Accurately estimating all strain components in quasi-static ultrasound elastography is crucial for the full analysis of biological media. In this paper, 2D strain tensor imaging is investigated, using a partial differential equation (PDE)-based regularization method. More specifically, this method employs the tissue property of incompressibility to smooth the displacement fields and reduce the noise in the strain components. The performance of the method is assessed with phantoms and in vivo breast tissues. For all the media examined, the results showed a significant improvement in both lateral displacement and strain but also, to a lesser extent, in the shear strain. Moreover, axial displacement and strain were only slightly modified by the regularization, as expected. Finally, the easier detectability of the inclusion/lesion in the final lateral strain images is associated with higher elastographic contrast-to-noise ratios (CNRs), with values in the range [0.68 -9.40] vs [0.09 -0.38] before regularization.
Accurately estimating all strain components in quasi-static ultrasound elastography is crucial for the full analysis of biological media. In this study, 2D strain tensor imaging was investigated, focusing on the use of a regularization method to improve strain images. This method enforces the tissue property of (quasi-) incompressibility, while penalizing strong field variations, to smooth the displacement fields and reduce the noise in the strain components. The performance of the method was assessed with numerical simulations, phantoms, and in vivo breast tissues. For all the media examined, the results showed a significant improvement in both lateral displacement and strain, while axial fields were only slightly modified by the regularization. The introduction of penalty terms allowed us to obtain shear strain and rotation elastograms where the patterns around the inclusions/lesions were clearly visible. In phantom cases, the findings were consistent with the results obtained from the modeling of the experiments. Finally, the easier detectability of the inclusions/lesions in the final lateral strain images was associated with higher elastographic contrast-to-noise ratios (CNRs), with values in the range of [0.54–9.57] versus [0.08–0.38] before regularization.
Reconstructing tissue elastic properties from displacements measured in quasi-static ultrasound elastography is a challenging task. Indeed, it requires to solve an ill-posed inverse problem, with generally no available boundary information and solely 2D estimated displacements, whereas the problem is inherently three-dimensional. In this paper, a method based on the virtual work principle is investigated to reconstruct Young's modulus maps from the knowledge of internal displacements and the force applied. The media examined are assumed to be linear elastic and isotropic. Moreover, for these first developments, the plane stress problem is investigated to overcome the lack of 3D data. The developed method is assessed with plane-stress and 3D simulations, as well as with experimental data. For all the media examined, regions of different stiffnesses are clearly revealed in the reconstructed Young's modulus maps. The stiffness contrast between regions is accurately estimated for the plane stress simulations but underestimated for the 3D simulations, which could be expected as plane stress conditions are no longer satisfied in this last case. Finally, similar comments can be made for the phantom results, with an inclusion-to-background Young's modulus ratio of 2.4 lower than the reference ratio of around 3, provided by the manufacturer.
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