Equivalence of double and single wave vector diffusion contrast at low diffusion weighting

Multiple pulsed field gradient diffusion sequences have received renewed interest in recent years as a potentially new type of MRI contrast. This attention is largely a result of the ability to measure pore sizes using low-amplitude diffusion gradients, and to distinguish between macroscopically isotropic systems of anisotropic pores and systems of isotropic pores. In this article, it is shown that, under many circumstances, the same type of information can be obtained by combining two or more standard single pulse diffusion-weighted experiments acquired at different diffusion times. Similarly, information from multiple pulsed field gradient diffusion can be reconstructed from several single pulsed diffusion experiments. This possibility is rooted in the information contained in the time dependence of the diffusion tensor, which provides a complete description of the diffusion-weighted MR signal at low gradient amplitudes. The new information arising at the fourth order in the cumulant expansion is discussed. The coupling of the wave vectors at long mixing times is found to be controlled by the variance of the single pore mean displacement tensor. In particular, a discussion is given concerning the way in which the sensitivity of the fourth-order term to the pore shape anisotropy is modulated by pore orientation anisotropy and vanishes in coherently oriented homogeneous ensembles. For macroscopically isotropic systems, a new index of pore shape anisotropy is proposed.