Synopsis

Keywords: Low-Field MRI, Low-Field MRI

Traditional B₀ gradients have several drawbacks including high acoustic noise, PNS, bulkiness, and high cost. To address this, we present a coil system for Bloch-Siegert (BS) RF encoding comprising an optimized square root solenoid with a bucking coil for high efficiency encoding and a nested uniform saddle coil for the imaging Tx/Rx coil at 47.5mT (2MHz), a field strength that is especially attractive due to its low SAR and accessibility. The coil designed for in-vivo imaging was evaluated in simulation including SAR measurements and experimentally on a resolution phantom using a 3D BS phase-encoded imaging and optimized ‘U’ shaped pulses.

Introduction

Conventional B₀ gradients are loud, compromising patient comfort, and are expensive¹. As an alternative to B₀ gradients, RF gradient encoding has the potential to bring about low-cost, compact, and silent MR imaging. Here we demonstrate the use of the Bloch-Siegert shift² due to its ability to produce linear phase/frequency shifts in the transverse plane without modulating the magnitude of the magnetization, at low-field using an optimized coil system for extremity(wrist) in-vivo imaging as well as SAR calculations as pulses used for BS encoding are SAR intensive.

Methods

The encoding coil optimization is done using a method like Ref³ which was modified to produce a target field of a square-root field. While this can provide a linear field, it is also essential to be as close to 0 as possible on one end of the coil since only the slope of the field matters and a non-zero intercept on one end represents wasted power. To achieve this, 12 bucking windings were then manually added to the optimized coil design to cancel the fringe $$$B_1^+$$$-field at the low $$$B_1^+$$$-field end. The coil (d=16cm, L=30cm, Total number of windings=52) has ROI of 19cm for the square root field, constructed using Litz wire with two distributed capacitors. The encoding coil and the winding pattern are shown in Figure 1A-B. The measured values of the coil were: L=164uH and Q=60. Due to arcing considerations in in-vivo imaging, a minimum gap of 1mm was used between windings. These bucking windings also reduced the overall inductance of the coil since they are in an opposing series configuration(without bucking L=250uH). A uniform saddle coil was constructed for imaging experiments. Figure 1C-F show the exploded view of the coils and the overall setup for wrist imaging including the phantoms used for validation. Additionally, interchangeable imaging coils (Saddle, loop, and double loop for parallel Rx) can be attached to the imaging coil holder as shown in Figure 2A-C along with the wrist placement in the saddle coil. Figure 2D shows the decoupling between the saddle imaging and encoding coil with and without loading. Since the frequency and phase shifts applied to an object by BS encoding are proportional to $$$B_1^2$$$, Figure 3A shows the $$$B_1^+$$$map acquired through simulations and the average $$$B_1^2$$$profiles.
The FDA limits specific absorption rate (SAR) for extremity imaging with a local transmit coil to 20W/kg averaged over 6 mins⁴. We performed SAR calculations for the wrist using the optimized encoding coil in the magneto-quasistatic simulator in Sim4life (Medtech, Zurich, Switzerland). The Yoon-sun hand model shown in Figure 4A was used with dielectric properties given in Figure 4B. Figures 4C-D show the peak-spatial SAR (psSAR) for 1g of tissue for in the sagittal and coronal planes respectively in the center slices of the hand model. Given our calculations are in continuous-wave mode, we can calculate the SAR for a pulse sequence:
$$SAR = \frac{SAR_{B1} \times \tau }{TR} =SAR_{B1} \times D$$

Where $$$\tau$$$ is the length of the BS pulse and D is the Duty-cycle of the pulse. We used a maximum pulse length of 16ms with a minimum TR of 350ms. Two 8ms optimized BS phase-encoding pulses⁵ with BS frequency-offset=10KHz and K_bs=43 each were used to apply phase encoding. A 3D GRE sequence (Sequence parameters: TE=27.3ms, TR=439ms, N_PE=67, N_FE=128, N_averages=10) reported previously⁶ was used with a phase drift navigator on the 47.5 mT scanner (Sigwa, Boston NMR, Boston, MA). The RF coils were placed in a shielded box and remaining EMI was removed using EDITER⁷. To map the $$$B_1^+$$$field of the encoding coil and to produce the encoding fields using the Bloch Siegert technique⁸, a rounded cylinder phantom (16cm (L) x 7.5(D)) filled with Mineral oil was used. The$$$B_1^+$$$maps that were experimentally obtained are shown in Figure 2B. Additionally, to validate phase encoding, a resolution phantom (Figure 1C) that was also filled with mineral oil was imaged. To verify RF phase encoding capabilities, the BS pulse amplitude was varied for across 33 amplitudes and two frequency polarities (total encodes=66). The transceiver saddle coil was used with an active TR switch⁹. The optimized coil was used for encoding. B₀ gradients were used for frequency encoding along the Z-direction(k_x). Image reconstruction was done using the method described previously⁶. The encoding fields used are shown in Figure 5A. The B₀ encoded image, a NUFFT and the full-model reconstruction of the resolution phantom are shown in Figure 5B-D.

Results

The coil simulation and experimental B₁² linear fit had R² = 0.9974 and 0.9994 with both y-intercepts at 0. The measured decoupling between the coils was ~32dB. The shift between unloaded and loaded conditions was minimal(<3KHz). For the peak B₁ of 0.55G and duty-cycle of 0.0457, the simulation yielded a Volume-average SAR= 2.01milliWatts/kg, psSAR averaged over 1g of tissue= 15.1milliWatts/kg and psSAR averaged over 10g of tissue= 7.2milliWatts/kg. All these values are well below the FDA limitations.

Discussion and conclusion

In this work we show an optimized coil setup that can do wrist in-vivo BS spatial encoding in one dimension. EMI and B₀ shim challenges will be addressed to achieve in-vivo imaging in the future. We also plan to image with the parallel Rx for higher SNR.

Acknowledgements

This work was supported by NIH grant R01 EB030414.