Fiber-orientation independent component of R₂* obtained from single-orientation MRI measurements in simulations and a...

The effective transverse relaxation rate (R₂*) is sensitive to the microstructure of the human brain like the g-ratio which characterises the relative myelination of axons. However, the fibre-orientation dependence of R₂* degrades its reproducibility and any microstructural derivative measure. To estimate its orientation-independent part (R_2,iso*) from single multi-echo gradient-recalled-echo (meGRE) measurements at arbitrary orientations, a second-order polynomial in time model (hereafter M2) can be used. Its linear time-dependent parameter, β₁, can be biophysically related to R_2,iso* when neglecting the myelin water (MW) signal in the hollow cylinder fibre model (HCFM). Here, we examined the performance of M2 using experimental and simulated data with variable g-ratio and fibre dispersion. We found that the fitted β₁ can estimate R_2,iso* using meGRE with long maximum-echo time (TE_max ≈ 54 ms), but not accurately captures its microscopic dependence on the g-ratio (error 84%). We proposed a new heuristic expression for β₁ that reduced the error to 12% for ex vivo compartmental R₂ values. Using the new expression, we could estimate an MW fraction of 0.14 for fibres with negligible dispersion in a fixed human optic chiasm for the ex vivo compartmental R₂ values but not for the in vivo values. M2 and the HCFM-based simulations failed to explain the measured R₂*-orientation-dependence around the magic angle for a typical in vivo meGRE protocol (with TE_max ≈ 18 ms). In conclusion, further validation and the development of movement-robust in vivo meGRE protocols with TE_max ≈ 54 ms are required before M2 can be used to estimate R_2,iso* in subjects.