Biofilms as poroelastic materials

TL;DR

This work develops a three‑dimensional poroelastic model for biofilms spreading on an agar/air interface, treating the biofilm as a biphasic mixture of biomass and interstitial liquid. Elastic deformation, fluid transport, osmotic effects, and chemical species are coupled, with two moving boundaries described by Von Kármán equations at the biofilm–agar interface and lubrication theory at the biofilm–air interface. The authors couple the continuum model to discrete cellular activity via cellular automata to generate residual growth stresses, and they introduce an image‑processing–based ROF denoising step to smooth these tensors for stable numerical integration. This framework enables unified analysis of swelling, wrinkle formation, and spreading driven by nutrient uptake and osmotic flux, with potential implications for understanding biofilm resilience and infection control.

Abstract

Biofilms are bacterial aggregates encased in a self-produced polymeric matrix which attach to moist surfaces and are extremely resistant to chemicals and antibiotics. Recent experiments show that their structure is defined by the interplay of elastic deformations and liquid transport within the biofilm, in response to the cellular activity and the interaction with the surrounding environment. We propose a poroelastic model for elastic deformation and liquid transport in three dimensional biofilms spreading on agar surfaces. The motion of the boundaries can be described by the combined use of Von Karman type approximations for the agar/biofilm interface and thin film approximations for the biofilm/air interface. Bacterial activity informs the macroscopic continuous model through source terms and residual stresses, either phenomenological or derived from microscopic models. We present a procedure to estimate the structure of such residual stresses, based on a simple cellular automata description of bacterial activity. Inspired by image processing, we show that a filtering strategy effectively smooths out the rough tensors provided by the stochastic cellular automata rules, allowing us to insert them in the macroscopic model without numerical instability.

Figures (3)

• Figure 1: Schematic representation of a biofilm: (a) Microscopic structure containing biomass (cells, polymeric mesh forming the extracellular matrix), fluid and dissolved substances, (b) Macroscopic view of the configuration under study: a biofilm growing on an agar block in contact with air.
• Figure 2: Wrinkle branching and coarsening in a spreading film.
• Figure 3: (a) $\varepsilon_{11}^0$ component of the residual strain tensor when $N=1$. (b) Averaged $\varepsilon_{11}^0$ component when $N=10$. (c) Averaged $\varepsilon_{11}^0$ component when $N=100$. (d) Filtered $\varepsilon_{11}^0$ component when $N=1$. (e) Filtered $\varepsilon_{11}^0$ component when $N=10$. (f) Filtered $\varepsilon_{11}^0$ component when $N=100$. The light peaks mark regions where the inicial cell population is larger. In those regions, the nutrient concentration depletes while the waste concentration increases, triggering cell dead by lack of resources and biochemical stress. Stresses become higher in the outer ring due to higher availability of resources and higher division rates. As the number of averaged $N$ runs of the cellular automata step grows, the averages become smoother and the underlying spatial structure is better defined. Using filters, the spatial structure is already visible when $N=1$ and is well defined with a few more trials.