Longitudinal motion of focused shear wave beams in soft elastic media

Focused Shear Wave Beam Propagation in Tissue-Mimicking Phantoms

OBJECTIVE

Ultrasound transient elastography (TE) technologies for liver stiffness measurement (LSM) utilize vibration of small, flat pistons, which generate shear waves that lack directivity. The most common cause for LSM failure in practice is insufficient shear wave signal at the needed depths. We propose to increase shear wave amplitude by focusing the waves into a directional beam. Here, we demonstrate the generation and propagation of focused shear wave beams (fSWBs) in gelatin.

METHODS

Directional fSWBs are generated by vibration at 200-400 Hz of a concave piston embedded near the surface of gelatin phantoms and measured with high-frame-rate ultrasound imaging. Five phantoms with a range of stiffnesses are employed. Shear wave speeds assessed by fSWBs are compared with those by radiation-force-based methods (2D SWE). fSWB amplitudes are compared to predictions using an analytical model.

RESULTS

fSWB-derived shear wave speeds are in good agreement with 2D SWE. The amplitudes of fSWBs are localized to the LSM region and are significantly greater than unfocused shear waves. Overall agreement with theory is observed, with some discrepancies in the theoretical source condition.

CONCLUSION

Focusing shear waves can increase the signal in the LSM region for TE. Challenges for translation include coupling piston vibration with the patient skin and increased attenuation in vivo compared to the phantoms employed here.

SIGNIFICANCE

Fibrosis is the most predictive measure of patient outcome in non-alcoholic fatty liver disease. Increased shear wave amplitude in the LSM region can reduce fibrosis assessment failure rates by TE, thus reducing the need for invasive methods like biopsy.

Nonlinear propagation of quasiplanar shear wave beams in soft elastic media with transverse isotropy

Model equations are developed for shear wave propagation in a soft elastic material that include effects of nonlinearity, diffraction, and transverse isotropy. A theory for plane wave propagation by Cormack [J. Acoust. Soc. Am. 150, 2566 (2021)] is extended to include leading order effects of wavefront curvature by assuming that the motion is quasiplanar, which is consistent with other paraxial model equations in nonlinear acoustics. The material is modeled using a general expansion of the strain energy density to fourth order in strain that comprises thirteen terms defining the elastic moduli. Equations of motion for the transverse displacement components are obtained using Hamilton's principle. The coupled equations of motion describe diffraction, anisotropy of the wave speeds, quadratic and cubic plane wave nonlinearity, and quadratic nonlinearity associated with wavefront curvature. Two illustrative special cases are investigated. Spatially varying shear vertical wave motion in the fiber direction excites a quadratic nonlinear interaction unique to transversely isotropic soft solids that results in axial second harmonic motion with longitudinal polarization. Shear horizontal wave motion in the fiber plane reveals effects of anisotropy on third harmonic generation, such as beam steering and dependence of harmonic generation efficiency on the propagation and fiber directions.