Spatial Effect on Separatrix of Two-Cell System and Parameter Sensitivity Analysis

Abstract

Inflammation in biological tissues follows a dynamical process where upon injury, interactions between cell types and exchange of growth factors occur. Depending on the distribution of different cell types in space, healing or fibrosis occurs. This process is clearly spatially heterogeneous. An existing modeling framework for this process assumes a spatially homogeneous distribution of fibroblasts and macrophages and is therefore unable to capture spatial effects. We extend this framework to obtain a spatially heterogeneous two-cell circuit also containing cell migration, chemotaxis and cytokine diffusion. By means of a physical property of the resulting PDE model, a decoupled multiscale solution strategy can be derived, where each linear problem is approximated by finite element methods. A numerical investigation illustrates a clear impact of spatial effects on the separatrix of the PDE model. We use non-intrusive methods from the field of uncertainty quantification to conduct a sensitivity analysis of the most uncertain model parameters, enabling us to quantify this impact.