Reducing discrepancies between 3D and 2D simulations due to cell packing density

Modelling all three spatial dimensions is often much more computationally expensive than modelling a two-dimensional simplification of the same system. Researchers comparing these approaches in individual-based models of microbial biofilms report quantitative, but not qualitative, differences between 2D and 3D simulations. We show that a large part of the discrepancy is due to the different space packing densities of circles versus spheres, and demonstrate methods to compensate for this: the internal density of individuals or the distances between them can be scaled. This result is likely to be useful in similar models, such as smoothed particle hydrodynamics.