An analytical poroelastic model for ultrasound elastography imaging of tumors

The mechanical behavior of biological tissues has been studied using a number of mechanical models. Due to the relatively high fluid content and mobility, many biological tissues have been modeled as poroelastic materials. Diseases such as cancers are known to alter the poroelastic response of a tissue. Tissue poroelastic properties such as compressibility, interstitial permeability and fluid pressure also play a key role for the assessment of cancer treatments and for improved therapies. At the present time, however, a limited number of poroelastic models for soft tissues are retrievable in the literature, and the ones available are not directly applicable to tumors as they typically refer to uniform tissues. In this paper, we report the analytical poroelastic model for a non-uniform tissue under stress relaxation. Displacement, strain and fluid pressure fields in a cylindrical poroelastic sample containing a cylindrical inclusion during stress relaxation are computed. Finite element simulations are then used to validate the proposed theoretical model. Statistical analysis demonstrates that the proposed analytical model matches the finite element results with less than 0.5% error. The availability of the analytical model and solutions presented in this paper may be useful to estimate diagnostically relevant poroelastic parameters such as interstitial permeability and fluid pressure, and, in general, for a better interpretation of clinically-relevant ultrasound elastography results.