A New Deterministic Spatio-Temporal Continuum Model for Biofilm Development
Open Access
- 1 January 2001
- journal article
- Published by Hindawi Limited in Journal of Theoretical Medicine
- Vol. 3 (3), 161-175
- https://doi.org/10.1080/10273660108833072
Abstract
A new mathematical model for the development of spatially heterogeneous biofilm structures is presented. Unlike previous hybrid discrete/continuum models it is a continuum model throughout, describing the interaction of nutrient availability and biomass production. Spatial biomass spreading is described by a nonlinear density-dependent diffusion mechanism. The diffusion operator degenerates for small biomass densities and is singular at the biomass density bound. The model can be interpreted as a predator-prey model for biomass and nutrients. First numerical simulations show that the model is able to predict experimentally observed cluster-and-channel biofilm structures. The results are reliable and in qualitatively good agreement with experimental expectations.Keywords
Funding Information
- European Commission (ERBFM RX-CI 97-0114, ERBFM C;E-CT 95--005 1)