A novel reconstruction method for magnetic resonance elastography based on the Helmholtz decomposition

We present a novel reconstruction method for magnetic resonance elastography, in which the shear modulus and viscosity of biological tissues are estimated from the externally oscillated displacement field obtained using magnetic resonance imaging. The proposed method is based on an integral representation of the stress field derived from the Helmholtz identity for tensor fields and is more robust against measurement noise than conventional methods using the Laplacian of the measured displacement field. We tested the proposed method by numerical simulations and compared it with two methods: the standard “algebraic inversion of the differential equation” method and our previously proposed integral-based method that is restricted to two-dimensional cases. The results showed that the proposed method could reconstruct both the shear modulus and viscosity stably even when noise was added to the data. In the future, we intend to validate the method via experimental data. © 2022 The Authors