Numerical study of a macroscopic finite pulse model of the diffusion MRI signal

International audienceDiffusion magnetic resonance imaging (dMRI) is an imaging modality that probes the diffusion characteristics of a sample via the application of magnetic field gradient pulses. The dMRI signal from a heterogeneous sample includes the contribution of the water proton magnetization from all spatial positions in a voxel.If the voxel can be spatially divided into different Gaussian diffusion compartmentswith inter-compartment exchange governed by linear kinetics, thenthe dMRI signal can be approximated using the macroscopic Karger model,which is a system of coupled ordinary differential equations (ODEs), under the assumption that the duration of the diffusion-encoding gradient pulses is shortcompared to the diffusion time (the narrow pulse assumption). \soutnew{Recently, a new macroscopic ODE model of the dMRI signal, the Finite Pulse ODE (FP-ODE) model,was derived from the Bloch-Torrey partial differential equation (PDE), without the narrow pulse restriction, using periodic homogenization techniques.}{Recently, a new macroscopic model of the dMRI signal,without the narrow pulse restriction, was derived from the Bloch-Torrey partial differential equation (PDE)using periodic homogenization techniques.} \soutnew{When restricted to narrowpulses, the FP-ODE model has the same form as the Karger model.}{When restricted to narrowpulses, this new homogenized model has the same form as the Karger model.} We conduct a numerical study of the \soutnew{FP-ODE}{new homogenized} model for voxels that are made up of periodic copies of a representativevolume that contains spherical and cylindrical cells of various sizes and orientationsand show that the signal predicted by the \soutnew{FP-ODE}{new} model approaches the reference signalobtained by solving the full Bloch-Torrey PDEin $O(\veps^2)$, where $\veps$ is the ratio between the size of the representativevolume and \soutnew{the diffusion displacement}{a measure of the diffusion length}.When the narrow gradient pulse assumption is not satisfied, the \soutnew{FP-ODE}{new homogenized} model offers a much better approximation of the full PDE signal than the Karger model.Finally, preliminary results of applying the \soutnew{FP-ODE}{new} model to a voxel that is not made up of periodic copies of a representativevolume are shown and discussed