Scattering and Diffraction of Elastodynamic Waves in a Concentric Cylindrical Phantom for MR Elastography

Aim: The focus of this paper is to report on the design and construction of a multiply connected phantom for use in magnetic resonance elastography (MRE) - an imaging technique that allows for the noninvasive visualization of the displacement field throughout an object from externally driven harmonic motion - as well as its inverse modeling with a closed-form analytic solution which is derived herein from first principles. Methods: Mathematically, the phantom is described as two infinite concentric circular cylinders with unequal complex shear moduli, harmonically vibrated at the exterior surface in a direction along their common axis. Each concentric cylinder is made of a hydrocolloid with its own specific solute concentration. They are assembled in a multistep process for which custom scaffolding was designed and built. A customized spin-echo-based MR elastography sequence with a sinusoidal motion-sensitizing gradient was used for data acquisition on a 9.4 T Agilent small-animal MR scanner. Complex moduli obtained from the inverse model are used to solve the forward problem with a finite-element method. Results: Both complex shear moduli show a significant frequency dependence (p < 0.001) in keeping with previous work. Conclusion: The novel multiply connected phantom and mathematical model are validated as a viable tool for MRE studies. Significance: On a small enough scale much of physiology can be mathematically modeled with basic geometric shapes, e.g., a cylinder representing a blood vessel. This study demonstrates the possibility of elegant mathematical analysis of phantoms specifically designed and carefully constructed for biomedical MRE studies.