An analytical poroelastic model of a spherical tumor embedded in normal tissue under creep compression.
An analytical model for a spherical poroelastic tumor embedded in normal poroelastic tissues under creep compression is presented in this paper. The tissue is modeled as a cylindrical sample containing a spherical inclusion having different material properties. Analytical expression for the volumetric strain generated inside the inclusion during creep compression is obtained. Error analysis is carried out by comparing the results from the developed analytical model with corresponding results obtained from an established finite element software for a number of samples with different material properties. The error is found to be below 2.5% for the samples with a small inclusion and 7% in the samples with a large inclusion. The analytical solutions reported in this paper can greatly impact elasticity imaging techniques aiming at reconstructing mechanical properties of tumors such as Young's modulus, Poisson's ratio, interstitial permeability and vascular permeability.