A Hertzian contact mechanics based formulation to improve ultrasound elastography assessment of uterine cervical tissue stiffness

Abstract

Clinical practice requires improved techniques to assess human cervical tissue properties, especially at the internal os, or orifice, of the uterine cervix. Ultrasound elastography (UE) holds promise for non-invasively monitoring cervical stiffness throughout pregnancy. However, this technique provides qualitative strain images that cannot be linked to a material property (e.g., Young's modulus) without knowledge of the contact pressure under a rounded transvaginal transducer probe and correction for the resulting non-uniform strain dissipation. One technique to standardize elastogram images incorporates a material of known properties and uses one-dimensional, uniaxial Hooke's law to calculate Young's modulus within the compressed material half-space. However, this method does not account for strain dissipation and the strains that evolve in three-dimensional space. We demonstrate that an analytical approach based on 3D Hertzian contact mechanics provides a reasonable first approximation to correct for UE strain dissipation underneath a round transvaginal transducer probe and thus improves UE-derived estimates of tissue modulus. We validate the proposed analytical solution and evaluate sources of error using a finite element model. As compared to 1D uniaxial Hooke's law, the Hertzian contact-based solution yields significantly improved Young's modulus predictions in three homogeneous gelatin tissue phantoms possessing different moduli. We also demonstrate the feasibility of using this technique to image human cervical tissue, where UE-derived moduli estimations for the uterine cervix anterior lip agreed well with published, experimentally obtained values. Overall, UE with an attached reference standard and a Hertzian contact-based correction holds promise for improving quantitative estimates of cervical tissue modulus.