Numerical simulation of diffusion MRI signals using an adaptive time-stepping method

Jing-Rebecca Li 1 Donna Calhoun 2 Cyril Poupon 3 Denis Le Bihan 3
1 DeFI - Shape reconstruction and identification
CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique, Inria Saclay - Ile de France
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.
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Jing-Rebecca Li, Donna Calhoun, Cyril Poupon, Denis Le Bihan. Numerical simulation of diffusion MRI signals using an adaptive time-stepping method. Physics in Medicine and Biology, IOP Publishing, 2013, ⟨10.1088/0031-9155/59/2/441⟩. ⟨hal-00763888v2⟩

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