Agazi Samuel Tesfai^{1}, Johannes Fischer^{1}, Ali Caglar Oezen^{1}, Ute Ludwig^{1}, and Michael Bock^{1}

A software tool (Multiparameter Analysis Method for B1 Acquisition - MAMBA) to design volume coils is presented for short T2* samples that optimizes relative SNR. MAMBA includes relevant RF coil parameters and evaluates performance. Sample and pulse sequence properties such as T2* relaxation times and echo time (TE) are considered. The tool is tested in a comparison of a commercial head coil and an optimized birdcage coil for imaging of an Egyptian mummy head.

** **MAMBA was designed with Mathematica (Wolfram Research, Inc., Oxfordshire, UK) to support the design and construction of RF coils. It considers multiple coil properties, for example the type (e.g., low pass birdcage coil), conductor shape (round or rectangle) and dimensions for legs and end rings. MAMBA provides the equivalent inductance and capacitor values^{5} to construct the coil, it can verify the resonant frequency, and it gives an approximation of the resistive losses and the Q-factor^{6}. Another important parameter is relative SNR that can be approximated by^{7}

$$SNR\approx { \gamma B_0}\cdot \frac{B_1}{I} \cdot \frac{V_{0}M_{T}}{\sqrt{4k_bT_{coil}R_{eq}\Delta f}}\sqrt{t_{o}/t_{R}}\sqrt{t_{scan}}.$$

By reducing the above equation to purely coil and sample related parameters, a figure of merit (FoM) can be calculated, consisting mainly of coil sensitivity^{8} (B1/I), all resistive losses (e.g. R_{coil}) and transverse magnetization decay^{9} M_{T}(T2*) as followed for birdcage:

$$FoM= \frac{\frac{B_1}{I}\cdot{2 \pi f_0}}{\sqrt{R_{eq}}}=\frac{2\mu_0}{\pi d}\frac{l}{\sqrt{l^{2}+d^{2}}}(1+\frac{d^2}{l^{2}+d^{2}})\zeta(\frac{2\pi f_0}{\sqrt{R_{coil}+R_{sample}+R_{parasitic}}})M_T.$$

A screenshot of the MAMBA user interface is shown in Figure 1. The input values show the properties and dimensions of a newly constructed Tx/Rx birdcage coil (Figure 2a). For comparison, a commercial Tx/Rx head coil (SIEMENS Healthineers, Erlangen, Germany) is used with a high pass birdcage coil design, 16 conductive legs, a diameter of 30cm and a length of 29cm (Figure 2b). The properties of this product coil were also analyzed with MAMBA, and both coils were used for the measurement of an ancient head of an Egyptian mummy (1300 BC, former collection of Musée d’Orbe, Suisse, Figure 3a). Imaging experiments were conducted on a 3T clinical MR system (PRISMA, Siemens Healthcare, Erlangen, Germany) with a 3D UTE sequence using the following parameters: TR=2.5ms, TE=70µs, α=12°, FoV=280mm³, BW=2600Hz/Pixel, 300000 radial spokes, averages=5, TA=1.25h. Further, a T2* map was determined by measuring a range of additional TE (70, 100, 150, 300, 500 and 750µs) with the commercial coil.

MR images of the mummified head acquired with both coils are shown in Figure 3b and c and the corresponding T2* map in Figure 4. Both MR images of the mummy head show an SNR > 40 so that all relevant short T2* tissues such as bone and even the embalming material can be visualized. The MR images were co-registered to allow SNR comparison of selected tissues (cf. Figure 3c), and the results are summarized in Table 1 together with their corresponding T2* times. For example, cortical bone shows an SNR improvement of about 2.1, dentin of 2 and the embalming material of 1.9. The FoM calculated for the custom coil was 2.24 (Figure 1) compared to 1.13 of the product coil, so that MAMBA predicts an SNR gain of 1.98, which is in good agreement with the measurements. The requirement of comparing SNR between different coils is the use of the same measurement protocol (MR system and sequence protocol) which allows determination of a reference value of e.g.

$$$\psi_{ref}=\frac{SNR_{absolut}}{FoM_{coil}}=\frac{SNR_{dentin}}{FoM_{custom}}=\frac{118}{2.24}=52.67.$$$

This allows comparison with other coil designs for same sample and selected ROI. To improve SNR estimation accurate knowledge of T2* and spin density of the different tissues is required. Difference in T2* is small due to close time range (136-161µs) and spin density is not quantified.

MAMBA allows for comparison of various coil designs (e.g. birdcage) and estimation of possible SNR gain based on a FoM including sample properties (short T2* times). Using an absolute SNR value from an initial MR measurement as reference, it can predict the coil performance for modified coil designs by calculating the effective SNR gain with high accuracy (2-7%).

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