Purpose: The viscoelasticity (storage modulus and loss modulus) of living tissues is known to be related to diseases. Magnetic resonance elastography (MRE) is a quantitative method for non-invasive measuring viscoelasticity. The viscoelasticity is calculated from the elastic wave images using an inversion algorithm. The estimation accuracy of the inversion algorithm is degraded by background noise. This study aims to propose novel inversion algorithms that are applicable for noisy elastic wave images.

Methods: The proposed algorithms are based on the Voigt-type viscoelastic equation. The algorithms are designed to improve the noise robustness by avoiding direct differentiation of measurement data by virtue of Green's formula. Similarly, stabilization is introduced to the curl-operator which works to eliminate the compression waves in measurement data. To clarify the characteristics of the algorithms, the proposed algorithms were compared with the conventional algorithms using isotropic and anisotropic voxel numerical simulations and phantom experimental data.

Results: From the results of the numerical simulations, normalized errors of stiffness of proposed algorithms were 3% or less. The proposed algorithms mostly showed better results than the conventional algorithms despite noisy elastic wave images. From the gel phantom experiment, we confirmed the same tendency as the characteristics of the algorithms observed in the numerical simulation results.

Conclusion: We have developed a novel inversion algorithm and evaluated it quantitatively. The results confirm that the proposed algorithms are highly quantitative and noise-robust methods for estimating storage and loss modulus regardless of noise, voxel anisotropy, and propagation direction. Therefore, the proposed algorithms will appropriate to various three-dimensional MRE systems.