Seunghoon Ha^{1}, Adam Morris^{1}, Jay Berres^{1}, and Jonathan Nass^{1}

The demand about invivo multi-nuclear MRI/MRS has increased
according to introduction of higher tesla MR system. The development of the dual
frequencies RF coil array keeps pace with this interest. At the overlay of both the proton and second-nucleus frequencies coil loops, inductive
coupling between coils has resolved to retain proton sensitivity and coil
tuning stability by LLC and LC tank circuit. However, they cause another mutual
coupling issue between the circuits and coil loops. Therefore, we introduce a simpler
and more efficient decoupling method than LLC and LC tank circuit in this study.

Our approach preventing from coupling by the higher frequency is to add
the LC series circuit on the loop tracer for x-nucleus frequency ad shown by figure 1(a). The
impedance of the LC series circuit is matched to selectively block current
induced at the proton frequency while minimizing the coil sensitivity at the lower
x-nucleus frequency. It is simply calculated as the equation (1-2). The series resistance (*R*_{s}) by the extra components, especially the inductor, to
the low frequency coil causes slight drop of the coils’ sensitivity. However,
it is adjustable by change of the total blocking impedance determination for the
proton frequency.

$$$Z_{p} = R_{s} + jX_{L} + 1/jX_{c} \approx$$$ high reactance at the proton frequency (1)

$$$Z_{x} = R_{s} + jX_{L} + 1/jX_{c} \approx$$$ zero reactance at the x-nucleus frequency (2)

To verify our proposal, we designed a pair of coplanar
concentric loop coils to simulate the current distribution on the copper loop
tracer and B_{1}^{+} field flux induced in a numerical phantom
with HFSS (ver.15.0, Ansys.Inc, USA). The inner loop coil (10cm outer diameter,
0.5cm width, 1mil thickness) is tuned at the sodium (33.8MHz) and the outer
loop coil (12cm outer diameter, 0.5cm width, 1mil thickness) is targeted at the
proton (127.7MHz) for 3T MRI. The coil geometries are driven by Eigen mode with
1W source. 22AWG hand-wound inductor (2929SQ series, Coilcraft, USA), as the
decoupling inductor, is used with the series resistance (*R*_{s}). Two
buildable hand-wound inductors (508nH and 960nH) with high Q-factor (150) at
the sodium frequency are determined on the equation (1-2). After, the proton
blocking impedances are easily derived as 380ohm and 720ohm. To generate B_{1} field, the numerical phantom,
the conductivity ($$$\sigma$$$) of 0.719s/m and the relative permitity ($$$\epsilon_{r}$$$)
63.5 referred as the muscle tissue, dimensions 14cm diameter and 10cm height.
It is nested 0.5cm above the coils surface (figure 1b). On the pair of coplanar concentric
loop coils, our concept is competed to no-decoupling and LC & LLC tank
circuit presented from previous studies. The frequency response (S11) of each
loop coil, electric current density (J) flowed on the coil surface, B_{1}^{+} field
induced into the phantom are analyzed while these decoupling circuits are
employed on the coils.

1. M. Meyerspeer et al., Magn. Reson. Med. 72:584-590, 2014.

2. J.V. Rispoli et al., Concepts in Magn Reson.46B:4:162-168, 2016.

Figure 1. (a) Circuit diagram for the pair of coplanar
concentric loop coils with LC series decoupling circuit (red dot box). The inner loop is for x-nucleus frequency and the other is for proton frequency. (b) the
aperture about the coil and the phantom setup in HFSS.

Figure 2. Frequency response (S11) calculated with no-decoupling
(a), LCC tank circuit decoupling (b), and LC series circuit decoupling at the
phantom loaded on the coil pair. The response of the coils using LC tank
circuit also kept similar coupling pattern with (b).

Figure 3. Current density distribution on the coil pair,
B_{1}^{+} field induced in the numerical phantom according to different
decoupling methods.

Figure 4. The midline B_{1}^{+} field profile in the phantom. (a) proton frequency field
profile, (b) sodium frequency field profile. The red dot line (no-decoupling),
blue dot line (LCC tank circuit), green dot line (LC tank circuit), blue solid
line (LC series circuit: 720ohm), green solid line (LC series circuit: 380ohm)
are representative for the corresponding circuits.