Introduction

Recent advancements in radiofrequency imaging (RFI) utilizing B₁ gradients to encode spatial information have shown the potential to produce images of equal or better quality than conventional MRI¹. While there are distinct advantages to RFI-based methods, advanced reconstructions techniques must be employed to correct the image distortions caused by nonlinear B₁ and B₀ inhomogeneities. To overcome these distortions, we propose a new reconstruction technique based on an iterative approach utilizing a full Bloch simulation and receiver coil sensitivities.

Methods

A recently developed RFI method called FREE (Frequency-modulated Rabi-Encoded Echoes)¹ encodes spatial information in a manner resembling rotating frame zeugmatography², except the magnetization rotates about a time-dependent effective field B_eff(t) during an adiabatic sweep^3,4. However, image distortions from nonlinear B₁ and B₀ inhomogeneity are observed in images acquired with FREE when Fourier-based image reconstruction is used.
To overcome limitations in reconstruction, we propose utilizing an iterative first-order proximal gradient method to solve the regularized linear inverse problem of the form $$$||\mathbf{\mathit{Ax}}-\mathbf{\mathit{y}}||_{2}^2 + \lambda\Omega(\mathbf{\mathit{x}})$$$ where $$$\mathbf{\mathit{A}}$$$ represents the encoding matrix determined via full Bloch simulation with known field inhomogeneities and receive coil sensitivities^5,6.
Initial in-vivo experiments were previously performed on a 1.5T, 90-cm Oxford magnet with a Siemens gradient system utilizing a multi- shot FREE double spin- echo (DSE) sequence¹. Two phantom simulations were also performed with parameters comparable to previously acquired in-vivo data. These simulations focused on acceleration by under-sampling and the effect of performing FREE in a highly inhomogeneous B₀ field with a constant linear gradient⁷. The first simulation considered FREE along two spatial dimensions with an acceleration factor of 4 and acquired on 8 separate receive channels. The latter considered the effect of a highly inhomogeneous static B₀ field and a permanent linear B₀ gradient producing 0.3 G/cm across a 5 cm FOV.

Results

A comparison between FFT-based and the proposed model-based reconstructions is shown in Fig. 1. FREE spatial encoding was performed with the surface coil’s (nonlinear) B₁ gradient in the vertical (y-axis) direction, while conventional B₀ frequency-encoding was used in the horizontal (x-axis) direction. Images depict the occipital lobes of a healthy subject. By including the B₁ and B₀ inhomogeneity in the forward model much of the image distortion was corrected using the proposed reconstruction approach.
Fig. 2 shows a reconstruction created from a Bloch simulation of a 2-dimensional DSE FREE experiment, using identical surface coils along both dimensions. The data were acquired on 8 separate receive coils with an acceleration factor of 4 and complex white Gaussian noise added. By incorporating the B₁ maps and receive coil sensitivity profiles into the forward model, the distortions are substantially removed and an alias free image is recovered.
Finally, an extreme example (Fig. 3) shows a reconstruction based on Bloch simulation of the DSE FREE experiment, using a surface coil for FREE (x-axis) and the calculated permanent B₀ gradient (y-axis) generated from a passive shim set in a compact 1.5T head magnet. This result demonstrates that FREE, when combined with a permanent B₀ gradient for frequency encoding, can generate good images with B₁ and B₀ maps included in the forward model.

Discussion

A primary limitation to model-based reconstruction is the need to accurately characterize the imaging system and address any mismatches between the encoding matrix and the physical experiment that can lead to artifacts in the reconstructed image. The latter can be challenging for some MRI methods that use B₀ gradients for spatial encoding, since imperfections with pulsed B₀ gradients (eg, eddy currents) can be more difficult to model⁸, whereas RF modulations typically have high fidelity. As such, RFI-based sequences that employ a B₁ gradient to perform spatial encoding are highly predictable and reproducible. Moreover, the results herein show that at 1.5T a simple static Biot-Savart simulation is enough to adequately model the transmit coil profile. Incorporating this transmit profile into the encoding matrix led to significant improvement in the reconstructed image quality, especially compared to the traditional Fourier-based reconstruction. However at large distances from transmit coil, the object becomes heavily blurred as the strength of the B₁ gradient decreases.
When applied to accelerated FREE-based acquisitions with noise added, the proposed method reconstructs highly distorted, aliased images, while eliminating most of the artifacts. Despite these artifacts, the reconstructed image is significantly better than that of FFT-based methods. The reconstruction method was then applied to a simulation of an object in the presence of a highly inhomogeneous static B₀ field and a nonlinear surface coil. The resulting Fourier reconstructed image is highly distorted along both dimensions due to the presence of the nonlinear fields. However, by incorporating these fields into the encoding matrix, the proposed reconstruction method was still able to produce images that are relatively distortion-free.

Conclusion

Standard Fourier based reconstruction has often produced artifacts when used in conjunction with RFI-based methods, limiting their adoption in clinical settings. However, the proposed reconstruction method presented here has shown that the artifacts can be eliminated and even enables accelerated acquisition. With these new tools, RFI-based imaging methods become more clinically viable and should ultimately produce comparable images to conventional acquisitions.

Acknowledgements

This work was supported by the National Institutes of Health grants U01 EB025153 and P41 EB027061.

References

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