The interference of gradient-echo signals from the different compartments of white matter produces non-linear phase evolution and magnitude signal decay that is not well characterised by a single exponential^[1,3,4]. This interference is a result of the different frequency offsets in the myelin, axonal and external compartments, which are well explained by a hollow cylinder fibre model incorporating the effect of the anisotropic magnetic susceptibility of myelin and the short $$$T_2^*$$$ relaxation time of the myelin water^[1,4,5]. Analysis of the complex signal evolution allows to separate the contributions of the different compartments, thus providing useful information about white matter microstructure. Multi-echo GE measurements of white matter structure are generally carried out using sequences with short TR-values and low flip-angles, giving rise to some $$$T_1$$$-weighting of signals. Recent work has suggested that there may be a component of myelin water with a much shorter $$$T_1$$$ than that of the external/axonal compartments^[2]. Flip-angle variation at fixed TR should thus vary the weighting of the different compartments providing additional microstructural information and potentially allowing the $$$T_1$$$ of the different compartments to be determined.

Data acquisition was performed on eight healthy subjects on an Achieva 7.0T scanner (Philips Healthcare). Single-slice, sagittal GE images ($$$\text{TE}1/\Delta\text{TE}/\text{TR}=2.2/2.2/127\,\text{ms},\,n_\text{echoes}=20,\,n_\text{averages}=10,$$$ $$$(\text{P}\times\text{R}\times\text{S})_\text{voxel}=1\times1\times5\,\text{mm}^3$$$) were acquired at nominal flip-angles of $$$\alpha=[10^\circ\,60^\circ\,90^\circ]$$$. We focused on the corpus callosum since this is a highly myelinated region with nerve fibers aligned perpendicular to $$$\vec{B_0}$$$ thus providing the largest frequency differences between compartments^[1]. In initial experiments we found that there were in-flow-related artefacts in high-flip-angle images, particularly adjacent to the anterior cerebral artery, which could be significantly suppressed by saturation of the signal in a thick, axial band positioned just below the corpus callosum (Figure1). Saturation band excitation prior to each excitation was therefore used for all flip-angles in this study. Each protocol included $$$B_1$$$-map-acquisition for the determination of the actual flip-angles applied in the different ROIs.

The complex signal from white matter at echo-time $$$t=\text{TE}_n=\text{TE}_1+(n-1)\Delta\text{TE}$$$ was described using a three-pool-model $$\qquad\qquad\qquad\qquad{}S(t)=\left(\frac{A_\text{a}}{A_\text{e}}e^{-i\langle\omega_\text{a}\rangle{}t}+\frac{A_\text{m}}{A_\text{e}}e^{-r_{2\text{m}}^*t}e^{-i\langle\omega_\text{m}\rangle{}t}+1\right)\cdot{}e^{-R_2^*t}e^{i\Omega{}t}e^{i\Phi_0},\qquad\qquad\qquad\qquad\qquad\qquad\qquad(1)$$ where the labels $$$\text{a}$$$, $$$\text{m}$$$ and $$$\text{e}$$$ denote the axonal, myelin and external compartments, $$$A$$$- and $$$\omega$$$-values characterise the amplitudes and frequencies of signals, while $$$r^*_\text{2m}$$$ is the additional relaxation rate of the myelin water signal. $$$\Omega$$$ and $$$\phi_0$$$ represent the uninteresting effects of large length scale field variation and RF-related phase offsets, which were removed by calculation of frequency difference values $$$\mathrm{arg}\left(\frac{S(\text{TE}_n)\cdot{}S(\text{TE}_1)^{n-2}}{S(\text{TE}_2)^{n-1}}\right)\cdot\frac{1}{\Delta\text{TE}(n-1)}$$$. These and the scaled magnitude values $$$\mathrm{abs}\left(\frac{S(\text{TE})}{S(\text{TE}_1)}\right)$$$, were averaged over ROIs in the genu, body and splenium of the CC (Figure1) for each data set and the resulting values were fitted to (1). Data from three flip-angles were fitted simultaneously for each ROI. The value of $$$A_\text{m}/A_\text{e}$$$ was allowed to vary with flip-angle to accommodate the expected relative change in saturation of the myelin compartment, all other parameters were assumed to be the same for all flip-angles, including equal $$$T_1$$$-values for the axonal and external compartments.

The resulting values of $$$A_\text{m}/A_\text{e}$$$ were fitted to $$\frac{A_\text{m}}{A_\text{e}} = c\cdot\frac{L_\text{m}}{L_\text{e}}$$ with $$L_\text{a,m}=\sin(\alpha)\cdot\frac{1-\exp(-\text{TR}/T^\text{a,m}_1)}{1-\cos{\alpha}\exp(-\text{TR}/T^\text{a,m}_1)}$$ at the corrected $$$\alpha$$$-values calculated for each ROI using the $$$B_1$$$-maps.

Figure2 shows the variation of FDM and magnitude data with TE in the splenium for one subject. The faster rate of magnitude signal decay at short TE and the larger negative frequency offsets in the data acquired with larger flip-angles are consistent with there being a relative increase in the amplitude of the myelin water signal as a result of its shorter $$$T_1$$$, and consequently lesser saturation than occurs in the external and axonal pools. Figure3 shows frequency difference maps acquired from the same subject at the three different flip-angles with and without saturation bands. The increased frequency offset with increasing flip-angle is evident, along with the reduction of in-flow artefacts manifested at high flip-angles through use of saturation band. Figure2 indicates that the three-pool model provides good fits to the experimental data. The best-fitting model parameters averaged over subjects are shown in Table1. These are in reasonable agreement with previously reported frequency offset and relaxation rate values^[1,4]. Table1 also details the $$$T_1$$$-values in the different compartments, found by fitting $$$A_\text{m}/A_\text{e}$$$ versus flip-angle for each compartment. Figure4 shows example data from the splenium of all subjects, displaying the expected relative increase in the myelin-compartment-amplitude at higher flip-angles. The calculated myelin $$$T_1$$$-values (Table1) are lower than in the external/axonal compartment as expected, but the $$$T_1$$$-values in the different compartments are much closer in size than reported in previous work based on double inversion-recovery at 3T^[2]. This may be a result of magnetization transfer effects and inter-compartmental exchange, which should be incorporated into future modelling.