Comparative analysis of signal models for microscopic fractional anisotropy estimation using q-space trajectory encoding.

Microscopic diffusion anisotropy imaging using diffusion-weighted MRI and multidimensional diffusion encoding is a promising method for quantifying clinically and scientifically relevant microstructural properties of neural tissue. Several methods for estimating microscopic fractional anisotropy (µFA), a normalized measure of microscopic diffusion anisotropy, have been introduced but the differences between the methods have received little attention thus far. In this study, the accuracy and precision of µFA estimation using q-space trajectory encoding and different signal models were assessed using imaging experiments and simulations. Three healthy volunteers and a microfibre phantom were imaged with five non-zero b-values and gradient waveforms encoding linear and spherical b-tensors. Since the ground-truth µFA was unknown in the imaging experiments, Monte Carlo random walk simulations were performed using axon-mimicking fibres for which the ground truth was known. Furthermore, parameter bias due to time-dependent diffusion was quantified by repeating the simulations with tuned waveforms, which have similar power spectra, and with triple diffusion encoding, which, unlike q-space trajectory encoding, is not based on the assumption of time-independent diffusion. The truncated cumulant expansion of the powder-averaged signal, gamma-distributed diffusivities assumption, and q-space trajectory imaging, a generalization of the truncated cumulant expansion to individual signals, were used to estimate µFA. The gamma-distributed diffusivities assumption consistently resulted in greater µFA values than the second order cumulant expansion, 0.1 greater when averaged over the whole brain. In the simulations, the generalized cumulant expansion provided the most accurate estimates. Importantly, although time-dependent diffusion caused significant overestimation of µFA using all the studied methods, the simulations suggest that the resulting bias in µFA is less than 0.1 in human white matter.