Hongpyo Lee^{1}, Yoonho Nam^{2}, and Dong-Hyun Kim^{1}

Recently, myelin water fraction has been investigated using mGRE data. The purpose of this study is to investigate effects of the range of TE in GRE based MWF using different three fitting models. The results of simulation and in-vivo data suggest that complex model can be helpful to overcome bias due to susceptibility anisotropy compared to magnitude based models.

**[Simulation]**
A
series of Monte Carlo simulations (300 repetitions for each case) were
performed to test the bias and noise performance of MWF estimation with respect
to the range of TE. Simulations were carried out within a 100 ms range of TE. A
hollow cylinder fiber model was used for the simulation^{4} with the following
parameters: volume fraction for the myelin, axon, and extra-cellular space were
32%, 41%, and 27% respectively, with g-ratio of 0.75. Water compartment of
myelin volume set to be 40%^{5}, and for axonal or extra-cellular space
set to 85%. Consequently, the fractional contribution to the total water signal
for the myelin, axon, and extra-cellular space were 18%, 49%, and 33%,
respectively. Isotropic susceptibility of -0.13 ppm and anisotropic
susceptibility of -0.15 ppm were used^{6}. Frequency shifts were
calculated using the formula in Table1 of Ref 4. Fig. 1 shows the parallel and
perpendicular examples of frequency shift of simulation data using the hollow
cylinder model. T2* components were generated for myelin water, axonal water,
and extra-cellular water with relaxation times 10ms, 64ms, 48ms^{1}.
Complex signal evolution was performed with the effect of hollow cylinder model
for four different orientations. Complex Gaussian noise was added to the
simulated signal for SNR of 300. Water exchange and diffusion effects were not
considered in this simulation.

**[Data acquisition] **
Data
from four healthy volunteers were acquired on a clinical 3 Tesla MRI scanner
(Tim Trio, Siemens Medical Solution, Erlangen, Germany) using a 12-channel head
coil for signal reception. The 3D mGRE data were acquired for the MWF mapping.
The imaging parameters were as follows: TR = 120 ms, flip angle = 30°, field of
view = 256 × 256 × 88 mm^{3}, spatial resolution = 2 × 2 × 2 mm^{3}.
To test the effect of range of echo times onto MWF, 80 echoes were acquired;
first TE = 1.6 ms, echo spacing = 1 ms, Last TE = 84 ms. Additionally, MPRAGE
and diffusion tensor imaging (DTI) was obtained to determine the structure and fiber
orientation information.

**[Data Processing]
**
Three different fitting models are used
and analyzed in this study (table 1); magnitude multi-component model (eqn.1), magnitude
three-component model (eqn.2), and complex three-component model (eqn.3). For
magnitude multi-pool model, the rNNLS algorithm was used to estimate the
parameters. For both three-pool models, non-linear least squares method was applied.
In the simulation,
of the complex model was ignored.

1. Nam Y, et al. Improved Estimation of Myelin Water Fraction using Complex Model Fitting. NueroImage, 2015;116:214-221

2. Du YP, et al. Fast multislice mapping of the myelin water fraction using multicompartment analysis of T2* decay at 3T: a preliminary postmortem study. MRM 2007;58(5):865-870

3. Hwang D, et al. In vivo multi-slice mapping of myelin water content using T 2* decay. NeuroImage 2010;52(1):198-204.

4. Wharton S, Bowtell R. Fiber orientation-dependent white matter contrast in gradient echo MRI. PNAS, 2012;109(45):18559-18564.

5. Vandenheuvel FA. Structural studies of biological membranes: The structure of myelin. Annals of the New York Academy of Sciences 1965;122(1):57-76.

6. Liu C. Susceptibility tensor imaging. Magnetic resonance in medicine 2010;63(6):1471-1477.

Figure
1. Examples of simulations of hollow cylinder model with anisotropic
susceptibility of the myelin at 3T. The frequency shifts (a,b,e,f) are
different for parallel (a,b) and perpendicular (e,f) fiber orientation.
Magnitude decay (c,g) and phase evolution (d,h) against TE are shown with
different fiber orientation. For comparison, it also shows signals which do not
consider susceptibility anisotropic effect.

Figure 2.
Simulations of estimated MWFs (a) and its standard deviations (b) of different
three models as a function of TE. Simulated signals were generated with ES =
1ms. The True MWF value is 18% indicated as a black line. Different four
orientation angles (0°, 30°, 60°, 90°) of myelin fibers were simulated.

Figure 3. In-vivo results of MWFs from
different echoes used in fitting at 3T. (a) The estimated MWF maps from
different three models. (b) The corresponding MPRAGE and (c) the DTI maps. (d)
The MWFs of the parallel ROI (yellow box drawn on DTI), and perpendicular ROI
(red box).

Table 1. Three different fitting models.