Introduction

In conventional MRI, signal is localized using B₀ gradients that link spatial position to signal frequency, but they are expensive, loud, induce PNS, and are prone to breakage. B₁⁺ gradients can alleviate these problems [1-8]. However, RF coils producing the appropriate B₁⁺ gradients are challenging to build. Solenoids with square-root pitch for Bloch-Siegert (BS) encoding need to be made longer than the imaging volume to achieve the desired square-root field in the imaging ROI, which limits their efficiency. To address this, we propose an optimized square root solenoid with a Bucking coil for encoding for BS spatial encoding, with a geometrically decoupled saddle coil inside it for excitation and reception. We demonstrate a phase encoding experiment with optimized frequency swept ‘U’-shaped BS pulses for phase encoding on a 47.5mT system with three reconstruction techniques.

Methods

2D phase encoded imaging was implemented on a 47.5mT scanner (Sigwa 48.7mT, Boston NMR, Boston, MA) shown in Figure 1A. The RF coils were placed in a shielded box and remaining EMI was removed using EDITER [9] with two external EMI detector coils.

Figure 1B shows the two-coil setup with 1) The 2.075MHz litz-wire optimized square root coil for phase encoding, and 2) A uniform saddle coil (OD of 3D printed former = 3.5cm, length = 12cm) for imaging. Optimization of the square-root coil was done numerically by minimizing the B₁⁺-field of a regular square-root solenoid to be close to an ideal square-root B₁⁺-field. The winding pattern of an optimized coil is shown in Figure 1C. Figure 1D shows the isolation (-36dB) between the geometrically decoupled solenoid and saddle coils. Bucking coil windings were added to cancel fringe B₁⁺-field at the low B₁⁺-field edge of the solenoid coil and make the coil more efficient. This effect can be seen in Figure 2A wherein an analytic square root coil is compared to the optimized coil with and without the bucking coil windings (Total # of windings for each = 34, excluding the bucking coil). Since the frequency and phase shifts applied to an object by BS encoding are proportional to B₁⁺², Figure 2B shows average B₁⁺² profiles across the ROI along with linear fits and their R². Figure 1C shows Experimental B₁⁺ maps which were obtained from a 11.5cm(L) x 3cm(D) tube mineral oil phantom using the optimized ‘U’ shaped BS pulse [10] shown in Figure 3A (BS frequency-offset =20KHz and Kbs[11] =43.5). Figure 1D shows the average B₁⁺² profile across the tube phantom along with a linear fit and its R².

The same optimized BS pulse was used for phase encoding in a 2D GRE sequence (Sequence parameters: TE=17ms, TR=534ms, N_PE=67, N_FE=128, N_averages=5) shown in Figure 3B. The BS pulse amplitude was varied for BS phase encoding (N_BS=37). The uniform saddle coil was used for Tx/Rx for imaging with an active T/R switch [12]. The optimized solenoid was used for encoding. B0 gradients were used for frequency encoding along the Z direction(k_x). A scanner drift navigator sequence was interleaved with the acqusition.

The Reconstruction pipeline is shown in Figure 4. Here, the full phase encoded tube dataset was taken and then scanner drift corrected. This resulting dataset was used to create an encoding matrix (E). A full model-based reconstruction(R) done using the following equation:
$$ R = {(E'E + \lambda I)}^{-1} E S$$
Where, S is the hybrid (x-k_y) data for a two-ball mineral(2cm) oil phantom and $$$\lambda$$$ is the regularization parameter. Additionally, a least-squares NUFFT reconstruction was performed by calculating the slopes of the BS phase encoded lines of the tube phantom to determine the actual ky locations. A partial Fourier reconstruction was performed using 70% of the ky lines which comprised all the positive encodes and 40% of the negative encodes. MATLAB’s lsqnonlin (Mathworks,Natick,MA) was used to reconstruct the image, holding the phase image fixed to match a zero-filled recon.

Results

Linear fits of B₁⁺² and their R² in Figure 2B show that the optimized square root solenoid had the highest linearity (R²=0.9987) which agreed with the R²(0.9960) of the linear fit for the experimental results in Figure 2D. Since efficiency depends on the slope of the B₁⁺²-field the y-intercepts are shown for each fit (retaining same slopes) to show that the optimized coil with the bucking windings was 20% more efficient than the one without the bucking windings. Figures 5A-D show the results from the three types of reconstructions in comparison to a fully B₀-encoded two-ball phantom image. Figure 5E shows two-ball phantom 1D profiles at the same points in all the reconstruction methods and from Figure 5F we can observe that the FWHM’s closely align with the B₀-encoded image. The NUFFT reconstruction had the closest fit to the B₀-encoded image.

Discussion

We demonstrated a robust method to perform B₁⁺ phase encoding using an optimized square root solenoid. Adding the Bucking coil to null the low-field, we obtained a 20% power efficiency improvement compared to the optimized design. The interleaved drift navigator scans could be eliminated by adding an FID measurement during the dead time between the excitation and BS encoding pulse. In future work, we will linearize the phase encodes to enable Cartesian FFT reconstruction.

Acknowledgements

Funding source R01 EB030414. We would like to thank Siddhant Gandhi for helpful discussions about RF coil design.

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