Radial TRASE: 2D RF encoding through mechanical rotation and active digital decoupling

Abstract

Purpose: Two-dimensional (2D) transmit array spatial encoding (TRASE) previously required four radiofrequency fields; however, interactions between transmit (Tx) array elements caused significant challenges for 2D imaging. Here, we present a low-cost, 2D radial encoding scheme (Radial TRASE) using a simplified two-coil array.

Theory and methods: The system consists of two B₁ phase gradient coils capable of encoding any one transverse direction. By incremental mechanical rotation over a 90° range, the encoding axis can be changed, allowing a complete radial k-space acquisition. As a first demonstration, a wrist-sized coil pair was experimentally verified on a 2-MHz Halbach magnet, incorporating a static B₀ slice-selection gradient. Although a high level of isolation is achievable geometrically, for a more robust implementation, we demonstrate the capability of active digital decoupling in eliminating residual coupling through a parallel-transmit system.

Results: Radial TRASE-encoded images of water phantoms were acquired, achieving a resolution better than 1.67 mm. Rotation of the Tx array was performed during the recovery period, which caused no imaging delays. All acquired images show minimal distortions, indicating the advantage of the simplified Tx array. The active digital decoupling technique is demonstrated to eliminate residual coupled currents, effectively increasing the isolation of the two-coil array to -50 dB. Sequential axial slice images were demonstrated using a uniform B₀ coil to shift the slice position.

Conclusion: Two-coil Radial TRASE can encode a 2D slice without rapidly switched B₀ gradients. Compared with previous three-coil or four-coil Cartesian TRASE, the design and isolation of the Tx array are significantly simplified.

Keywords: RF coil rotation; TRASE MRI; active digital decoupling; radial encoding; radiofrequency (RF) transmit array; twisted solenoid.

FIGURE 1

The 1D TRASE sequence and trajectory through k‐space. The TRASE sequence consists of a long echo train with refocusing pulses alternating between the two differing phase gradient coils ( A and B ). In k‐space, each refocusing pulse causes a reflection of the spin states about that coil's k‐space origin ( k _A and k _B ). The resulting trajectory through k‐space is a repeated jumping fashion, with each echo (e.g., e1, e2, e3) corresponding to a single point in k‐space with separation $∆{\mathit{k}}_{\mathit{AB}}=2\left|{\mathit{k}}_A-{\mathit{k}}_B\right|$.

FIGURE 2

Illustration of the twisted solenoid phase gradient direction changing under rotation in a vertical B₀ field. (A) The 1D TRASE Tx array consisting of a twisted solenoid pair ( A and B ) with opposite phase gradients (G _1,A and G _1,B) along the x‐axis. After a mechanical rotation of $\alpha$ about the coil's axis (z‐direction), the two phase gradients are shifted by an angle $2\alpha$. (B) TRASE k‐space acquisition from the initial (I) and rotated configuration (II). In the initial configuration, the 1D‐TRASE sequence encodes the x‐axis. After the rotation by $\alpha$, the shifted phase gradient fields (and corresponding k‐space origins k _A and k _B ) encode in the direction $2\alpha$. To fully sample two‐dimensional k‐space radially, the phase gradients need to be incrementally shifted over a 180° span, which is achieved by physical incremental rotation over a 90° range.

FIGURE 3

B₁ field simulations in the center of the outer coil (z = 0 plane) for four physical rotation angles (0°, 30°, 60°, and 90°) showing the B₁ magnitude (A), B₁ phase (B), and B₁ phase gradient (C). The horizontal axis in each plot is along the encoding direction for each rotational angle. The black dotted lines designate the boundaries of the optimized imaging volume (80‐mm diameter). Within these bounds, the B₁ phase and magnitude are relatively unchanged during rotation in their respective encoding directions. The small variation that does exist is primarily due to the pitch of the radiofrequency coil (i.e., not tightly wound), resulting in the zero spatial phase location being slightly off‐center.

FIGURE 4

Circuit diagram depicting the current monitoring transformer and a photo of the coil electronics. (A) Circuit diagram of the outer coil. The values of C_M and C_T (2 to 120 pF) represent the matching and tuning capacitors, respectively. The two fixed capacitors (C₁ and C₂) both had a value of 470 pF. The values of L_T and L_D (combined 37.2 μH) represent the outer twisted solenoid and its decoupling solenoid, respectively. A transformer was placed within the resonance circuit to measure the current amplitude and phase in the RF coils. (B) Photograph of the coil electronics outside the magnet. Both decoupling solenoids are wound around their own formers, with their exact position used to control the isolation (S₁₂). The current monitoring transformers are kept on the circuit boards away from the twisted and decoupling solenoids.

FIGURE 5

Depiction of the mechanical rotation system. (A) Image of the connected motor outside the RF shielding. The drive rod connects to the motor and is passed directly through a waveguide to the coils. (B) A Fusion360 model of the coil pair within the magnet. The RF coils (red and yellow) rest on the bore tube (green), which positions the coils centrally and guides rotation. A three‐dimensional‐printed connection (gray) affixes the coils to the drive rod (blue) axially and houses their circuit boards.

FIGURE 6

Demonstration of the ADD compensation pulse in eliminating residual coil coupling. The coils were geometrically isolated to $S_{12}=-20\mathrm{dB}$. Transformers within the resonance circuits monitored the coil currents as an induced electromagnetic field (EMF) (Faraday's law). For a refocusing pulse transmitted on the inner coil (yellow), the coupled induced current was measured on the outer coil (blue) without (A) and with (B) an ADD compensation pulse. Initially, an EMF magnitude of 232 mV was induced on the outer coil. From this measurement (magnitude and phase), an ADD pulse was applied to the outer coil under the same conditions. This ADD pulse reduced the EMF magnitude from 232 to 8 mV, effectively improving the coil isolation by a further −29.3 dB.

FIGURE 7

TRASE experimental results with ADD and a geometric isolation of $S_{12}=-20\mathrm{dB}$. The pulse sequence consisted of 200‐μs hard pulses, echo train length of 128, echo time of 2000 μs, repetition time of 3000 ms, and 201 radial spokes. (A) The imaged phantom contains seventeen 8‐mm‐diameter water vials. One vial is placed centrally with eight vials each positioned in rings of diameter 60 mm and 90 mm. The two Radial TRASE images were obtained without (B) and with (C) an ADD compensation pulse. Both images have identical displays and wide windowing. In comparison, ADD effectively reduced the blurring of most outer vials.

FIGURE 8

Radial TRASE resolution experimental results of a custom line‐pair phantom. The pulse sequence consisted of 200‐μs hard pulses, echo train length of 128, echo time of 2000 μs, repetition time of 3000 ms, and 201 radial spokes. (A) The three‐dimensional‐printed line‐pair phantom consisting of 5, 4, 3.33, 3, 2.5, and 2‐mm/lp water‐filled segments. (B) The two‐dimensional filtered back‐projection image. The 3.33‐mm/lp segment is clearly resolvable, indicating an in‐plane spatial resolution of at least 1.67 mm, which is similar to the expected resolution of 1.23 mm. (C) The constructed sinogram from the radial one‐dimensional (1D) TRASE profiles, showing the TRASE spatial axis (vertical) and radial projections (horizontal). Although a smooth center of mass correction was applied to the sinogram, some spoke alignment errors remain.

FIGURE 9

Demonstration of sequential slice Radial TRASE imaging. The pulse sequence for each slice consisted of 200‐μs hard pulses, echo train length of 128, echo time of 2000 μs, repetition time of 1000 ms, acquisition window of 1000 μs, four averages, and 201 radial spokes. A uniform B₀ coil within the magnet bore is used to shift the resonance slice due to the static axial gradient. Imaging was performed with a phantom containing nine 8‐mm‐diameter water vials. One vial is positioned centrally, with the remaining eight angled toward the center by 24°. (A) Sequential slice images were obtained for B₀ shift coil currents of −3, −1.5, 0, 1.5, and 3 A. The expected shift between each slice is 10.4 mm with a reconstructed partition thickness of 3.36 mm. From left to right, the ring of vials spreads outward, indicating successful shifting of the resonance slice position by the uniform B₀ coil. (B) Fusion360 model with a different perspective of the imaged vial phantom.