The effects of surrounding media on the shear wave propagation in plates as related to the dispersion velocity
Abstract— The calculation of dispersion curves and, therefore, the rheological properties is possible by analyzing how the different phase velocity modes behave in the medium of interest. Shear wave propagation in “thin” organs is affected by the mechanical properties of the tissues surrounding those organs. In order to obtain the proper mechanical properties of such boundary sensitive organs, an analytical solution for the dispersion curves on a plate surrounded by semi-infinite solids was derived and validated.
Keywords — Shear wave; Dispersion Curves; Ultrasound Elastography
Introduction
Through the last decades the use of Shearwave Dispersion Ultrasound Vibrometry (SDUV) has become a powerful tool on the diagnosis and follow-up in many pathologies. This technic is based on the propagation of the shear wave in a medium, applying either acoustic radiation force (ARF) or external actuator [1].
The Dispersion, which is the dependence of the Shear Wave (SW) phase velocity on its frequency, is then used to characterize changes in tissue stiffness, what is often related to pathologies. The calculation of dispersion curves and, therefore, the rheological properties is possible by analyzing how the different phase velocity modes behave in the medium of interest [2].
In many cases this point of interest is located far apart from any boundaries, and can be treated as part of an infinite medium, e.g. organs such as the liver, breast and kidney. But in thin layers, the geometry and border conditions have an important role in how it behaves during shear stress, e.g. organs such as the spleen, myocardium, arteries, bladder and pancreas. In addition, shear wave propagation in “thin” organs is affected by the mechanical properties of the tissues surrounding those organs.
In this paper, we derive an analytical solution for the dispersion curves in plates embedded in semi-infinite solids. Commercial softwares, along with Shear wave propagation in
PVA (Polyvinyl
Keywords — Shear wave; Dispersion Curves; Ultrasound Elastography
Introduction
Through the last decades the use of Shearwave Dispersion Ultrasound Vibrometry (SDUV) has become a powerful tool on the diagnosis and follow-up in many pathologies. This technic is based on the propagation of the shear wave in a medium, applying either acoustic radiation force (ARF) or external actuator [1].
The Dispersion, which is the dependence of the Shear Wave (SW) phase velocity on its frequency, is then used to characterize changes in tissue stiffness, what is often related to pathologies. The calculation of dispersion curves and, therefore, the rheological properties is possible by analyzing how the different phase velocity modes behave in the medium of interest [2].
In many cases this point of interest is located far apart from any boundaries, and can be treated as part of an infinite medium, e.g. organs such as the liver, breast and kidney. But in thin layers, the geometry and border conditions have an important role in how it behaves during shear stress, e.g. organs such as the spleen, myocardium, arteries, bladder and pancreas. In addition, shear wave propagation in “thin” organs is affected by the mechanical properties of the tissues surrounding those organs.
In this paper, we derive an analytical solution for the dispersion curves in plates embedded in semi-infinite solids. Commercial softwares, along with Shear wave propagation in
PVA (Polyvinyl
References: Chen S, Fatemi M, Greenleaf JF. Quantifying elasticity and viscosity from measurement of shearwave speed dispersion. J Acoust Soc Am. 2004; 115:2781–5. [PubMed: 15237800] Chen S, Urban MW, Pislaru C, Kinnick R, Zheng Y, Yao A, Greenleaf JF. Shearwave dispersion ultrasound vibrometry (SDUV) for measuring tissue elasticity and viscosity. IEEE Trans Ultrason Ferroelectr Freq Control. 2009; 56:55–62. [PubMed: 19213632] Michael J. S. Lowe Matrix Techniques for Modeling Ultrasonic Waves in Multilayered Media, IEEE TRANSACTIONS ON ULTRASONICS, FERROELECTRICS, AND FREQUENCY CONTROL, VOL. 42, NO. 4, JULY 1995 D. Alleyne and P. Cawley, "A two-dimensional Fourier transform method for the measurement of propagating multimode signals," J. Acoust. Soc. Am., vol. 89, pp. 1159-1168, 1991. M. Bernal, I. Nenadic, M. W. Urban, and J. F. Greenleaf, "Material property estimation for tubes and arteries using ultrasound radiation force and analysis of propagating modes," J. Acoust. Soc. Am., vol. 129, pp. 1344-1354, 2011.