Speaker
Description
Many biological systems contain material components that are repaired and replaced over time. One common example is the extra-cellular matrix, an interconnected network of proteins that provides chemical and mechanical protection and support in many systems, for example in tissue basement membranes and bacterial biofilms. The building blocks in these systems can be supplied by accompanying cells, with stressed, damaged or degraded material extracted, leading to a turnover in the underlying material of the network. Questions remain as to how the bulk mechanical properties of the material is affected by this microscale material replacement.
I will present a mathematical model, based on a system of springs, that aims to capture how microscale replacement of elastic material can lead to different observed bulk mechanical behaviours. This model evolves an underlying distribution of material via a population-style model governed by underlying energy barriers, with feedback between the material distribution and the local mechanical deformation. Numerical experiments and mathematical analysis reveal emergent viscoelastic behaviours over sufficiently long times, despite the system behaving purely elastically at any instant. We use this to determine effective bulk parameters from supplied microscale behaviours. Despite the model’s simplicity, it has interesting characteristics that are biologically-relevant.
