Daniel Højrup Johansen^{1}, Juan Diego Sanchez-Heredia^{1}, Vitaliy Zhurbenko^{1}, and Jan Henrik Ardenkjær-Larsen^{1,2}

Significant increase of the signal-to-noise ratio (SNR) is possible by cooling receive coils to cryogenic temperatures, if they are not highly sample noise dominated. Conventionally, the noise of the preamplifier is excluded leading to an overestimation of the achievable SNR gain. In this work, we show that for the case of a small-animal birdcage coil for ^{13}C at 3T cooled with liquid nitrogen to 77K, the SNR is overestimated by approximately 40% if the effect of the room temperature preamplifier is excluded. Hence, the preamplifier should either be included in the SNR gain estimation or cooled with the coil.

The SNR gain when comparing a room temperature coil with a cryogenic coil is often described by

$$\Psi_{\textrm{coil}}=\sqrt{\frac{T^{\left(\textrm{r}\right)}\cdot{Q_{\textrm{u}}^{\left(\textrm{r}\right)}}^{-1}+T^{\left(\textrm{r}\right)}\cdot{Q_{\textrm{s}}^{\left(\textrm{r}\right)}}^{-1}}{T^{\left(\textrm{c}\right)}\cdot{Q_{\textrm{u}}^{\left(\textrm{c}\right)}}^{-1}+T^{\left(\textrm{r}\right)}\cdot{Q_{\textrm{s}}^{\left(\textrm{c}\right)}}^{-1}}},$$

where superscripted $$$\left(\textrm{r}\right)$$$ and $$$\left(\textrm{c}\right)$$$ refers to the room temperature and cryogenic coil, respectively. $$$T$$$ is the temperature of the coil, $$$Q_{\textrm{u}}$$$ is the unloaded Q-factor, and $$$Q_{\textrm{s}}^{-1}=Q_{\textrm{l}}^{-1}-Q_{\textrm{u}}^{-1}$$$ where $$$Q_{\textrm{l}}^{-1}$$$ is the loaded Q-factor. For the above equation, it is assumed that the preamplifier only adds a negligible amount of noise. However, if the preamplifier is used for both the room temperature and cryogenic coil, the noise figure (and thus the SNR impairment) increases as the reference temperature drops. This is because the noise figure is a relative measure. The usual reference is the equivalent noise generated by resistor at a temperature of $$$T_{\textrm{ref}}=290$$$K (as per the IEEE definition). Hence, when the reference temperature changes the noise figure also changes. The equivalent noise temperature is defined as

$$T_{\textrm{e}}^{\left(\textrm{r}\right)}=T_{\textrm{ref}}\left(F^{\left(\textrm{r}\right)}-1\right),$$

where $$$F^{\left(\textrm{r}\right)}$$$ is the noise figure of the preamplifier measured at a given reference temperature $$$T_{\textrm{ref}}$$$. Hence as the reference temperature is decreased by cooling the coil, while the equivalent noise temperature of the preamplifier remains constant, the resulting cryogenic noise figure increases as described by

$$F^{\left(\textrm{c}\right)}=\frac{T_{\textrm{e}}^{\left(\textrm{r}\right)}}{T^{\left(\textrm{c}\right)}}+1.$$

Extending the first equation with the following two yields

$$\Psi_{\textrm{coil+preamp}}=\Psi_{\textrm{coil}}\frac{F^{\left(\textrm{r}\right)}}{F^{\left(\textrm{c}\right)}}=\sqrt{\frac{T^{\left(\textrm{r}\right)}\cdot {Q_{\textrm{u}}^{\left(\textrm{r}\right)}}^{-1}+T^{\left(\textrm{r}\right)}\cdot{Q_{\textrm{s}}^{\left(\textrm{r}\right)}}^{-1}}{T^{\left(\textrm{c}\right)}\cdot{Q_{\textrm{u}}^{\left(\textrm{c}\right)}}^{-1}+T^{\left(\textrm{r}\right)}\cdot{Q_{\textrm{s}}^{\left(\textrm{c}\right)}}^{-1}}}\cdot\frac{F^{\left(\textrm{r}\right)}T^{\left(\textrm{c}\right)}}{T_{\textrm{ref}}\left(F^{\left(\textrm{r}\right)}-1\right)+T^{\left(\textrm{c}\right)}}.$$

For SNR comparisons, a room temperature and cryogenic eight-rung low-pass quadrature transmit-receive (T/R) birdcage coil was constructed. The birdcage coils are mounted on a fiberglass tube with an inner diameter of 50mm and a thickness of 1.5mm. The coils have a length of 100mm and an inner diameter of 53mm. The conductor is 2mm diameter copper wire. A self-built RF front end consisting of a T/R switch, quadrature coupler, and preamplifier was used with a total noise figure of 1dB (at reference temperature of 290K) for the receive path. The cryostat is built using a styrofoam box where the cryogenic coil is completely submerged in LN. See Fig. 1. for pictures of the room temperature coil, cryogenic coil, and the RF front end.

The two coils were measured at 32.1MHz (^{13}C) in a clinical 3T scanner (MR750, GE Healthcare, Waukesha, WI, USA) using a CSI sequence with TR=500ms and 30 degree flip angle. The sample was a 50ml tube with 30mm diameter and length of 120mm filled with ethylene glycol mixed with 1.7 NaCl g/L (to provide adequate loading).

Simulated results are seen in Fig. 2 and 3. Bench measurements show $$$Q_{\textrm{u}}^{\left(\textrm{r}\right)}=362$$$, $$$Q_{\textrm{l}}^{\left(\textrm{r}\right)}=356$$$, $$$Q_{\textrm{u}}^{\left(\textrm{c}\right)}=627$$$, and $$$Q_{\textrm{l}}^{\left(\textrm{c}\right)}=616$$$. The corresponding SNR gain calculated using the first equation yields 2.5 whereas using the final equation yields 1.6.

Imaging experiments, seen in Fig. 4, yielded a room temperature SNR of 55.5 and a cryogenic SNR of 89.7. Hence, the measured SNR gain is 1.62.

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