Brigham, John C.

We implemented a three-dimensional solver for simulating the ultrasound radiation force induced shear wave motion in viscoelastic media using a mapped Chebyshev pseudospectral method. The solver used a body force field that is simulated by the Field II program as the excitation. Then, a velocity-stress formulation was used to calculate the shear wave motion. We used a Voigt model to describe tissue viscoelasticity, and the viscosity is introduced by memory variables and auxiliary differential equations. The top boundary of the domain had a fixed boundary condition to mimic the interaction between an ultrasound probe and the tissue surface. All other sides of the domain were surrounded by perfectly matched layers to minimize the reflections. Time stepping was implemented with the LSODE integrator with variable step sizes. Results show that the waveform of the simulated shear wave is close to experimental observations and equivalent FEM simulations. We used a Fourier-based method to estimate the phase velocities of the shear waves between 100–1000 Hz and a nonlinear regression to estimate the Voigt model parameters. The reconstructions matched within 10% error compared with the true values.

In conventional shear wave elastography materials are assumed to be linear, elastic, homogeneous, and isotropic. These assumptions are important to account for in certain tissues because they are not always appropriate. Many tissues such as skeletal muscle, the kidney, and the myocardium are anisotropic. Shear waves can be used to investigate the directionally dependent mechanical properties of anisotropic media. To study these tissues in a systematic way and to account for the effects of the anisotropic architecture, laboratory-based phantoms are desirable. We will report on several phantom-based approaches for studying shear wave anisotropy, assuming that these materials are transversely isotropic. Phantoms with embedded fibers were used to mimic anisotropic tissues. Homogeneous phantoms were compressed to induce transverse isotropy according to the acoustoelastic phenomenon, which is related to nonlinear behavior of the materials. The fractional anisotropy of these phantoms was quantified to compare with measurements made in soft tissues. In addition, soft tissues are also viscoelastic, and we have developed a method to model viscoelastic transversely isotropic materials with the finite element method (FEM). The viscoelastic property estimation from phantom experiments and FEM simulations will also be discussed.

This work presents an approach to inversely determine material properties for solids immersed in fluids through the use of steady-state dynamic response. The methodology uses measured acoustic pressure amplitudes in the fluid surrounding a structure being vibrated with a harmonic force to determine the parameters for elastic and viscoelastic material models. Steady-state dynamic finite element analysis is used to compute the frequency response function of homogeneous and heterogeneous solids. The frequency response is then used to inversely estimate material parameters. In order to solve the inverse problem, an optimization method is presented which combines the global search capabilities of the random search method with the reduced computational time of a surrogate model approach. Through numerical and laboratory experiments, this work shows that acoustic emissions hold sufficient information for quantifying both elastic and viscoelastic material behaviors. Furthermore, the examples show that the surrogate model accelerated random search algorithm is an efficient and accurate method for solving these types of inverse problems. This research has direct and important implications in nondestructive evaluation of material properties in general. However, the examples shown in this paper are based on applications related to noninvasive characterization of biological materials through methodologies currently applied to medical imaging.