Accurate estimation of microscopic diffusion anisotropy and its time dependence in the mouse brain

Abstract: Microscopic diffusion anisotropy ({\mu}A) has been recently gaining increasing attention for its ability to decouple the average compartment anisotropy from orientation dispersion. Advanced diffusion MRI sequences, such as double diffusion encoding (DDE) and double oscillating diffusion encoding (DODE) have been used for mapping {\mu}A. However, the time-dependence of {\mu}A has not been investigated insofar, and furthermore, the accuracy of {\mu}A estimation vis-`a-vis different b-values was not assessed. Here, we investigate both these concepts using theory, simulation, and experiments in the mouse brain. In the first part, simulations and experimental results show that the conventional estimation of microscopic anisotropy from the difference of D(O)DE sequences with parallel and orthogonal gradient directions yields values that highly depend on the choice of b-value. To mitigate this undesirable bias, we propose a multi-shell approach that harnesses a polynomial fit of the signal difference up to third order terms in b-value. In simulations, this approach yields more accurate {\mu}A metrics, which are similar to the ground truth values. The second part of this work uses the proposed multi-shell method to estimate the time/frequency dependence of {\mu}A. The data shows either an increase or no change in {\mu}A with frequency depending on the region of interest, both in white and gray matter. When comparing the experimental results with simulations, it emerges that simple geometric models such as infinite cylinders with either negligible or finite radii cannot replicate the measured trend, and more complex models, which, for example, incorporate structure along the fibre direction are required. Thus, measuring the time dependence of microscopic anisotropy can provide valuable information for characterizing tissue microstructure.