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.