  Purpose: This study aims to evaluate two distinct approaches for fibre radius
estimation using diffusion-relaxation MRI data acquired in biomimetic
microfibre phantoms that mimic hollow axons. The methods considered are the
spherical mean power-law approach and a T2-based pore size estimation
technique. Theory and Methods: A general diffusion-relaxation theoretical model
for the spherical mean signal from water molecules within a distribution of
cylinders with varying radii was introduced, encompassing the evaluated models
as particular cases. Additionally, a new numerical approach was presented for
estimating effective radii (i.e., MRI-visible mean radii) from the ground truth
radii distributions, not reliant on previous theoretical approximations and
adaptable to various acquisition sequences. The ground truth radii were
obtained from Scanning Electron Microscope images. Results: Both methods show a
linear relationship between effective radii estimated from MRI data and
ground-truth radii distributions, though some discrepancies were observed. The
spherical mean power-law method overestimated fibre radii. Conversely, the
T2-based method exhibited higher sensitivity to smaller fibre radii but faced
limitations in accurately estimating the radius in one particular phantom,
possibly due to material-specific relaxation changes. Conclusion: The study
demonstrates the feasibility of both techniques to predict pore sizes of hollow
microfibres. The T2-based technique, unlike the spherical mean power-law
method, does not demand ultra-high diffusion gradients but requires calibration
with known radius distributions. This research contributes to the ongoing
development and evaluation of neuroimaging techniques for fibre radius
estimation, highlights the advantages and limitations of both methods and
provides datasets for reproducible research.
