Introduction

R₂*(T₂*) contrast is commonly utilized for diagnostics in liver and kidney using-multi echo gradient echo (GRE) acquisitions^1-5. Previously, Dixon imaging along with the R₂*(T₂*) relaxometry was utilized for liver imaging^3-5.
In this work, Bilateral Orthogonality Generative Acquisitions (BOGA) method⁶ was implemented at a 3T scanner with a dual channel transmit body coil and adapted for simultaneous R₂*(T₂*) relaxometry and Dixon imaging in order to obtain homogeneous images without the central brightening effects due to the transmit field, B₁⁺, inhomogeneity.

Theory

The original BOGA method⁶ requires 4 small angle GRE acquisitions denoted as circularly polarized (CP) mode image $$$S_1={\rho}E^*_{2,2}(q_1+q_2)\beta$$$ , adding a transmit phase of 180° to the first transmit channel to achieve an orthogonal excitation pattern $$$S_2={\rho}E^*_{2,2}(-q_1+q_2)\beta$$$ and two single channel transmit acquisitions $$$S_{3,4}={\rho}E^*_{2,1}(q_{1,2})\beta$$$. For Dixon encoding two GRE images with a phase difference between water and fat, is required. Combining both methods introducing an optimum $$${\Delta}TE$$$ for water and fat separation between S_1,2 and S_3,4 two intermediate images can be computed as follows⁶:$$C=\begin{bmatrix}C_1\\C_2\end{bmatrix}=\begin{bmatrix}S_3^*&S_4\\S_4^*&-S_3\end{bmatrix}\begin{bmatrix}S_1\\S_2^*\end{bmatrix}={\rho}^2E^*_{2,1}E^*_{2,2}\begin{bmatrix}q_1^*{\beta}&q_2{\beta}\\q_2{\beta}^*&-q_1{\beta}\end{bmatrix}\begin{bmatrix}e^{i\gamma}&0\\0&e^{-i\gamma}\end{bmatrix}\begin{bmatrix}q_1&q_2\\q_2^*&-q_1^*\end{bmatrix}\begin{bmatrix}{\beta}\\{\beta}\end{bmatrix}={\rho}^2E^*_{2,1}E^*_{2,2}{\beta}^2\begin{bmatrix}{|q_1|^2e^{i\gamma}+|q_2|^2e^{-i\gamma}+(e^{i\gamma}-e^{-i\gamma})q_1^*q_2}\\{|q_1|^2e^{-i\gamma}+|q_2|^2e^{i\gamma}+(e^{i\gamma}-e^{-i\gamma})q_1q_2^*}\end{bmatrix}$$Similarly, a complimentary set of intermediary images can also be written as follows:$$D=\begin{bmatrix}D_1\\D_2\end{bmatrix}=\begin{bmatrix}S_3^*&-S_4\\S_4^*&S_3\end{bmatrix}\begin{bmatrix}S_1\\S_2^*\end{bmatrix}={\rho}^2E^*_{2,1}E^*_{2,2}\begin{bmatrix}q_1^*{\beta}&-q_2{\beta}\\q_2{\beta}^*&q_1{\beta}\end{bmatrix}\begin{bmatrix}e^{i\gamma}&0\\0&e^{-i\gamma}\end{bmatrix}\begin{bmatrix}q_1&q_2\\q_2^*&-q_1^*\end{bmatrix}\begin{bmatrix}{\beta}\\{\beta}\end{bmatrix}={\rho}^2E^*_{2,1}E^*_{2,2}{\beta}^2\begin{bmatrix}{|q_1|^2e^{i\gamma}-|q_2|^2e^{-i\gamma}+(e^{i\gamma}+e^{-i\gamma})q_1^*q_2}\\{-|q_1|^2e^{-i\gamma}+|q_2|^2e^{i\gamma}+(e^{i\gamma}+e^{-i\gamma})q_1q_2^*}\end{bmatrix}$$ $$$\gamma=2\pi{\Delta}B_0{\Delta}TE$$$ is the phase accumulated between echoes, $$${\Delta}B_0$$$ denotes the main field inhomogeneity, $$${\Delta}TE$$$ denotes the difference between echo times, $$$q$$$ denotes the channel effects, $$$\beta$$$ is the flip angle and $$$E_2^*$$$ is the $$$T_2^*$$$ decay. Using these intermediate images C and D and defining $$$E=S_3^*S_3+S_4^*S_4$$$ , homogeneous final images $$$I$$$ with accumulated phase can be calculated as $$$F=0.25(C_1+D_1+C_2+D_2+(C_1-D_1+C_2-D_2)^*)$$$ and $$$I=F/E$$$.
For Dixon imaging, a normalized complex ($$$F^N$$$ ) combined image, represents the phase encoding acquired to distinguish water and fat due to their chemical shift difference. Complex water and fat masks, denoted as $$$WM$$$ and $$$FM$$$ respectively, are then calculated as $$$WM=0.5(1+F^N)$$$ and $$$FM=0.5(1-F^N)$$$ . Since fat and water content does not change between echoes and same masks can be used for every echo for obtaining water only and fat only images and R₂* images.
By applying BOGA method to every echo except the first one and the logarithmic identities, R₂* is estimated without exponential fitting as follows using N echoes. $$$M_k$$$ denotes the mask for water only and fat only images, for the joint image it is 1. $$$K=0.5N(N-1)$$$ is the total duration for the R₂* decay from all echoes.$$R^*_{2,s}=\frac{1}{K}\sum^N_{i=2}-(i-1)(ln(|M_kF_i|)-ln(|M_k|^2E|))$$

Methods

For the acquisition of the data, a 3T Philips Healthcare Achieva human MRI system with two transmit channel body coil is used along with the large body surface receive coil. For a healthy volunteer, two multi-echo 3D spoiled GRE acquisitions with breath holding were acquired with voxel size of 2x2x5 mm, 224x224x5 acquisition matrix and 5^o flip angle. $$$TE1/{\Delta}TE/TR=1.1/1.2/16$$$ ms with 2 averages and 12 echoes. Transversal and coronal slice orientation is used for liver and kidney acquisitions respectively. Total scan time for the data is 30 seconds. First echoes of each GRE acquisitions are used for calculating S₃ and S₄,whereas other echoes used as S₁ and S₂.

Results

In Figure 1 and 2, 11 echoes of the GRE acquisitions that are used as S₁ and S₂ for the BOGA method are given. Using these images homogeneous T₂* images are obtained and R₂* are estimated. Figure 3, illustrates the single channel images S₃ (a, e) and S₄ (b, f) (shortest TE) used for obtaining the homogeneous images in combination with S₁ and S₂. Calculated water only and fat only masks for Dixon imaging are presented in (c) and (d) respectively. These figures indicate a shimming problem prominent in the right side of the body, which results inaccuracies in the water and fat masks.
In Figure 4, magnitude of the homogeneous T₂* images are shown for echoes 2 to 12. Compared to the conventional CP mode images in Figure 1 block, images in Figure 3 are free of central brightening and present pure T₂* weighted contrast.
In Figure 5, images without Dixon imaging, water only and fat only images are presented for liver and kidneys using the 12th echo.Clear difference between water only and fat only images can be observed. Calculated R₂* images, with and without Dixon imaging, using the 11 echoes for each slice are shown in Figure 5 second block.

Discussion and Conclusion

In this work, it is shown that the BOGA method, which was introduced for 7T MRI system and used for whole brain imaging, can be utilized in body imaging at a 3T system with a dual channel body coil for homogeneous T₂* image contrast, R₂* estimation and Dixon imaging as it is demonstrated in liver and kidneys. As future work, shimming will be improved to counteract the inaccuracies in the water and fat masks.

Acknowledgements

This work was performed in the Advance Imaging Research Center at University of Texas Southwestern Medical center Dallas. This work was supported by Cancer Prevention and Research Institute of Texas (CPRIT) grant / RR180056.