Does powder averaging remove dispersion bias in diffusion MRI diameter estimates within real 3D axonal architectures?

Noninvasive estimation of axon diameter with diffusion MRI holds potential to investigate the dynamic properties of the brain network and pathology of neurodegenerative diseases. Recent methods use powder averaging to account for complex white matter architectures, such as fibre crossing regions, but these have not been validated for real axonal geometries. Here, we present 120 - 313 m long segmented axons from X-ray nano-holotomography volumes of a splenium and crossing fibre region of a vervet monkey brain. We show that the axons in the complex crossing fibre region, which contains callosal, association, and corticospinal connections, are larger and exhibit a wider distribution than those of the splenium region. To accurately estimate the axon diameter in these regions, therefore, sensitivity to a wide range of diameters is required. We demonstrate how the q-value, b-value, signal-to-noise ratio and the assumed intra-axonal parallel diffusivity influence the range of measurable diameters with powder average approaches. Furthermore, we show how Gaussian distributed noise results in a wider range of measurable diameter at high b-values than Rician distributed noise, even at high signal-to-noise ratios of 100. The number of gradient directions is also shown to impose a lower bound on measurable diameter. Our results indicate that axon diameter estimation can be performed with only few b-shells, and that additional shells do not improve the accuracy of the estimate. Through Monte Carlo simulations of diffusion, we show that powder averaging techniques succeed in providing accurate estimates of axon diameter across a range of sequence parameters and diffusion times, even in complex white matter architectures. At sufficiently low b-values, the acquisition becomes sensitive to axonal microdispersion and the intra-axonal parallel diffusivity shows time dependency at both in vivo and ex vivo intrinsic diffusivities.