Diffusion magnetic resonance imaging (dMRI) encodes water displacement due to diffusion and is a powerful tool for obtaining information on the tissue microstructure. An important quantity measured in dMRI in each voxel is the apparent diffusion coefficient ($ADC$), and it is well established from imaging experiments that, in the brain, in vivo, the $ADC$ is dependent on the measured diffusion time. To aid in the understanding and interpretation of the $ADC$, using homogenization techniques, we derived a new asymptotic model for the dMRI signal from the Bloch--Torrey equation governing the water proton magnetization under the influence of diffusion-encoding magnetic gradient pulses. Our new model was obtained using a particular choice of scaling for the time, the biological cell membrane permeability, the diffusion-encoding magnetic field gradient strength, and a periodicity length of the cellular geometry. The $ADC$ of the resulting model is dependent on the diffusion time. We numerically validated this ...
['Houssem Haddar', 'Jing-Rebecca Li', 'Simona Schiavi']
A Macroscopic Model for the Diffusion MRI Signal Accounting for Time-Dependent Diffusivity