It had been previously shown that an idealized version of the two-wave-vector extension of the NMR pulsed-field-gradient spin echo diffusion experiment can be used to determine the apparent radius of geometries with restricted diffusion. In the present work, the feasibility of the experiment was demonstrated in an NMR imaging experiment, in which the apparent radius of axons in white matter tissue was determined. Moreover, numerical simulations have been carried out to determine the reliability of the results. For small diffusion times, the radius is systematically underestimated. Larger gradient area, finite length gradient pulses, and a statistical distribution of radii within a voxel all have a minor influence on the estimated radius. Pulsed-field-gradient spin echo (PGSE) NMR experiments have been used to measure apparent diffusion in liquids and biological tissue (1,2). In the narrow gradient pulse limit (i.e., using infinitely short pulses), the signal obtained with the PGSE experiment corresponds to the Fourier transform of the diffusion propagator (3,4). Using this so-called q-space imaging technique, the evolution of the diffusion propagator can be measured by acquiring images or spectra with increasing delays between the pulsed diffusion gradients (5,6) and has been used to characterize the diffusion propagator in liquids (6), red blood cells (7,8), and nerve cells (5). The shape of the diffusion propagator carries information about the microstructure of the sample (e.g., biological tissue) and allows the study of compartments that are much smaller than typical sizes that can be resolved by morphological MRI methods (6,9,10).A two-wave-vector extension to the standard PGSE experiment using two pairs of pulsed gradients in a double spin echo, a so called two-wave-vector exper- iment, has been used to study flow effects in more detail than possible with a single gradient pair (11). In general, two-wave-vector experiments carry more details than obtainable through a one wave vector experiment. For example, a two-wave-vector experiment can distinguish between diffusion in different compartments and diffraction-like behavior which is caused by restricted diffusion (12).In the case of restricted diffusion, theoretical calculations by Mitra have shown that the two-wave-vector experiment can be used to determine the radius of gyration of pores using several approximations (12). The same is true for any geometry with restricted diffusion. Potential applications of this theoretical work include the measurement of the size of microscopic structures in biological tissue, as for example done in (13)(14)(15).In the present work, the theory (12) has been successfully applied to quantify the apparent cell radius in an NMR imaging experiment of biological tissue. Furthermore, it has been investigated how deviations from the idealized assumptions affect the apparent radius. Among the effects studied are finite widths of gradient pulses and radius distributions. The term apparent refers to the fact that the determination...
