Doohee Lee^{1}, Jingu Lee^{1}, Jongho Lee^{1}, and Yoonho Nam^{2}

In this study, we propose a single-scan GRE-MWI method that corrects for the effects of macroscopic field inhomogeneity using a modified z-shimming. In addition, a new three-component magnitude model corresponding to the modified sequence is proposed. Compared to the conventional method, the results showed an improved MWF estimation, particularly in frontal lobe regions.

*Single-scan z-shim sequence:*

To acquire signal decay curve for GRE-MWI with z-shim, a conventional 2D
multi-slice GRE sequence was modified as shown in Fig. 1. Since myelin water
signal has a short T_{2}^{*} (<10 ms) and is mostly lost after 10 ms, z-shim blips
were applied after 10 ms of TE to reserve most of the myelin water signal.
Since the effects of the macroscopic susceptibility induced field gradient increase
linearly with time, both compensation gradients and rewinding gradients were
also increased with time.

*MWF
fitting and post processing:*

The
three-pool magnitude model suggested by previous studies was given by ^{1-2,7}:

$$S_{uncorr}(t)=A_{my}e^{-t/T_{2,my}^*}+A_{ax}e^{-t/T_{2,ax}^*}+A_{ex}e^{-t/T_{2,ex}^*}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:[Eq.\:1]$$

where $$$A_{my}$$$, $$$A_{ax}$$$, and $$$A_{ex}$$$ represent
the amplitude of the myelin (my), axonal (ax) and extracellular (ex) water pools respectively,
and $$$T_{2,my}^*$$$, $$$T_{2,ax}^*$$$
, and $$$T_{2,ex}^*$$$ represent T_{2}^{*} of the three water pools. Additional signal decay that
originates from the macroscopic field inhomogeneity was modeled by M(∙),
which assumed linear spin dephasing in slice-select direction and included a non-ideal
excitation profile. Then the signal decay is modeled as follows:

$$S_{corr}(t)=S_{uncorr}(t)\cdot M(G_{z,susc}t)\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:[Eq.\:2]$$

where G_{z,susc} represents
susceptibility induced field gradient in slice-select direction.
When this model is applied to the modified
z-shimming sequence, one can generate the following equations.

$$S_{proposed}(t)=\begin{cases}S_{uncorr}(t)\cdot M(G_{z,susc}t) & (for\:not\:z-shimmed\:echoes)\\S_{uncorr}(t)\cdot M( (G_{z,susc}-G_c)t) & (for\:z-shimmed\:echoes)\end{cases}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:[Eq.\:3]$$

where G_{c}
represents the amplitude of compensation gradient.
When estimating the model parameters, the
signals were first fitted to a one-component model, then the resulting parameters
were used to determine initial values for a two-component model. The results
were used for initial values for the three-component model.^{8}

*Data acquisition and processing:*

Three healthy volunteers (mean age 24 ± 1)
were scanned at 3T. ** GRE:** The conventional GRE and the z-shim sequence were
acquired with following parameters: 1 ms Hanning windowed sinc RF pulse, TR = 1 s, TE(n) = 2 + (n-1)∙2
ms, number of echoes = 16, flip angle = 68°,
in-plane resolution = 1.4 × 1.4
mm

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