Wave speeds and Green’s tensors for shear wave propagation in incompressible, hyperelastic materials with uniaxial stretch

Assessing elastic material properties from shear wave propagation following an acoustic radiation force impulse (ARFI) excitation is difficult in anisotropic materials because of the complex relations among the propagation direction, shear wave polarizations, and material symmetries. In this paper, we describe a method to calculate shear wave signals using Green's tensor methods in an incompressible, hyperelastic material with uniaxial stretch. Phase and group velocities are determined for SH and SV propagation modes as a function of stretch by constructing the equation of motion from the Cauchy stress tensor determined from the strain energy density. The Green's tensor is expressed as the sum of contributions from the SH and SV propagation modes with the SH contribution determined using a closed-form expression and the SV contribution determined by numerical integration. Results are presented for a Mooney-Rivlin material model with a tall Gaussian excitation similar to an ARFI excitation. For an experimental configuration with a tilted material symmetry axis, results show that shear wave signals exhibit complex structures such as shear splitting that are characteristic of both the SH and SV propagation modes

Measuring elastic nonlinearity in a soft solid using a tilted acoustic radiation force for shear wave excitation

Excitation of multiple wave modes using shear wave elastography can result in additional information about the tissue's material characteristics and, potentially, improve disease diagnosis. Theoretically, tilting the acoustic radiation force excitation axis with respect to the material's symmetry axis should excite several wave modes in the material. In this work, we have experimentally demonstrated proof of concept in a uniaxially stretched phantom, while increasing the stretch level. Tilted acoustic radiation force experiments showed a clearly visible second wave mode across the stretch direction for larger stretches (>160%)

Bayesian multiresolution algorithm for PET reconstruction

We introduce a spatially non-homogeneous adaptive image model and multiresolution reconstruction algorithm for Bayesian tomographic reconstruction. In contrast to existing approaches, the proposed image model is formulated in a multiresolution wavelet domain and relies on training data to incorporate the expected characteristics of typical reconstructions. The actual tomographic reconstruction is performed in the space domain to simplify enforcement of the positivity constraint. We apply the proposed algorithm to simulated data and to data acquired using the IndyPET dedicated research scanner. Our experimental results indicate that our algorithm can improve reconstruction quality over fixed resolution Bayesian methods.

Analysis of multiple shear wave modes in a nonlinear soft solid : experiments and finite element simulations with a tilted acoustic radiation force

Tissue nonlinearity is conventionally measured in shear wave elastography by studying the change in wave speed caused by the tissue deformation, generally known as the acoustoelastic effect. However, these measurements have mainly focused on the excitation and detection of one specific shear mode, while it is theoretically known that the analysis of multiple wave modes offers more information about tissue material properties that can potentially be used to refine disease diagnosis. This work demonstrated proof of concept using experiments and finite element simulations in a uniaxially stretched phantom by tilting the acoustic radiation force excitation axis with respect to the material's symmetry axis. Using this unique set-up, we were able to visualize two propagating shear wave modes across the stretch direction for stretches larger than 140%. Complementary simulations were performed using material parameters determined from mechanical testing, which enabled us to convert the observed shear wave behavior into a correct representative constitutive law for the phantom material, i.e. the Isihara model. This demonstrates the potential of measuring shear wave propagation in combination with shear wave modeling in complex materials as a non-invasive alternative for mechanical testing