Introduction

Preamplifier decoupling is a well-known technique to decouple nearby elements^[1-3] in MRI receive arrays. The main objective is to present a high impedance Z_block to the coil port so that a minimum current flows in the coil, thereby reducing mutual induction in neighbouring coils. Usually, the low-input impedance of a preamplifier is transformed into a high impedance at the coil port thanks to a LC resonant circuit^[2,4]. Iterative procedure with two well-decoupled probes^[2] is needed both in simulation and practical implementation to get optimal decoupling, which is difficult to achieve for high-count channel arrays. Recently, alternative circuit designs were proposed^[5]. We developed here high-input impedance preamplifiers that can be directly connected to the coil, easing tuning procedure but requiring new simulation methods. The optimal Z_block to present to the coil was determined thanks to simulation. Note that this method is also applicable to the traditional low-input impedance scheme since this impedance is also transformed into Z_block. Optimal implementation relies on the ability to simulate SNR according to the circuit design. We tested this methodology on a new receive array design at 7T, made of non-overlapping loops arranged in two layers thereby requiring more demanding preamplifier decoupling performance.

Methods

A 32-channel phased array has been designed with Ansys Electronics Desktop (Pennsylvania, USA) and transferred to circuit co-simulation for analysis (Fig.1). The inner layer consists of 25 small loops arranged in three rows in z-direction, mainly devoted to peripheral imaging (two loops at the top of the head are combined for signal reception), and 8 larger loops are placed in an outer layer to increase penetration performance. It also aims at improving sensitivity of non-overlapping areas of small loops. Elements within the same layer are chosen to be non-overlapped to facilitate positioning and improve g-factor in parallel imaging^[6]. Only one simulation is performed with a homemade head model including 10 different tissues, considering all environmental objects (detuned transmission coil with shielding, bed, etc.). Lossy capacitors are placed in the HFSS design in series with the loops to make them resonate approximately at the Larmor frequency, and a port is placed at the top of each loop. After HFSS simulation, the dynamically linked component composed of the 32 channels is placed in circuit design. Circuit co-simulations are performed according to Fig. 2: first, each loop is fine-tuned to the Larmor frequency thanks to an adjustable series capacitor (i.e. the impedance Z_coil is made purely resistive). This fine-tuning capacitor is placed in co-simulation to avoid repeated HFSS simulations (the HFSS simulation took about 13 hours with Intel Gold 6250, 3.90 GHz, 768 Go RAM). Then, each port impedance is set to a variable Z_block to emulate preamplifier decoupling. To normalize the B₁^- field to 1W dissipated power, a voltage source (Fig.2) is scaled according to $$$V_{gen}=\sqrt{\frac{2\mid\tilde{Z}_{block} + \tilde{Z}_{coil}\mid^2}{Real(\tilde{Z}_{coil})}}$$$. This formula was derived from an equivalent Thevenin generator and impedance transformation so that the real part of the complex power is equal to 1W.
Each loop, even the one being excited in the simulation, is now preamplifier-decoupled. Magnetic field maps are extracted and post-processed with Matlab for SNR computation based on the theorem of reciprocity^[7]; this process is automated and repeated for each element. The impedance Z_block of an in-house developed preamplifier was measured with a network analyzer (Fig. 3). Therefore, Z_block can be used in simulations to evaluate the potential coil performance and reciprocally, circuit can be optimized according to simulations. Provided |Z_coil| is low enough, only |Z_block| matters for decoupling: in simulation, Z_block was taken such as Re(Z_block)<Im(Z_block).

Results

Fig. 4 presents normalized SNR as computed in the brain model for different Z_block values. The last plot shows SNR for |Z_block|=2000 Ω as no further increase was found above this value, even at 1 MΩ (Fig.5). Results show that |Z_block|=330 Ω can already reach 88% of the maximum SNR (averaged over the whole brain), whereas |Z_block|=160 Ω and 75 Ω give only 75% and 54% of the best SNR respectively. Strong coupling observed at |Z_block|=75 Ω, truly downgrades the global performance.

In principle, it is always possible to increase |Z_block| so that coupling losses are minimized. Nevertheless, these results show that increasing |Z_block| above 400 Ω would only provide a maximum gain of 10% in SNR, but might compromise the preamplifier noise-matching, which is not taken into account in this study. To predict SNR as measured at the preamplifier output, transistor and noise-matching circuit should be included to account for noise figure and components losses. Moreover, Z_block can be optimized for a group of loops with the same geometry. This design was compared in simulation to a commercial state-of-the-art 32-channel array and showed equivalent SNR for |Z_block|=160 Ω: 20% extra gain can be expected with |Zblock|=400 Ω.

Conclusion

A simple method to evaluate the impact of preamplifier decoupling on thermal SNR has been proposed based on the measurement of the impedance Z_block as seen by the coil. This methodology was illustrated on a 32-channel receive array with non-overlapping loops at 7T. A value of |Z_block| higher than 400 Ω provides a close-to-perfect decoupling at least from the SNR point of view.

Acknowledgements

These research activities have received funding from the European Union's Horizon 2020 research and innovation programme under grant agreement No 952106 (M-ONE project).