Suchit Kumar^{1}, Jeong-Hee Kim^{2}, Heung-Kyu Lee^{3}, and Chang-Hyun Oh^{1,4,5,6}

The elliptical whole-body radiofrequency (RF) coil can be used for RF transmission/reception in magnetic resonance (MR)-guided treatment or MR-fused system with space between the RF shield and the gradient coil available for other imaging/treatment modality. The elliptical birdcage has higher B1^{+} field uniformity than circular birdcage due to increased filling factor between the RF coil and target. In this work, the asymmetric elliptical birdcage is proposed to improve overall performance through electromagnetic simulations. This work compares the 2-port and 4-port excitations and their effects on B1^{+} field uniformity and SAR deposition for both circular and elliptical coil with symmetrical/asymmetrical structures.

In symmetric elliptical birdcage, all
legs are equally distributed in angular direction, and their B1+
field distributions do not seem to provide sufficient uniformity even for
elliptical subjects. To improve the uniformity, asymmetric elliptical birdcage
is introduced by shifting the legs near the RF shield to the optimum position,
and each capacitance is calculated and implemented for EM simulations. Figure 1
shows the circular, elliptical symmetric, and asymmetric birdcage designs and
their dimensions.
To calculate the optimum end-ring
capacitor, the elliptical birdcage theory (eq.1~5) is implemented to calculate
the total inductance and impedance of each leg and end-ring segments including the mirror elements due to the RF shield^{4}.

The optimum current distribution, $$I(θ)=\frac{I_0B^2 cos(θ))}{B^2 cos^2(θ)+A^2 sin^2(θ)}$$ (1)

where A and B are the radius of major- and minor-axes, respectively, and is the angle of each leg position.

The
self-inductance, L_{α,α}, of the end-ring segment, $$ L_{α,α}=2l\left[ln\left(\frac{2l}{w+t}\right)+\frac{1}{2}\right]$$ (2)

where l, w, and t are the length, width, and thickness of the rectangular conductor, respectively.

The mutual inductance, L_{n,m}, between two legs, $$L_{n,m}=2l\left[ln(\frac{l}{d}+\sqrt{1+\frac{l^2}{d^2}})-\sqrt{(1+\frac{d^2}{l^2
})}+\frac{d}{l}\right]$$ (3)

where d is the distance between two legs in centimeters and l is the length of leg.

The total impedance of
each leg, Z_{n}, and the total impedance of one end-ring segment, Z_{α},
are calculated as $$Z_n = \sum_{m=1}^{16} \frac{I_m}{I_n}
j\omega L_{n,m}+\sum_{m=1}^{16}\frac{I_{m^{'}}}{I_n}
j\omega L_{n,{m^{'}}}$$
and $$Z_\alpha=\sum_{\beta=1}^{16}\frac{I_\beta}{I_\alpha}j\omega L_{\alpha,\beta}$$ (4)

Finally,
the optimum capacitor, C_{α}, is calculated as, $$V_n-V_{n+1}=I_α\left[\frac{1}{jωC_α}+Z_α\right]$$ (5)

where $$V_n=\frac{1}{2}I_nZ_n$$ (using Ohm’s law).

EM simulation analysis based on finite-difference
time-domain (FDTD) method was performed using Sim4Life V4.0 in 3-dimensional
(3D) human model^{5,6}. Then, through the EM simulation platform, B1^{+}
field distribution, SAR distribution, and total power required are evaluated
and compared. For the reference, the circular birdcage is implemented with the identical
length and number of legs. In addition, 4- port excitation was evaluated and
compared with 2-port excitation. Figure 2 shows the configuration of simulated
birdcage coils evaluated and compared in this work. After the EM simulation, B1^{+} field uniformity is measured using
the National Electrical Manufacturers Association (NEMA) standard in the 3D region
of interest (ROI) described in Fig. 3. The SAR averaged over any 10g of tissue
in the shape of a cube (10g-avg SAR) and total power normalized to 1 µT are calculated to ensure that the
SAR is under the safety limits provided by regulatory board.

- Kurczewski R, et al. Design of elliptically shaped quadrature pediatric body coils. ISMRM. 1992; 4025.
- Li CS and Smith MB. Theoretical calculations of the optimum current distribution for an elliptical birdcage RF coil. ISMRM. 1993; 1342.
- Ibrahim TS, et al. Comparison between linear, quadrature, and 4-port excitations from 1.5 T to 4.7 T. ISMRM. 1999; 423.
- Li S. et al. A method to create an optimum current distribution and homogeneous B1 field for elliptical birdcage coils. Magnetic resonance in Medicine. 1997; 37(4): 600-608.
- Sim4Life, ZMT, <http://www.zurichmedtech.com>.
- Gosselin MC, et al. Development of a new generation of high-resolution anatomical models for medical device evaluation: the Virtual Population 3.0. Physics in Medicine & Biology 2014: 59(18): 5287.

Figure 1. Schematics
of
circular, symmetric elliptical, and asymmetric elliptical birdcage
coils.

Figure 2. Configuration of circular, symmetric elliptical, and asymmetric
elliptical birdcage coils with 2-port and 4-port.

Figure 3. Description of 3-dimensional region of interest for
B1^{+} field uniformity measurement.

Figure 4. a) B1^{+} field distribution, b) SAR field
distribution in coronal (top) and axial (bottom) planes.

Table 1. B1^{+} field uniformity, total power, mean
10g-avg SAR, and peak 10g-avg SAR [normalized to 1 µT] of all simulated coils. Note: red box represents
the most optimized case.