Wave Propagation: Theories and Applications
Chapter in a Book
Studies have found that shear moduli, having the dynamic range of several orders of magnitude for various biological tissues, are highly correlated with the pathological statues of human tissue such as livers. Shear moduli can be investigated by measuring the attenuation and velocity of the shear wave propagation in a tissue region. Many efforts have been made to measure shear wave propagations induced by different types of force, which include the motion force of human organs, external applied force, and ultrasound radiation force.
In the past 15 years, ultrasound radiation force has been successfully used to induce tissue motion for imaging tissue elasticity. Vibroacoustography (VA) uses bifocal beams to remotely induce vibration in a tissue region and detect the vibration using a hydrophone. The vibration center is sequentially moved in the tissue region to form a two-dimensional image. Acoustic Radiation Force Imaging (ARFI) uses focused ultrasound to apply localized radiation force to small volumes of tissue for short durations and the resulting tissue displacements are mapped using ultrasonic correlation based methods. Supersonic shear image remotely vibrates tissue and sequentially moves vibration center along the beam axis to create intense shear plan wave that is imaged at a high frame rate (5000 frames per second). These image methods provide measurements of tissue elasticity, but not the viscosity.
Because of the dispersive property of biological tissue, the induced tissue displacement and the shear wave propagation are frequency dependent. Tissue shear property can be modeled by several models including Kelvin-Voigt (Voigt) model, Maxwell model, and Zener model. The Voigt model effectively describes the creep behavior of tissue, The Maxwell model effectively describes the relaxation process, and the Zener model effectively describes both creep and relaxation but it requires one extra parameter. The Voigt model is often used by many researchers because of its simplicity and the effectiveness of modeling soft tissue. The Voigt model consists of a purely viscous damper and a purely elastic spring connected in parallel. For Voigt tissue, the tissue motion at a very low frequency largely depends on the elasticity, while the motion at a very high frequency largely depends on the viscosity. In general, the tissue motion depends on both elasticity and viscosity, and estimates of elasticity by ignoring viscosity are biased or erroneous.
In 1951, Dr. Oestreicher published his work to solve the wave equation for the Voigt soft tissue with harmonic motions. With assumptions of isotropic tissue and plane wave, he derived equations that relate the shear wave attenuation and speed to the elasticity and viscosity of soft tissue. However, Oestreicher’s method was not realized for applications until the half century later.
In the past ten years, Oestreicher’s method was utilized to quantitatively measure both tissue elasticity and viscosity. Ultrasound vibrometry has been developed to noninvasively and quantitatively measure tissue shear moduli. It induces shear waves using ultrasound radiation force and estimates the shear moduli using shear wave phase velocities at several frequencies by measuring the phase shifts of the propagating shear wave over a short distance using pulse echo ultrasound. Applications of the ultrasound vibrometry were conducted for viscoelasticities of liver, bovine and porcine striated muscles, blood vessels, and hearts. A recent in vivo liver study shows that the ultrasound vibrometry can be implemented on a clinical ultrasound scanner of using an array transducer.
One potential application of ultrasound vibrometry is to characterize shear moduli of livers. The shear moduli of liver are highly correlated with liver pathology status. Recently, the shear viscoelasticity of liver tissue has been investigated by several research groups. Most of these studies applied ultrasound radiation force in liver tissue regions, measured the phase velocities of shear wave in a limited frequency range, and inversely solved the Voigt model with an assumption that liver local tissue is isotropic without considering boundary conditions. Because of the boundary conditions, shear wave propagations are impacted by the limited physical dimensions of tissue. Studies shows that considerations of boundary conditions should be taken for characterizing tissue that have limited physical dimensions such as heart, blood vessels, and liver, when ultrasound vibrometry is used.
Zheng, Yi; Chen, Xin; Yao, Aiping; Lin, Haoming; Shen, Yuanyuan; Zhu, Ying; Lu, Minhua; Wang, Tianfu; and Chen, Siping, "Shear Wave Propagation in Soft Tissue with Ultrasound Vibrometry" (2013). Electrical and Computer Engineering Faculty Publications. 1.