Analytical theory, circuit and numerical simulations to design a splittable degenerate birdcage for MSK applications.
Riccardo Stara1,2,3, Fabio Morsani2, Gianluigi Tiberi4,5, Maria Evelina Fantacci2,3, Massimo Marletta6, Virna Zampa6, Brian Rutt1, Alessandra Retico2, and Michela Tosetti5

1Stanford University, Stanford, CA, United States, 2Istituto Nazionale di Fisica Nucleare (Pisa), Pisa, Italy, 3Dipartimento di Fisica, Universita' di Pisa, Pisa, Italy, 4IMAGO7, Pisa, Italy, 5IRCCS Stella maris, Calambrone (Pisa), Italy, 6Dipartimento di radiologia diagnostica ed interventistica AOU, Pisa, Italy

Synopsis

The degenerate birdcage is not a common design for ultra-high field transmit array due to the technical difficulties in its construction, such as the interdependence of tuning and degeneracy on the value of capacitors. We present here a combination of an analytical theory, circuit simulations and numerical simulations to be used for an efficient design and construction of the degenerate birdcage at 7T. We demonstrate satisfactory performance in terms of decoupling, B1+ homogeneity and B1+ efficiency on the workbench and with scanner measurements on phantoms and human volunteers.

Purpose

The birdcage coil is still by far the most common design for MRI quadrature coils, mostly thanks to its intrinsic efficiency and B1+ field uniformity. However, the “degenerate” version of this design1, is rarely used for multichannel transmit arrays, especially at ultra high field (≥7T). We introduce here a combination of analytical theory and simulations to design a knee-sized transmit-and-receive degenerate birdcage at 7T. These methods resulted in excellent performance, despite the asymmetry introduced by the splittable design. A prototype was constructed, and demonstrated satisfactory by workbench and scanner measurements on phantom and human volunteers.

Methods

The birdcage theory2,3 was rewritten in term of variables more suited for the “degenerate” application, obtaining a mode equation dependent only on the mutual inductances, the ratio R and series combination T of leg and end-ring capacitance values. As shown in Figure 2, while a true degenerate solution does not exist3, several almost-degenerate spectra can be obtained, depending on the value of R. The mode equation can be inverted to obtain a relationship between the resonant frequency and the mutual inductances, to be used in an iterative way to find optimal values of R and T. The theory was used in combination with circuit and numerical simulations using Agilent ADS and Altair FEKO to obtain an estimate of optimal capacitance values, B1 efficiency, and S matrix. All FEKO simulations were performed using a cylindrical phantom model (OD=12 cm, σ=0.6, er=78). The coil model was imported into CST to evaluate the SAR and B1+ inside a realistic human head model (Ella from the Virtual Family). The coil was then fabricated on an ABS cylindrical former (ID 180 mm, OD 240 mm, length 236) using Kapton and ARLON FR25 as PCB substrate for the coil legs and end rings respectively. The 0.05 mm Kapton shield consist of 2-layers of overlapping strips. Workbench measurements were performed with a saline 0.1M NaCl cylindrical phantom (OD 12 cm). A Butler matrix4 was simulated (using ADS and FEKO) and built to interface the degenerate birdcage to the 2-channel MRI scanner. It consisted of three layers containing four microstrip quadrature hybrids each and microstrip connection lines of variable length. The substrate was 3 mm thick RO3010. Different layers were connected by carefully calibrated RG405 semi-rigid coaxial cables. The power loss, amplitude and phase balance were measured and compared to simulations. A set of 8 TR switches was built on 3mm thick RG5880 substrate. The circuit uses two λ/4 lumped element lines with shunt Microsemi UM4906PIN diodes. Insertion loss, transmit power loss, preamp isolation and preamp gain were measured.

Results

The simulated and measured capacitor values are shown in Table 1. The simulation correctly predicted the R value, while some adjustment (around 15%) was needed to correctly tune the coil to 300 MHz. The mesh that spanned the split required slightly different values of both R and T. As shown in Figure 3, the simulated coil is correctly matched and decoupled, although some residual coupling (-11 dB) exists between next-neighbor meshes. The measurements show an average reflection coefficient of -16.8 dB and coupling coefficients better than -10.4 dB. The simulated and measured B1+ maps are shown in Figure 4. The coil in CP mode has good efficiency (44.4$\frac{μT}{\sqrt{kW}$ in the simulation and 56.5 $\frac{μT}{\sqrt{kW}$ in the measurement) and the qualitative agreement with simulation (and the birdcage theory) is good for all modes. The simulation on the human phantom shows a CP mode efficiency of 44 $\frac{μT}{\sqrt{kW}$ and a maximum local SAR of 1.05 W/kg normalized to 1 μT average B1+ across a central slice. Regarding the Butler matrix the mean phase error was ±3.8o for the measurement and ±1.4o for the simulation, while the measured power loss was 14.6%. The TR switches insertion loss during reception was 0.219 dB, while the attenuation during Tx was 0.161 dB. The preamp isolation was -50 dB. The coil, in combination with the Butler matrix and T/R switches, was used in CP mode for knee imaging in vivo (see Figure 1).

Discussion and Conclusions

A knee-sized splittable degenerate birdcage was constructed at 7T, with good performance in terms of B1+ efficiency and element decoupling. The modified birdcage theory, together with circuit and numerical simulations, provided an effective strategy for design and construction. The coil was successfully used in vivo for knee imaging and MSK applications. This coil can be used for RF shimming and pTx solutions on both 2-channel and 8-channel MRI systems.

Acknowledgements

No acknowledgement found.

References

1. Alagappan V. et al. Degenerate mode band-pass birdcage coil for accelerated parallel excitation. Magnet Reson Med; 57(6), 1148-1158, 2007.

2. Tropp J. Mutual inductance in the bird-cage resonator. J Magn Reson; 126(1), 9-17, 1997.

3. Cheng Y.C. et al. A degeneracy study in the circulant and bordered-circulant approach to birdcage and planar coils. MAGMA; 16(2), 103-111, 2003.

4. Yazdanbakhsh P. and Solbach K.. Microstrip Butler matrix design and realization for 7 T MRI. Magnetic Resonance in Medicine, 66(1):270–280, 2011.

Figures

Figure 1: Coil prototype (a); 3D Fiesta-C TR=8.4 ms, TE=3.2 ms, NEX=1, Acquisition matrix=512x480, FA=40, Slice thickness=1.2 mm (b).

Figure 2: Birdcage coil spectrum for three choices of R: minimum spread including the end ring mode (a) or not including it (b) and degenerate homogeneous and linear mode (c)

Table 1: Capacitor values in simulation and in the prototype. The values under bracket are relative to the splittable meshes.

Figure 3: Simulated (a) and measured (b) S matrix. Degenerating the homogeneous and linear mode is equivalent to decoupling adjacent meshes. Some residual coupling is present for next-neighbor elements.

Figure 4: Simulated (second and fourth rows) and measured (first and third rows) B1+ maps, for single channel excitation (first and second rows) and butler matrix modes (third and fourth rows).



Proc. Intl. Soc. Mag. Reson. Med. 24 (2016)
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