MRI has the potential to provide excellent soft tissue contrast for diagnosing complications surrounding metallic implants. However, the presence of metal induces $$$B_0$$$ field perturbations and causes severe image distortions. 3D Multi-Spectral Imaging (MSI) methods, including SEMAC^[1], MAVRIC^[2], and MAVRIC-SL^[3], are able to correct for the metal-induced off-resonance artifacts, but at a cost of prolonged scan time. In this work, we introduce a novel model-based method to accelerate 3D MSI. We demonstrate in phantom and in vivo experiments that the proposed method can accelerate MAVRIC-SL acquisitions by a factor of 4 when used alone, and 13-17 when combined with other acceleration methods.

In MAVRIC-SL or SEMAC, thin slices are excited, and 3D spatial encoding with view-angle tilting (VAT)^[4] is used to resolve the distorted slice profile (Fig.1A). Conventionally, the 3D images of different spectral bins (distorted slices) are reconstructed separately, including prior compressed-sensing approaches^[5,6]. We propose to exploit the signal model (Fig.1 BC) of the spectral bins to reduce the unknowns from over 20 bin images to 2 parameter maps. The image of spectral bin b is represented by $$$m_b(\rho(\textbf{r}),f(\textbf{r}))=\rho(\textbf{r})\cdot G(f(\textbf{r})-f_b)\quad \mathrm{(1)}$$$, where $$$G(f)$$$ is the frequency profile of RF pulses and $$$f_b$$$ is the center frequency of the bin. $$$G(f)$$$ and $$$f_b$$$ are usually known for a given sequence. The parameters to be estimated include the $$$B_0$$$ field map $$$f(\textbf{r})$$$, and the magnetization map $$$\rho(\textbf{r})$$$. If $$$M_b$$$ represents the under-sampling mask of bin b, F{} represents the Fourier transform, the acquired k-space of the bin is $$$y_b=M_b \cdot F\{\rho(\textbf{r})G(f(\textbf{r})-f_b)\}$$$. The proposed method directly solves for $$$\rho(\textbf{r})$$$ and $$$f(\textbf{r})$$$ using k-space data of all bins as, $$\mathrm{minimize}_{\rho(\textbf{r}),f(\textbf{r})}{\Sigma_b{\|M_b \cdot F\{\rho(\textbf{r})\cdot G(f(\textbf{r})-f_b)\} -\hat{y}_b \|_2^2} + \lambda\mathrm{TV}(\rho(\textbf{r}))}, \quad \mathrm{(2)}$$ where TV represents the total variation. A nonlinear conjugate gradient algorithm^[7,8] is used to solve $$$\mathrm{(2)}$$$.

The reconstruction procedure is outlined in Fig. 2. The raw k-space data should be demodulated at a single frequency for all bins before solving $$$\mathrm{(2)}$$$, so that off-resonance and VAT will induce the same pixel displacements in the readout direction for all bins. To correct for the distortions in the resulting parameter maps, the bin images $$$m_b$$$ are synthesized based on $$$\mathrm{(1)}$$$, and then demodulated at the center frequency of each bin. In the final step, the bin images are summed to a composite image.

The proposed method was tested in a MAVRIC-SL scan of an agar gel phantom with a Ti/CoCr shoulder prosthesis on a GE 3T MRI system. The fully sampled data were retrospectively under-sampled by a factor of 3.8 using Poisson-disc sampling (Fig.3A). Different (randomly selected) under-sampling patterns were applied to different bins. The proposed method, integrated with 2x2 parallel imaging and half-Fourier acquisition, was compared with a bin-by-bin L1-ESPIRiT^[9] reconstruction, in a MAVRIC-SL hip scan with a total hip replacement on a GE 1.5T MRI system. The acquired k-space data were further under-sampled by factors of 2 and 3 by multiplying the uniform sampling mask (Fig.4A) with Poisson-disc sampling masks (Fig.4CF). The scan parameters are detailed in Table 1.

In the phantom experiment (Fig.3), the proposed model-based reconstruction was applied alone without other acceleration methods, and the composite image reconstructed with 26% sampled data preserved most fine structures. The results of proposed method in the in vivo scan (Fig.4) demonstrated sharper details compared with L1-ESPIRiT at both 2x and 3x additional subsampling. In both phantom and in vivo results, the reconstructed image showed improved SNR compared with the reference images and L1-ESPIRiT results, likely because the fitting suppressed noise and slice-direction ringing that was not consistent with the model.

In the in vivo scan, artificial signal oscillations appeared in a small area above the implant with the proposed method (dashed arrows in Fig.4), which was more obvious at 3x additional subsampling. This was caused by imperfection of the model where the spins in one voxel have largely varying off-resonance frequencies. The large off-resonance gradient also caused pile-up artifacts in the reference images and L1-ESPIRiT results^[10].

Currently, the same uniform under-sampling was applied to all bins prospectively in the in vivo scan. Using prospective under-sampling with different patterns for each bin will probably improve the quality of reconstructed images, and permit a higher under-sampling factor.

By incorporating the signal model of 3D MSI, the proposed model-based reconstruction is able to provide high-quality images near metallic implants using 4x under-sampled k-space, as demonstrated in the phantom experiment. We also demonstrated in vivo that the proposed method can be integrated with partial Fourier and parallel imaging and further accelerate MAVRIC-SL by a factor of 2 to 3.