Feasibility Study of High Resolution Mapping for Myelin Water Fraction and Frequency Shift using Tissue Susceptibility
Zhe Wu1,2, Hongjian He1,2, Ying Chen1,2, Song Chen1,2, Hui Liu3, Yiping P. Du2, and Jianhui Zhong1,2

1Center for Brain Imaging Science and Technology, Zhejiang University, Hangzhou, China, People's Republic of, 2Department of Biomedical Engineering, Zhejiang University, Hangzhou, China, People's Republic of, 3NEA MR Collaboration, Siemens Ltd., China, Shanghai, China, People's Republic of

### Synopsis

A three-step method for high resolution myelin water fraction (MWF) and frequency shift mapping of white matter components using tissue susceptibility is presented in this study. Tissue susceptibility induced phase was calculated by the simultaneously acquired QSM from the same multi-echo GRE (mGRE) dataset, and was used as the phase part of complex data for a subsequent fitting to a three-pool white matter model. Benefit from the background phase removal and magnetic dipole deconvolution procedures during QSM calculation, the result reveals much less misfitting when comparing with direct fitting to original mGRE data. These generated quantitative maps can be potentially used for quantitative studies of demyelinated diseases.

### Target Audience

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

### Introduction

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.

### Methods

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 1st 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 $MWF=\frac{A_{my}}{A_{my}+A_{ax}+A_{ex}}$.

### Results

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.

### Discussion

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]

### Conclusion

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.

### Acknowledgements

This work was supported by National Natural Science Foundation of China (NSFC) 81371518.

### References

[1] Du YP, Chu R, Hwang D, et al. Fast Multislice Mapping of the Myelin Water Fraction Using Multicompartment Analysis of T2* Decay at 3T: A Preliminary Postmortem Study. Magn. Reson. Med. 2007; 58: 865–870.

[2] van Gelderen P, de Zwart JA, Lee J, et al. Nonexponential T2* Decay in White Matter. Magn. Reson. Med. 2012; 67:110–117.

[3] Nam Y, Lee J, Hwang D, Kim DH. Improved estimation of myelin water fraction using complex model fitting. NeuroImage. 2015; 116: 214–221.

[4] Li W, Wu B, Liu C. iHARPERELLA: an improved method for integrated 3D phase unwrapping and background phase removal. Proc. Intl. Soc. Mag. Reson. Med. 2015; 23: 3313.

[5] Li W, Wang N, Yu F, et al. A method for estimating and removing streaking artifacts in quantitative susceptibility mapping. NeuroImage. 2015; 108: 111–122.

[6] Sati P, van Gelderen P, Silva AC, et al. Micro-compartment specific T2* relaxation in the brain. NeuroImage. 2013; 77: 268–278.

### Figures

Fig. 1 Myelin water fraction (MWF) map, frequency offset maps for myelin water ($f_{my}$), axonal water ($f_{ax}$) and extracellular water ($f_{ex}$), calculated from original data (upper row), only magnitude denoised data (middle row), and the proposed method (bottom row). Note the effect of phase processing on $f_{ax}$ and $f_{ex}$ maps.

Fig. 2 Frequency map of myelin water and axonal water. The solid circles indicate the fibers perpendicular to the $B_0$ field, while the dashed circles indicate the fibers that are parallel to the $B_0$ field. Note the difference of these two kinds of fibers on $f_{my}$ and $f_{ax}$ maps.

Proc. Intl. Soc. Mag. Reson. Med. 24 (2016)
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