Chemomechanical models for soft tissues based on the reconciliation of porous media and swelling polymer theories

The interstitial fluid plays an important role for the deformability of soft biological tissues. While its high bulk modulus is often taken as an argument for tissue incompressibility, its ability to move through the interstitial space and across the boundary permits reversible changes of tissue volume through fluid exchange with the environment, which in turn is affected by the osmotic activity of the tissue constituents. Such coupled phenomena of fluid flow and deformation are characteristic both for hydrated biological tissues and swelling polymers, typically treated within the theory of porous media and chemoelasticity, respectively. In this contribution, the two theories are reconciled for biphasic materials with incompressible constituents and an inviscid liquid phase. Based on this analogy, and starting from the chemoelastic approach, a lean theoretical framework for the modelling of biphasic chemomechanical effects in soft biological tissues is presented. It provides access to fluid flux, variations in chemical potential and osmotic pressure in addition to stress and strain in the tissue. The framework is exemplified in application to arterial tissue, modifying and complementing an established monophasic, incompressible model, and the benefits of the alternative chemomechanical representation are illustrated in numerical examples.