Inverse analysis of material parameters in coupled multi-physics biofilm models

Abstract

In this article we propose an inverse analysis algorithm to find the best fit of multiple material parameters in different coupled multi-physics biofilm models. We use a nonlinear continuum mechanical approach to model biofilm deformation that occurs in flow cell experiments. The objective function is based on a simple geometrical measurement of the distance of the fluid biofilm interface between model and experiments. A Levenberg-Marquardt algorithm based on finite difference approximation is used as an optimizer. The proposed method uses a moderate to low amount of model evaluations. For a first presentation and evaluation the algorithm is applied and tested on different numerical examples based on generated numerical results and the addition of Gaussian noise. Achieved numerical results show that the proposed method serves well for different physical effects investigated and numerical approaches chosen for the model. Presented examples show the inverse analysis for multiple parameters in biofilm models including fluid-solid interaction effects, poroelasticity, heterogeneous material properties and growth.

Bayesian calibration of coupled computational mechanics models under uncertainty based on interface deformation

“…Euclidean distance at measurement points The first approach is an Euclidean distance measure as presented in [12]. At several selected points on the experimentally observed biofilm surface, specific directions are chosen and the distance to the corresponding deformed interface resulting from the forward model simulation is measured.…”

“…At several selected points on the experimentally observed biofilm surface, specific directions are chosen and the distance to the corresponding deformed interface resulting from the forward model simulation is measured. As discussed in [12] measurement points should be selected in regions of significant, characteristic displacements. Measurement directions should be chosen normal to the observed interface.…”

“…Although the presented calibration approach is equivalently applicable for single field problems with deformable boundaries we take the challenge of a coupled multi-physics model of FSI because we want to advertise the benefit of the approach in such applications. A variety of different models for biofilms are available and also further effects can be included (see, e.g., [12,51]), which would just lead to different forward models.…”

“…We chose the same problem setup as presented in [12]. The biofilm geometry is inspired by analyses done on experimental results in [11,14].…”

“…Biofilms usually develop on surfaces exposed to fluid flows and therefore a mechanical model must include the FSI between biofilm surface and the fluid. As the capability of computational mechanical models of fluid-solid interaction increases, the inclusion of such models in deterministic inverse analysis of biofilms has emerged in recent years [11,12]. One of the best approaches to acquire image data of biofilms is via optical coherence tomography (OCT) in flow cell experiments, as used in, e.g., [11,13,14].…”