title: Numerical study of a macroscopic finite pulse model of the diffusion MRI signal.
abstract: Diffusion 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 compartments with inter-compartment exchange governed by linear kinetics, then the 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 short compared to the diffusion time (the narrow pulse assumption). 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. When restricted to narrow pulses, this new homogenized model has the same form as the Karger model. We conduct a numerical study of the new homogenized model for voxels that are made up of periodic copies of a representative volume that contains spherical and cylindrical cells of various sizes and orientations and show that the signal predicted by the new model approaches the reference signal obtained by solving the full Bloch-Torrey PDE in O(ε(2)), where ε is the ratio between the size of the representative volume and a measure of the diffusion length. When the narrow gradient pulse assumption is not satisfied, the new homogenized model offers a much better approximation of the full PDE signal than the Karger model. Finally, preliminary results of applying the new model to a voxel that is not made up of periodic copies of a representative volume are shown and discussed.
authors.affiliation: INRIA Saclay-Equipe DEFI CMAP, Ecole Polytechnique, France. Electronic address: jingrebecca.li@inria.fr.
authors.forename: Jing-Rebecca
authors.initials: JR
authors.lastname: Li
authors.affiliation: NeuroSpin, CEA Saclay Center, 91191 Gif-sur-Yvette Cedex, France.
authors.forename: Hang Tuan
authors.initials: HT
authors.lastname: Nguyen
authors.affiliation: INRIA Saclay-Equipe DEFI CMAP, Ecole Polytechnique, France.
authors.forename: Dang Van
authors.initials: DV
authors.lastname: Nguyen
authors.affiliation: INRIA Saclay-Equipe DEFI CMAP, Ecole Polytechnique, France.
authors.forename: Houssem
authors.initials: H
authors.lastname: Haddar
authors.affiliation: INRIA Saclay-Equipe DEFI CMAP, Ecole Polytechnique, France.
authors.forename: Julien
authors.initials: J
authors.lastname: Coatléven
authors.affiliation: NeuroSpin, CEA Saclay Center, 91191 Gif-sur-Yvette Cedex, France.
authors.forename: Denis
authors.initials: D
authors.lastname: Le Bihan
mesh_terms: D000465:Algorithms; D000818:Animals; D003198:Computer Simulation; D038524:Diffusion Magnetic Resonance Imaging / Q000379:methods*; D006801:Humans; D007089:Image Enhancement / Q000379:methods; D007090:Image Interpretation, Computer-Assisted / Q000379:methods*; D021621:Imaging, Three-Dimensional / Q000379:methods*; D008954:Models, Biological; D009716:Numerical Analysis, Computer-Assisted; D015203:Reproducibility of Results; D012680:Sensitivity and Specificity; D012815:Signal Processing, Computer-Assisted
keywords: Diffusion MRI; Effective medium; Homogenization; Karger model; Macroscopic model; Signal model