Kohjiro Iwasawa^{1}, Yosuke Otake^{1}, Hisaaki Ochi^{1}, Hideta Habara^{2}, Masayoshi Dohata^{2}, and Yoshihisa Soutome^{1}

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.

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.

Simulation

We
used an in-house built EM simulator based on method of moments^{3} 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 decoupling^{4} 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 (NiCl_{2} 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.

- Farivar R, et al. Dense, Shape-Optimized Posterior 32-Channel Coil for Submillimeter Functional Imaging of Visual Cortex at 3T. Magn Reson Med. 2016;76:321-328.
- Kumar A, et al. Noise Figure Limits for Circular Loop MR Coils. Magn Reson Med. 2009;61:1201-1209.
- Ochi H, et al. Calculation of Electromagnetic Field of an MRI Antenna Loaded by a Body. In: Proc SMRM 11th Ann Mtg. 1992:4021.
- Roemer PB, et al. The NMR Phased Array. Magn Reson Med. 1990;16:192-225.

Schematics of simulation model of phantom and
10-channel receiver coil. (a) Bird’s-eye view. (b) Front view. (c) Side view.

Experimental setup of phantom and
10-channel receiver coil of three sizes with diameters of (a) Φ178, (b) 203, and
(c) 254 mm, respectively.

Losses of RF receiver coil. Percentages are
shown for Φ178-mm coil at
1.5 T. Sample loss was calculated from measured Qu/Ql. Measured coil-component
losses are shown in right pie chart in ohms. R_{cond}: conductor loss, R_{cd}, R_{ct},
R_{cp}, R_{ca}, and R_{cm}: losses of each capacitor (R_{cd}: dividing capacitor, R_{ct}:
tuning capacitor, R_{cp}: capacitor at passive decoupler, R_{ca}: capacitor at active
decoupler, R_{cm}: matching capacitor), R_{ic}: inductive coupler loss, R_{p}: passive
decoupler circuit loss, and R_{a}: active decoupler circuit loss.

Calculated SNR_{OPT} maps from electromagnetic simulation and measurement for coil diameters of Φ178, 203, and 254 mm.

Calculated
SNR_{OPT} from EM simulation scaled to measured SNR_{OPT} for
(a) mean of ROI A and (b) mean of ROI B. X marks are simulation results scaled to Φ254 mm, and plus marks are those scaled to Φ178 mm. Red crosses are simulation results
considering coil loss. Blue crosses are shown for comparison when noise
correlations were calculated without coil loss.