Shear modulus reconstruction by ultrasonically measured strain ratio

Abstract

In addition to a description of our three previously developed one-dimensional (1D) methods from the viewpoint of shear modulus reconstruction using the strain ratio, two new methods for stabilizing the 1D methods are described, together with their limitations. As confirmed using human in vivo breast tissues, method 1 for evaluating the strain ratio itself is useful when the measurement accuracy of the strain distribution is high. However, because tissues having high shear moduli, such as scirrhous carcinoma, often form singular points/regions, both methods 2 and 3 using the strain ratio (initial estimate) and a regularization method are effective for realizing a unique, stable, useful shear modulus reconstruction. Because method 3 carries out implicit integration only at singular points/regions, whereas method 2 carries out implicit integration throughout the region of interest (ROI), the smaller number of singular points enables more rapid shear modulus reconstruction by method 3 than by method 2. Like method 1, method 3 is also useful when the measurement accuracy of the strain distribution is high. However, when evaluating strain distribution in an ROI with a high spatial resolution to obtain a shear modulus reconstruction having a high spatial resolution, shear modulus reconstructions obtained by methods 1, 2, and 3 often become laterally unstable due to the instability and low accuracy of the strains in the reference regions (reference strains), i.e., regularization in methods 2 and 3 cannot reduce the instability in the initial estimate. To cope with this instability, (i) the reconstruction obtained by calculating the strain ratio should be low-pass filtered; for breast tissues, in particular, the reconstruction of the inverse shear modulus should be low-pass filtered, not the reconstruction of the shear modulus. (ii) Otherwise, when using homogeneous regions as a reference, such as a block of reference material, fatty tissue, or parenchyma, evaluation of the reference strains with a low spatial resolution is effective. Although such evaluation yields a stable reconstruction with a high spatial resolution compared with that obtained by the low-pass filtering of the strain ratio, we confirmed through simulations that, when reducing artifacts due to a 1D reconstruction of the shear modulus, the evaluation yields a low-accuracy reconstruction value of inhomogeneity. In contrast, in such a case the low-pass filtering of the strain ratio yields a more accurate reconstruction value. All the above-mentioned methods using the strain ratio realize real-time shear modulus reconstruction and should be selected appropriately in conventional ultrasonic imaging equipment by considering the application of the reconstruction (i.e., in accordance with the measurement accuracy of the strains and the occurrence of artifacts).