Introduction

The variable flip angle (VFA) T₁ mapping with a spoiled gradient-echo (SPGR), though it has a shorter scanning time than the inversion recovery method, is affected by B₁ inhomogeneity caused by a transmitted radiofrequency pulse. In this situation, B₁ inhomogeneity correction is required for accurate T₁ estimation. The typical methods of B₁ correction, are Bloch-Siegert shift, double flip angle (DFA), and actual flip angle methods. On the other hand, these methods need additional scanning for B₁ mapping, except the main scan for T₁ estimation; these methods require a longer total scan time. In this study, we developed a self-calibrating B₁ correction method based on the DFA technique without additional scanning. The purpose of this study is to determine the accuracy of the B₁ correction in our developed method using a cylindrical digital phantom and a digital brain phantom.

Methods

In this study, data acquisition was used a Bloch simulator (MRIsimulations Inc.). Figure 1 shows a schematic diagram of self-calibrating B₁ correction for VFA T₁ mapping in this study. Built-in VFA datasets for cylindrical phantom and brain phantom were acquired using a three-dimensional spoiled gradient-echo (3D-SPGR) sequence. Table 1 summarizes relaxation times of each sample in the built-in a numerical phantom. A cylindrical phantom consisted of nine tubes having different relaxation times; T₁ range, 367-1616 ms; T₂ range, 32-110 ms. The digital brain phantom we used was a Colin 27 Average Brain (http://www.bic.mni.mcgill.ca//ServicesAtlases/Colin27Highres). The SPGR signal $$$S_{SPGR}$$$ is described as follows:
$$S_{SPGR} = M_{0}\sin(\alpha)\frac{1-\exp(-\frac{TR}{T_{1}})}{1-\exp(-\frac{TR}{T_{1}})\cos(\alpha)}, (Eq. 1)$$
where $$$M_{0}$$$ is the equilibrium magnetization, $$$\alpha$$$ is flip angle (FA), and TR is repetition time (TR). In this study, the imaging parameters were TR = 10 and 100 ms, echo time (TE) = 4 ms, FA = 2-16 and 5-70 degrees (8 point, respectively), and matrix size = 256×256×256. After acquiring each VFA dataset, B₁ inhomogeneity distribution was generated in the in-plane and slice direction using a Gaussian distribution. B₁ inhomogeneity distribution was applied to each SPGR image. Next, DFA function $$$B_{1,DFA}^{function}$$$ was defined with DFA method and Gaussian distribution as follows:
$$B_{1,DFA}^{function} = \arccos(\frac{S_{2\alpha}}{2S_{\alpha}})\times{A}\times\left[-\frac{(x-\mu)^{2}}{2\sigma_x^2}-\frac{(y-\mu)^{2}}{2\sigma_y^2}-\frac{(z-\mu)^{2}}{2\sigma_z^2}\right], (Eq. 2)$$
where $$${A}$$$ is coefficient, $$$\sigma$$$ is standard deviation, and $$$\mu$$$ is mean. To generate DFA function, Eq. 1 and 2 were used and the simulation parameters were set to $$$M_{0}$$$ =1000, TR = 10 and 100 ms, FA = 15,30 and 30, 60 degrees, T₁ = 300-3500, A = 0.8, $$$\mu$$$ = 0.5, and $$$\sigma_{x,y,z}$$$ = 0.5-1.0. Finally, the T₁ measurement was applied to SPGR dataset of different FAs by linear least squares approximation as follows:
$$\left(\begin{array}{c}\frac{S_{1}}{\sin(B_{1,DFA}^{function}\times{\alpha_{1})}}\\\frac{S_{2}}{\sin(B_{1,DFA}^{function}\times{\alpha_{2})}}\\\ \vdots\\ \frac{S_{n}}{\sin(B_{1,DFA}^{function}\times{\alpha_{n})}}\end{array}\right)=\begin{pmatrix}\frac{S_{1}}{\tan(B_{1,DFA}^{function}\times{\alpha_{1}})} & 1 \\\frac{S_{2}}{\tan(B_{1,DFA}^{function}\times{\alpha_{2}})} &1 \\\vdots &\vdots \\\frac{S_{n}}{\tan(B_{1,DFA}^{function}\times{\alpha_{n}})} &1 \\\end{pmatrix}\cdot\left(\begin{array}{c}\exp(-\frac{TR}{T_{1}})\\ M_{0}(1-\exp(-\frac{TR}{T_{1}}))\end{array}\right), (Eq. 3)$$
In the experiment using the cylindrical phantom, T₁ measurements were evaluated in each region in the in-plane and slice direction. Then, the relative uncertainties for the original and with T₁ applied to B₁ correction were calculated for each sample. For the brain phantom experiment, the brain segmentation was performed using statistical parametric mapping software which was divided into white matter (WM), gray matter (GM) and cerebrospinal fluid (CSF). The mean T₁ values were measured at each segmented region. Additionally, the relative uncertainties map between original and T₁ applied to B₁ correction were calculated and the in-plane and slice direction were evaluated.

Results & Discussion

Figure 2 shows the results of calculated T₁ maps and the graphs for the relationship between T₁ value and the relative uncertainties found in the cylindrical phantom. Figure 3 shows the relationship between T₁ values in eight samples and slice position on the cylindrical phantom. Figure 4 shows the relative uncertainties map with and without B₁ correction in each region of the brain phantom. The yellow images show the masked region of each brain component. In the cylindrical phantom experiment, comparing the B₁ correction accuracy of each sample in-plane, the relative error of each T₁ value was found to be less than 5%. These results indicate that there is sufficient correction accuracy. In addition, the relative error values of long T₁ samples were smaller than that of short T₁ samples. When there is a long TR, the accuracy of B₁ correction was almost equal to short TR (Fig. 3). This enabled us to accurately corrected for the slice direction at No.7 sample. On the other hand, for the No.8 sample, there were increasing T₁ values at the end-slice positions (Fig. 3, red arrows). We demonstrated that our B₁ correction method was successful without additional scanning. In this experiment, although T₁ values were calculated using eight-data points, some data points remain a matter of research: the use of a fewer data points leads to the accomplishment of shorter acquisition times. In the future, the accuracy of our B₁ correction method needs to be more investigated using fewer data points.

Conclusion

It was found that our self-calibrating B₁ correction method has high accuracy for in-plane and slice direction. Our B₁ correction method makes it possible to calculate a 3D-T₁ map using VFA method of the brain without additional scanning.

Acknowledgements

No acknowledgement found.