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A new macroscopic model for the diffusion MRI accounting for time-dependent diffusivity

Houssem Haddar 1 Jing-Rebecca Li 1 Simona Schiavi 1 
1 DeFI - Shape reconstruction and identification
CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique, Inria Saclay - Ile de France
Abstract : Diffusion Magnetic Resonance Imaging (dMRI) encodes water displacement due to diffusion and is a powerful tool to obtain information on the tissue micro-structure. 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, {\it 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 model for a wide range of diffusion times for two dimensional geometrical configurations.
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Submitted on : Monday, October 19, 2015 - 5:03:49 PM
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Houssem Haddar, Jing-Rebecca Li, Simona Schiavi. A new macroscopic model for the diffusion MRI accounting for time-dependent diffusivity. SIAM Journal on Applied Mathematics, 2016, 76 (3), pp.930-949. ⟨10.1137/15M1019398⟩. ⟨hal-01217537⟩



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