Biofilm growth: a multi-scale and coupled fluid-structure interaction and mass transport approach

In this paper, we propose a novel approach for modelling biofilm growth. It is based on a finite element method and includes both fluid-structure interaction (FSI) as well as scalar transport effects. Due to the different time-scales of the involved phenomena, the growth of the biofilm structure is coupled with the FSI and mass transport through a multi-scale approach in time. In each hydrodynamic time step, first the non-linear FSI problem is solved followed by the scalar transport equations, using the information on velocities and deformations obtained in the FSI step. After a steady state solution is reached, information on mass fluxes and stresses are passed to the growth model. At this point, the growth is calculated for a biological time step larger than the hydrodynamic one and based on the mass flux through the interface and on normal and shear stresses on it. This type of approach can significantly contribute to the understanding of biofilm development in fluid flows, since the influence of hydrodynamic conditions and availability of nutrients is well known to have effects on biofilm development. Therefore, for the purpose of understanding biofilm macro-scale dynamics, it is essential to adopt a modeling approach, which takes into account all the relevant aspects, like fluid flow, structure deformation, mass transport and their effect on biofilm growth and erosion. First numerical examples demonstrate the suitability of the proposed model to catch the main features of a growing biofilm structure.