MR elastography inversion by compressive recovery

Direct inversion (DI) derives tissue shear modulus by inverting the Helmholtz equation. However, conventional DI is sensitive to data quality due to the ill-posed nature of Helmholtz inversion and thus providing reliable stiffness estimation can be challenging. This becomes more problematic in the case of estimating shear stiffness of the lung in which the low tissue density and short T2* result in considerably low signal-to-noise ratio during lung MRE. In the present study, we propose to perform MRE inversion by compressive recovery (MICRo). Such a technique aims to improve the numerical stability and the robustness to data noise of Helmholtz inversion by using prior knowledge on data noise and transform sparsity of the stiffness map. The developed inversion strategy was first validated in simulated phantoms with known stiffness. Next, MICRo was compared to the standard clinical multi-modal DI (MMDI) method forin vivoliver MRE in healthy subjects and patients with different stages of liver fibrosis. After establishing the accuracy of MICRo, we demonstrated the robustness of the proposed technique against data noise in lung MRE with healthy subjects. In simulated phantoms with single-directional or multi-directional waves, MICRo outperformed DI with Romano filter or Savitsky and Golay filter, especially when the stiffness and/or noise level was high. In hepatic MRE application, agreement was observed between MICRo and MMDI. Measuringin vivolung stiffness, MICRo demonstrated its advantages over filtered DI by yielding stable stiffness estimation at both residual volume and total lung capacity. These preliminary results demonstrate the potential value of the proposed technique and also warrant further investigation in a larger clinical population.