NMR diffusion simulation based on conditional random walk

The authors introduce here a new, very fast, simulation method for free diffusion in a linear magnetic field gradient, which is an extension of the conventional Monte Carlo (MC) method or the convolution method described by Wong et al. (in 12th SMRM, New York, 1993, p.10). In earlier NMR-diffusion simulation methods, such as the finite difference method (FD), the Monte Carlo method, and the deterministic convolution method, the outcome of the calculations depends on the simulation time step. In the authors' method, however, the results are independent of the time step, although, in the convolution method the step size has to be adequate for spins to diffuse to adjacent grid points. By always selecting the largest possible time step the computation time can therefore be reduced. Finally the authors point out that in simple geometric configurations their simulation algorithm can be used to reduce computation time in the simulation of restricted diffusion.

[1]  M. H. Blees,et al.  The Effect of Finite Duration of Gradient Pulses on the Pulsed-Field-Gradient NMR Method for Studying Restricted Diffusion , 1994 .

[2]  H Gudbjartsson,et al.  Simultaneous calculation of flow and diffusion sensitivity in steady‐state free precession imaging , 1995, Magnetic resonance in medicine.

[3]  E. Purcell,et al.  Effects of Diffusion on Free Precession in Nuclear Magnetic Resonance Experiments , 1954 .

[4]  Gary P. Zientara,et al.  Spin‐echoes for diffusion in bounded, heterogeneous media: A numerical study , 1980 .

[5]  J. E. Tanner,et al.  Spin diffusion measurements : spin echoes in the presence of a time-dependent field gradient , 1965 .

[6]  H. C. Torrey Bloch Equations with Diffusion Terms , 1956 .

[7]  J S Petersson,et al.  MRI simulation using the k-space formalism. , 1993, Magnetic resonance imaging.

[8]  R M Henkelman,et al.  On the Transverse relaxation rate enhancement induced by diffusion of spins through inhomogeneous fields , 1991, Magnetic resonance in medicine.

[9]  B. Rosen,et al.  Microscopic susceptibility variation and transverse relaxation: Theory and experiment , 1994, Magnetic resonance in medicine.

[10]  Baldwin Robertson,et al.  Spin-Echo Decay of Spins Diffusing in a Bounded Region , 1966 .

[11]  Per Linse,et al.  The NMR Self-Diffusion Method Applied to Restricted Diffusion. Simulation of Echo Attenuation from Molecules in Spheres and between Planes , 1993 .

[12]  B. Rosen,et al.  MR Contrast Due to Microscopically Heterogeneous Magnetic Susceptibility: Numerical Simulations and Applications to Cerebral Physiology , 1991, Magnetic resonance in medicine.

[13]  S. H. Koenig,et al.  Transverse relaxation of solvent protons induced by magnetized spheres: Application to ferritin, erythrocytes, and magnetite , 1987, Magnetic resonance in medicine.