Mathematical model of biofilm growth

The aim of the paper is to derive a mathematical model of bacterial biofilm growth in two-dimensions using an Individual-Based model (IbM) to describe cell growth behaviour in prescribed environments. The approach extends the ideas of Xavier et al. [1] and Drasdo and Hohme [2]. Bacteria are treated as volume occupying particles that respond in various ways to the concentrations of substrates present, whereby new cellular growth requires can lead to the repositioning of neighbouring cells in order to accommodate the changes in local volume. A Metropolis algorithm is applied to handle the cellular positioning adjustment and the coupled reaction-diffusion equations for each of the substrates are solved using finite-difference methods. The advantage of an IbM approach is that it can easily be extended to include multiple bacteria species with varying traits responding to multiple diffusible substrates. As an example, results are presented for a biofilm consisting of two species, which have differing tolerances to low nutrient environments.