Analyzing Shear Wave Propagation in Magnetic Resonance Elastography Using Finite Element Modeling

Principal Investigator: Kai-Nan An, Ph.D.
Project Coordinator: Qingshan Chen — chen.qingshan@mayo.edu

Finite element modeling serves as a powerful simulation tool in MRE study. Better understanding of the wave propagation can be obtained by comparing the wave motion data in the finite element model to the wave image data of MRE. In addition, one of the keys to the clinical success of MRE is how well the wave image data is converted into a stiffness map, using specific reconstruction methods called inversion algorithms. Finite element modeling can be a potential inversion algorithm. We have successfully developed homogenous 2-D finite element models with various types of complicated boundary conditions and axial pre-tensions. It was found that MRE measurements can be either dispersive or non-dispersive depending on the boundary conditions, and that the axial pre-tension elongates the propagating shear wavelength in a dispersive system. This is significant because skeletal muscles are subjected to tension. Homogenous 3-D finite element models with various geometries were also developed and the results agree well with wave theories in elastic media. A 3-D finite element model with fibers embedded in a simple rectangular prism was also developed. The fiber and the matrix materials were assumed to be isotropic and linear elastic with different moduli than the material in which they were embedded. Depending on the fiber density, either a planar wave-front or a v-shaped wave-front was observed.