Analytical Solutions to Axisymmetric Plane Strain Porous Media-Transport Models in Large Arteries

Theoretical and numerical finite element models (FEMs) have been developed for analysis of coupled structural-fluid-species transport in soft tissues [1–3]. Here analytical solutions for coupled diffusive-convective transport of a single, neutral species in soft tissues are presented. Based on experimental observations [4], osmotic pressure and partial Onsager coupling of species transport can be neglected for large mobile species in rabbit carotid arteries. These analytical solutions provide a starting point for development of solutions to more complex problems and allow verification of the associated FEMs under development in our laboratory. The analytical solutions will allow comparison of elastic and poroelastic-species transport for axisymmetric, plane strain in thick-walled arteries including expressions for displacement, strain, stress, pore fluid pressure, and concentration fields. The initial models considered here will be steady state (SS) solutions for compressible, linear, isotropic materials undergoing small strains.