Finite Element Implementation of Neutral Solute Transport in Porous Biological Soft Tissues Under Finite Deformation

The physiological function of biological tissues and cells is critically dependent on the transport of various solutes, such as nutrients, cytokines, hormones, and waste products. Transport in such media may be significantly hindered by the porous solid matrix, which may impart anisotropic transport properties to the solutes. Furthermore, large deformations of soft tissues and cells may significantly alter these transport properties due to concomitant alterations in pore volume and structure. Another potential influence of the porous solid matrix is steric volume exclusion resulting from the ratio of solute size and pore size distribution. This steric effect implies that solute concentration inside a tissue or cell may be less than the concentration in a surrounding bath, and this limit on solubility may be exacerbated under finite deformation due to changes in pore volume. Finally, the osmotic pressurization of the interstitial fluid may deviate from ideal physico-chemical behavior and this deviation may be dependent on the state of strain in the solid matrix. Therefore, a finite element framework that can accommodate solid-solute momentum exchanges, strain-induced anisotropy in transport properties and solubility, and strain-dependent non-ideal osmotic response, can provide an important modeling tool in the biomechanics of soft tissues and cells.