Journal of Theoretical Medicine
Volume 3 (2001), Issue 3, Pages 161-175
doi:10.1080/10273660108833072

A New Deterministic Spatio-Temporal Continuum Model for Biofilm Development

Herman J. Eberl,1,3 David F. Parker,2 and Mark C. M. Van Loosdrecht3

1GSF National Research Center for Environment and Health Inst. Biomathematics and Biometry, 85764 Neuherberg, Gennany
2Department of Mathematics and Statistics, University of Edinburgh, EH9 3JZ, UK
3Department of Biochemical Engineering, Delft UT, 2628BC Delft, The Netherlands

Received 22 March 2000; Accepted 28 July 2000

Copyright © 2001 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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.