Synopsis

Multi-Spectral Imaging (MSI) enables MRI near metallic implants, but suffers from prolonged scan times. Model-based reconstruction accelerates MSI by enforcing a signal model along the spectral dimension to reduce the number of unknowns in image reconstruction. The previous signal model assumes that spins in one voxel have the same off-resonance frequency, which tends to fail where the off-resonance field changes rapidly. Here we propose a more flexible MSI signal model that allows multiple frequencies within a voxel, and demonstrate improvements with both simulated and in-vivo data. 3x net additional acceleration above partial-Fourier and parallel-imaging alone (20x in total) was achieved.

Purpose

Imaging near metallic implants is challenging due to large magnetic field perturbations induced by metal. Multi-Spectral Imaging (MSI) techniques, such as SEMAC¹ and MAVRIC-SL², resolve the field perturbations by acquiring separate 3D spatial encodings for multiple spectral bins, at the cost of long scan time. Various methods have been investigated to accelerate MSI^3-9, among which model-based reconstruction⁹ has the advantage of fully exploiting the correlation between spectral bins by enforcing a signal model to describe the signal profile across bins. This reduces the number of unknowns in the reconstruction from 20+ spectral bins to 2 parameters.

The previous MSI signal model assumes that spins in one voxel have the same off-resonance frequency. This assumption tends to fail near high-susceptibility implants where the off-resonance field changes rapidly, resulting in artifacts in the reconstructed images. Here we propose a flexible MSI signal model that allows multiple frequencies within a voxel, and demonstrate improvements using both simulated and in-vivo data.

Theory

As shown in Fig.1, over 20 spectral bin images are acquired at different center frequencies in MSI. Based on the Gaussian RF pulses used in MAVRIC-SL, the original signal model uses two parameters, magnetization $$$\rho(r)$$$ and off-resonance frequency $$$f(r)$$$, to represent the bin images as$$m_b^{\mathrm{original}}(r)=\rho(r)\cdot\exp\{-(f(r)-f_b)^2/2\sigma^2\}\hspace{10mm}(\mathrm{Eq.1})$$

where $$$b$$$ is the bin index, $$$f_b$$$ denotes the center frequency of bin $$$b$$$ and $$$\sigma$$$ denotes the width of RF frequency profile. $$$f_b$$$ and $$$\sigma$$$ are known sequence parameters. All bins are demodulated at a single frequency, so that off-resonance-induced pixel displacements match across bins. However, with this demodulation scheme, spins with varying off-resonance frequencies can be shifted to the same location, and the signal profile across bins will have a broader peak or even two peaks (Fig.2). The second peak in the signal model only appears in a small region near metal where the off-resonance frequency varies rapidly in the readout direction. This effect is considered in the new double-peak model given by$$m_b^{\mathrm{double-peak}}(r)=\Sigma_{p=1,2}{\rho_p(r)\cdot\exp\{-(f_p(r)-f_b)^2/2s_p(r)\}}\hspace{10mm}(\mathrm{Eq.2})$$

where $$$s_p(r)$$$ denotes the width of the signal profile, two sets of parameter maps indexed by $$$p$$$ are used to represent the double-peak situation. The second set of parameters is only included in a small region near metal determined during initialization.

The reconstruction problem is$$ \mathrm{minimize}_{\rho_p(r),f_p(r),s_p(r)}{\Sigma_b\|M_b\cdot{}F\{m_b^{\mathrm{double-peak}}(r)\}-\hat{y}_b\|_2^2+\lambda\Sigma_{p=1,2}{\mathrm{TV}(\rho_p(r))}}\hspace{10mm}(\mathrm{Eq.3})$$

where $$$M_b$$$ represents the under-sampling mask, $$$F$$$ represents the Fourier transform, and $$$\hat{y}_b$$$ represents the acquired k-space data. A limited-memory BFGS algorithm¹⁰ is used to solve (3). The spectral bin images are synthesized from the resulting parameter maps, demodulated at the center frequency of each bin, and combined by root-sum-of-squares to form the composite image.

Method

Results & Discussion

As both simulated and in-vivo results in Fig.2 show, in most places the original model described the signal profile across bins well, while the double-peak model was necessary in regions of rapidly varying off-resonance, like voxel B. The double-peak model effectively reduced the fitting residual in these regions. The remaining residual for the double-peak model came from the asymmetric peaks in signal profiles, such as voxel B in Fig. 2d.

The comparison of reconstructed images in Figs.3&4 shows that incorporating the double-peak model suppressed the artifacts (signal oscillations and signal loss) near the surface of the implants compared to results of the original model (arrowheads). The locations of these artifacts were consistent with the areas where the original model had large residuals in Fig.2a&c. Both model-based reconstruction results showed sharper details compared with bin-by-bin PI&CS(dashed arrows).

Conclusion

Acknowledgements

References