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%)

Phase and group velocities for shear wave propagation in an incompressible, hyperelastic material with uniaxial stretch

Abstract Objective. Determining elastic properties of materials from observations of shear wave propagation is difficult in anisotropic materials because of the complex relations among the propagation direction, shear wave polarizations, and material symmetries. In this study, we derive expressions for the phase velocities of the SH and SV propagation modes as a function of propagation direction in an incompressible, hyperelastic material with uniaxial stretch. Approach. Wave motion is included in the material model by adding incremental, small amplitude motion to the initial, finite deformation. Equations of motion for the SH and SV propagation modes are constructed using the Cauchy stress tensor derived from the strain energy function of the material. Group velocities for the SH and SV propagation modes are derived from the angle-dependent phase velocities. Main results. Sample results are presented for the Arruda–Boyce, Mooney–Rivlin, and Isihara material models using model parameters previously determined in a phantom. Significance. Results for the Mooney–Rivlin and Isihara models demonstrate shear splitting in which the SH and SV propagation modes have unequal group velocities for propagation across the material symmetry axis. In addition, for sufficiently large stretch, the Arruda–Boyce and Isihara material models show cusp structures with triple-valued group velocities for the SV mode at angles of roughly 15° to the material symmetry axis.</jats:p

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. 1 INTRODUCTION One of the major challenges in Bayesian tomographic reconstruction is the design of edge-preserving prior models. Existing prior models are largely based on spatially homogeneous Markov random field (MRF) implementations. A disadvantage of such models is..

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.