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Simulating Biofilm Deformation and Detachment with the Immersed Boundary Method

Part of: Basic methods in fluid mechanics Coupling of solid mechanics with other effects Incompressible viscous fluids Materials of strain-rate type and history type, other materials with memory

Published online by Cambridge University Press:  16 March 2016

Rangarajan Sudarsan ,
Sudeshna Ghosh ,
John M. Stockie  and
Hermann J. Eberl
Rangarajan Sudarsan*
Affiliation:
Department of Mathematics and Statistics and Biophysics Interdepartmental Graduate Program, University of Guelph, ON, N1G 2W1, Canada
Sudeshna Ghosh
Affiliation:
Department of Mathematics, Simon Fraser University, Burnaby, BC, V5A 1S6, Canada
John M. Stockie
Affiliation:
Department of Mathematics, Simon Fraser University, Burnaby, BC, V5A 1S6, Canada
Hermann J. Eberl
Affiliation:
Department of Mathematics and Statistics and Biophysics Interdepartmental Graduate Program, University of Guelph, ON, N1G 2W1, Canada
*
*Corresponding author. Email addresses:[email protected] (R. Sudarsan), [email protected] (S. Ghosh), [email protected] (J. M. Stockie), [email protected] (H. J. Eberl)
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Abstract

We apply the immersed boundary (or IB) method to simulate deformation and detachment of a periodic array of wall-bounded biofilm colonies in response to a linear shear flow. The biofilm material is represented as a network of Hookean springs that are placed along the edges of a triangulation of the biofilm region. The interfacial shear stress, lift and drag forces acting on the biofilm colony are computed by using fluid stress jump method developed by Williams, Fauci and Gaver [Disc. Con-tin. Dyn. Sys. B 11(2):519–540, 2009], with a modified version of their exclusion filter. Our detachment criterion is based on the novel concept of an averaged equivalent continuum stress tensor defined at each IB point in the biofilm which is then used to determine a corresponding von Mises yield stress; wherever this yield stress exceeds a given critical threshold the connections to that node are severed, thereby signalling the onset of a detachment event. In order to capture the deformation and detachment behaviour of a biofilm colony at different stages of growth, we consider a family of four biofilm shapes with varying aspect ratio. For each aspect ratio, we varied the spacing between colonies to investigate role of spatial clustering in offering protection against detachment. Our numerical simulations focus on the behaviour of weak biofilms (with relatively low yield stress threshold) and investigate features of the fluid-structure interaction such as locations of maximum shear and increased drag. The most important conclusions of this work are: (a) reducing the spacing between colonies reduces drag by from 50 to 100% and alters the interfacial shear stress profile, suggesting that even weak biofilms may be able to grow into tall structures because of the protection they gain from spatial proximity with other colonies; (b) the commonly employed detachment strategy in biofilm models based only on interfacial shear stress can lead to incorrect or inaccurate results when applied to the study of shear induced detachment of weak biofilms. Our detachment strategy based on equivalent continuum stresses provides a unified and consistent IB framework that handles both sloughing and erosion modes of biofilm detachment, and is consistent with strategies employed in many other continuum based biofilm models.

Keywords

Immersed boundarymethodbiofilmsdetachmentvon Mises yield stressinterfacial shear stressdrag and lift force

MSC classification

Secondary: 74D10: Nonlinear constitutive equations 74F10: Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.) 76D05: Navier-Stokes equations 76M20: Finite difference methods
Type
Research Article
Information
Communications in Computational Physics , Volume 19 , Issue 3 , March 2016 , pp. 682 - 732
Copyright
Copyright © Global-Science Press 2016 

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