A New Deterministic Spatio-Temporal Continuum Model for Biofilm Development. Issue 3 (2001)

• Record Type: Journal Article
• Authors: Eberl Eberl, Herman J. Herman J.; Parker Parker, David F. David F.; Van Loosdrecht Van Loosdrecht, Mark C. M. Mark C. M.
• Is Part Of: Journal of theoretical medicine. Volume 3:Issue 3(2001)
• Page Start: 161
• Page End: 175
• Publication Date: 2001
• Subjects: biofilms -- spatio-temporal mathematical modelling -- density-dependent diffusion -- numerical experiments; Biological models -- Periodicals; Biological systems -- Mathematical models -- Periodicals
• DOI: 10.1080/10273660108833072
• Languages: English
• ISSNs: 1027-3662

Abstract

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.