Researchers and clinicians who are interested in multi-component white matter analysis and demyelination diseases.

Multiple echo GRE (mGRE) preserves information for both T₂* and phase evolution, which offers opportunity for white matter (WM) components analysis^[1] together with their frequency shifts^[2]. The feasibility of WM components analysis using direct complex fitting to the following model was recently validated on low spatial resolution (2×2×2mm³) mono-polar readout mGRE data^[3]:

$$S(t)=[A_{my}e^{-(1/T^*_{2,my}+j2\pi{f_{my}})}+A_{ax}e^{-(1/T^*_{2,ax}+j2\pi{f_{ax}})}+A_{ex}e^{-(1/T^*_{2,ex}+j2\pi{f_{ex}})}]e^{j\phi_0}~~~~~~[1]$$

Here, $$$my$$$=myelin water, $$$ax$$$=axonal water, $$$ex$$$=extracellular water; $$$A$$$ and $$$f$$$ respectively represent signal magnitudes and frequency offsets of each WM component; $$$\phi_0$$$ is the initial phase offset.

In this study, with the mGRE acquisition and the above WM three-pool complex model, we present a three-step method for high resolution myelin water fraction and frequency shift mapping, using tissue susceptibility from simultaneously acquired quantitative susceptibility maps (QSM) by the same mGRE sequence.

Data Acquisition: Data were acquired on a 3T scanner (MAGNETOM Prisma, Siemens Healthcare A.G., Erlangen, Germany) with informed consent letters for all three healthy volunteers. A 3D mGRE data acquisition was used for whole cerebral myelin water fraction and frequency shift mapping: 32-echo bi-polar readout train, TE of 1^st echo = 2.7 ms, echo spacing = 1.5 ms, TR = 62 ms, readout bandwidth = 930 Hz/pixel, voxel size = 0.94×0.94×2mm³, acquisition matrix = 256×256×64. DTI data were also acquired to obtain WM fiber orientation map.

Data Processing: The mapping for myelin water fraction and frequency shift was done in three steps.

Step 1: Calculating QSM from the odd echoes of mGRE data. iHARPERELLA method^[4] was used for background field removal, and iLSQR method^[5] was used for QSM calculation.

Step 2: Pre-processing of the magnitude and phase of the complex mGRE data. The magnitude part was filtered with a 3D anisotropic diffusion filter (ADF), and the phase part was replaced by $$$\phi_i=f_{tissue}TE_i$$$, with $$$i$$$ being the echo number. The tissue induced local frequency $$$f_{tissue}$$$ is represented by Lorentzian sphere approximation $$$f_{tissue}=\frac{4}{3}\pi\chi{f_0}$$$, where $$$f_0$$$ is the MR center frequency, and $$$\chi$$$ is the susceptibility value of QSM calculated in Step 1.

Step 3: Complex fitting was performed using the same model as Eq. [1] where the magnitude and phase of $$$S(t)$$$ are replaced by those generated from Step 2. The myelin water fraction (MWF) was calculated as $$$MWF=\frac{A_{my}}{A_{my}+A_{ax}+A_{ex}}$$$.

Fig. 1 demonstrates the quantitative maps of MWF, $$$f_{my}$$$, $$$f_{ax}$$$, and $$$f_{ex}$$$ from three methods: direct fitting of original complex data^[3] (upper row), fitting of complex data with only magnitude part filtered by ADF (middle row), and the proposed three-step method (bottom row). Fig. 2 demonstrates the relationships of $$$f_{my}$$$ versus fiber orientation, and of $$$f_{ax}$$$ versus fiber orientation.

As shown in Fig. 1, the proposed method outperforms the direct fitting: the direct fitting without phase processing failed in $$$f_{ax}$$$ and $$$f_{ex}$$$ mapping (upper and middle rows in Fig. 1), possibly due to a much lower SNR and a higher sensitivity to inhomogeneous $$$B_0$$$ field in smaller voxels. This problem is resolved by using tissue susceptibility induced phase from simultaneously acquired QSM in Step 2, which benefits from the background phase removal and magnetic dipole deconvolution procedures during QSM calculation. MWF map with a higher homogeneity (zoomed in sub images), and a higher sensitivity for $$$f_{my}$$$ estimation (black circles) are also observed.

Fig. 2 shows a relatively large positive $$$f_{my}$$$ on fibers perpendicular to $$$B_0$$$ (solid circles), and a small positive $$$f_{my}$$$ on fibers parallel to $$$B_0$$$ (dashed circles). Slight negative frequency shifts for axonal water were also observed in fibers perpendicular to $$$B_0$$$, with much smaller values than that in $$$B_0$$$ parallel fibers. These results correspond well with previous literature.^{[3, 6]}

We present a novel method for high spatial resolution WM multi-component imaging by using tissue susceptibility induced phase with no requirement for additional QSM data acquisition. Comparing with direct fitting, this method take the advantage of the background phase removal and magnetic dipole deconvolution procedures during QSM calculation to avoid the misfitting possibly caused by a smaller voxel size. The generated high-resolution MWF and frequency shift maps can be potentially used for quantitative studies of demyelinated diseases.