Effect of lesion boundary conditions on axial strain elastograms: a parametric study

Ultrasound elastography produces strain images of compliant tissues under quasi-static compression. When a material is compressed, there are several parameters that affect the stress-distribution and, hence, the strain distribution in the material. The state of bonding of an inclusion to the background material is a critical parameter. Heretofore, in the field of elastography, the inclusion was considered to be firmly bonded to the background material and analytical solutions were derived for the elasticity problem involving simple geometries like circular inclusion (for two dimensional [2D]) and spherical inclusion (three dimensional [3D]). Under these conditions, simple analytical expressions relating the strain contrast to the modulus contrast were derived. However, it is known that the state of bonding of some tumors to their surrounding tissues depends on the type of the lesion. For example, benign lesions of the breast are known to be loosely bonded to the surrounding tissue, while malignant breast lesions are firmly bonded. In this study, we perform a parametric study using finite element modeling (FEM) to investigate the validity of the analytical expression relating the strain contrast to the modulus contrast, when the state of bonding at the inclusion/background interface spans a large dynamic range. The results suggest that estimated modulus contrast using the analytical expression is sensitive to the region-of-interest within the inclusion that is considered in the computation of the strain contrast. By considering the inclusion region lying along the axis of lateral symmetry instead of whole region of the inclusion, the estimated modulus contrast (obtained using the analytical expression present in the literature) can be computed to within a systematic error of 10% of the actual modulus contrast. Additional estimation errors are expected to accrue in experimental and in vivo conditions.