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.

翻译：生物膜是由细菌自产聚合物基质包裹而成的聚集体，附着于潮湿表面，对化学物质和抗生素具有极强的抗性。最新实验表明，其结构由弹性变形与生物膜内液体传输之间的相互作用所决定，这种相互作用响应于细胞活动及与周围环境的交互。我们提出一个多孔弹性模型，用以描述在琼脂表面扩展的三维生物膜中的弹性变形与液体传输。边界运动可通过联合使用冯·卡门型近似（描述琼脂/生物膜界面）和薄膜近似（描述生物膜/空气界面）来描述。细菌活动通过源项和残余应力（无论是现象学模型还是源自微观模型）影响宏观连续模型。我们提出一种基于简单元胞自动机描述细菌活动的方法，用于估算此类残余应力的结构。受图像处理启发，我们证明了一种滤波策略可有效平滑由随机元胞自动机规则产生的粗糙张量，从而使其能够在不引发数值不稳定的情况下嵌入宏观模型中。