All-in-one approach for constrained all-voxel tri-exponential IVIM model identification: Application to Diffusion-Weighted MR Imaging in the Liver

Diffusion and perfusion evaluation is important for liver pathologies. Intravoxel incoherent motion (IVIM) diffusion weighted magnetic resonance imaging (DW-MRI) is a good method to quantify the apparent diffusion coefficient (ADC) and perfusion fraction $(PF)$. However the existence of large blood vessels in the liver leads to a confounding effect on the conventional bi-exponential IVIM model. Actually, such confounding effect can be considered as a third contribution of the image signal. In this study, an all-in-one approach for blood vessels localization and tissue diffusion/perfusion estimation based on an all-voxel tri-exponential IVIM model in human liver is proposed. The proposed approach assumes sparse distribution of blood vessels in the considered region of interest. Besides, it deals with the non-negativity of the model parameters by resorting to a change of variables into square. Model parameters are estimated alternatively in an iterative way following the spirit of the ADMM algorithm. The good behavior of the proposed approach is assessed using both realistic and real diffusion-weighted magnetic resonance imaging in the liver.