On the feasibility of quantifying mechanical anisotropy in transversely isotropic elastic materials using acoustic radiation force (ARF)-induced displacements

Abstract

Many soft tissues, including skeletal muscle and kidney, can be modeled astransversely isotropic (TI) materials defined by an axis of symmetry (AoS) perpendicular to a plane of isotropy. In such materials, mechanical properties differ along versus across the AoS. The degree of mechanical anisotropy in TI materials was previously assessed as the ratio of peak displacement (PD) achieved when the long axis of an asymmetric acoustic radiation force (ARF) excitation point spread function (PSF) was aligned along versus across the material’s AoS, but the measurement was qualitative. The objectives of this work were: (i) to derive an empirical model describing the relationship between the PD ratio and shear moduli ratio; (ii) to investigate the impact of ARF excitation PSF aberration due to speed of sound (c), attenuation (α), and dimension of ARF excitation PSF on the empirical model; and (iii) to estimate mechanical anisotropy in excised pig biceps femoris muscles and in vivo pig kidney using the empirical model. The empirical model was derived by simulating ARF Impulse (ARFI) imaging of ‘train’ TI materials (shear moduli ratios varying from 1.0 to 10 in steps of 0.75) and validated on ‘test’ materials (shear moduli ratios varying from 1.25 to 8.75 in steps of 0.75) using finite element method (FEM) models. Siemens VF73 transducer parameter with lateral F/1.5 was simulated for ARFI imaging. The speed of sound and attenuation was set to1540 ms-1 and 0.5 dB/cm/MHZ, respectively for train materials and was set to1540 or 1620 ms-1 and 0.5 or 1.0 dB/cm/MHZ, respectively for test materials. To find the impact of ARF excitation PSF dimension, a matrix array was simulated and the lateral and elevational F/# was set to 2.0 and 3.4, respectively for train materials and was set to 2.0 or 3.0 and 3.4 or 5.1, respectively for test materials. Ultrasound tracking of FEM displacements was performed in Field II with an SNR of 30 dB. The average absolute percent error in predicting shear moduli ratio of all ‘test’ materials was 1.6%. The empirical model was not impacted by the deviation from expected attenuation, sound speed, and ARF excitation PSF dimension. Shear moduli ratios derived using the empirical model matched those derived from shear wave elasticity imaging (SWEI) in pig muscle (model: 4.44 ± 0.47 and SWEI: 4.38 ± 0.27), renal medulla (model: 1.31 ± 0.07 and SWEI: 1.32 ± 0.04) and renal cortex (model: 2.0 ± 0.19 and SWEI: 1.99 ± 0.06). These results suggest the feasibility of using the PD empirical model to quantify mechanical anisotropy in biological tissues.