An Improved Postprocessing Method to Mitigate the Macroscopic Cross-Slice B0 Field Effect on R2* Measurements in the Mouse Brain at 7T

Abstract

The MR transverse relaxation rate, R2*, has been widely used to detect iron and myelin content in tissue. However, it is also sensitive to macroscopic B₀ inhomogeneities. One approach to correct for the B₀ effect is to fit gradient-echo signals with the three-parameter model, a sinc function-weighted monoexponential decay. However, such three-parameter models are subject to increased noise sensitivity. To address this issue, this study presents a two-stage fitting procedure based on the three-parameter model to mitigate the B₀ effect and reduce the noise sensitivity of R2* measurement in the mouse brain at 7T. MRI scans were performed on eight healthy mice. The gradient-echo signals were fitted with the two-stage fitting procedure to generate R2corr_t*. The signals were also fitted with the monoexponential and three-parameter models to generate R2nocorr* and R2corr*, respectively. Regions of interest (ROIs), including the corpus callosum, internal capsule, somatosensory cortex, caudo-putamen, thalamus, and lateral ventricle, were selected to evaluate the within-ROI mean and standard deviation (SD) of the R2* measurements. The results showed that the Akaike information criterion of the monoexponential model was significantly reduced by using the three-parameter model in the selected ROIs (p = 0.0039-0.0078). However, the within-ROI SD of R2corr* using the three-parameter model was significantly higher than that of the R2nocorr* in the internal capsule, caudo-putamen, and thalamus regions (p = 0.0039), a consequence partially due to the increased noise sensitivity of the three-parameter model. With the two-stage fitting procedure, the within-ROI SD of R2corr* was significantly reduced by 7.7-30.2% in all ROIs, except for the somatosensory cortex region with a fast in-plane variation of the B₀ gradient field (p = 0.0039-0.0078). These results support the utilization of the two-stage fitting procedure to mitigate the B₀ effect and reduce noise sensitivity for R2* measurement in the mouse brain.

Keywords: B0 inhomogeneity; R 2 *; T 2 *; background gradients; brain; gradient-echo; iron; myelin; noise; post-processing; quantitative MRI.

Figure 1

Illustration of the two-stage fitting procedure. In the first stage of fitting, the voxel-wise multi-echo GRE signals shown in (a) were fitted with the three-parameter model (Equation (1)) to generate corrected $R_2^{*}$ ($R_{2corr}^{*}$) (b) and γΔB₀ maps (c). Based on the assumption that the γΔB₀ map is smooth on the x-y plane, a 2D Gaussian filter with a σ_gaussian of 390 µm was applied to the γΔB₀ map to generate γΔB_0smooth (d). In the second stage of fitting, the multi-echo GRE signals of each image voxel were divided by the $sinc(\gamma {∆B}_{0smooth}\mathrm{T}\mathrm{E}/2$)) and were then fit with the monoexponential model to generate the $R_{2corr\_t}^{*}$ map with reduced sensitivity to noise (e).

Figure 2

(a) Representative $R_2^{*}$ measurements of three mice using the monoexponential model ($R_{2nocorr}^{*}$), three-parameter model ($R_{2corr}^{*}$), and two-stage fitting procedure ($R_{2corr\_t}^{*}$), respectively, along with the anatomical T₂-weighted images (b) as a reference.

Figure 3

${\chi }_{\nu }^2$ maps corresponding to the voxel-wise fittings using the monoexponential model, three-parameter model, and two-stage fitting procedure, respectively, to generate the $R_2^{*}$ measurements as shown in Figure 2.

Figure 4

Illustration of the workflow of image co-registrations for the ROI analysis. Firstly, structural labels and the P56 Mouse Brain atlas images shown in (a) were brought into the space of individual anatomical images shown in (b) through a non-linear co-registration. Secondly, they were brought into the space of individual GRE images through a linear co-registration. (c) The selected six ROIs extracted from the structural labels on the individual GRE image space. ROIs were manually adjusted before they were applied to the $R_2^{*}$ maps for quantification analysis.

Figure 5

Comparison of the within-ROI mean AIC values on the eight mice using the monoexponential model, three-parameter model, and two-stage fitting procedure. * indicates that the AIC of the monoexponential model was significantly higher than that of the three-parameter model or two-stage fitting procedure. The comparisons were evaluated using the one-tailed Wilcoxon signed rank test (p < 0.0078).

Figure 6

Comparison of the within-ROI mean (a) and SD (b) values of the $R_2^{*}$ measurements on the eight mice using the monoexponential model ($R_{2nocorr}^{*}$), three-parameter model ($R_{2corr}^{*}$), and two-stage fitting procedure ${(R}_{2corr\_t}^{*}$). * in (b) indicates that the SD of the $R_{2corr}^{*}$ was significantly higher than that of the $R_{2nocor}^{*}$ or $R_{2corr\_t}^{*}$. The comparisons were evaluated using the one-tailed Wilcoxon signed-rank test (p < 0.0078).

Figure 7

Illustration of the γΔB_0smooth map for the two-stage fitting procedure using different smoothing kernels (the σ_gaussian: 234, 390, 546, and 702 µm).

Figure 8

The effect of the different smoothing kernels (the σ_gaussian: 234, 390, 546, and 702 µm) on the within-ROI mean (a) and SD (b) values of the γΔB_0smooth map for the eight mice using the two-stage fitting procedure.

Figure 9

The effect of the different smoothing kernels (the σ_gaussian: 234, 390, 546, and 702 µm) on the within-ROI mean (a) and SD (b) values of the $R_{2corr\_t}^{*}$ for the eight mice using the two-stage fitting procedure.

Figure 10

Illustration of the $R_2^{*}$ (a–c) and γΔB₀ (d,e) measurements using simulations with a cross-slice ΔB₀ effect. One-hundred sets of noisy signals were generated using the three-parameter model (Equation (1)) with an SNR of 50, $R_2^{*}$ of 30 Hz, 6 TEs of 2.5–22.5 ms in increments of 4 ms, and γΔB₀ of 45 Hz over 100 repeated trials. They were fitted with the monoexponential model, three-parameter model, and two-stage fitting procedure to generate the $R_2^{*}$ measurements (a–c). The γΔB₀ measurements in (d) were obtained through the three-parameter fit. They were smoothed by a 1D Gaussian filter with a σ_gaussian of 25 data points to generate γΔB_0smooth (e) for the two-stage fitting procedure.

Figure 11

The RMSE of $R_2^{*}$ (a) and γΔB₀ (b) measurements across the different true γΔB₀ values used in the simulations as described in Figure 10. Here, one thousand repeated trials were used to generate noisy signals to reduce the variability in the RMSE.

Figure 12

The RMSE of the $R_2^{*}$ (a) and γΔB₀ (b) measurements across the different SNRs used in the simulations with a true $R_2^{*}$ of 30 Hz and true γΔB₀ of 45 Hz as described in Figure 10. Here, one thousand repeated trials were used to generate noisy signals to reduce the variability in the RMSE.