Special transformations for pentamode acoustic cloaking.

The acoustic cloaking theory of Norris [Proc. R. Soc. London, Ser. A 464, 2411-2434 (2008)] permits considerable freedom in choosing the transformation f from physical to virtual space. The standard process for defining cloak materials is to first define f and then evaluate whether the materials are practically realizable. In this paper, this process is inverted by defining desirable material properties and then deriving the appropriate transformations which guarantee the cloaking effect. Transformations are derived which result in acoustic cloaks with special properties such as (1) constant density, (2) constant radial stiffness, (3) constant tangential stiffness, (4) power-law density, (5) power-law radial stiffness, (6) power-law tangential stiffness, and (7) minimal elastic anisotropy.

Elastic nonlinearity imaging.

Previous work has demonstrated improved diagnostic performance of highly trained breast radiologists when provided with B-mode plus elastography images over B-mode images alone. In those studies we have observed that elasticity imaging can be difficult to perform if there is substantial motion of tissue out of the image plane. So we are extending our methods to 3D/4D elasticity imaging with 2D arrays. Further, we have also documented the fact that some breast tumors change contrast with increasing deformation and those observations are consistent with in vitro tissue measurements. Hence, we are investigating imaging tissue stress-strain nonlinearity. These studies will require relatively large tissue deformations (e.g., > 20%) which will induce out of plane motion further justifying 3D/4D motion tracking. To further enhance our efforts, we have begun testing the ability to perform modulus reconstructions (absolute elastic parameter) imaging of in vivo breast tissues. The reconstructions are based on high quality 2D displacement estimates from strain imaging. Piecewise linear (secant) modulus reconstructions demonstrate the changes in elasticity image contrast seen in strain images but, unlike the strain images, the contrast in the modulus images approximates the absolute modulus contrast. Nonlinear reconstructions assume a reasonable approximation to the underlying constitutive relations for the tissue and provide images of the (near) zero-strain shear modulus and a nonlinearity parameter that describes the rate of tissue stiffening with increased deformation. Limited data from clinical trials are consistent with in vitro measurements of elastic properties of tissue samples and suggest that the nonlinearity of invasive ductal carcinoma exceeds that of fibroadenoma and might be useful for improving diagnostic specificity. This work is being extended to 3D.

Linear and nonlinear elasticity imaging of soft tissue in vivo: demonstration of feasibility.

We establish the feasibility of imaging the linear and nonlinear elastic properties of soft tissue using ultrasound. We report results for breast tissue where it is conjectured that these properties may be used to discern malignant tumors from benign tumors. We consider and compare three different quantities that describe nonlinear behavior, including the variation of strain distribution with overall strain, the variation of the secant modulus with overall applied strain and finally the distribution of the nonlinear parameter in a fully nonlinear hyperelastic model of the breast tissue.

Evaluation of the adjoint equation based algorithm for elasticity imaging.

Recently a new adjoint equation based iterative method was proposed for evaluating the spatial distribution of the elastic modulus of tissue based on the knowledge of its displacement field under a deformation. In this method the original problem was reformulated as a minimization problem, and a gradient-based optimization algorithm was used to solve it. Significant computational savings were realized by utilizing the solution of the adjoint elasticity equations in calculating the gradient. In this paper, we examine the performance of this method with regard to measures which we believe will impact its eventual clinical use. In particular, we evaluate its abilities to (1) resolve geometrically the complex regions of elevated stiffness; (2) to handle noise levels inherent in typical instrumentation; and (3) to generate three-dimensional elasticity images. For our tests we utilize both synthetic and experimental displacement data, and consider both qualitative and quantitative measures of performance. We conclude that the method is robust and accurate, and a good candidate for clinical application because of its computational speed and efficiency.