Sigrun Goluch-Roat^{1}, Martin Vit^{1,2,3}, Albrecht Ingo Schmid^{1}, and Elmar Laistler^{1}

^{31}P-MR spectroscopy measures
cardiac energetics in vivo directly
by means of ATP and PCr, but is limited due to low SNR due to the low MR
sensitivity of the 31P nucleus and limitation by the achievable B_{1}^{+}.
Comprehensive RF coil design considerations and planning help fully exploit the
SNR gain by increase of B_{0}. In this simulation study we compare 28
different ^{31}P 7T RF coil array designs with respect to their
transmit field performance and obtain a 3-channel array as the best variant.

**Introduction**

**Methods**

*Coil design*: Suitable RF coil designs were intended to cover the
average human heart size of 12x8x6 cm^{3} and its location
approximately 2 cm below the sternum [3]. Additionally, the existing ^{1}H
coil housing and 12-channel layout [2] constrained the maximum number of
elements, coil sizes, and shapes. Figure 1 shows all considered RF coil array
configurations, ranging from 2- to 4-channel arrays differing in size and
position, yielding a total number of 28 simulated arrays to be compared.

*3D electromagnetic simulation (EMS)*: The coil designs were constructed
in XFdtd 7.7 (Remcom, State College, PA, USA) using 1 mm thick wire, modeled as
perfect conductor. All capacitors were replaced by 50Ω voltage sources to
enable RF co-simulation in ADS (Keysight Technologies, Santa Rosa, CA, USA) [4].
All designs were simulated as overlap-decoupled arrays, where additional
decoupling, when necessary, was achieved in RF co-simulation with counter-wound
inductances. An overlap factor of 0.86 was used [5]. Realistic loss estimations
for inductances, capacitances, and solder joints were modeled as series
resistances. The array was loaded with a realistic human body model (“Duke”, Virtual Family, IT’IS
Foundation, Zurich, Switzerland). Post-processing of 3D EM data and
co-simulation results was performed in Matlab 2017b (Mathworks, Natick, MA, USA). To compare the
performance of the designs, static B1+ shimming was
obtained by varying the relative phase shift between the array
elements in 5° steps for the 2- and 3- element arrays (72 and 5184 phase sets),
and 10° steps for the 4 element arrays (46656 phase sets), respectively. The
optimum was determined for each array by maximizing a merit function f that is a normalized and equally weighted combination of power
efficiency (PE), SAR efficiency (SE), and relative homogeneity (RH) for a ROI
comprising the heart lumen and muscle identified from the human body model:

$$\small \textbf{PE} = \frac{\overline{B_1^+}}{\sqrt{P_{in}}}, \hspace{0.5cm}\textbf{SE} = \frac{\overline{B_1^+}}{\sqrt{max(SAR_{10g})}},\hspace{0.5cm} \textbf{RH} = 1-\frac{std(B_1^+)}{\overline{B_1^+}},\hspace{0.5cm} \textbf{f}=\frac{1}{3}\left( \frac{PE}{max(PE)} + \frac{SE}{max(SE)}+\frac{RH}{max(RH)}\right)$$

where the maximum refers to the maximum encountered value within all simulated phase combinations for one array layout.

*Choice of the best array*: From the 28 B_{1}^{+}-shim optimized arrays,
the best array was chosen by again calculating the merit function *f*, but with the maximum function in the
formula referring to the maximum value encountered within the set of the 28
individually optimized arrays.

**Results and Discussion**

Matching for all elements was <
-55 dB, inter-element decoupling was always < -14 dB.
Fig. 2 summarizes the results for
the 28 individually optimized designs, together with the merit function* f*. The best design is the 3-channel
array with 9.4x14.1 cm² elements, centered above the heart, the corresponding B_{1}^{+}
maps are shown in Fig. 3. The optimal phase combination for this design
was 0°/-85°/-145°. The mean B_{1}^{+} in the heart ROI was 23.4 µT/sqrt(kW)
and the
10-g maximum SAR was 0.49 kg^{-1}.

**Conclusion**

[1] Valkovič et al. Using a whole-body 31P
birdcage transmit coil and 16-element receive array for human cardiac metabolic
imaging at 7T. PLoS One. 2017; 12(10): e0187153.

[2] Hosseinnezhadian S et al. A flexible 12-channel
transceiver array of transmission line resonators for 7 T MRI. J Magn Reson
2018; 296:47-59

[3] Gordon et al. Anatomy & Physiology. OpenStax 2013

[4] Kozlov M et al. Fast MRI coil analysis based on 3-D electromagnetic and RF
circuit co-simulation. J Magn Reson 2009; 200(1):147-52

[5] Mispelter et al. NMR Probeheads for Biophysical and Biomedical Experiments.
Imperial College Press 2006