Oscillating-gradient spin-echo diffusion-weighted imaging (OGSE-DWI) with a limited number of oscillations: I. Signal equation

The oscillating-gradient spin-echo (OGSE) sequence has been promoted as a promising diffusion-weighted magnetic resonance imaging (DWI) technique for probing in vivo tissue microstructure in the frequency domain. However, due to practical restrictions on the duration and number of oscillations that a motion-probing gradient can have, the technique has limited spectral resolution and range. This work re-examines the OGSE-DWI method to clarify how these limitations are reflected in the signal model. There are several aspects of the revised framework that distinguish it from the conventional description employed for OGSE DWI. In particular, while the conventional OGSE signal model implies that the spectral density of molecular diffusion may be directly sampled in experiments, in practice information about the spectral density can be only indirectly obtained.