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Multiparameter Analysis Method for B1 Acquisition (MAMBA): A tool for RF coil design and SNR estimation for short T2* samples
Agazi Samuel Tesfai1, Johannes Fischer1, Ali Caglar Oezen1, Ute Ludwig1, and Michael Bock1

1Department of Radiology, Medical Physics, Medical Center University of Freiburg, Faculty of Medicine, University of Freiburg, Freiburg, Germany

### Synopsis

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.

### Introduction

In RF coil design, one aim is to achieve an effective SNR gain over existing commercially available coils. Construction and manufacturing of multiple coil iterations or numerical simulations1 are time-consuming and not very cost-effective – thus, it is desirable to have a fast and efficient tool to compare coil performances. Available software tools2,3 mostly focus on construction of the RF coil and do not provide information about the attainable performance. In this work, the software tool MAMBA (Multiparameter Analysis Method for B1 Acquisition) is demonstrated which is based on analytical expressions of coil properties. MAMBA allows for estimation of the relative SNR improvement of volume coil designs. In particular, the work focuses on imaging of ancient remains which is challenging due to their ultra-short T2* relaxation times4. T2* is also considered in MAMBA as it requires fast coil switching times (short TE) for optimal signal acquisition. The aim of this experiment is to quantify the estimated SNR improvement of an available product coil compared to a newly constructed birdcage coil for an Egyptian mummy head.

### Materials and Methods

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 values5 to construct the coil, it can verify the resonant frequency, and it gives an approximation of the resistive losses and the Q-factor6. Another important parameter is relative SNR that can be approximated by7

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

By reducing the above equation to purely coil and sample related parameters, a figure of merit (FoM) can be calculated, consisting mainly of coil sensitivity8 (B1/I), all resistive losses (e.g. Rcoil) and transverse magnetization decay9 MT(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.

### Results and Discussion

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.

### Conclusion

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%).

### Acknowledgements

Grant support from the Deutsche Forschungsgemeinschaft (DFG) under grant numbers BO 3025/8-1 and UL 1187/6-1 is gratefully acknowledged.

### References

[1] N. Gurler et al. "Numerical methods and software tools for simulation, design, and resonant mode analysis of radio frequency birdcage coils used in MRI." Concepts in Magnetic Resonance Part B: Magnetic Resonance Engineering 45.1 S. 13-32. 2015.

[2] G. Giovannetti et al. "A fast and accurate simulator for the design of birdcage coils in MRI." Magnetic Resonance Materials in Physics, Biology and Medicine 15.1-3 S. 36-44. 2002.

[3] C.L. Chin et al. "BirdcageBuilder: design of specified‐geometry birdcage coils with desired current pattern and resonant frequency." Concepts in Magnetic Resonance: An Educational Journal 15.2 S 156-163. 2002.

[4] A.C. Özen et al. "Comparison of ultrashort echo time sequences for MRI of an ancient mummified human hand." Magnetic resonance in medicine 75.2 S 701-708. 2016.

[5] G. Giovannetti Birdcage coils: "Equivalent capacitance and equivalent inductance." Concepts in Magnetic Resonance Part B: Magnetic Resonance Engineering, 44(2) S 32-38. 2014.

[6] D.I. Hoult & P.C. Lauterbur “The sensitivity of the zeugmatographic experiment involving human samples” Journal of Magnetic Resonance (1969), 34(2), S 425-433. 1979.

[7] L. Darrasse. "Perspectives with cryogenic RF probes in biomedical MRI". Biochimie 85.9, S 915–937. 2003.

[8] J. Mispelter. "NMR probeheads for biophysical and biomedical experiments". Imperial College Press and Distributed by World Scientific, 2006.

[9] F. Springer et al. "Effects of in-pulse transverse relaxation in 3D ultrashort echo time sequences: Analytical derivation, comparison to numerical simulation and experimental application at 3 T." Journal of Magnetic Resonance 206.1 S 88-96. 2010.

### Figures

Figure 1: The user interface of the MAMBA tool for setting all required RF coil parameters by means of sliders or buttons. The results are displayed immediately in the output window and show calculated values for a lumped element, noise levels and SNR gain to a reference value.

Figure 2: Experimental setup with used RF coils and inserted Mummy head sample in a) the newly constructed Tx/Rx high-pass birdcage coil that runs in circular polarized (CP) mode and b) the commercial Tx/Rx head birdcage coil with 16 rugs and CP mode.

Figure 3: (a) Egyptian mummy head and corresponding sagittal MR images acquired with (b) the custom and (c) the commercial RF coil. Regions of Interest (ROI) for SNR calculation are displayed in yellow.

Figure 4: Acquired T2* map of the corresponding slice with commercial RF coil.

Table 1: SNR comparison of different tissues between investigated coils and comparison with Figure of Merit (FoM) calculation using measured T2* value. The ROIs for SNR calculation are displayed in Fig. 3.

Proc. Intl. Soc. Mag. Reson. Med. 27 (2019)
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