Francesca Maggiorelli^{1,2,3}, Alessandra Retico^{2}, Eddy Boskamp^{4}, Fraser Robb^{5}, Angelo Galante^{6}, Marco Fantasia^{6}, Marcello Alecci^{6}, Gianluigi Tiberi^{3}, and Michela Tosetti^{3}

We present a systematic comparison between two dual-tuned (DT) RF coil
models through electromagnetic simulations. The first model (*imbricated*) consists of two
concentrically placed birdcages, whereas the second model (*four-rings*) consists of two High-Pass birdcage-like structures
nested over an internal Low-Pass birdcage. For both DT-RF coil models, the dimensional
parameters have been varied in order to optimize the B_{1}^{+}
field homogeneity and the coil efficiency at the proton (298.03MHz) and sodium
(78.86MHz) Larmor frequency at 7T. Results show that the longest four-rings DT-RF coil model has the best
performances.

**Introduction**

**Methods**

It has been demonstrated that birdcage
coils allow to achieve a superior B_{1}^{+} field homogeneity with
respect to other coil designs, and, in case of quadrature driving, an improved
efficiency^{5}. Both DT-RF coil models we analysed are based on the
birdcage design. Both have been driven in quadrature by two ports positioned
90° apart.
For
each model, the B_{1}^{+} field homogeneity and the coil
efficiency have been computed through full electromagnetic simulation, varying
the model geometrical parameters. The B_{1}^{+} field maps have
been evaluated in the transverse plane (z=0), in the presence of a spherical
phantom that mimics dimension and electrical properties of the human head (radius
r=90mm, electric conductivity σ=0.6S/m, dielectric constant ε_{r}=80), by
means of an electromagnetic simulator (CST MWS) using the Finite-Difference-Time-Domain
(FDTD) algorithm. The B_{1}^{+} field homogeneity has been
evaluated as^{6},

[1-(max(|B_{1}^{+}|)-min(|B_{1}^{+}|)/(max(!B_{1}^{+}|)+min(|B_{1}^{+}|)]

before performing the matching in order to avoid having to restore the unavoidable asymmetries caused by the insertion of the matching network, and thus achieving more reproducible results. Instead, the coil efficiency, evaluated as ,

average(|B_{1}^{+}|/√P_{in})

has been evaluated from
the B_{1}^{+} field maps computed after the matching procedure,
so to neglect power reflection at ports. The two models and the related
variations of the geometrical parameters are reported in Tab.
1.

**Results**

**Discussion**

**Conclusion**

1. J. R. Fitzsimmons, B. L. Beck, H. R. Brooker. Double resonant quadrature birdcage. Magn.Reson. Med. 1993; vol. 30, pp 107-114.

2. A. Galante, M. Fantasia, M. Alecci. Optimization study of a double-tuned nested birdcage RF coil for ^{1}H/^{23}Na
MRI. Proc. Intl. Soc. Mag. Reson. Med. 2018; vol. 26, pp. 1719.

3. J. Murphy-Boesch, R.
Srinivasan, L. Carvajal, R. R. Brown. Two configurations of the four-ring
birdcage coil for 1H imaging and ^{1}H decoupled ^{31}P
spectroscopy of the human head. J. Magn. Reson. 1994; B103, pp 103-114.

4. Maggiorelli
et al. Double Tuned ^{1}H-^{23}Na Birdcage Coils for MRI at 7 T
: Performance evaluation through electromagnetic simulations. 2018 IEEE International Symposium on Medical
Measurements and Applications (MeMeA)
4. Hoult, C. Chen, V.
Sank. Quadrature detection in the laboratory frame. Magn, Reson. Med. 1984;
vol. 1, no. 3.

5. National Electrical Manufacturers Association. Determination of Image Uniformity in Diagnostic Magnetic Resonance Images. NEMA Standards Publication, MS 3-2008 (R2014).

Tab. 1 In a) Geometrical
configurations of the *four-ring* DT-RF coil model. In b) Geometrical configurations of the *imbricated* DT-RF
coil model.

Tab. 2 In
a) B_{1}^{+} field homogeneity evaluated for the *four-ring* (in
a.1, a.3 and a.5) and for the *imbricated* model (in a.2, a.4 and a.6). In b)
DT-RF coil efficiency evaluated for the *four-ring* (in b.1, b.3 and b.5) and for
the *imbricated* model (in b.2, b.4 and b.6).