Characterizing intra-axonal water diffusion with direction-averaged triple diffusion encoding MRI

For large diffusion weightings, the direction-averaged diffusion MRI (dMRI) signal from white matter is typically dominated by the contribution of water confined to axons. This fact can be exploited to characterize intra-axonal diffusion properties, which may be valuable for interpreting the biophysical meaning of diffusion changes associated with pathology. However, using just the classic Stejskal-Tanner pulse sequence, it has proven challenging to obtain reliable estimates for both the intrinsic intra-axonal diffusivity and the intra-axonal water fraction. Here we propose to apply a modification of the Stejskal-Tanner sequence designed for achieving such estimates. The key feature of the sequence is the addition of a set of extra diffusion encoding gradients that are orthogonal to the direction of the primary gradients, which corresponds to a specific type of triple diffusion encoding (TDE) MRI sequence. Given direction-averaged dMRI data for this TDE sequence, it is shown how the intra-axonal diffusivity and the intra-axonal water fraction can be determined by applying simple, analytic formulae. The method is illustrated with numerical simulations, which suggest that it should be accurate for b-values of about 4000 s/mm² or higher.