Numerical and experimental investigation of multi-species bacterial co-aggregation

This paper deals with the mathematical modeling of bacterial co-aggregation and its numerical implementation in a FEM framework. Since the concept of co-aggregation refers to the physical binding between cells of different microbial species, a system composed of two species is considered in the modeling framework. The extension of the model to an arbitrary number of species is straightforward. In addition to two-species (multi-species growth) dynamics, the transport of a nutritional substance and the extent of co-aggregation are introduced into the model as the third and fourth primary variables. A phase-field modeling approach is employed to describe the co-aggregation between the two species. The mathematical model is three-dimensional and fully based on the continuum description of the problem without any need for discrete agents which are the key elements of the individual-based modeling approach. It is shown that the use of a phase-field-based model is equivalent to a particular form of classical diffusion-reaction systems. Unlike the so-called mixture models, the evolution of each component of the multi-species system is captured thanks to the inherent capability of phase-field modeling in treating systems consisting of distinct multi-phases. The details of numerical implementation in a FEM framework are also presented. Indeed, a new multi-field user element is developed and implemented in ANSYS for this multiphysics problem. Predictions of the model are compared with the experimental observations. By that, the versatility and applicability of the model and the numerical tool are well established.