Adaptive slice-specific z-shimming for 2D spoiled gradient-echo sequences

Abstract

Purpose: To reduce the misbalance between compensation gradients and macroscopic field gradients, we introduce an adaptive slice-specific z-shimming approach for 2D spoiled multi-echo gradient-echoe sequences in combination with modeling of the signal decay.

Methods: Macroscopic field gradients were estimated for each slice from a fast prescan (15 seconds) and then used to calculate slice-specific compensation moments along the echo train. The coverage of the compensated field gradients was increased by applying three positive and three negative moments. With a forward model, which considered the effect of the slice profile, the z-shim moment, and the field gradient, $R_2^{\ast }$ maps were estimated. The method was evaluated in phantom and in vivo measurements at 3 T and compared with a spoiled multi-echo gradient-echo and a global z-shimming approach without slice-specific compensation.

Results: The proposed method yielded higher SNR in $R_2^{\ast }$ maps due to a broader range of compensated macroscopic field gradients compared with global z-shimming. In global white matter, the mean interquartile range, proxy for SNR, could be decreased to 3.06 s^-1 with the proposed approach, compared with 3.37 s^-1 for global z-shimming and 3.52 s^-1 for uncompensated multi-echo gradient-echo.

Conclusion: Adaptive slice-specific compensation gradients between echoes substantially improved the SNR of $R_2^{\ast }$ maps, and the signal could also be rephased in anatomical areas, where it has already been completely dephased.

Keywords: ${\mathrm{R}}_2^{\ast }$ relaxometry; ${\mathrm{T}}_2^{\ast }$ relaxometry; field inhomogeneities; gradient-echo; z-shim.

FIGURE 1

Schematic overview of the compared sequences. A, Spoiled multi‐echo gradient‐echo (mGRE) sequence without z‐shimming. B, In the global z‐shim approach, moments are applied through alternating pairs (same color) with a linear increase along TE. The first moment in each pair is calculated based on a single positive or negative ${\overline{G}}_c^{+/‐}$, and the second moment balances the compensation moment to acquire a gradient‐echo (GRE) image with zero net moment. C, The proposed slice‐specific approach, with ${\overline{G}}_c^{+/‐}\left[n\right]$ estimated from a prescan individually for each slice n. In addition, ${\overline{G}}_c^{+/‐}\left[n\right]$ is split up with factors $\left[\frac{1}{3},\frac{2}{3},\frac{3}{3}\right]{\overline{G}}_c^{+/‐}\left[n\right]$ (dashed boxes) followed by compensation of all moments. To correct for physiological fluctuations, a navigator echo is acquired at TE_navi

FIGURE 2

Comparison of the measured averaged normalized signal decay $S_{\mathit{norm}}\left(T{E}_i\right)=S\left(T{E}_i\right)/S\left(T{E}_1\right)$ and the estimated dephasing functions $F_{z‐shim}\left({\mathit{TE}}_i\right)$ within one slice. A, The magnitude images of $T{E}_{10}$ to $T{E}_{20}$. B, Regions of interest (ROIs) were defined within different field gradient intervals, $G_z$. In these ROIs, the $S_{\mathit{norm}}\left(T{E}_i\right)$ (C) and the averaged $F_{z‐shim}\left(T{E}_i\right)$ (D) were estimated. The lines in (C) and (D) show the results from a spoiled mGRE sequence without z‐shim gradients in blue, with the global z‐shim approach ( $|{\overline{G}}_c^{+/‐}|=100\mu T/m$) in red, and with the proposed slice‐specific z‐shimming in yellow. Note: The interpolation between echoes is solely for illustration purposes

FIGURE 3

Comparison of the measured averaged normalized $S_{\mathit{norm}}\left(T{E}_i\right)=S\left(T{E}_i\right)/S\left(T{E}_1\right)$ (middle) and the averaged estimated dephasing functions $F_{z‐shim}\left({\mathit{TE}}_i\right)$ (right) in three slices (A, B, and C). In each slice, averaging was performed in a ROI defined by different intervals of field gradients $G_z$ (left). The lines in the plots show the results from a spoiled mGRE sequence without z‐shim gradients in blue, with the global z‐shim approach ( $|{\overline{G}}_c^{+/‐}|=100\mu T/m$) in red, and with the proposed slice‐specific z‐shimming in yellow. Note: The interpolation between echoes is solely for illustration purposes

FIGURE 4

Comparison of estimated ${\mathrm{R}}_2^{\ast }$ maps of a homogenous phantom. A, The field gradient map $G_z$. B, The ${\mathrm{R}}_2^{\ast }$ maps were calculated from the spoiled mGRE data by assuming a mono‐exponential signal model neglecting $G_z$ ( $F_{z‐shim}=1)$. The other ${\mathrm{R}}_2^{\ast }$ maps were calculated with the proposed signal model using the data of the spoiled mGRE (C), from the global z‐shim ( $|{\overline{G}}_c^{+/‐}|=100\mu T/m$) (D), and from the proposed slice‐specific approach (E)

FIGURE 5

A,B, The ${\mathrm{R}}_2^{\ast }$ values obtained from the phantom experiments as a function of the field gradient $G_z$ (bin size = 10 µT/m) with different scaling of the ${\mathrm{R}}_2^{\ast }$ axes . From the spoiled mGRE data, ${\mathrm{R}}_2^{\ast }$ values were first estimated assuming a mono‐exponential signal model (blue line) neglecting $G_z$ ( $F_{z‐shim}=1)$, and second by using the proposed model (red line). Furthermore, ${\mathrm{R}}_2^{\ast }$ values from the global z‐shim approach (| ${\overline{G}}_c^{+/‐}|=100\mu \frac{T}{m})$ (yellow) and the proposed slice‐specific method (purple) are plotted. The ${\mathrm{R}}_2^{\ast }$ values are shown as median and 25^th and 75^th percentiles (whiskers)

FIGURE 6

Last five GRE images from TE₁₂ to TE₁₆ acquired with a spoiled mGRE sequence without z‐shimming (A), with the global z‐shim (B), and with the proposed slice‐specific z‐shimming approach (C). At TE₁₂ as well as at TE₁₆, the sum of the compensation moments (M_c,12, M_c,16) is zero for all sequences. With the proposed approach, the signal can also be rephased in areas where it has already been completely dephased (arrows). The complete series of the echoes with z‐shim gradients is illustrated in Supporting Information Figure S2

FIGURE 7

Axial views of estimated in vivo ${\mathrm{R}}_2^{\ast }$ maps (left), with detailed views of the blue rectangular regions (right). A, The ${\mathrm{R}}_2^{\ast }$ maps were directly calculated from the spoiled mGRE data by assuming a mono‐exponential signal model neglecting $G_z$ ( $F_{z‐shim}=1)$. The other ${\mathrm{R}}_2^{\ast }$ maps were calculated using the proposed signal model for the spoiled mGRE (B), the global z‐shim ( $|{\overline{G}}_c^{+/‐}|=220\mu T/m$) (C), and the proposed slice‐specific approach (D) data. An increase in SNR can be observed from (C) to (D) due to higher signal recovery