An Analytical Model of Tumors With Higher Permeability Than Surrounding Tissues for Ultrasound Elastography Imaging

Abstract

Cancerous tissues are known to possess different poroelastic properties with respect to normal tissues. Interstitial permeability is one of these properties, and it has been shown to be of diagnostic relevance for the detection of soft tissue cancers and for assessment of their treatment. In some cases, interstitial permeability of cancers has been reported to be lower than the surrounding tissue, while in other cases interstitial permeability of cancers has been reported to be higher than the surrounding tissue. We have previously reported an analytical model of a cylindrical tumor embedded in a more permeable background. In this paper, we present and analyze a poroelastic mathematical model of a tumor tissue in cylindrical coordinate system, where the permeability of the tumor tissue is assumed to be higher than the surrounding normal tissue. A full set of analytical expressions are obtained for radial displacement, strain, and fluid pressure under stress relaxation testing conditions. The results obtained with the proposed analytical model are compared with corresponding finite element analysis results for a broad range of mechanical parameters of the tumor. The results indicate that the proposed model is accurate and closely resembles the finite element analysis. The availability of this model and its solutions can be helpful for ultrasound elastography applications such as for extracting the mechanical parameters of the tumor and normal tissue and, in general, to study the impact of poroelastic material properties in the assessment of tumors.