Estimation of degree of anisotropy in transversely isotropic (TI) elastic materials from Acoustic Radiation Force (ARF)-induced peak displacements

Abstract

In this work, we evaluate if directional differences in the mechanical properties of transversely anisotropic (TI) materials may be interrogated using Acoustic Radiation Force Impulse (ARFI) imaging. We hypothesize that ARFI-induced peak displacements (PDs) will vary depending on the orientation of the ARFI excitation to the TI material's axis of symmetry (AoS) when an asymmetrical ARFI excitation is employed, but not when a symmetrical ARFI excitation is used. We further hypothesize that the ratio of the PDs induced with the long axis of an asymmetrical ARFI excitation oriented along versus across the material AoS will be related to the degree of anisotropy of the material. These hypothesizes were tested in silico using finite element method (FEM) models and Field II. ARFI excitations had F/1.5, 3, 4, or 5 focal configurations, with the F/1.5 case having the most asymmetrical and the F/5 case having the most symmetrical point spread function (2D PSF) at the focal depth. These excitations were implemented for ARFI imaging in 18 different TI materials with varying degrees of anisotropy. The ratio of PDs at the focal depth when the AoS was oriented along versus across the long axis of the ARFI-2D PSF was calculated. The degree of anisotropy in the materials was represented by the ratio of the longitudinal and transverse shear modulus and by the ratio of the longitudinal and transverse Young's modulus. To describe the relationship between the ratio of PDs and material anisotropy, piecewise linear regression of the ratio of PDs versus the ratio of shear moduli and of the ratio of PDs versus the ratio of Young's moduli were calculated. The slopes were highest for the F/1.5 ARFI excitation, indicating that the ratio of PDs was most strongly impacted by the material orientation when the ARFI impulse was most asymmetrical. On the contrary, the slope was roughly zero for the F/5 ARFI excitation, which indicates that PD did not depend on the orientation of the material when the ARFI excitation was symmetrical. These results suggest that symmetrical ARFI focal configurations are desirable when the orientation of the ARFI excitation to the AoS is not specifically known and standardization of measurement is important, such as for longitudinal or cross-sectional studies of anisotropic organs. However, asymmetrical focal configurations are useful for exploiting anisotropy. Finally, the ratio of PDs reflects degree of anisotropy in TI materials.