Introduction

TRASE is an MR imaging technique that performs k-space encoding through the use of RF transmit phase gradients, rather than gradients of the main magnetic field. The replacement of B₀ gradients by RF transmit phase gradients allows alternative low-cost MRI systems to be constructed from small permanent magnets, such as a Halbach array¹.

The twisted solenoid has been previously demonstrated as a promising coil for TRASE imaging². High one-dimensional spatial resolutions have been achieved with the twisted solenoid in phantom studies^2,3; however, this specific coil geometry creates large gaps at the end of the RF transmit coils due to the protruding twisted turns (See Fig. 1a). The gaps created by the twisted turns lead to a decreased B₁ magnitude uniformity towards the end of the coils, requiring the twisted solenoid to be significantly longer relative to its usable imaging volume. In this study we modified the coils by truncation to better fit coil conductors upon a cylindrical former of limited length, while maintaining or improving imaging performance.

Methods

The design process of the truncated twisted solenoid was as follows: (1) the axial truncation distance is specified (2) for the first coil turn, any portion of the turn beyond the truncation distance is flattened (3) each successive turn with a portion beyond the truncation point is then flattened a fix distance below the previously flattened turn. A truncated twisted solenoid compared to an untruncated twisted solenoid are shown in Fig. 1.

The truncated twisted solenoid can be described by the following geometric parameters: coil turn radius, coil length, modulation amplitude, pitch, and number of turns. Coil optimization was performed by first selecting the coils diameter and length based on the desired target imaging volume and physical constraints. Optimization was performed through a parameter search using Biot‐Savart simulations with the BSMag MATLAB package. As required by the TRASE sequence, the B₁ magnitude inhomogeneity was restricted to ±10% and a mean B₁ phase gradient strength greater than 5.0 deg/cm over the target imaging volume^2,4. Coils were primarily optimized for B₁ magnitude uniformity.

Results

For a target imaging volume 100mm in length and 80mm in diameter, two truncated twisted solenoids were constructed, a 125mm diameter 15-turn outer coil and a 100mm diameter 16-turn inner coil. Before truncation, the length of the outer coil and inner coils were 320mm and 290mm respectively; both coils were truncated to a length of 200mm. Coils were wound with 20 AWG wire around a 3D printed PLA cylindrical former. The coil pair was geometrically decoupled using a short 30mm long 6-turn clockwise and 5-turn counterclockwise regular solenoid added to the end of the outer and inner truncated twisted solenoids respectively (See Fig. 2)³. The geometric parameters, mean phase gradient strength, and mean B₁ magnitude for the inner and outer coils from the optimization simulation results are given in Fig. 3. Within the 100mm target imaging volume length, the optimized coils had a B₁ magnitude uniformity better than ±10% at 80% the coils diameter, as shown in Fig. 4.

The one-dimensional TRASE sequence was performed on a Halbach array with a central resonant frequency of 2.836 MHz¹. The coil pair and a cylindrical bottle phantom of diameter 35mm and length 40mm containing a molar concentration of 61.6 mM NaCl and 7.8 mM CuSO₄ was centered within the magnet. The sequence consisted of a 200 µs hard pulse for both excitation and refocusing, an echo spacing of 2000 µs, repetition time of 2000ms, an echo train length of 128, and 16 averages. The obtained one-dimensional TRASE profile is shown in Fig. 5. The width of the 1D phantom profile was roughly 30 pixels. For the 35mm diameter phantom this corresponds to a mean pixel size of 1.16mm/pixel and a mean B₁ phase gradient of G_x = 12.1 deg/cm. In tandem, the truncated coil pair have a simulated effective field gradient strength of G_x = 11.0 deg/cm and expected mean pixel size of 1.28mm/pixel.

Discussion

Simulations indicate the truncated design, while significantly shorter, maintains a similar imaging volume and spatial resolution (i.e. phase gradient strength) to the untruncated twisted solenoid. The truncated coil set presented here boasted a high level of B₁ magnitude uniformity. The 200mm long nested coil pair allowed an imaging volume 100mm in length and 80mm in diameter. This coil pair is roughly half the length of previously published untruncated twisted solenoid pairs whilst obtaining a slightly larger target imaging volume³.

The experimental one-dimensional TRASE image resembles the expected peaked excited volume caused by the Halbach arrays B₀ pattern (Fig. 5)¹. The phase gradient strength determined from the pixel size is slightly greater than expected, but within an acceptable level of uncertainty.

Conclusion

Based on the simulation studies conducted, this new truncated twisted solenoid design is significantly shorter than the predecessor untruncated version whilst maintaining similar imaging quality. This truncated coil will allow practical imaging volumes to be obtained for a more compact TRASE RF transmit coil. Experimental results indicate that TRASE using the truncated twisted solenoid can be performed on small portable Halbach array, which could lead to the development of a low-cost, accessible MR imaging system.

Acknowledgements

No acknowledgement found.