Fast Monte-Carlo simulations of diffusion MRI signals of the brain microstructure

The diffusion magnetic resonance imaging (dMRI) experiments are sensitive to the restricted diffusion of water molecules within a confined geometry and can thus reveal essential information about the brain microstructure. Nowadays, significant progress are made in the development of models of the brain microstructure that can provide rich information about the complex organization of cellular structures in the brain. However, the validation of a model is made through the synthesizing of his respective dMRI signal. This signal from simple geometrical microstructure model is known analytically but remains difficult to found for complex geometries like extra-cellular spaces. A common numerical method to approximate a dMRI signal in extra-cellular space is to use a Monte-Carlo simulation. This technique simulates the Brownian motion of the water molecules by creating a succession of small random fixed length steps between adjacent positions. It can provide accurate results but requires a large amount of computational time. This thesis develops a new fast Monte-Carlo simulation for PGSE sequence in extra-cellular space. Compared to the "classic" Monte-Carlo simulation, the length steps between adjacent positions are continuously adapted in function of their local position in their geometrical environment. This new fast Monte-Carlo simulation is through this thesis, described, analyzed and compared to the fixed length step Monte-Carlo simulation.