Bucaro, Joseph A.

In this paper, we present recent developments in the characterization of anisotropic, biological media utilizing displacements measured with dynamic MRE. In one approach, a waveguide constrained analysis is applied to physical structures (such as muscle), which evaluates the velocities of wave propagation along arbitrarily oriented fibers or fiber bundles in a local fashion, utilizing a spectral filter and a sliding window, spatial Fourier transform. In a second approach, the anisotropic equations of elasticity, in variational form, are inverted for a determination of the complex moduli comprising the medium. Issues concerning ill-conditioning, the effects of boundary conditions, and multiaspect excitation requirements will be addressed, as well as a discussion concerning the models which are appropriate for various physical situations. These two complementary methods of analysis will be demonstrated utilizing both phantom as well as in vivo dynamic displacement measurements.

In this paper, the feasibility of extending previously described magnetic resonance elastography (MRE) dynamic displacement (and associated elasticity) measurement techniques, currently used successfully in tissue, to solid materials which have much higher shear rigidity and much lower nuclear spin densities, is considered. Based on these considerations, the MRE technique is modified in a straightforward manner and used to directly visualize shear wave displacements within two polymeric materials, one of which is relatively stiff.

A novel algorithm based on the variational formulation is presented for the determination of the material parameters (λ+2μ)/ρ and μ/ρ throughout inhomogeneous media given volumetric displacement information. The performance of the inversion algorithm is subsequently investigated when applied to measured displacement data throughout an inhomogeneous test phantom. The vector displacement components throughout the test phantom subject to monochromatic shear excitation measured in time using MRI (Magnetic Resonance Imaging) were temporally Fourier transformed to extract the components of monochromatic excitation, and the data were delivered to the inversion algorithm. A sequence of studies is presented on the basis of subsequent wavenumber filtering, polarization selection, and variation in the size of the volume elements of resolution. The resulting performance is assessed and recommendations for future efforts are discussed. [Work supported by ONR and NIH.]