MR Elastography Reconstruction Based on a Linear Integral Equation Derived from the Helmholtz Identity

This paper presents a novel reconstruction method for MR Elastography. Unlike most conventional methods that solve Navier's partial differential equation (PDE), the proposed approach solves a linear integral equation derived from Helmholtz’s identity. The proposed method can reconstruct the complex shear modulus without calculating higher-order derivatives of the measured displacement data, nor solving a nonlinear minimization problem that could result in local minima. Our preliminary study by numerical simulations demonstrated that the proposed method could robustly estimate the complex shear modulus. Future work is to compare the effectiveness of the proposed method with the PDE-based conventional methods.