Analytical Solutions and Simulations for Spin-Echo Measurements of Diffusion of Spins in a Sphere with Surface and Bulk Relaxation

Permeability Coefficients from NMR q-Space Data: Models with Unevenly Spaced Semi-permeable Parallel Membranes

“…The latter implies the short gradient pulse approximation that is the basis of the simple form of the integral (e.g., 5,18); this integral contrasts with the more complicated one used for relatively large ␦ values or even a constant field gradient (e.g., 19). The exponential term with its imaginary exponent already implies a solution that is periodic in qz.…”

“…P is a Green's function and its use in solving the present class of problem is described more fully elsewhere (e.g., 19,22). In more detail, Eq.…”

Use, misuse, and abuse of apparent diffusion coefficients

“…[6]). A number of works are devoted to numerical computations of the spin-echo ADC by using Monte Carlo simulations, finite-difference, or finite-element methods (26)(27)(28)(29)(30)(31)(32) [for further references, see review (2)].…”

Theory of Spin Echo in Restricted Geometries under a Step-wise Gradient Pulse Sequence

“…Ϫ͑⌬Ϫ␦͒⌳ ⅐ e Ϫ␦V* ⅐ U, [47] and taking into account the fact that U n ϭ ␦ n,0 for perfectly reflecting boundaries,…”

“…One is termed the Gaussian phase approximation in the NMR literature, which is otherwise known as the truncated cumulant expansion. This approximation prevailed until recently (27,38,(41)(42)(43)(44)(45)(46)(47). The cumulant expansion result for the echo signal is…”