Transformation Elastography

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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. Reconstruction in isotropic materials, with the same mechanical properties regardless of direction, is easier than in anisotropic materials, whose properties vary with direction. Transformation Elastography is based on the idea of distorting the material as part of the reconstruction algorithm to make the anisotropic problem become isotropic. This strategy, which has been shown to work in simple two-dimensional reconstruction problems, will be extended to more complex three-dimensional problems. Elastography is a potentially transformative measurement technology for basic research into material mechanics. Extending it to anisotropic materials is essential to advance its application in geophysical exploration, fiber composite analysis, and medical diagnosis of diseases of the brain, skeletal muscle, heart and other organs with aligned fibers for which changes in stiffness and viscosity have been proven to correlate with disease. This research supports NSF's mission to promote the progress of science and advance national health. Research developments will be integrated into courses and multimedia educational materials for a diverse group of students at multiple levels, from K-12 through graduate level engineering.Elastography relies on a constitutive model of mechanical wave motion in the viscoelastic material to interpret the noninvasive measurements. To make the modeling 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 are computationally expensive and yield less physical insight. A new strategy, Transformation Elastography, is planned that involves spatial distortion in order to make an anisotropic problem become isotropic. Development and experimental validation of this new strategy requires inverting the algorithm and extending initial developments from two- to three-dimensional problems with inhomogeneity.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.