Synopsis

Peak local specific absorption rate (SAR) is a limiting factor for many high and ultrahigh field MRI applications. Therefore, improving the SAR performance of the transmitters is the scope of many studies. In this study, we used the SAR efficiency (B₁⁺/sqrt(peak local SAR)) as a metric to evaluate the SAR performance of transmitters and investigated its upper bound, defined as Ultimate Intrinsic SAR Efficiency (UISARE). For proof of concept, we derived the UISARE values at 1.5T and 10.5T and compared to the SAR efficiencies of a 1.5T birdcage coil and a 10.5T eight-channel array of fractionated dipoles.

Introduction

Demand for high-field (HF, B0≥3T) MRI is continuously increasing due to its numerous benefits such as significant increase in the SNR^1,2. However, peak local SAR becomes a limiting factor in many applications.^3,4 Using transmit array (TxArray) coils with properly designed elements may provide a good solution to this issue.^5,6

Various TxArray coil designs such as an 8-channel loop array at 3T,⁷ a 16-channel loop-dipole array at 7T,⁸ and a 10-channel fractionated dipole array at 10.5T⁹ were proposed to overcome the SAR issue. However, researchers are still seeking for new designs to improve the SAR performance of the transmitters and introduced the SAR-efficiency¹⁰ (B₁⁺/sqrt(peak local SAR)) as a metric for this performance.

In this study, we utilize EM analytic relations to determine an upper bound for the SAR-efficiency inside a cylindrical homogeneous sample. We introduce this upper bound as the ultimate intrinsic SAR-efficiency (UISARE). For proof of calculations, we compared the results at 1.5T and 10.5T with the results achieved using a commercial EM-simulator.

Theory and Method

The SAR-efficiency at the point of interest (POI) r_i can be defined as follows:

$$\xi =\frac{{{s^T}({r_i})\alpha}}{{\sqrt{{\alpha^H}R({r_p})\alpha}}}$$

where $$${\alpha}$$$ is a complex vector contains coefficients of the cylindrical harmonics. $$$s({r_i})$$$ contains H₁⁺’s corresponding to each cylindrical harmonic with unit coefficient at the POI inside the cylindrical sample. $$$R({r_p})$$$ is the local SAR matrix¹¹ at the position r_p where the peak local SAR occurs.

To maximize the SAR-efficiency at the POI, the following optimization problem can be defined¹²:

$$\begin{array}{*{20}{c}} {{\rm{min}}}&{{\alpha^H}R({r_p})\alpha}&{}&{\alpha\in {C^{2MN\times1}}}\\ {}&{}&{}&{R\in{C^{2MN\times2MN}}}\\ {{\rm{s.t.}}}&{{s^T}({r_i})\alpha=1}&{}&{s\in{C^{2MN \times1}}} \end{array}$$

M and N are the numbers of the cylindrical harmonics in ϕ- and z-directions, respectively. The peak local SAR is defined as P₀. Since R’s are positive semi-definite matrices, the minimization problem above is convex and can be solved for a global optimum. We applied the KKT conditions¹³ to obtain the optimal coefficients and peak local SAR as follows:

$$\begin{array}{l}\alpha=\frac{{{R^{-1}}({r_p}){s^*}({r_i})}}{{{s^T}({r_i}){R^{ -1}}({r_p}){s^*}({r_i})}}\\{P_0}=\frac{{{s^T}({r_i}){R^{-1}}({r_p}){s^*}({r_i})}}{{{{\left|{{s^T}({r_i}){R^{-1}}({r_p}){s^*}({r_i})} \right|}^2}}}\end{array}$$

In this work, a uniform cylindrical sample electrical properties of ε_r=80 and σ=0.6S/m was used for calculations. We investigated how many cylindrical modes would be needed to reach the UISARE for different B₀ field-strengths ranging from 1.5T to 10.5T. Further, at each field strength, UISARE was calculated for different POIs inside the sample.

For proof of the calculations, the-EM simulation of a quadrature-excited birdcage coil (Fig.1a) was performed using an EM-simulator (HFSS) at 1.5T and the result was compared to the UISARE estimated for the center of the sample.

Eventually, the UISARE at the center of the sample at 10.5T was compared to the SAR-efficiency achieved using an 8-channel TxArray coil of fractionated dipoles (Fig.1b). Note that, this array was driven by an RF shimming solution calculated with virtual observation points14 to maximize SAR-efficiency at the origin.

For both 1.5T and 10.5T cases, to determine the limiting factor of the excitation, UISARE at the center was compared to the ultimate intrinsic transmit efficiency^15-17 (UITXE) as well. Furthermore, the 1g-averaging was chosen as the local-averaging to reduce the calculation time.

Results

Fig.2 shows the number of cylindrical modes that is necessary for convergence of the UISARE in different field strengths for different POIs on the central transverse plane.

Utilizing adequately large number of modes, Fig.3a shows the UISARE at different POIs on the x-axis for each of B₀ values, separately. Correspondingly, Fig.3b shows the UISARE versus B₀ values at different POIs.

Fig.4 shows the SAR efficiency maps in 1.5T and 10.5T on a central transverse plane obtained by using the UISARE at the origin and performing EM simulations on the structures of Fig.1.

Considering 2 W/kg and 10 W/kg limits¹⁸ for the whole body and local SAR, respectively, Fig.5a shows that the ultimate whole body SAR^16,17 and local SAR restrict the maximum B₁⁺ at the center at 1.5T and 10.5T, respectively. However, for the simulated birdcage coil, local SAR is the limiting factor. Fig.5b shows the upper bounds of B₁⁺ that can be excited at the center of the 80kg cylindrical uniform sample with consideration of corresponding SAR limits in each case.

Discussion and Conclusion

In this study, we considered the SAR-efficiency as a metric for SAR performance of the transmitters, and calculated the UISARE as an upper bound for this metric. Results show that UISARE can almost be achieved in UHF (B0≥7T) using the recently used TxArray coils with proper shimming strategy. However, at a lower field strength (B0≤3T) the upper bound is significantly higher than the SAR efficiencies achievable with the commonly used birdcage coils. On the other hand, the results show that the limiting cases at 1.5T and 10.5T are whole body and local SAR constraint, respectively.

Our future work will be to characterize the ideal current patterns¹⁷ for UISARE and study the UISARE in realistic body models¹⁹.

Acknowledgements

References

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