Linear Bloch-Siegert phase-encoded low-field MRI: RF coils, pulse sequence, and image reconstruction.

Conventional $B_0$ gradient systems have several weaknesses including high cost and bulk. As a step towards addressing these while providing new degrees of freedom for spatial encoding and system design in Magnetic Resonance Imaging (MRI), a radio frequency (RF) gradient encoding system and pulse sequence for phase encoding using the Bloch-Siegert (BS) shift were developed. Optimized BS spatial encoding coils with bucking windings (counter-wound loops) were designed and constructed, along with compatible homogeneous imaging coils for excitation and signal reception. Two coil systems were developed: one for phantom imaging and a second for human wrist imaging. BS phase-encoded imaging and BS RF pulse simulations were performed. Pulse sequences were designed for linear stepping in k-space and implemented on a 47.5-mT scanner to image resolution phantoms in both coil setups. Reconstructions were performed using both the full $B_1^{+}$ -based encoding fields for each BS pulse amplitude and using inverse discrete Fourier transforms. A $B_0$ gradient was used for frequency encoding during signal readout, and the third axis was projected. Specific absorption ratio (SAR) calculations were performed for the wrist coil to determine the safety of BS-based RF encoding for $B_0$ fields in the low field MRI regime. The optimized RF spatial encoding coils resulted in higher linearity ( $R^2=0.9981$ and 0.9921 in the phantom and wrist coils, respectively) than coils used in previous work. The phantom and wrist imaging coils were validated in simulations and experimentally to produce a peak $B_1^{+}=1.35$ G and 0.8 G with 12-W input power, respectively, in the field-of-view (length = 11 cm) used for imaging. Nominal imaging resolutions of 5.22 and 7.21 mm were, respectively, achieved by the two-coil systems in the RF phase-encoded dimension. Coil systems, pulse sequences, and image reconstructions were developed for linear RF phase encoding using the BS shift and validated using a 47.5-mT open low field scanner, establishing a key component required for $B_0$  gradient-free imaging at low $B_0$  field strengths.