Deciphering the fibre-orientation independent component of R2* (R2,iso*) in the human brain with a single multi-echo gradient-recalled-echo measurement under varying microstructural conditions

The effective transverse relaxation rate (R2*) is sensitive to the microstructure of the human brain, e.g. the g-ratio characterising the relative myelination of axons. However, R2* depends on the orientation of the fibres relative to the main magnetic field, degrading its reproducibility and that of any microstructural derivative measure. To decipher its orientation-independent part (R2,iso*), a second-order polynomial in time (M2) can be applied to single multi-echo gradient-recalled-echo (meGRE) measurements at arbitrary orientation. The linear-time dependent parameter, β1, of M2 can be biophysically related to R2,iso* when neglecting the signal from the myelin water (MW) in the hollow cylinder fibre model (HCFM). Here, we examined the effectiveness of M2 using experimental and simulated data with variable g-ratio and fibre dispersion. We showed that the fitted β1 effectively estimates R2,iso* when using meGRE with long maximum echo time (TEmax ≈ 54 ms) but its microscopic dependence on the g-ratio was not accurately captured. This error was reduced to less than 12% when accounting for the MW contribution in a newly introduced biophysical expression for β1. We further used this new expression to estimate the MW fraction (0.14) and g-ratio (0.79) in a human optic chiasm. However, the proposed method failed to estimate R2,iso* for a typical in-vivo meGRE protocol (TEmax ≈ 18 ms). At this TEmax and around the magic angle, the HCFM-based simulations failed to explain the R2*-orientation-dependence. In conclusion, estimation of R2,iso* with M2 in vivo requires meGRE protocols with very long TEmax ≈ 54 ms. ### Competing Interest Statement The Max Planck Institute for Human Cognitive and Brain Sciences has an institutional research agreement with Siemens Healthcare. NW holds a patent on acquisition of MRI data during spoiler gradients (US 10,401,453 B2). NW was a speaker at an event organized by Siemens Healthcare and was reimbursed for the travel expenses.