Synopsis

Electromagnetic simulation is a powerful tool to evaluate optimal radio frequency (RF) coil design without costly prototypes. However, RF receiver coils have accessory circuits, such as decoupler circuits, that make it difficult to reflect accurate coil loss. This leads to calculation error which can be non-negligible even in high static magnetic fields, especially for small loop coils. We measured the coil-component losses and took them into account for the simulation to calculate the signal-to-noise ratio (SNR). The calculated SNR had less than 5% error when compared to SNR measured with a 1.5-T MRI scanner for 10-channel receiver-array coils, confirming high accuracy of multi-channel SNR simulation.

Introduction

Recent increase in the number of receiver channels enables high-density RF array coils. For RF receiver coils with a large number of channels, electromagnetic (EM) simulation is a powerful tool to evaluate optimal design without costly prototypes. However, coil loss can become comparable to sample loss as the loop-size decreases, even in high static magnetic fields.¹ It is important to include accurate coil loss to the simulation model to calculate the signal-to-noise ratio (SNR) with high accuracy using EM simulation.² However, RF receiver coils have accessory circuits, such as decoupler circuits, that make it difficult to reflect accurate coil loss. Therefore, large estimation error of coil loss is an issue for SNR simulation.

In this study, we assessed the coil loss of each coil component through measurement and incorporated each loss to the simulation model. We applied this to 10-channel (ch) array coils and evaluated SNR calculation error by comparing the simulated SNR to that measured using a 1.5-T MRI scanner.

Methods

Simulation

We used an in-house built EM simulator based on method of moments³ which enables sub-millimeter overlap adjustments. Figure 1 shows the 10-ch array model. Neighbor channels were decoupled with overlap,⁴ and next-neighbor channels were decoupled with inductive coupling. Preamp decoupling⁴ was applied to all channels with preamps of 2 Ω input impedance. Three types of coil diameters, Φ178, 203, and 254 mm, were investigated with a cylindrical phantom of Φ165 mm (cell size (4 mm)³, σ=0.58 S/m, ε_r=86). Coil loss of passive and active decoupling circuits and decoupling inductors were assessed from unloaded Q measurements of a loop coil with/without the components. Capacitor loss was assessed from the manufacture’s datasheet. Residual loss was assessed as the conductor loss including solders. The noise correlation matrix was calculated as $$\Psi^s_{ij} = \frac{R_{ij}}{\sqrt{R^\ast_{ii}R_{jj}}},$$ $$R_{ij} = \sigma\int_V \vec{E_{i}}(x,y,z)\cdot\vec{E_{j}}^{\ast}(x,y,z)dV,$$ $$R_{ii} = \sigma \left( 1+\frac{1}{Q_{ui}/Q_{li}-1} \right) \int_V \left| \vec{E_{i}}(x,y,z) \right|^2 dV$$ (where $$$V$$$: volume of phantom, $$$\vec{E_i}$$$: electric field of ch $$$i$$$, $$$Q_{ui}/Q_{li}$$$: ratio of unloaded to loaded Q of ch $$$i$$$). The SNR was calculated as $$$SNR_{OPT} = \sqrt{{\bf {S^\ast_s \cdot (\Psi^s})^{-1}\cdot {}^t\!S_s}}$$$, where $$${\bf S_s}$$$ is the sensitivity of all channels.⁴

Measurement

We fabricated three types of 10-ch receiver coils in accordance with the simulation. The SNR was measured using a 1.5-T MRI scanner (Hitachi Ltd., Japan). Figure 2 shows the experimental setup including the coils and phantom (NiCl₂ 0.2%, NaCl 0.25%). A central axial slice was scanned with a 2D GrE sequence. The noise correlation matrix was measured as $$$\Psi^m_{ij} = (\Sigma^M_{k=1} n_{i,k}n^\ast_{j,k})/M$$$ (where $$$n_{i,k}$$$: noise of ch $$$i$$$ at pixel $$$k$$$, $$$M$$$: number of pixels). The SNR was calculated as $$$SNR_{OPT} = \sqrt{{\bf {S^\ast_m \cdot (\Psi^m})^{-1}\cdot {}^t\!S_m}}$$$, where $$${\bf S_m}$$$ is the signal of all channels.⁴

SNR evaluation

1) Signal intensity errors: $$$\sqrt{{\bf {S^\ast_s \cdot {}^t\!S_s}}}$$$ and $$$ \sqrt{{\bf {S^\ast_m \cdot {}^t\!S_m}}}$$$ were compared.

2) Noise correlation errors: SNR_OPT calculated with noise correlations $$${\bf {\Psi^s}}$$$ and $$${\bf {\Psi^m}}$$$ for the same signal ($$${\bf S_s}$$$) were compared.

3) SNR error: First, the estimated calculation error was evaluated as the root-sum-square of independent errors from 1) and 2) according to error propagation. Second, SNR_OPT of simulation and measurement were compared for confirmation.

[For all evaluations]: Two region of interests, ROI A: Φ146.5 mm (75% area) and ROI B: Φ30 mm (center region), were analyzed. Simulated results were scaled to measured results (at Φ254 and 178 mm, respectively), and the maximum error was evaluated.

Results

Discussion

Conclusion

Acknowledgements

References

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2. Kumar A, et al. Noise Figure Limits for Circular Loop MR Coils. Magn Reson Med. 2009;61:1201-1209.
3. Ochi H, et al. Calculation of Electromagnetic Field of an MRI Antenna Loaded by a Body. In: Proc SMRM 11th Ann Mtg. 1992:4021.
4. Roemer PB, et al. The NMR Phased Array. Magn Reson Med. 1990;16:192-225.