title: Numerical simulation of diffusion MRI signals using an adaptive time-stepping method.
abstract: The effect on the MRI signal of water diffusion in biological tissues in the presence of applied magnetic field gradient pulses can be modelled by a multiple compartment Bloch-Torrey partial differential equation. We present a method for the numerical solution of this equation by coupling a standard Cartesian spatial discretization with an adaptive time discretization. The time discretization is done using the explicit Runge-Kutta-Chebyshev method, which is more efficient than the forward Euler time discretization for diffusive-type problems. We use this approach to simulate the diffusion MRI signal from the extra-cylindrical compartment in a tissue model of the brain gray matter consisting of cylindrical and spherical cells and illustrate the effect of cell membrane permeability.
authors.affiliation: INRIA Saclay-Equipe DEFI, CMAP, Ecole Polytechnique Route de Saclay, F-91128, Palaiseau Cedex, France. NeuroSpin, CEA Saclay Center 91191 Gif-sur-Yvette Cedex, France.
authors.forename: Jing-Rebecca
authors.initials: JR
authors.lastname: Li
authors.forename: Donna
authors.initials: D
authors.lastname: Calhoun
authors.forename: Cyril
authors.initials: C
authors.lastname: Poupon
authors.forename: Denis
authors.initials: D
authors.lastname: Le Bihan
mesh_terms: D001921:Brain / Q000166:cytology; D002463:Cell Membrane Permeability; D038524:Diffusion Magnetic Resonance Imaging / Q000379:methods*; D007091:Image Processing, Computer-Assisted; D008954:Models, Biological; D013997:Time Factors