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Elastography refers to mapping mechanical properties in a material based on measuring wave motion in it using noninvasive optical, acoustic or magnetic resonance imaging methods. For example, increased stiffness will increase wavelength. Stiffness and viscosity can depend on both location and direction. A material with aligned fibers or layers may have different stiffness and viscosity values along the fibers or layers versus across them. Converting wave measurements into a mechanical property map or image is known as reconstruction. To make the reconstruction problem analytically tractable, isotropy and homogeneity are often assumed, and the effects of finite boundaries are ignored. But, infinite isotropic homogeneity is not the situation in most cases of interest, when there are pathological conditions, material faults or hidden anomalies that are not uniformly distributed in fibrous or layered structures of finite dimension. Introduction of anisotropy, inhomogeneity and finite boundaries complicates the analysis forcing the abandonment of analytically-driven strategies, in favor of numerical approximations that may be computationally expensive and yield less physical insight. A new strategy, Transformation Elastography (TE), is proposed that involves spatial distortion in order to make an anisotropic problem become isotropic. The fundamental underpinnings of TE have been proven in forward simulation problems. In the present paper a TE approach to inversion and reconstruction is introduced and validated based on numerical finite element simulations.
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Analytical solution based on spatial distortion for a time-harmonic Green's function in a transverse isotropic viscoelastic solid
A strategy of spatial distortion to make an anisotropic problem become isotropic has been previously validated in two-dimensional transverse isotropic (TI) viscoelastic cases. Here, the approach is extended to the three-dimensional problem by considering the time-harmonic point force response (Green's function) in a TI viscoelastic material. The resulting wave field, exactly solvable using a Radon transform with numerical integration, is approximated via spatial distortion of the closed form analytical solution to the isotropic case. Different distortions are used, depending on whether the polarization of the wave motion is orthogonal to the axis of isotropy, with the approximation yielding differing levels of accuracy.
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- Award ID(s):
- 1852691
- PAR ID:
- 10593598
- Publisher / Repository:
- Acoustical Society of America (ASA)
- Date Published:
- Journal Name:
- The Journal of the Acoustical Society of America
- Volume:
- 149
- Issue:
- 4
- ISSN:
- 0001-4966
- Format(s):
- Medium: X Size: p. 2283-2291
- Size(s):
- p. 2283-2291
- Sponsoring Org:
- National Science Foundation
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