EFFECTS OF RESTRICTED DIFFUSION ON MICROSCOPIC NMR IMAGING

Computer simulations were undertaken to study the effect of spatial molecular diffusion on NMR microscopic images. Solutions to Torrey's equation describing the time evolution of the complex transverse magnetization in the presence of a o:)nstant field gradient following a 90° pulse were obtained for a sphere, disc, and 1D box using random walk simulations. The 1 D case was also solved by spatially discretizing Torrey's equation and solving the resultant matrix equation by Fourier-Laplace inversion. The absorption spectra obtained can be classified using the dimensionless scaling parameter d = 4πD/γGL3 where D is the self-diffusion coefficient, γ the gyromagnetic ratio, G the field gradient, and L the characteristic length of the object. For 0 < d < 0.1, there are, relative to theD = 0 case, a gradual decrease in spectral width as d increases and an increase in spectral intensity near the boundaries. For d increasing beyond 0.1, there is a rapid decrease in spectral width due to motional narrowing. For the self diffusion of water at room temperature in a 5 G/cm gradient, the value of d is 0.1 at L = 29 μm. Because 3D microscopic resolution of (10 μm)3 has been attained, such effects may become important in practical experiments. © 1991.