Homogenised model linking microscopic and macroscopic dynamics of a biofilm: Application to growth in a plug flow reactor

We propose a new “hybrid” model for the simulation of biofilm growth in a plug flow bioreactor, that combines information from three scales: a microscopic one for the individual bacteria, a mesoscopic or “coarse-grained” one that homogenises at an intermediate scale the quantities relevant to the attachment/detachment process, and a macroscopic one in terms of substrate concentration. In contrast to existing partial differential equations models, this approach is based on a description of biological mechanisms at the individual scale, thus bringing in a biological justification of the attachment/detachment process responsible of the macroscopic behaviour. We found that compared to purely individual based or purely macroscopic models,
• the approximate coarse-grained scale simplifies the change of scales from micro to macro, and speeds up the computation,
• additional information about the stochasticity of the solution, especially at small populations, is revealed compared with the numerical simulations of partial differential equations models. Furthermore, the coarse-grained model can be much more easily adapted to various attachment/detachment hypotheses, that are at the core of the biofilm development.

► A new hybrid discrete continuous model of biofilm growth in a plug flow reactor.
► A coarse grained scale that homogenises the attachment detachment process.
► Comparison of the simulations with solutions of macroscopic PDE.