Double diffusion encoding is a magnetic resonance technique with applications in measuring microstructure. In many tissues, cell size (which is of a few micrometers) is an important biological parameter. Estimating an arbitrary pore size distribution from a diffusion attenuated signal usually relies on varying a single experimental setting. This inversion process is numerically unstable. Numerical simulations are presented, where multiple experimental settings are varied concomitantly. The inversion's results show good agreement with ground truth.

Double diffusion encoding (DDE) MRI is a technique in which two diffusion weighted periods are applied between excitation and acquisition. This allows to acquire structural information (as pore size and shape) and molecular exchange between compartments, in terms of apparent exchange rate (AXR). However, it has not been well investigated yet whether the diffusion restriction underlying DDE size estimation may compromise AXR results.Numerical simulations for impermeable spheres have shown that in case of small pores (diameter < 10 µm) the restriction effect may be neglected. Yet, for larger pores, the restriction effect can be relevant and needs to be considered in the analysis of experiments.Here, we present experiments performed on a 3 T clinical MRI system using a water-in-oil emulsion in which no exchange between compartments is expected. The results show that a nonzero apparent exchange rate may be estimated in a sample with impermeable pores. This shows that, as predicted in simulations, the restriction effect affects the AXR results. The use of perpendicular diffusion gradients may be a solution for this problem in isotropic samples.

Objective To study the origin of compartment size overestimation in double diffusion encoding MRI (DDE) in vivo experiments in the human corticospinal tract. Here, the extracellular space is hypothesized to be the origin of the DDE signal. By exploiting the DDE sensitivity to pore shape, it could be possible to identify the origin of the measured signal. The signal difference between parallel and perpendicular diffusion gradient orientation can indicate if a compartment is regular or eccentric in shape. As extracellular space can be considered an eccentric compartment, a positive difference would mean a high contribution to the compartment size estimates. Materials and methods Computer simulations using MISST and in vivo experiments in eight healthy volunteers were performed. DDE experiments using a double spin-echo preparation with eight perpendicular directions were measured in vivo. The difference between parallel and perpendicular gradient orientations was analyzed using a Wilcoxon signed-rank test and a Mann–Whitney U test. Results Simulations and MR experiments showed a statistically significant difference between parallel and perpendicular diffusion gradient orientation signals ($$\alpha =0.05$$ α = 0.05 ). Conclusion The results suggest that the DDE-based size estimate may be considerably influenced by the extra-axonal compartment. However, the experimental results are also consistent with purely intra-axonal contributions in combination with a large fiber orientation dispersion.