Synopsis

In this study, we propose an extension to GRE based myelin water fraction techniques based on 3-comparment models. The new model includes T₁ and chemical exchange effects between a free water pool and a myelin water pool and can be fitted to a variable flip angle acquisition strategy. Furthermore, we demonstrate that it can both correct the T₁ dependency in MWF, make the fitting procedure less ill-posed and more SNR efficient, resulting in robust estimation across subjects.

Introduction

Theory

Standard mGRE-MWF considers 3 water pools in white matter (WM)⁴: myelin water (MW), intra-axonal water (IW) and extracellular water (EW). With a variable flip angle acquisition strategy⁶, the signal measured for each flip angle $$$\alpha$$$, $$$S_{\alpha}$$$, can be modelled as:

$$S_{\alpha}(t)=\left[\sum_{n=\left\{MW,IW,EW\right\}}M_{0,n}\sin\alpha\frac{1-e^{-TR{\cdot}R_{1,n}}}{1-e^{-TR{\cdot}R_{1,n}}\cos\alpha}e^{t(-R_{2,n}^{*}+i\omega_{n})}\right]e^{i(\omega_{b}t+\psi)}$$

$$=\sum_{n=\left\{MW,IW,EW\right\}}SS_{\alpha,n}e^{t(-R_{2,n}^{*}+i\omega_{n})}e^{i(\omega_{b}t+\psi)}[Eq.1]$$

Each pool has a different proton density, $$$M_{0,n}$$$ , frequency shift $$$\omega_{n}$$$, longitudinal, $$$R_{1,n}$$$, and transverse relaxation rates, $$$R_{2,n}^{*}$$$ . $$$\omega_{b}$$$ and $$$\psi$$$ represent the background field and initial phase offset. Preliminary analysis (data not shown) suggested that imperfect RF spoiling (particularly for large flip angles) and the presence of inter-compartmental water exchange cannot be ignored in the steady state calculation while IW and EW could be assumed to have the same $$$R_{1}$$$. These three factors can be accounted for using an Extended Phase Graph (EPG-X⁷) approach where two pools are considered, MW and free water (OW=IW+EW)⁸. In Eq.1 the steady-state signal is given by:

$$SS_{\alpha,MW or IW,EW}=EPGX(M_{IW+EW},R_{1,IW+EW},M_{WM},R_{1,MW},k,\alpha,TR)[Eq.2]$$

where k is the exchange rate from the OW to MW⁷.

Method

All scans were performed at 3T (Siemens, Erlangen, Germany) using a 32-channel array in 6 healthy volunteers. The imaging protocol consisted of:

• Whole-brain T₁ scan using MP2RAGE⁹ with res=1mm isotropic, Tacq=4mins;
• 2D-MB EPI-DWI multiband=3, isotropic resolution 1.6mm, TR/TE=3350/71.20ms, 2-shell (b=0/1250/2500 s/mm2,17/165/165 measurements), Tacq=15mins;
• Monopolar 3D mGRE with 12 echoes, TR/TE=46/2.15:3.05:35.70ms, res=1.8mm isotropic, $$$\alpha$$$=[5,10,20,30,40,50,70]° and GRAPPA=2. Six additional datasets with $$$\alpha$$$=20° were acquired (order was randomised), Tacq=3.5mins per flip angle.

Furthermore, B1 map was acquired to correct B1+ inhomogeneity when fitting Eq.1 and 2.

MP2RAGE images were segmented using FSL (www.fmrib.ox.ac.uk). DWI images were pre-processed in FSL and DTI was used to estimate the principal fibre direction.

All (mGRE, and processed DWI and MP2RAGE) data were co-registered to the middle mGRE acquisition using ANTs¹⁰. Eddy current artifacts, prevalent in the first echo of the mGRE phase data, were corrected using first-order polynomial fit. The model described in Eq.1 and 2 was fitted to the complex-valued 7 flip angles data in a voxel-wise manner. Each acquisition was assumed to have a separate $$$\omega_{b}$$$ and $$$\psi$$$ (14 parameters) to account for small variations in head position, resulting on 26 parameters to be estimated. The 7 flip angle 20 (Ernst angle) mGRE data were averaged (after co-registration, eddy current and frequency correction) and fitted to a standard 3-pool model⁴ consisting of 10 parameters.

To evaluate the robustness of the most relevant parameters (MWF, R₂* and R₁) of the different water compartments, histograms of these parameters within WM and grey matter (GM) masks were compared across subjects and across regions

Results and Discussion

Figs.2&3 demonstrates the quality of volumetric parameter estimation in 2 subjects. The proposed model produces MWF maps and frequency maps with higher SNR than the standard approach (Fig.2), with highly-myelinated fibres appearing more pronounced. Additionally, our method allows the computation of two R₁ maps with different spatial patterns.

Fig.4 shows the histograms of the different compartments R₁ (4A-B), R₂* (4C-E) as well as MWF (4F) in WM and GM for all subjects, demonstrating the reproducibility of the measurements.

As expected, R₁ values of free water are shorter than those predicted by the MP2RAGE, while the myelin water is higher than both and less distinguishable between grey and white matter (Fig.5A). Surprisingly, MWF estimated by our method was higher in both GM and WM than in the standard mGRE-MWF, with our histograms distributions being significantly narrower (Fig.5B). R₂* maps of each compartment have an increased contrast between GM and WM in the proposed method.

Conclusion

Acknowledgements

References

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