Improving Specific Absorption Rate Efficiency and Coil Robustness of Self-Decoupled Transmit/Receive Coils by Elevating Feed and Mode Conductors

Self-decoupling technology was recently proposed for radio frequency (RF) coil array designs. Here, we propose a novel geometry to reduce the peak local specific absorption rate (SAR) and improve the robustness of the self-decoupled coil. We first demonstrate that B1 is determined by the arm conductors, while the maximum E-field and local SAR are determined by the feed conductor in a self-decoupled coil. Then, we investigate how the B1, E-field, local SAR, SAR efficiency, and coil robustness change with respect to different lift-off distances for feed and mode conductors. Next, the simulation of self-decoupled coils with optimal lift-off distances on a realistic human body is performed. Finally, self-decoupled coils with optimal lift-off distances are fabricated and tested on the workbench and MRI experiments. The peak 10 g-averaged SAR of the self-decoupled coil on the human body can be reduced by 34% by elevating the feed conductor. Less coil mismatching and less resonant frequency shift with respect to loadings were observed by elevating the mode conductor. Both the simulation and experimental results show that the coils with elevated conductors can preserve the high interelement isolation, B1+ efficiency, and SNR of the original self-decoupled coils.

Decoupling is crucial to RF arrays because interelement coupling decreases the SNR and Tx efficiency, reduces the encoding capability, and makes individual B 1 profiles less distinct. To date, many decoupling approaches have been proposed and used for coil arrays, such as geometric overlap, transformers, interconnecting L/C networks, and induced current elimination [3,[26][27][28][29][30][31][32]. We recently proposed self-decoupled coils, which proved to be a simple and efficient approach to maintain extremely low interelement coupling without the need for any decoupling approaches [33]. In particular, they can be applied for Tx coils as well as Rx coils, as the mode of operation is independent of the subsequent circuit parameters, such as preamplifier impedance.
The self-decoupled coil uses intentionally uneven capacitor/current distributions along the conductor to generate dipole-mode (or electric) coupling to cancel the loop-mode (magnetic) coupling [33]. Our previous results revealed that it exhibits almost the same performance compared to an ideal conventional coil in terms of SNR, B 1 + efficiency, and SAR efficiency when positioned several centimeters away from the loading [33]. The SAR efficiency is evaluated as the B 1 + strength per root of the square of the maximum 10 gaveraged local SAR (maxSAR 10g ), representing the achievable B 1 + for a given local SAR limit. Note that the SAR efficiency is also known as the B 1 + SAR efficiency, and the two terms are interchangeably used here. When the self-decoupled coil was placed close to the loading, e.g.,~1 cm away from the loading in the transmit/receive applications, we noted that the strong current on the conductor near the feed port (herein referred to as the feed conductor) leads to a higher maximum local SAR. Meanwhile, we noted that the coil impedance and resonant frequency of self-decoupled coils are more sensitive to loading, partly because small mode capacitors (C mode ) are more likely to be affected by the parasitic capacitance between the coil and loading.
When looking into the electromagnetic fields generated by different conductors in a self-decoupled coil, we found that (1) the rotating magnetic fields (B 1 = B x ± iB y ) [34] are determined by the currents along the arm conductors; (2) the maximum electrical (E-) field and local SAR are determined by the feed conductor where the strongest current occurs; and (3) the coil is sensitive to loading, partly because of the small capacitors on the mode conductor. Therefore, we might be able to reduce the maximum local SAR (i.e., improve the B 1 + SAR efficiency) and improve the coil robustness by elevating only the feed conductor and mode conductor. Note that the arm conductors would NOT be elevated to maintain the transmit efficiency and coil sensitivity. Therefore, unlike the conventional self-decoupled coil where all conductors are on the same planar surface [33], the proposed method here is a three-dimensional design in which the conductors are arranged intentionally on an uneven surface.
In this work, we first numerically investigated how the B 1 efficiency and local SAR change with a spaced mode conductor and a spaced feed conductor but unchanged arm conductors on a water phantom. Then, we simulated the self-decoupled coil array with optimal lift-off distances on the human body and evaluated its performance. Next, a pair of transmit/receive self-decoupled coils with optimal lift-off distances was built and tested on the workbench. Finally, their B 1 + efficiency and SNR, which are expected to be the same as those of the original self-decoupled coils, were tested and compared through MRI experiments.

Concept
Based on Ampere's Law, the magnetic field generated by a straight conductor wraps around it. Therefore, magnetic fields from the feed conductor (orange in Figure 1A) and mode conductor (yellow in Figure 1A) are mainly along the z-direction, which contributes much less to B 1 . Meanwhile, the feed conductor with the strongest current generates the strongest E-field and thus determines the maximum local SAR. Figure 1B plots the magnitudes of the B 1 + field (central axial slice) and E-field (coronal slice close to the coil) generated by these four individual conductors. Each conductor was driven with a series of current sources, with current magnitudes set to match those in a same-sized self-decoupled coil (10 × 10 cm 2 ). The simulated B 1 and E-fields clearly validated the assumption that B 1 is unlikely to decrease when elevating feed and mode conductors, providing the foundation for this work. The concept simulations and the subsequent simulations for optimal lift-off distances were performed with an FEM-based Maxwell solver (HFSS, Ansys, Canonsburg, PA, USA) and an RF circuit simulator (Designer, Ansys, Canonsburg, PA, USA).
lift-off distances were performed with an FEM-based Maxwell solver (HFSS, Ansys, Canonsburg, PA, USA) and an RF circuit simulator (Designer, Ansys, Canonsburg, PA, USA).  Figure 1A), while the maximum local E field is determined by the feed conductor (orange in Figure 1A).

Simulation
We first numerically investigated how the E-field, B1, local SAR, B1 + SAR efficiency, coil impedance, and resonant frequency change when elevating the mode conductor. As shown in Figure 2A, pairs of 10 × 10 cm 2 self-decoupled coils were modeled (conductor width 5 mm, coils are 5 mm apart) in Ansys HFSS. Similar to the design in the original self-decoupled coil [33], each coil has a parallel capacitor for matching (Cm), two lumped components on the arm conductors for tuning (Xarm), and five Cmodes for decoupling. Various lift-off spacings of the mode conductor (Dmode in Figure 2A, from 0 cm to 4 cm in steps of 0.5 cm) were investigated, with all other conductors unchanged. In this assessment, a cuboidal phantom (30 × 15 × 15 cm 3 ) was placed 1 cm below the coil as the loading. The electromagnetic (EM) properties of the phantom were chosen to be similar to those of human tissue and the same as those of a practical saline phantom, with conductivity σ = 0.6 S/m and relative permittivity εr = 78. The B1 efficiencies correspond to the B1 magnitudes normalized to the 1-watt input power. Considering that RF safety at ultrahigh fields is most likely limited by the local SAR instead of the global SAR [35][36][37], we did not investigate the global SAR changes. For each Dmode, self-decoupled coils were first welltuned/matched/decoupled when the coil-to-phantom distance was 1 cm. Then, the coils were moved closer or further away from the phantom, with no retuning or rematching. The resonance frequency shift and impedance matching were recorded when moving the coils.
Similarly, we numerically investigated how the E-field, B1 + , B1 − , and B1 + SAR efficiency change when elevating the feed conductor. Various lift-off spacings of the feed conductor (Dfeed in Figure 2B, from 0 cm to 4 cm in steps of 0.5 cm) were investigated, with all other conductors unchanged. To ascertain whether elevating the feed conductor affects the decoupling performance, we also recorded the transmission coefficient (S21) between the elements of the self-decoupled coil array. To match the real case, these self-decoupled coils were all well-tuned, matched, and decoupled following the method described in our previous work [33].
Furthermore, we simulated a pair of self-decoupled coil arrays with an optimal Dfeed of 2 cm on the human spine ( Figure 2D) and compared them to the original self-decoupled  Figure 1A), while the maximum local E field is determined by the feed conductor (orange in Figure 1A).

Simulation
We first numerically investigated how the E-field, B 1 , local SAR, B 1 + SAR efficiency, coil impedance, and resonant frequency change when elevating the mode conductor. As shown in Figure 2A, pairs of 10 × 10 cm 2 self-decoupled coils were modeled (conductor width 5 mm, coils are 5 mm apart) in Ansys HFSS. Similar to the design in the original self-decoupled coil [33], each coil has a parallel capacitor for matching (C m ), two lumped components on the arm conductors for tuning (X arm ), and five C modes for decoupling. Various lift-off spacings of the mode conductor (D mode in Figure 2A, from 0 cm to 4 cm in steps of 0.5 cm) were investigated, with all other conductors unchanged. In this assessment, a cuboidal phantom (30 × 15 × 15 cm 3 ) was placed 1 cm below the coil as the loading. The electromagnetic (EM) properties of the phantom were chosen to be similar to those of human tissue and the same as those of a practical saline phantom, with conductivity σ = 0.6 S/m and relative permittivity ε r = 78. The B 1 efficiencies correspond to the B 1 magnitudes normalized to the 1-watt input power. Considering that RF safety at ultrahigh fields is most likely limited by the local SAR instead of the global SAR [35][36][37], we did not investigate the global SAR changes. For each D mode , self-decoupled coils were first welltuned/matched/decoupled when the coil-to-phantom distance was 1 cm. Then, the coils were moved closer or further away from the phantom, with no retuning or rematching. The resonance frequency shift and impedance matching were recorded when moving the coils.
Similarly, we numerically investigated how the E-field, B 1 + , B 1 − , and B 1 + SAR efficiency change when elevating the feed conductor. Various lift-off spacings of the feed conductor (D feed in Figure 2B, from 0 cm to 4 cm in steps of 0.5 cm) were investigated, with all other conductors unchanged. To ascertain whether elevating the feed conductor affects the decoupling performance, we also recorded the transmission coefficient (S 21 ) between the elements of the self-decoupled coil array. To match the real case, these self-decoupled coils were all well-tuned, matched, and decoupled following the method described in our previous work [33].
Furthermore, we simulated a pair of self-decoupled coil arrays with an optimal D feed of 2 cm on the human spine ( Figure 2D) and compared them to the original self-decoupled coil array ( Figure 2C). All coils are simulated for 7T, with an RF/Larmor frequency of 298 MHz. Both the local SAR and B 1 + SAR efficiency were evaluated.
coil array ( Figure 2C). All coils are simulated for 7T, with an RF/Larmor frequency of 298 MHz. Both the local SAR and B1 + SAR efficiency were evaluated.

Coil Fabrication, Bench Test, and MRI Experiment
Based on the numerical investigations, we built a pair of self-decoupled coils with optimal Dmode and Dfeed. Details of the choices of Dmode and Dfeed are provided in the Results section. For comparison, we also built a pair of original self-decoupled coils without any elevated conductors [33]. The values of all lumped elements were initially chosen based on the simulation results and then finely tuned by adjusting the trimmers (Johanson Manufacturing, 52 H Series, Boonton, NJ, USA) and air-core inductors (~25 nH). Bench tests were performed on an octagonal body phantom (~45 L, 1.24 g/L CuSO4 × 6H2O and 2.6 g/L NaCl) using a four-port Vector Network Analyzer (Keysight 5071C).
We measured B1 + maps on a body-shaped phantom (1 cm below coils) using the original and optimized self-decoupled coils. Individual B1 + maps were measured using the DREAM method [38] (field of view (FOV) = 400 × 224 mm 2 , TR = 1000 ms, voxel size = 2 × 2 mm 2 and slice thickness = 10 mm) with the same input power. We also acquired lowflip-angle gradient echo (GRE, TR/TE = 1000/2.5 ms, FOV = 400 × 256 mm 2 , nominal flip angle = 15°, voxel size = 2 × 2 mm 2 and slice thickness = 5 mm) images of individual coils for SNR assessment. SNR values were calculated from individual GRE images as SI/std(noise) × 0.655, where SI is the signal and std(noise) is the standard deviation of the noise maps. MRI experiments were performed on a Philips Achieva 7T whole-body scanner (Philips Healthcare, Best, The Netherlands).

Coil Fabrication, Bench Test, and MRI Experiment
Based on the numerical investigations, we built a pair of self-decoupled coils with optimal D mode and D feed . Details of the choices of D mode and D feed are provided in the Results section. For comparison, we also built a pair of original self-decoupled coils without any elevated conductors [33]. The values of all lumped elements were initially chosen based on the simulation results and then finely tuned by adjusting the trimmers (Johanson Manufacturing, 52 H Series, Boonton, NJ, USA) and air-core inductors (~25 nH). Bench tests were performed on an octagonal body phantom (~45 L, 1.24 g/L CuSO 4 × 6H 2 O and 2.6 g/L NaCl) using a four-port Vector Network Analyzer (Keysight 5071C).
We measured B 1 + maps on a body-shaped phantom (1 cm below coils) using the original and optimized self-decoupled coils. Individual B 1 + maps were measured using the DREAM method [38] (field of view (FOV) = 400 × 224 mm 2 , TR = 1000 ms, voxel size = 2 × 2 mm 2 and slice thickness = 10 mm) with the same input power. We also acquired low-flip-angle gradient echo (GRE, TR/TE = 1000/2.5 ms, FOV = 400 × 256 mm 2 , nominal flip angle = 15 • , voxel size = 2 × 2 mm 2 and slice thickness = 5 mm) images of individual coils for SNR assessment. SNR values were calculated from individual GRE images as SI/std(noise) × 0.655, where SI is the signal and std(noise) is the standard deviation of the noise maps. MRI experiments were performed on a Philips Achieva 7T whole-body scanner (Philips Healthcare, Best, The Netherlands). E-field and local SAR were plotted on the coronal slice that was closest to the coil. We chose this slice to present the E-field and local SAR results because that is where the maximum E-field and SAR occur. Figure 3B,D plot the average B 1 + and B 1 + SAR efficiency at the surface and middle areas with respect to D mode . The average B 1 + values were taken from two regions fixed in the phantom. The surface area (1.5 × 1.5 cm 2 ) was immediately below the top surface of the phantom. The middle area (1.5 × 1.5 cm 2 ) was 5 cm below the top surface of the phantom. Figure 4C plots the maxSAR 10g with different D mode . The B 1 efficiency, B 1 + SAR efficiency, and maxSAR 10g remain the same, even when D mode increases to 4 cm. Figure 3E plots the largest frequency shifts when moving coils closer to or further away from the phantom. Coils exhibit less frequency shift as D mode increases. This occurs because C mode is not easily affected by the parasitic capacitance (between coil and loading) when the mode conductor and mode capacitors are elevated. Figure 3F,G plot the coil impedance (evaluated by S 11 and S 21 ) with respect to D mode . The impedance variation shows a similar trend to that of the frequency shift. However, the improvement in impedance is modest, which could be attributed to coils' wide bandwidth (i.e., low quality factor), so the return loss does not change much when the resonant frequency is shifted. The curves in Figure 3E-G start to flatten when D mode > 1 cm. In this work, we chose a D mode of 2 cm for practical coil fabrication.  Figure 3A shows the B1 + , E-field, and local SAR maps with respect to Dmode. B1 + maps and B1 + SAR efficiency were plotted on the central axial slice of the phantom, while E-field and local SAR were plotted on the coronal slice that was closest to the coil. We chose this slice to present the E-field and local SAR results because that is where the maximum Efield and SAR occur. Figure 3B,D plot the average B1 + and B1 + SAR efficiency at the surface and middle areas with respect to Dmode. The average B1 + values were taken from two regions fixed in the phantom. The surface area (1.5 × 1.5 cm 2 ) was immediately below the top surface of the phantom. The middle area (1.5 × 1.5 cm 2 ) was 5 cm below the top surface of the phantom. Figure 4C plots the maxSAR10g with different Dmode. The B1 efficiency, B1 + SAR efficiency, and maxSAR10g remain the same, even when Dmode increases to 4 cm. Figure 3E plots the largest frequency shifts when moving coils closer to or further away from the phantom. Coils exhibit less frequency shift as Dmode increases. This occurs because Cmode is not easily affected by the parasitic capacitance (between coil and loading) when the mode conductor and mode capacitors are elevated. Figure 3F,G plot the coil impedance (evaluated by S11 and S21) with respect to Dmode. The impedance variation shows a similar trend to that of the frequency shift. However, the improvement in impedance is modest, which could be attributed to coils' wide bandwidth (i.e., low quality factor), so the return loss does not change much when the resonant frequency is shifted. The curves in Figure 3E-G start to flatten when Dmode > 1 cm. In this work, we chose a Dmode of 2 cm for practical coil fabrication.  Figure 4A shows the simulated B1 + , B1 − , B1 + SAR efficiency, E-field, and local SAR maps with respect to Dfeed. Figure 4B plots the average B1 + at the surface and middle areas  Figure 4A shows the simulated B 1 + , B 1 − , B 1 + SAR efficiency, E-field, and local SAR maps with respect to D feed . Figure 4B plots the average B 1 + at the surface and middle areas with respect to D feed . It is noted that B 1 + efficiency was not affected when D feed was 2 cm or less, with the B 1 + variation <3%. This is also true for B 1 − efficiency, as shown in Figure 4C. These results indicate that elevating the feed conductor would not impair the B 1 + efficiency or receive SNR, as expected from the Concept section. Figure 4D shows the maxSAR 10g with different D feed s. Up to a 26% reduction of a maximum of 10 g SAR was observed when the feed conductor was elevated by 2 cm. The B 1 + SAR efficiency (both the surface and middle areas) achieves the highest value when D feed is approximately 2 cm, as shown in Figure 4E. A D feed of 2 cm was thereby chosen for simulation on human spine and practical coil fabrication. with respect to Dfeed. It is noted that B1 + efficiency was not affected when Dfeed was 2 cm or less, with the B1 + variation <3%. This is also true for B1 − efficiency, as shown in Figure 4C.

Simulation Results
These results indicate that elevating the feed conductor would not impair the B1 + efficiency or receive SNR, as expected from the Concept section. Figure 4D shows the maxSAR10g with different Dfeeds. Up to a 26% reduction of a maximum of 10 g SAR was observed when the feed conductor was elevated by 2 cm. The B1 + SAR efficiency (both the surface and middle areas) achieves the highest value when Dfeed is approximately 2 cm, as shown in Figure 4E. A Dfeed of 2 cm was thereby chosen for simulation on human spine and practical coil fabrication.  Figure 5 plots the B1 + efficiency, SAR10g, and B1 + SAR efficiency maps of the original self-decoupled coil [33] and optimized self-decoupled coil with a Dfeed of 2 cm. B1 + maps and B1 + SAR efficiency are shown in the central axial slice, while SAR10g is shown in the axial slice that is close to the feed port. We chose this slice to show SAR10g, as the maximum SAR10g is located near the feed conductor. Compared with the original self-decoupled coil, the B1 + SAR efficiency of the optimized self-decoupled coil has 11.5% and 18.8% improvements at the surface and in the middle areas of the human body, respectively.  Figure 5 plots the B 1 + efficiency, SAR 10g , and B 1 + SAR efficiency maps of the original self-decoupled coil [33] and optimized self-decoupled coil with a D feed of 2 cm. B 1 + maps and B 1 + SAR efficiency are shown in the central axial slice, while SAR 10g is shown in the axial slice that is close to the feed port. We chose this slice to show SAR 10g , as the maximum SAR 10g is located near the feed conductor. Compared with the original self-decoupled coil, the B 1 + SAR efficiency of the optimized self-decoupled coil has 11.5% and 18.8% improvements at the surface and in the middle areas of the human body, respectively.  Figure 6A shows the fabricated original and optimized self-decoupled coils, and Figure 6B plots the measured scattering (S-) parameters when they were placed 1 cm above the phantom. Note that a cable trap was employed for each coil to suppress the commonmode current, but it is not shown in Figure 6A. Both the original and optimized coils achieve excellent decoupling performance, with S21 < −20 dB. Figure 6C,D compare their measured B1 + and SNR. As expected, coils without and with elevated conductors exhibit almost the same B1 + and SNR. Figure 6E shows the resonant frequency shift and coils' input impedance with respect to the coil-to-phantom distance. Consistent with the simulation, the coil with elevated conductors demonstrated more robust tuning/matching performance, with the worst S11 of −11.3 dB (vs. −7.5 dB) and the largest frequency shift of 17.2 MHz (vs. 28.2 MHz).  Figure 6A shows the fabricated original and optimized self-decoupled coils, and Figure 6B plots the measured scattering (S-) parameters when they were placed 1 cm above the phantom. Note that a cable trap was employed for each coil to suppress the common-mode current, but it is not shown in Figure 6A. Both the original and optimized coils achieve excellent decoupling performance, with S 21 < −20 dB. Figure 6C,D compare their measured B 1 + and SNR. As expected, coils without and with elevated conductors exhibit almost the same B 1 + and SNR. Figure 6E shows the resonant frequency shift and coils' input impedance with respect to the coil-to-phantom distance. Consistent with the simulation, the coil with elevated conductors demonstrated more robust tuning/matching performance, with the worst S 11 of −11.3 dB (vs. −7.5 dB) and the largest frequency shift of 17.2 MHz (vs. 28.2 MHz).

Discussion
For all scenarios with different Dmodes and Dfeeds, the coil isolation is at the same level of approximately −20 dB, as shown in Figure 7. This means only ~1% power crosstalk between the coils, which is sufficient for both Rx and Tx applications. This also indicates that the lift-off of the feed and/or mode conductor does not affect the decoupling performance and does not need to be considered during the optimization of Dmode and Dfeed.

Discussion
For all scenarios with different D mode s and D feed s, the coil isolation is at the same level of approximately −20 dB, as shown in Figure 7. This means only~1% power crosstalk between the coils, which is sufficient for both Rx and Tx applications. This also indicates that the lift-off of the feed and/or mode conductor does not affect the decoupling performance and does not need to be considered during the optimization of D mode and D feed .
The lift-off conductor design is mainly for transmit/receive applications where the selfdecoupled coil is positioned close to the loading/tissue to maximize the receive sensitivity. For the Tx-only self-decoupled coil, which is typically several centimeters away from loading, there is significantly less improvement or even a decrease in B 1 + SAR efficiency. Figure 8 shows how the B 1 and maximum local SAR change when elevating the feed conductor for a self-decoupled coil that was already positioned 4 cm away from the loading.
We noted that the B 1 + SAR efficiency in the middle area increased by only~1%, and this efficiency at the surface area even decreased for any lift-off distance. The lift-off conductor design is mainly for transmit/receive applications where the self-decoupled coil is positioned close to the loading/tissue to maximize the receive sensitivity. For the Tx-only self-decoupled coil, which is typically several centimeters away from loading, there is significantly less improvement or even a decrease in B1 + SAR efficiency. Figure 8 shows how the B1 and maximum local SAR change when elevating the feed conductor for a self-decoupled coil that was already positioned 4 cm away from the loading. We noted that the B1 + SAR efficiency in the middle area increased by only ~1%, and this efficiency at the surface area even decreased for any lift-off distance. It should be noted that simply elevating all conductors would significantly reduce the B1 + and B1 − efficiency and is therefore not recommended, as shown in the first row of Figure 9. It is interesting that as the lift-off distance increases, the B1 + (also B1 − ) efficiency at the surface area decreases much faster than that at the middle area. As a result, the B1 +  The lift-off conductor design is mainly for transmit/receive applications where the self-decoupled coil is positioned close to the loading/tissue to maximize the receive sensitivity. For the Tx-only self-decoupled coil, which is typically several centimeters away from loading, there is significantly less improvement or even a decrease in B1 + SAR efficiency. Figure 8 shows how the B1 and maximum local SAR change when elevating the feed conductor for a self-decoupled coil that was already positioned 4 cm away from the loading. We noted that the B1 + SAR efficiency in the middle area increased by only ~1%, and this efficiency at the surface area even decreased for any lift-off distance. It should be noted that simply elevating all conductors would significantly reduce the B1 + and B1 − efficiency and is therefore not recommended, as shown in the first row of Figure 9. It is interesting that as the lift-off distance increases, the B1 + (also B1 − ) efficiency at the surface area decreases much faster than that at the middle area. As a result, the B1 + It should be noted that simply elevating all conductors would significantly reduce the B 1 + and B 1 − efficiency and is therefore not recommended, as shown in the first row of Figure 9. It is interesting that as the lift-off distance increases, the B 1 + (also B 1 − ) efficiency at the surface area decreases much faster than that at the middle area. As a result, the B 1 + SAR decreased by up to 23% in the surface area, while it slightly increased in the middle area when the whole coil was elevated by 4 cm. SAR decreased by up to 23% in the surface area, while it slightly increased in the middle area when the whole coil was elevated by 4 cm. Figure 9. Simulated B1 + efficiencies, E-fields, local SARs, and B1 + SAR efficiencies of self-decoupled coils when elevating the whole coil, i.e., all conductors, instead of only the mode and feed conductors. An obvious B1 decrease was observed and therefore this design is not recommended.
For simplicity and clarity, we optimized Dmode and Dfeed separately, which is reasonable considering that the SAR efficiency and coil robustness are separately determined by Dfeed and Dmode. In addition to the loop-type self-decoupled coil studied here, this elevated conductor design could be extended to loopole-mode [39,40] self-decoupled coils where the feed conductor orientates along the z-direction instead of perpendicular to the z-direction. In this case, the feed conductor plays two roles in B1 + SAR efficiency: its lift-off will change B1 + as well as the maximum SAR. Another parameter one can optimize for improved B1 + SAR efficiency and coil robustness is the dielectric constant of the substrate underneath the feed and mode conductors.

Conclusions
We propose a novel geometry to reduce the local SAR and improve the robustness of self-decoupled coils. A significant reduction in the maximum local SAR and a moderate improvement in the coil robustness were obtained by elevating the feed and mode conductors. We also confirmed that elevating these conductors does not impair the SNR or transmit efficiency.   For simplicity and clarity, we optimized D mode and D feed separately, which is reasonable considering that the SAR efficiency and coil robustness are separately determined by D feed and D mode . In addition to the loop-type self-decoupled coil studied here, this elevated conductor design could be extended to loopole-mode [39,40] self-decoupled coils where the feed conductor orientates along the z-direction instead of perpendicular to the z-direction. In this case, the feed conductor plays two roles in B 1 + SAR efficiency: its lift-off will change B 1 + as well as the maximum SAR. Another parameter one can optimize for improved B 1 + SAR efficiency and coil robustness is the dielectric constant of the substrate underneath the feed and mode conductors.

Conclusions
We propose a novel geometry to reduce the local SAR and improve the robustness of self-decoupled coils. A significant reduction in the maximum local SAR and a moderate improvement in the coil robustness were obtained by elevating the feed and mode conductors. We also confirmed that elevating these conductors does not impair the SNR or transmit efficiency.