Magnetic resonance elastography: Inversions in bounded media

Magnetic resonance elastography is a noninvasive imaging technique capable of quantifying and spatially resolving the shear stiffness of soft tissues by visualization of synchronized mechanical wave displacement fields. However, magnetic resonance elastography inversions generally assume that the measured tissue motion consists primarily of shear waves propagating in a uniform, infinite medium. This assumption is not valid in organs such as the heart, eye, bladder, skin, fascia, bone and spinal cord, in which the shear wavelength approaches the geometric dimensions of the object. The aim of this study was to develop and test mathematical inversion algorithms capable of resolving shear stiffness from displacement maps of flexural waves propagating in bounded media such as beams, plates, and spherical shells, using geometry-specific equations of motion. Magnetic resonance elastography and finite element modeling of beam, plate, and spherical shell phantoms of various geometries were performed. Mechanical testing of the phantoms agreed with the stiffness values obtained from finite element modeling and magnetic resonance elastography data, and a linear correlation of r² ≥ 0.99 was observed between the stiffness values obtained using magnetic resonance elastography and finite element modeling data. In conclusion, we have demonstrated new inversion methods for calculating shear stiffness that may be more appropriate for waves propagating in bounded media.