Beckman Institute for Advanced Science and Technology at the University of Illinois at Urbana-Champaign, Urbana, IL, USA.
IEEE Trans Ultrason Ferroelectr Freq Control. 2011 Feb;58(2):389-98. doi: 10.1109/TUFFC.2011.1816.
The Navier equation describing shear wave propagation in 3-D viscoelastic media is solved numerically with a finite differences time domain (FDTD) method. Solutions are formed in terms of transverse scatterer velocity waves and then verified via comparison to measured wave fields in heterogeneous hydrogel phantoms. The numerical algorithm is used as a tool to study the effects on complex shear modulus estimation from wave propagation in heterogeneous viscoelastic media. We used an algebraic Helmholtz inversion (AHI) technique to solve for the complex shear modulus from simulated and experimental velocity data acquired in 2-D and 3-D. Although 3-D velocity estimates are required in general, there are object geometries for which 2-D inversions provide accurate estimations of the material properties. Through simulations and experiments, we explored artifacts generated in elastic and dynamic-viscous shear modulus images related to the shear wavelength and average viscosity.
用有限差分时域（FDTD）方法数值求解描述三维粘弹性介质中剪切波传播的纳维方程。根据横向散射体速度波形成解，然后通过与非均匀水凝胶模型中的测量波场进行比较进行验证。该数值算法被用作研究在非均匀粘弹性介质中波传播对复杂剪切模量估计的影响的工具。我们使用代数亥姆霍兹反演（AHI）技术从二维和三维模拟和实验速度数据中求解复杂剪切模量。尽管通常需要三维速度估计，但对于某些物体形状，二维反演可以提供材料特性的准确估计。通过模拟和实验，我们研究了与剪切波长和平均粘度相关的弹性和动态粘性剪切模量图像中的伪影。
