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Comparative design study of a 3T 1H RF breast coil: Quadrature vs. Solenoid Design
Sören Bieling1,2, Mark E. Ladd1,2,3, and Arthur W. Magill1

1Medical Physics in Radiology, German Cancer Research Center (DKFZ), Heidelberg, Germany, 2Faculty of Physics and Astronomy, Heidelberg University, Heidelberg, Germany, 3Faculty of Medicine, Heidelberg University, Heidelberg, Germany

### Synopsis

In this work a comparative design study for the development of a new proton (1H) transmit/receive radio frequency (RF) coil for unilateral breast imaging at 3 Tesla (123MHz) is performed. The two most common RF breast coil designs, based on quadrature and solenoid coils, are compared against each other in terms of spatial homogeneity and first-order statistics (mean µ, standard deviation σ, spread σ/µ) of the circularly polarized RF excitation field (B1+) as well as B1+ scaled over the square root of the maximum 10g-averaged specific absorption rate (B1+/√(SARpeak)).

### Introduction

Among women, breast cancer is the most commonly diagnosed cancer and the leading cause of cancer death1.
In this work a comparative design study for the development of a new proton (1H) transmit/receive radio frequency (RF) coil for unilateral breast imaging at 3 Tesla (123MHz) is performed. The two most common2,3,4 RF breast coil designs, based on quadrature and solenoid coils, are compared against each other in terms of spatial homogeneity and first-order statistics (mean µ, standard deviation σ, spread σ/µ) of the circularly polarized RF excitation field ($\vec{B}_{1}^{+}$) as well as $\vec{B}_{1}^{+}$ scaled over the square root of the maximum 10g-averaged specific absorption rate ($\vec{B}_{1}^{+} /\sqrt{\mathrm{SAR}_{\mathrm{peak}}^{\mathrm{10g}}}$). Quadrature RF coil design refers in this context to an orthogonally crossed 2-channel coil design driven in quadrature and thereby directly exciting the circularly polarized excitation field $\vec{B}_{1}^{+}$ whereas a solenoid RF coil design refers to a single-channel solenoid coil exciting a full linearly polarized $\vec{B}_{1}=\vec{B}_{1}^{+}+\vec{B}_{1}^{-}$ field.

### Methods

CAD models for both the quadrature RF coil and three solenoid coil variants are shown in Fig.1. The quadrature design consists of two orthogonally crossed loops with the coil “flaps” proximal to the chest wall bent over to better accommodate the patient. The three solenoid designs considered consisted of 2, 3 or 4 equally spaced planar loops connected in series, each with the top loop being maximally close to the patient interface to allow for the most RF exposure into the chest region. In all cases an identical RF shield was added outside the RF coils. Either a homogenous tissue phantom ($\epsilon_{\mathrm{r}}=60$, $\sigma=0.5\frac{\mathrm{S}}{\mathrm{m}}$) or one of three different heterogeneous female anatomical torso voxel models4 were placed inside the different coils. The three torso models feature 1.2mm isotropic resolution and 17 different tissue types with their respective EM material properties following the IT’IS material database5. The models were positioned tightly within the coils by translation, minimal rotation, and scaling by not more than -5%. Electromagnetic RF simulations were performed with CST Studio Suite 2017 (CST AG, Darmstadt, Germany). All coils with their respective loads were tuned to resonate at 123 MHz and matched to better than -60dB. All loops were subdivided with appropriate capacitors in the picofarad range to break up standing wave effects of the RF current and were modeled together with a matching network prior to the RF feed in a network co-simulation (CST Design Studio).
Based on the simulation results, the 10g-averaged SAR6, the $\vec{B}_{1}^{+} /\sqrt{\mathrm{power}}$ and subsequently the scaled $\vec{B}_{1}^{+} /\sqrt{\mathrm{SAR}_{\mathrm{peak}}^{\mathrm{10g}}}$ fields were calculated.

### Results

Figure 3 shows the quadrature coil compared against solenoid designs with 2-4 loops using a homogeneous tissue phantom load. Going from quadrature to an increasing number of solenoid loops, the peak 10g SAR goes down as the $\vec{B}_{1}^{+} /\sqrt{\mathrm{power}}$ fields become more homogeneous, with the exception of a small increase in peak 10g SAR for the 4-loop solenoid. While the scaled $\left|\vec{B}_{1}^{+}\right|_{\mathrm{rms}} / \sqrt{\mathrm{SAR}_{\mathrm{peak}}^{\mathrm{10g}}}$ means are similar for all coils (around $1.8 \mu\mathrm{T}/\sqrt{\frac{\mathrm{W}}{\mathrm{kg}}}$), the non-uniformity (σ/µ) decreases from 42.0 % for the quadrature RF coil design to 15.9 % for the 4-loop solenoid. The gain in $\left|\vec{B}_{1}^{+}\right|_{\mathrm{rms}} / \sqrt{\mathrm{SAR}_{\mathrm{peak}}^{\mathrm{10g}}}$ homogeneity from 3 loops (19.5 %) to 4 loops (15.9 %) is minimal and can be easily matched by increasing the diameter of the 3 loops (e.g. +5mm yields 13.7 %). Therefore, in all further investigations the quadrature design was compared with the 3-loop solenoid, but now with the heterogeneous voxel models as load (Fig. 4 and Fig. 5).
Averaged over all three voxel models, the peak SAR is about 2.5x higher for the quadrature RF coil design. Conversely, the mean of the scaled $\left|\vec{B}_{1}^{+}\right|_{\mathrm{rms}} / \sqrt{\mathrm{SAR}_{\mathrm{peak}}^{\mathrm{10g}}}$ efficiency is on average 2.8x higher for the 3-loop solenoid design and its homogeneity on average 3x better (cf. Fig. 5).

### Discussion & Conclusion

Quadrature coil designs preferentially drive the $\vec{B}_{1}^{+}$ excitation field and can thus improve the transmit efficiency by a factor of $\sqrt{2}$ in $\vec{B}_{1}^{+} /\sqrt{\mathrm{power}}$. In contrast, solenoid coils can only be driven with linear polarization, but are inherently very efficient at generating a uniform magnetic field. In the case of the breast coil designs investigated here, the gains in efficiency and field homogeneity of the solenoid design outweigh the advantages offered by driving the crossed-loops in quadrature. In summary, for the homogeneous tissue phantom as well as the three realistic body models studied here, we can generally conclude that the solenoid variants and in particular the 3-loop variant represent the best choice in terms of peak SAR, $\vec{B}_{1}^{+} /\sqrt{\mathrm{SAR}_{\mathrm{peak}}^{\mathrm{10g}}}$ efficiency, and $\vec{B}_{1}^{+}$ homogeneity.

### Acknowledgements

The research leading to these results has received funding from the Deutsche Forschungsgemeinschaft (DFG) under grant number LA 1325/8-1.

### References

1. Bray F., Ferlay J., Soerjomataram I., Siegel R.L., Torre L.A., Jemal A. Global cancer statistics 2018: GLOBOCAN estimates of incidence and mortality worldwide for 36 cancers in 185 countries. CA: A Cancer Journal for Clinicians. 2018; doi:10.3322/caac.21492
2. Maillet D., Ruehle A., Reutens D.C., Vegh V. An adaptable MRI radiofrequency breast coil: Evaluation of size, coil diameter, and uniformity. Concepts Magn. Reson. 2012; 41B: 50-56. doi:10.1002/cmr.b.21211
3. Brown R., Storey P., Geppert C. et al. Breast MRI at 7 Tesla with a bilateral coil and T1-weighted acquisition with robust fat suppression: Image evaluation and comparison with 3 Tesla. Eur. Radiol. 2013; 23: 2969. doi: 10.1007/s00330-013-2972-1
4. Fiedler T.M., Ladd M.E., Bitz A.K. RF safety assessment of a bilateral four‐channel transmit/receive 7 Tesla breast coil: SAR versus tissue temperature limits. Med. Phys. 2017;44: 143-157. doi:10.1002/mp.12034
5. Hasgall P.A., Di Gennaro F., Baumgartner C., et al. IT’IS Database for thermal and electromagnetic parameters of biological tissues, Version 2.6; www.itis.ethz.ch/database
6. IEC/IEEE International Standard -- Determining the peak spatial-average specific absorption rate (SAR) in the human body from wireless communications devices, 30 MHz to 6 GHz - Part 1: General requirements for using the finite-difference time-domain (FDTD) method for SAR calculations IEC/IEEE 62704-1:2017. doi: 10.1109/IEEESTD.2017.8088404

### Figures

CAD models for both the quadrature RF coil design and the three solenoid RF coil variants are shown consisting of RF conductor (black), tuning capacitors (blue), RF feed port (red), RF shield (green), homogenous tissue phantom (magenta) which in further simulations was replaced by the three different heterogeneous female anatomical torso voxel models shown in Fig.2.

The three different heterogeneous female anatomical torso voxel models4 used for simulation are shown as well as their age and weight given. They feature 1.2mm isotropic resolution, 17 different tissue types with their respective EM material properties following the IT’IS material database5.

Cut views of scaled B1+/√(SARpeak) are shown in the central transversal plane. Corresponding key figures such as peak 10g-averaged SAR, the mean µ of scaled B1+/√(SARpeak) and its spread σ/µ (σ being its standard deviation) are calculated over the entire tissue phantom and stated. (Cf. CAD-models shown in Fig.1)

Central transversal plane cut views of scaled B1+/√(SARpeak) are shown for all combinations of quadrature and 3 loop solenoid RF coil design with all three heterogeneous female anatomical torso voxel models4 (Fig.2).

To Fig.4 corresponding key figures such as peak 10g-averaged SAR, the mean µ of scaled B1+/√(SARpeak) and its spread σ/µ (σ being its standard deviation) are calculated and stated for all combinations of quadrature and 3 loop solenoid RF coil design with all three heterogeneous female anatomical torso voxel models4 (Fig.2). While the 10g-averaged SAR has been evaluated over the entire voxel models, statistics for the scaled B1+/√(SARpeak) have been sensibly evaluated over the single breast positioned within the coil.

Proc. Intl. Soc. Mag. Reson. Med. 27 (2019)
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