe the motion of the flowing fluid. We discretize the fluid equations using finite differences and use a geometric multigrid method to solve the resulting equations at each time step.The use of multigrid is necessary because of the dramatically different densities and viscosities between the biofilm and the surrounding fluid. We investigate and simulate the model in both two and three dimensions.Our method differs from previous attempts of using IBM for modeling biofilm/flow interactions in the following ways: the density and viscosity of the biofilm can differ from the surrounding fluid, and the Lagrangian node locations correspond to experimentally measured bacterial cell locations from 3D images taken of Staphylococcus epidermidis in a biofilm.