Langevin equation approach to diffusion magnetic resonance imaging.
The normal phase diffusion problem in magnetic resonance imaging (MRI) is treated by means of the Langevin equation for the phase variable using only the properties of the characteristic function of Gaussian random variables. The calculation may be simply extended to anomalous diffusion using a fractional generalization of the Langevin equation proposed by Lutz [E. Lutz, Phys. Rev. E 64, 051106 (2001)] pertaining to the fractional Brownian motion of a free particle coupled to a fractal heat bath. The results compare favorably with diffusion-weighted experiments acquired in human neuronal tissue using a 3 T MRI scanner.
Cooke
Jennie M
JM
Institute of Neuroscience, Trinity College, Dublin 2, Ireland.
Kalmykov
Yuri P
YP
Coffey
William T
WT
Kerskens
Christian M
CM
D000465:Algorithms; D003198:Computer Simulation; D038524:Diffusion Magnetic Resonance Imaging / Q000379:methods*; D007090:Image Interpretation, Computer-Assisted / Q000379:methods*; D008954:Models, Biological