Abstract
Shear wave beams with spatially varying polarization are characterized here by stretching the medium in the plane perpendicular to the propagation direction. Such a beam is produced in a soft tissue by applying motion perpendicular to the source plane, as with a piston source, due to the quasi-incompressible nature of the medium. In the transversely isotropic (TI) soft tissue, such as muscle, this polarization causes extension and contraction in the fiber direction, resulting in nonlinear propagation effects that are unique to the TI tissue compared to propagation in an isotropic tissue [Cormack, J. Acoust. Soc. Am. 150, 2566 (2021)]. A KZ-type equation is presented that describes a special case of propagation of a shear wave beam with spatially varying polarization in the TI soft tissue, accounting for material anisotropy along with leading-order effects of nonlinearity and diffraction. Solutions for harmonic generation from a time-harmonic source are presented for focused and unfocused Gaussian-derivative distributions of transverse displacement in the source plane. Of practical interest is the longitudinal displacement in the shear wave field, which possesses a second-harmonic component on the axis that results from stretching in the fiber direction. This second harmonic, which is absent in isotropic tissues, may be measured using existing elastography techniques.
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