Radial 3D GRE imaging is increasingly used for various clinical routine applications due to its inherently higher robustness to motion¹. One major limitation consists in the strong blurring of off-resonant signal components such as fat, which makes it necessary to always use spectral fat suppression. However, spectral fat-suppression techniques typically fail in regions with large field inhomogeneities. Furthermore, use of fat suppression makes it impossible to assess the local fat content, as needed, e.g., for identifying fat-containing lesions such as angiomyolipomas. Therefore, clinical protocols currently still require acquisition of conventional Cartesian non-fat-suppressed T₁-weighted images in in-phase/opposed-phase conditions.

To overcome these limitations, we describe a model-based fat/water separation technique for radial sampling, which takes into account the off-resonant blurring of fat and integrates both compressed sensing and parallel imaging to achieve rapid acquisition.

Signal model:

The aim of the reconstruction approach is to estimate separate fat and water maps directly from the k-space data. The general optimization problem for this purpose can be written as²:

$$\text{argmin}\sum_{c,t}\|E(W,F,\Phi)_{c,t}-y_{c,t}\|_2^2+\lambda_W\text{TV}(W)+\lambda_F\text{TV}(F)+\lambda_\Phi\|\Theta\Phi\|_2^2$$

where $$$y$$$ is the acquired radial k-space data, and $$$E$$$ is the forward operator that synthesizes k-space data from the to-be-estimated water ($$$W$$$), fat ($$$F$$$), and B₀ field maps ($$$\Phi$$$). Compressed Sensing is included via total variation penalty terms for both the fat and water maps. In addition, a smoothness constraint $$$\Theta$$$ is applied to the field map. The forward operator $$$E$$$ is composed of the operations:

$$E(W,F,\Phi)_{c,t}=\text{FT}\left(C_c\cdot\exp\left(2\pi i\cdot\Phi\cdot t_n\right)\cdot W\right)+D(t)\cdot\text{FT}\left(C_c\cdot\exp\left(2\pi i\cdot\Phi\cdot t_n\right)\cdot F\right)$$

where $$$FT$$$ is the gridding operator and $$$t_n$$$ are the different echo times. To account for the off-resonant blurring of fat due to the applied radial acquisition scheme, $$$D(t)$$$ models the chemical shift in k-space³, taking into account the exact readout time points $$$t=t_n+\tau_{n,k}$$$ of the samples $$$k$$$ of each spoke:

$$D(t)=\sum_{m=1}^6\alpha_m\cdot\exp\left(2\pi i\cdot\Delta f_m\cdot(t_n+\tau_{n,k})\right)$$

In addition, a 6-peak multi-frequency model was applied. To incorporate parallel imaging, multiplications with the different coil sensitivity profiles $$$C_c$$$ were integrated into the forward operator.

Data acquisition and reconstruction:

IRB-approved abdominal scans of a healthy volunteer were performed during free-breathing on a 1.5T whole-body scanner (Magnetom Aera, Siemens Healthcare GmbH) using an 18-channel body-array and a 24-channel spine-array. A 3D stack-of-stars trajectory was employed for data acquisition, which performs Cartesian sampling along the slice direction and radial sampling in-plane according to the golden-angle scheme. Within each TR, three echoes were acquired using a bipolar readout. 64 partitions with each 256 radial projections were collected in 3:10min using the following parameters: FOV = 300x300x160mm³, matrix size = 256x256x64, resolution = 1.17x1.17x2.50mm³, TR = 11.6ms, TE = 2.34/5.59/8.84ms, BW = 330Hz/px, flip angle = 12deg.

Furthermore, both a volunteer and a patient were measured with IRB-approval on a 3T scanner (Magnetom Skyra). For these acquisitions, a readout bandwidth of 270Hz/px was used, while other acquisition parameters were similar to the 1.5T measurement. The patient measurement was conducted after contrast injection.

Reconstructions were performed offline in Matlab (Mathworks, MA) using a Gauss-Newton algorithm, in analogy to prior work on compressed-sensing-based fat/water separation for Cartesian data². Due to the non-convex cost function of the optimization problem, it is crucial to use a good initial guess for the field map. This was achieved by analytically calculating possible field map values with subsequent region growing². Coil sensitivity maps were estimated using the adaptive combination technique³.

Figure 1 shows the estimated water and fat maps, as well as synthetically generated in-phase/opposed-phase images from an exemplary transversal slice. Clear separation of fat and water could be achieved with only slight streaking artifacts due to breathing motion.

Figure 2 shows results of the patient measurement, revealing liver cysts (arrows) in the water image.

The effect of removing the fat blurring in the volunteer measurement at 3T is shown in Figure 3.

This work demonstrates how the combination of 3D radial stack-of-stars sampling and model-based reconstruction with fat/water separation enables motion-robust volumetric radial MRI without need for spectral fat suppression. Parallel imaging and compressed sensing can be incorporated by including coil-sensitivity profiles and L₁-based penalty terms into the optimization problem. The fat blurring is removed by including its frequency deviation into the signal model. For routine clinical use of the proposed method, a robust technique for initial field map estimation is necessary, which is ongoing work.

After estimation of the water and fat maps, in-phase/opposed-phase images can be generated synthetically. Therefore, the approach can be used to replace both, fat-suppressed (radial) acquisition and non-fat-suppressed (Cartesian) in-phase/opposed-phase acquisitions with only a single radial free-breathing scan. This promises to shorten abdominal MR examinations considerably and improve patient comfort.