Efficient sparsity-based algorithm for parameter estimation of the tri-exponential intra voxel incoherent motion (IVIM) model: Application to diffusion-weighted MR imaging in the liver

Jie Liu, Giulio Gambarota, Huazhong Shu, Longyu Jiang, Benjamin Leporq, Olivier Beuf, Ahmad Karfoul

Abstract: Tissue perfusion measurements by IntraVoxel Incoherent Motion (IVIM) Diffusion-Weighted Magnetic Resonance Imaging (DW-MRI) are of great interest for investigating liver pathologies. However, perfusion estimation in the liver is more challenging than in other organs due to the presence of several blood vessels (not capillaries) whose visual identification, in the considered Region-Of-Interest (ROI), is not evident. These blood vessels are the source of a confounding perfusion parameter, which can be modelled as a third exponential decay in the IVIM-MRI model. Thus, a new algorithm to estimate the tissue perfusion parameters including those confounding ones related to the potential presence of blood vessels is presented in this paper. Based on the sparsity of the spatial distribution of the blood vessels in the considered ROI, the parameter estimation of the tri-exponential IVIM model is performed in an iterative way following the spirit of the alternating direction method of multipliers where the Gauss-Newton method is employed to deal with the model nonlinearity. To the best of our knowledge, this is the first time a all-voxel tri-exponential IVIM-MRI model is considered in the IVIM-MRI framework. The efficiency of the proposed algorithm was validated on realistic DW-MR images. The estimated parametric maps of the water diffusion coefficient and tissue perfusion of the IVIM model were in good agreement with ground-truth values. A good performances of this algorithm was also observed on clinical MRI data in the liver.