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The technique relies on a transient mechanical vibration which is used to induce a shear wave into the tissue. The propagation of the shear wave is tracked using ultrasound in order to assess the shear wave speed from which the Young's modulus is deduced under hypothesis of homogeneity, isotropy and pure elasticity (E=3ρV²).
This formula is the wave equation applied to the vector quantity , which is the material's shear strain. Its solutions, the S waves, are linear combinations of sinusoidal plane waves of various wavelengths and directions of propagation, but all with the same speed β = μ / ρ {\textstyle \beta ={\sqrt {\mu /\rho }}} .
MR elastography for detection of liver fibrosis in two patients. The left column shows the anatomy, with the liver outlined. The middle row shows images of propagating shear waves in the liver, captured with the MRE technique. The right column shows elastograms computed from the wave images, with tissue stiffness depicted with on color scale.
The acoustoelastic effect is an effect of finite deformation of non-linear elastic materials. A modern comprehensive account of this can be found in. [1] This book treats the application of the non-linear elasticity theory and the analysis of the mechanical properties of solid materials capable of large elastic deformations.
Shearography uses the test object itself as the known reference; it shears the image so a double image is created. The superposition of the two images, a shear image, represents the surface of the test object at this unloaded state. This makes the method much less sensitive to external vibrations and noise.
In mechanics, strain is defined as relative deformation, compared to a reference position configuration. Different equivalent choices may be made for the expression of a strain field depending on whether it is defined with respect to the initial or the final configuration of the body and on whether the metric tensor or its dual is considered.
The shear modulus is one of several quantities for measuring the stiffness of materials. All of them arise in the generalized Hooke's law: . Young's modulus E describes the material's strain response to uniaxial stress in the direction of this stress (like pulling on the ends of a wire or putting a weight on top of a column, with the wire getting longer and the column losing height),
Elastography has been proven feasible for characterization of ocular tissues. [ 11 ] Tissue exhibits varying degrees of viscoelasticity (time-dependent response to a load), poroelasticity (presence of fluid-filled pores or channels), and anisotropy, as well as a nonlinear relationship between elasticity and the applied load.