• bayesian probability
• diffusion
• IVIM
• MRI
• non-linear fitting

Diffusion-Weighted magnetic resonance Imaging (DWI) is a method that uses the diffusion of water molecules to generate contrast in Magnetic Resonance (MR) images. The DWI diagnostic potential resides in its ability to provide information that reflects tissue cellularity and the integrity of cellular membrane.
Conventional DWI assumes that all water molecules behave the same within a voxel. IntraVoxel Incoherent Motion (IVIM) instead is an advanced diffusion modelling described by Le Bihan et al., which allows separation between the water molecular diffusion (due to Brownian motion) and the microcirculation of blood (also called pseudo-diffusion).
The first purpose of this thesis is to develop a customized platform for IVIM maps reconstruction of the liver using the major algorithms in literature. Indeed, one of the most important potential clinical application of IVIM is the liver fibrosis staging.
The second purpose is to compare the variability, precision, and accuracy of five different algorithms (three Levenberg–Marquardt based and two Bayesian-Probability based) for computing IVIM parameters. It will be shown how the Bayesian-Probability based algorithms should be preferred due their ability to reduce estimation uncertainty and to preserve spatial features in the parametric maps.