Introduction

Magnetic resonance imaging (MRI) is a widely used non-invasive medical imaging modality that provides a variety of high-resolution images of the human body, with versatile soft-tissue and functional contrast1. The radiofrequency (RF) coils used in an MRI scanner to transmit RF energy into the body and receive signals from it play a critical role in determining image quality in terms of signal-to-noise ratio (SNR) and image uniformity, as well as other technical constraints on scanner performance. For three decades, arrays of receive coils have been used in MRI to achieve flexible coverage of large imaging volumes with high SNR2,3, and to accelerate scans using parallel imaging techniques4,5,6,7,8. Advances in RF array performance have usually come through increasing the number of coils in the array6,9,10. For example, receive arrays with large numbers of coils (≥32) have been fundamental to recent advances in the speed, sensitivity and resolution of neuroimaging8,11,12. 3 Tesla MRI scanners used for clinical applications are today equipped with 32 receiver channels as standard, and array coils are used exclusively for signal reception. Array coils are also used for RF transmission at ultra-high magnetic field strengths (7 Tesla and higher), as a means to achieve spatially homogeneous transmit RF fields in a patient-adaptive manner, while controlling tissue heating (quantified as global and local specific absorption rate (SAR)13,14,15,16,17). In that application, increasing the number of coils in the array improves power efficiency and image uniformity. Current 7 Tesla scanners are typically equipped with 8 transmit channels, and there have been reports of systems developed with as many as 3218 channels. Even for scanners with a smaller number of transmit channels, the benefits of many-coil transmit arrays can be realized using array-compression networks19.

The most widely used RF coil array element is a resonant loop coil comprising a circle or rectangle of copper wire or tape, which is uniformly segmented along its length by identical impedances (usually capacitors) to achieve a uniform current distribution and avoid antenna effects. When assembled into an array, these loops electromagnetically couple to each other due to magnetic flux linkage, which is referred to as loop-mode coupling. Minimizing this coupling is a central challenge in building RF coil arrays with many coil elements. When receiving RF signals from the body, strong coupling can lead to noise amplification and may limit the degree to which image acquisition can be accelerated using parallel imaging. When transmitting RF energy into the body, coupled power is absorbed by protection circuits and wasted. These and other power losses necessitate the use of very large RF amplifiers, with high cost and siting requirements. Transmit coil coupling also limits the ability to control the shape of the RF fields produced within the subject being scanned, because each coil’s transmit field profile becomes less distinct from those of its neighbours.

The most common strategy to minimize array coil coupling is to partially overlap adjacent loops. In receive coil arrays, overlap** is combined with low-impedance preamplifier decoupling, which minimizes coupling between non-adjacent elements3. Other less common decoupling methods have been described including transformers20, inter-connecting capacitive/inductive networks21,22,23,24,25,26, and passive resonators47,48,49. In flexible coil designs, the single Cmode could instead be replaced by a transmission line to maintain coil flexibility, which may also lower local SAR. Self-decoupling was also effective in decoupling loops from other elements in a mixed loop–dipole array where it is challenging to decouple adjacent (non-overlap**) loop and dipole elements. Another concern for mixed arrays is coupling between adjacent dipole/monopole elements. However, several methods have been described to reduce coupling between closely spaced dipoles/monopoles, such as passive antennas50,51 and metamaterials52. This report focused on the characterization and validation of self-decoupling itself, and further work is needed to investigate combinations with these methods. Self-decoupling was also effective in decoupling next-adjacent loops and loops in multi-row loop arrays, and could be a key technique in the development of many-element parallel transmission array coils. We expect that decoupling would be improved in a flat self-decoupled array compared to the cylindrical array we built, because the optimal Cmode values for decoupling elements in the same row and different rows would be almost the same due to more similar coupling geometries.

In this report we have emphasized the broad applicability and simplicity of self-decoupled designs by building arrays that used only self-decoupling. Although two-dimensional (2-D) and cylindrical arrays are suitable for most applications, close-fitting receive-only three-dimensional (3-D) helmet arrays with 32 or more elements may be preferred to capture maximum SNR in brain imaging. For these arrays, the small size, close spacing and varying neighbour geometries may limit the degree of self-decoupling that can be achieved since coils must be decoupled from several neighbours simultaneously. Further optimization of self-decoupled coils may be needed to address this more complex coupling problem. Alternatively, self-decoupling could be paired with conventional decoupling methods such as overlap**, low-impedance preamplifiers, shielding, and transformers, to address coupling in arrays with complex geometries. In particular, for 3-D receive arrays self-decoupling could combined with preamplifier decoupling to achieve high isolation between all neighbours.

Self-decoupled loop coils are built with unequal capacitance and inductance distributions to intentionally generate electric coupling that cancels magnetic coupling. They are distinct from “loopole” coils40, in which vertical conductors are built with unequal capacitance distributions to generate unequal current distributions that approximate transmit- or receive-optimal current patterns at 7 Tesla. However, as shown in Supplementary Figure 7, if a self-decoupled coil is rotated by 90 degrees or fed at its corner, the currents on its two vertical conductors become different so its B1 field becomes more similar to that of a “loopole” coil40,46, which may be helpful to improve transmit or receive efficiency. It should be noted that this may increase coupling with dipole or monopole antennas in the same array. More broadly, self-decoupled coils should enable greater flexibility in RF array design, since they alleviate constraints on element overlap and spacing. As an example, Supplementary Figure 8 shows how decoupling can be made independent of overlap** area using the self-decoupled approach, which provides a new degree of freedom for RF array design to optimize parallel imaging performance and imaging coverage.

Although this work demonstrated the self-decoupled coil concept for 10 × 10 cm2 coils at 7 Tesla, it can be applied to other coil sizes and field strengths so long as the magnetic and electric field coupling can be balanced to cancel each other. Like a conventional loop, the resonant frequency of a self-decoupled coil is dominated by its inductance (self-inductance and Xarm) and capacitance. At lower frequencies and for smaller coils, the Xarm impedance needed to tune a self-decoupled coil’s resonant frequency may be an inductor. In particular, if the Cmode capacitor required for self-decoupling remained fixed as the coil size decreased, Xarm may have a large inductance which could lead to significant power loss. To give some insight on this matter, we simulated a series of square self-decoupled coils with lengths/widths from 10 cm down to 5 cm in 1 cm steps. We found that the Cmode increased approximately linearly as the coil size decreased (Supplementary Table 2), and that, for a 5 × 5 cm2 self-decoupled coil, the Cmode was around 0.8 pF so the required total inductance Xarm remained a relatively small 80 nH, which alleviates this concern. We also built a pair of 5 × 5 cm2 self-decoupled coils and a pair of 5 × 5 cm2 conventional coils. Similar to the 10 × 10 cm2 coil, the smaller self-decoupled coil had better decoupling and efficiency than the non-decoupled coils (Supplementary Figure 9). 5 × 5 cm2 is smaller than the 9.5 and 6.5 cm coils that have been used in state-of-the-art 32- and 64-coil head arrays, respectively8. Supplementary Figure 10 shows a study of self-decoupled coils at 3 Tesla and 1.5 Tesla, where it was found that the ideal B1- fields can be maintained at 3 Tesla for both 10 × 10 cm2 and 20 × 20 cm2 coils, but there was an SNR decrease (~20%) for the 10 × 10 cm2 coil at 1.5 Tesla due to inductor loss. This loss could be avoided using dielectric materials with high permittivity or meander lines, at the cost of increased manufacturing complexity. The radiation losses of the self-decoupled coils were similar to that of conventional coils, even though they behave more like antennas than conventional coils. This means that most of the coils’ power was directed into the high-permittivity and conductivity samples, which is consistent with results using straight dipole antennas53.

Methods

Numerical simulation setup

Electromagnetic (EM) simulations were performed using commercially available software (ANSYS Electromagnetics, Canonsburg, PA, USA). As in the experiments, the coils were tuned to 298 MHz (proton Larmor frequency at 7 Tesla) and matched to 50 Ohms (the characteristic impedance of MRI scanner RF chains). Values of all lumped elements were obtained using the EM and RF circuit co-simulation method54. During RF circuit optimization, tuning and matching performance were optimized by varying Xarm and Xmatch with a built-in module in the RF circuit software (ANSYS Designer), while the decoupling performance was optimized by varying Cmode manually. All conductors and lumped elements (capacitors and inductors) were set to be ideal without ohmic loss. The transmit RF fields (B1+) were extracted from the simulations using the relationship: \(B_1^ + = (B_{\mathrm{x}} + {\mathrm{i}}B_{\mathrm{y}})/2\)44, where Bx and By are the x- and y- components of the magnetic field. Local SAR averaged across 10 grams was calculated using the built-in Fields Calculator module in ANSYS HFSS.

For the loop–loop configuration, the feed port was positioned at one end with one Cmode positioned at the opposite end. Two loops (each sized 10 × 10 cm2) were mounted on a 25-cm-diameter former and positioned with a 1 cm gap. A cylindrical phantom (conductivity б = 0.6 S m-1 and relative permittivity ξr = 78) with 15 cm diameter and 20 cm length was placed 4.5 cm below the loops. For the loop–dipole configuration, the loop had one Cmode positioned at each end. The dipole had dimensions 23 × 0.75 cm2 and loop had dimensions 20 × 9.5 cm2; the two were spaced 4 cm apart. A tank phantom with dimensions 35 × 30 × 20 cm3 was placed 4.5 cm below the pair (б = 0.7 S m-1 and ξr = 55). The dipole was shortened using two inductors and was matched using a parallel capacitor55.

Coil construction and bench test setup

The fabricated self-decoupled coils in both loop–loop and loop–dipole configurations had the same geometry and circuit as those in the simulation. The conventional coils used in the comparisons had the same sizes but equally distributed capacitors along their conductors. All coils were constructed with 7.5-mm-wide copper (3 M, Minneapolis, MN). Fixed capacitors (Passive Plus, 111 C Series, Huntington, NY) were used as distributed capacitors and trimmer capacitors (Johanson Manufacturing, 52 H Series, Boonton, NJ) were used for tuning, matching and decoupling. Handmade inductors using American wire gauge (AWG)-18 copper wires were used for Xarm impedances when needed. In the simulations, six equally distributed Xarm impedances were used for generality. In the constructed coils, only one Xarm was used since the total inductance was only around 35 nH. To avoid confusion with the transformer decoupling method which uses a pair of adjacent windings, the inductors in the two coils were placed far away from each other. Bench tests were performed using a calibrated Agilent 5071 C ENA network analyzer. For the loop–loop configuration, a 3-liter cylindrical phantom (15-cm-diameter, with 0.26 g L−1 NaCl and 0.125 g L−1 NiSO4 × 6H2O) was used for loading. For the loop–dipole configuration, a 20-liter tank phantom (35 × 30 × 20 cm3, with 0.26 g L−1 NaCl and 0.125 g L−1 NiSO4 × 6H2O) was used for loading.

Phantom transmit (B 1 +) maps and receive sensitivity (B 1 -) maps

Phantom B1+ maps were acquired with the constructed loop–loop and dipole-loop arrays on a 7 Tesla Philips Achieva whole-body scanner (Philips Healthcare, Best, Netherlands). In all MR experiments, each coil element was measured individually with the other one terminated with 50 Ohms. B1+ maps were measured using the DREAM method with the same input power56. The DREAM sequence parameters for the loop–loop configuration (10 × 10 cm2) were: field of view (FOV) = 180 × 180 mm2, in-plane resolution = 2 × 2 mm2, slice thickness = 5 mm, TR = 1000 ms. For the multi-slice B1+ of the 10 × 10 cm2 loop coils, the in-plane resolution was set to 1 × 1 mm2. The parameters for the loop–dipole configuration were: FOV = 350 × 200 mm2, in-plane resolution = 1.8 × 1.8 mm2, slice thickness = 5 mm, TR = 1000 ms. To calculate the receive sensitivity (B1-) map of the 5 × 5 cm2 loop coils, low-flip-angle gradient-recalled echo (GRE) images were acquired using the following parameters: FOV = 180 × 180 mm2, nominal flip angle = 10 degree, in-plane resolution = 3 × 3 mm2, slice thickness = 5 mm, TR/TE = 1000/10 ms, bandwidth = 5020 Hz. The B1- was calculated as Signal Intensity/std(noise)/|B1+|, where std(noise) is the standard deviation of noise map acquired with no RF excitation. Then the B1- was normalized to the maximum B1- of the ideal single coils.

Coil robustness analysis

To evaluate self-decoupled coils’ sensitivity to coil separation, two self-decoupled coils were mounted on a flat acrylic board (thickness 1.2 mm) which had a lift-off of ~4 cm above the large tank phantom. The self-decoupled coils were initially tuned, matched and decoupled when the coils’ distance was 1 cm. Then the distance between the coils (Dcoil) was varied from 1 to 7 cm in steps of 1 cm. No re-tuning or re-matching was applied as Dcoil changed. Two conventional coils with the same Dcoil were measured for comparison. The same bench test was conducted for two conventional coils for comparison. During the test, care was taken to make sure the loading condition did not change.

To evaluate self-decoupled coils’ sensitivity to loading, two self-decoupled coils were mounted on a 25-cm-diameter cylindrical former, and were tuned and matched with the 15-cm-diameter cylindrical phantom positioned 4.5 cm below the coils. The coil-to-phantom distance was then increased to 7.5 cm (lighter loading) and decreased to 1.5 cm (heavier loading) in steps of 1 cm. The same bench test was conducted for two overlapped conventional coils for comparison. The overlapped area was optimized when Dphantom was 4.5 cm, and it was not readjusted when Dphantom changed. In both cases, S11 and S22 were measured to evaluate the matching performance. Note that coils may mismatch when their separation or loading conditions change, so normalized S21 (defined as \(\left| {S_{21}} \right|/\left( {\sqrt {1 - \left| {S_{11}} \right|^2} } \right)\)) was used to evaluate the decoupling performance.

1×3 array and 2×2 array

The three-coil self-decoupled array was constructed by adding a third coil to the previously described two-coil array. Adding the third coil had little impact on the decoupling performance of the original two coils but slightly changed the resonance frequency of the middle coil, so the Cmode capacitor and Xarm inductors in the middle coil were retuned manually to achieve isolation and bring its resonant frequency to 298 MHz. We also constructed conventional loop arrays using gapped and overlap** designs as comparisons. Since we focused on evaluating the decoupling between next adjacent elements, only two elements were built in conventional loop arrays. For the gapped array, the two loop elements had the same size (10 × 10 cm2) and the same separation (12 cm) as the self-decoupled coils. For the same coverage, the loop elements using an overlap** design had slightly larger size (12 × 10 cm2) and closer distance (8 cm). Shielded trap circuits were used for all coils to remove the common current along the cables.

The 2 × 2 array was constructed by adding another row to the two-coil array. As explained above, a suitable dipole mode is needed to cancel out the magnetic coupling and realize self-decoupling. Therefore, each coil in the 2 × 2 array was fed at one corner and the Cmode was positioned at the opposite corner to reduce coupling from different rows as well as that from the same row. Due to limited space for the 2 × 2 array, bazooka/sleeve baluns rather than cable traps were used to suppress common-mode current.

In vivo imaging

The 2-coil self-decoupled array (dimensions 10 × 10 cm2) was mounted on an open cylindrical acyclic former (16-cm diameter). To avoid high electric fields near small Cmode capacitors, five larger capacitors (four fixed 2.7 pF and one variable ~2.5 pF) were connected in series. The coils were initially tuned, matched and decoupled when loaded with a human head. A healthy male volunteer was imaged using the array on the 7 Tesla whole body scanner. B1+ maps and MR images were acquired with individual coils and both coils, respectively. When imaging using both coils, the array was operated in quadrature mode. The imaging sequence was a low-flip-angle GRE sequence with parameters: FOV = 220 × 220 mm2, nominal flip angle = 10 degrees, TR/TE = 1000/1.98 ms, in-plane resolution = 1 × 1 mm2, slice thickness = 5 mm, bandwidth = 887 Hz pixel-1, number of averages = 1. Turbo spin echo (TSE) images were also acquired with the parameters: FOV = 220 × 178 mm2, refocusing flip angle/flip angle = 120/90 degrees, TR/TE = 3000/76 ms, in-plane resolution = 0.5 × 0.5 mm2, slice thickness = 5 mm, bandwidth = 243 Hz pixel-1, TSE factor = 15, number of averages = 1. To achieve the same B1+ in this area, the required input power of the 2-coil self-decoupled array was 73% lower than for a commercial volume transmit array (28 cm diameter, Nova Medical Inc., Wilmington, MA). The human experimental procedures were approved by the local institutional review board of Vanderbilt University, and informed written consent was obtained from the participant.

Data Availability

The data that support the findings of this study are available from the corresponding author upon request.