Numerical simulation of wave propagation through interfaces using the extended finite element method for magnetic...

Area of Science:

• Biomedical Engineering
• Medical Imaging
• Computational Mechanics

Background:

• Magnetic Resonance Elastography (MRE) quantifies tissue stiffness using wave propagation.
• Finite Element Method (FEM) is standard for MRE modeling but struggles with complex inclusions.
• Complex interfaces in MRE models increase computational cost and meshing difficulty.

Purpose of the Study:

• To implement and evaluate the eXtended Finite Element Method (XFEM) for MRE.
• To assess XFEM's performance in modeling wave propagation and stiffness reconstruction with complex interfaces.
• To compare XFEM against traditional FEM in terms of accuracy, speed, and ease of use.

Main Methods:

• Utilized the eXtended Finite Element Method (XFEM), a FEM formulation for discontinuities.
• Employed a level-set method for mesh-independent interface representation.
• Conducted two simulation studies: wave propagation across an oblique interface and stiffness reconstruction of a random-shape inclusion.

Main Results:

• XFEM accurately predicted wave conversion rules at a linear interface, matching theoretical results.
• XFEM demonstrated superior convenience, accuracy, and speed compared to FEM in a pseudo-practical MRE application.
• The level-set approach in XFEM simplified meshing for complex inclusion geometries.

Conclusions:

• XFEM is a viable and advantageous alternative to FEM for modeling inclusions in MRE.
• XFEM enhances computational efficiency and accuracy in MRE stiffness reconstruction.
• This method shows significant promise for advancing MRE analysis of heterogeneous tissues.