Introduction

B₁ inhomogeneity is one of the main problems that limit the clinical application of ultra-high-field MRI. The spatially varying contrast and intensity influence diagnosis and need to be corrected. For magnetic resonance imaging at fields lower than, or equal to 3 T, B₁ shimming technology can provide more uniform B₁⁺, which is sufficient for clinical application. By comparing the signal intensity of coil arrays with the flat receive profile of a volume coil, we can estimate B₁^- and correct for this non-uniform intensity distribution. At the ultra-high field, the B₁ inhomogeneity is more severe and both above-mentioned methods are inadequate. Parallel transmission (pTx)¹ can excite a more uniform flip angle by accelerated spatially selective excitation. However, this method required special hardware and minor flip angle inhomogeneity together with B₁^- effect still exists after pTx excitation. The most widespread post-processing methods for B₁⁺ and B₁^- correction are nonparametric nonuniform intensity normalization (N3)², and its' improved version, N4ITK³. However, the assumption, the effect of bias field (the combining effect of B₁⁺ and B₁^-) can be approximate as a convolution of Gaussian function to the distribution of the true tissue intensity, is not applicable when the bias field is strong. To overcome these difficulties, we estimated the magnitude of B₁^- and proposed a bias-field correction method based on its signal dependence on B₁^- and B₁⁺.

Methods

For a spoiled gradient echo sequence at low flip-angle, the signal can be approximated as:
$$PD(r)=M_0 (r)⋅\alpha⋅|B_1^+ (r)|⋅|B_1^- (r)|⋅f(T1(r),T2(r),TE,TR)$$
, where f is the function of T1 and T2 relaxation and α is the nominal flip angle. We need the information of M₀, |B₁⁺| and $$$f(T1(r),T2(r),TE,TR)$$$ to estimate |B₁^-|. For brain imaging, low flip angle proton density weighted images usually present low tissue contrast ($$$M_0⋅f(T1(r),T2(r),TE,TR)\approx Constant$$$), and can be used to estimate $$$|B_1^-(r)|$$$ when $$$|B_1^+ (r)|$$$ is available.
Therefore, we approximated the bias field in the brain based on the proton density images:
$$B_1^±(r)=C⋅|B_1^+ (r)|⋅|B_1^- (r)|=Sfilter(PD(r))$$
,where Sfilter is an operator that approximates the images using multi-resolution 3D splines³.
For an imaging method, named MET, its signal can be expressed as:
$$I_{MET}(r)=|B_1^- (r)|⋅g_{MET}(T1(r),T2(r),α⋅|B_1^+ (r)|)⋅M_0(r)$$
,where g_MET is a method-dependent function that describes its signal dependence on T1, T2 and B₁⁺. With the information of $$$B_1^±(r)$$$ and $$$|B_1^+(r)|⋅$$$ The bias field corrected images can be calculated as:
$$I_{METcor}(r)=I_{MET}(r)/\frac{B_1^±(r)}{|B_1^+(r)|}/g_{MET}(T1(r),T2(r),\alpha⋅|B_1^+ (r)|).$$
In most situations as well as in this study, T1 and T2 maps are not available. Therefore, we approximated T1 and T2 by constants, $$$\bar{T1}$$$ and $$$\bar{T2}$$$. The PD-weighted images were acquired with parameters (TE/TR=2.41/20ms, flip angle=5^o, FOV=220x220x220mm³, and matrix size=80x80x80). The |B₁⁺| maps were acquired using pre-saturation TFL (FOV=220x220x220mm³, matrix size=64x64x30). We acquired 3D SPACE T2 weighted images (TE/TR=118/4000ms, ETL=119,FOV=212x150x170mm³, and matrix size=318x224x256) and 2D TSE T2 weighted images (TE/TR=54/320ms, ETL=11, FOV=209x209x72 mm³, matrix size=1176x1568x30, and slice thickness=2mm) to test the performance of the proposed method. The function g_MET for both methods were calculated based on phase graph theory⁴. One healthy volunteer was scanned at a 7T MRI system (MAGNETOM Terra, Siemens Healthineers, Erlangen, Germany).

Results

Figure 1A shows the PD-weighted images. The $$$B_1^±$$$ maps estimated from the PD-weighted images were shown in Figure 1B, and |B₁⁺| maps at the same slices were shown in Figure 1C. Figure 2A shows SPACE T2 weighted images at the same slices of Figure 1B without bias field correction. The bias field caused signal voids near the temporal lobe and inferior part of the cerebellum. Figure 2B are the images after N4ITK bias field correction. For most brain regions, the signal inhomogeneity was improved, however, it fails in regions of low B₁. Figure 2C shows the images using the proposed bias field correction. The image intensity is more homogeneous and the signal voids in the temporal lobe and cerebellum were recovered.
Figure 3A shows the T2 TSE images of the healthy volunteer. The image homogeneity, using the proposed post-processing method, improves significantly in figure 3B. There were more structural details that can be seen in the temporal lobe and inferior cerebellum.

Discussion and Conclusion

We proposed a method to estimate a B₁^- map. Together with the measured B₁⁺ map, we were able to correct the image intensity inhomogeneity caused by the bias field. This method can be applied to correct bias field effects for different imaging protocols or sequences using the same estimated bias field maps. On the contrary, for most post-processing methods, the bias field was estimated from the targeted images^3,5 and these estimation might be inaccurate if the targeted images only have limited coverage.
The signal intensity depends not only on the bias field but also on its T1 and T2 properties. Note that the proposed method cannot correct the contrast altered by the bias field. The pTx is a better solution to achieve homogeneous contrast by a more uniform excitation. However, the proposed method can be used to correct the B₁^- inhomogeneity and the residual flip angle inhomogeneity in images using pTx.
In most situations, we don't need extra proton density images. For example, we can use the magnitude images from field mapping with the least echo time, or the unsaturated images used for TFL B₁ mapping and thereby not adding additional scan time.

Acknowledgements

No acknowledgement found.