An Analytical Poroelastic Model of a Nonhomogeneous Medium Under Creep Compression for Ultrasound Poroelastography Applications—Part I

An analytical theory for the unconfined creep behavior of a cylindrical inclusion (simulating a soft tissue tumor) embedded in a cylindrical background sample (simulating normal tissue) is presented and analyzed in this paper. Both the inclusion and the background are considered as fluid-filled, porous materials, each of them being characterized by a set of mechanical properties. Specifically, in this paper, the inclusion is considered to be less permeable than the background. The cylindrical sample is compressed using a constant pressure within two frictionless plates and is allowed to expand in an unconfined way along the radial direction. Analytical expressions for the effective Poisson's ratio (EPR) and fluid pressure inside and outside the inclusion are derived and analyzed. The theoretical results are validated using finite element models (FEMs). Statistical analysis shows excellent agreement between the results obtained from the developed model and the results from FEM. Thus, the developed theoretical model can be used in medical imaging modalities such as ultrasound poroelastography to extract the mechanical parameters of tissues and/or to better understand the impact of different mechanical parameters on the estimated displacements, strains, stresses, and fluid pressure inside a tumor and in the surrounding tissue.