Inverse problems for a model of biofilm growth

TL;DR

This paper addresses the inverse problem of determining key parameters in a nonlinear PDE model of biofilm growth, providing theoretical guarantees and numerical methods for robust parameter reconstruction from measurements.

Contribution

It introduces a new inverse problem framework for biofilm models, including uniqueness proofs and numerical strategies for reconstructing multiple physical parameters.

Findings

Unique reconstruction of biofilm model parameters achieved.

Additional data improves parameter estimation accuracy.

Numerical methods demonstrate practical applicability.

Abstract

A bacterial biofilm is an aggregate of micro-organisms growing fixed onto a solid surface, rather than floating freely in a liquid. Biofilms play a major role in various practical situations such as surgical infections and water treatment. We consider a non-linear PDE model of biofilm growth subject to initial and Dirichlet boundary conditions, and the inverse coefficient problem of recovering the unknown parameters in the model from extra measurements of quantities related to the biofilm and substrate. By addressing and analysing this inverse problem we provide reliable and robust reconstructions of the primary physical quantities of interest represented by the diffusion coefficients of substrate and biofilm, the biomass spreading parameters, the maximum specific consumption and growth rates, the biofilm decay rate and the half saturation constant. We give particular attention to the constant coefficients involved in the leading-part non-linearity, and present a uniqueness proof and some numerical results. In the course of the numerical investigation, we have identified extra data information that enables improving the reconstruction of the eight-parameter set of physical quantities associated to the model of biofilm growth.