Parametric Analysis of SV Mode Shear Waves in Transversely Isotropic Materials Using Ultrasonic Rotational 3-D SWEI

Ultrasonic rotational 3-D shear wave elasticity imaging (SWEI) has been used to induce and evaluate multiple shear wave modes, including both the shear horizontal (SH) and shear vertical (SV) modes in in vivo muscle. Observations of both the SH and SV modes allow the muscle to be characterized as an elastic, incompressible, transversely isotropic (ITI) material with three parameters: the longitudinal shear modulus <inline-formula> <tex-math notation="LaTeX">$\mu _{L}$ </tex-math></inline-formula>, the transverse shear modulus <inline-formula> <tex-math notation="LaTeX">$\mu _{T}$ </tex-math></inline-formula>, and the tensile anisotropy <inline-formula> <tex-math notation="LaTeX">$\chi _{E}$ </tex-math></inline-formula>. Measurement of the SV wave is necessary to characterize <inline-formula> <tex-math notation="LaTeX">$\chi _{E}$ </tex-math></inline-formula>, but the factors that influence SV mode generation and characterization with ultrasonic SWEI are complicated. This work uses Green’s function (GF) simulations to perform a parametric analysis to determine the optimal interrogation parameters to facilitate visualization and quantification of SV mode shear waves in muscle. We evaluate the impact of five factors: <inline-formula> <tex-math notation="LaTeX">$\mu _{L}$ </tex-math></inline-formula>, <inline-formula> <tex-math notation="LaTeX">$\mu _{T}$ </tex-math></inline-formula>, <inline-formula> <tex-math notation="LaTeX">$\chi _{E}$ </tex-math></inline-formula>, fiber tilt angle <inline-formula> <tex-math notation="LaTeX">$\theta _{\text {tilt}}$ </tex-math></inline-formula>, and F-number of the push geometry on SV mode speed, amplitude, and rotational distribution. These analyses demonstrate that the following hold: 1) as <inline-formula> <tex-math notation="LaTeX">$\mu _{L}$ </tex-math></inline-formula> increases, SV waves decrease in amplitude so are more difficult to measure in SWEI imaging; 2) as <inline-formula> <tex-math notation="LaTeX">$\mu _{T}$ </tex-math></inline-formula> increases, the SV wave speeds increase; 3) as <inline-formula> <tex-math notation="LaTeX">$\chi _{E}$ </tex-math></inline-formula> increases, the SV waves increase in speed and separate from the SH waves; 4) as fiber tilt angle <inline-formula> <tex-math notation="LaTeX">$\theta _{\text {tilt}}$ </tex-math></inline-formula> increases, the measurable SV waves remain approximately the same speed, but change in strength and in rotational distribution; and 5) as the push beam geometry changes with F-number, the measurable SV waves remain approximately the same speed, but change in strength and rotational distribution. While specific SV mode speeds depend on the combinations of all parameters considered, measurable SV waves can be generated and characterized across the range of parameters considered. To maximize measurable SV waves separate from the SH waves, it is recommended to use an <inline-formula> <tex-math notation="LaTeX">${F}/{1}$ </tex-math></inline-formula> push geometry and <inline-formula> <tex-math notation="LaTeX">$\theta _{\text {tilt}} = {15}^{\circ} $ </tex-math></inline-formula>.