Odd-Leg Birdcages for Geometric Decoupling in Multinuclear Imaging and Spectroscopy

Te utility of interleaved odd-number leg birdcage coils is demonstrated for decoupling in double-and triple-tuned multinuclear applications. Te birdcage was designed to geometrically decouple from a planar double-tuned ( 1 H-23 Na) array and from a 31 P saddle coil insert to create a triple-tuned confguration. Comparisons between an actively detuned coil and a purely geometrically decoupled architecture were used to demonstrate the capabilities of the design. In particular cases, the simplicity and adaptability of the interleaved nine-leg design for multinuclear nuclear magnetic resonance (NMR) ofer a straightforward alternative to the often complex and lossy designs currently available for multinuclear birdcages and volume coils.


Introduction
Te development of multinuclear nuclear magnetic resonance (NMR) techniques yields many unique challenges for engineers in the clinical adoption of these methods. Sensitivity to X-nuclei such as 23 Na, 31 P, and 13 C has the potential to elucidate underlying physiological processes for the study and treatment of numerous disease states [1][2][3][4][5]. Tese nuclei, however, have much lower natural abundance and sensitivity than hydrogen and thus require specialized hardware for detection, such as array coils to increase sensitivity and signal-to-noise ratio (SNR) [6,7]. Additionally, achieving reliable shimming in X-nuclei studies is a challenge and immediately presents the need for doubletuning with 1 H [8]. Given the low sensitivity when detecting naturally abundant second nuclei, the short lifetime, expense, and nonuniform distribution in hyperpolarized applications, shimming requires the use of a 1 H coil without moving the X-nucleus coil between scans. Tis system of multinuclear transmit and receive hardware requires a complex chain of specialized coils, multiband amplifers, receivers, and often switching drivers, either for switch-tuned coils or active detuning. Te process of designing these multiband systems benefts from low-complexity coil designs to test individual components for the optimization of the resultant system, initially motivating the volume coil design presented here [9].
One of the most common transmit coil designs is the birdcage due to its highly homogeneous feld over a large volume [10,11]. Traditionally, birdcages are constructed of two end rings and integer multiples of four evenly spaced legs connecting these end rings to create the symmetry and respective highly homogeneous felds characteristic of birdcage coils [12]. To create multituned birdcages, one of the most common methods is to add traps on the rungs [13][14][15]. Tis design involves an iterative tuning process for multiple traps while maintaining the circular symmetry of the birdcage. Te result is therefore highly efective, but can be complex and results in a reported loss of quality factor (Q) [16]. A four-ring design also has been proposed in which an inner birdcage is constructed between two outer birdcages using common legs but diferent end rings [17][18][19]. Tis confguration creates a homogeneous double resonant structure, but with a diference in flling factors potentially limiting its scalability in size for clinical imaging. Interleaved birdcages for multinuclear applications attempt to minimize the losses in Q and flling factor discrepancies associated with other confgurations. Tis design has previously been reported at various feld strengths for hydrogen, sodium, and phosphorus [20][21][22]. Using interleaved odd-number leg birdcages enables a simple construction method to simultaneously create parallel linear felds at both frequencies, thus allowing for the possibility of geometrically decoupling from planar receive elements or any additional coil with orthogonal sensitivity. Specifcally, we report benchtop and imaging experimental data for interleaved nine-leg birdcages tuned to 1 H and 23 Na at 4.7 T designed to accommodate a planar double-tuned receive array. Additionally, we report benchtop characterizations for a 31 P volume saddle coil insert as a triple-tuned volume coil to further demonstrate the adaptability of the modular coil design.  23 Na), one interleaved double-tuned birdcage ( 1 H-23 Na), and one saddle ( 31 P). All three birdcage confgurations were constructed of 1oz copper-clad FR4 mounted on a 17.8 cm diameter acrylic former. Two nine-leg single-tuned birdcages were constructed: a 24.2 cm long sodium coil in a lowpass confguration with two capacitor breaks along the legs for distributed capacitances (1111C, Passive Plus), and a 21 cm long single-tuned bandpass birdcage for hydrogen. To account for nuances in the nine-leg design compared to conventional birdcages, the modes of the low-pass birdcage were mapped using a crossed probe. Te modes of a conventional eight-leg birdcage are well documented [23]. Te nine-leg birdcage showed similar behavior with multiple modes, the lowest mode of which was the homogeneous mode, and several degenerate modes at higher frequencies.

Materials and Methods
Similarly, the modes of the 1 H bandpass birdcage were also mapped. A unique characteristic of the bandpass birdcage is the greater control over the frequency of the modes based on design specifcs [24]. Tis was therefore an essential component of the tuning process to verify the frequencies of the homogeneous and degenerate modes. Te multinuclear birdcage was constructed by interleaving the nine-leg hydrogen coil and the nine-leg sodium coil on a single 17.8 cm diameter former. Conductor overlaps between the coils were electrically isolated using Kapton ® tape, and feed ports on opposite sides of the coil created a double-tuned coil with parallel felds at the two frequencies. Te coil was constructed by frst coarsely tuning the birdcages using the same distributed capacitances as their single-tuned counterparts. Te capacitances of the sodium coil were then adjusted on the legs on either side of the feed port to steer the felds to be precisely aligned, as verifed by a feld probe. All coils were matched and tuned with variable capacitors (NMAT 40HVE 1712, Voltronics Corp.). A shield was constructed for all three birdcages using overlapping sheets of 0.25 oz Pyralux ® copper-clad laminate on a 25.4 cm acrylic former.
A standard active detuning network was added to the multinuclear birdcage to be able to compare/evaluate using geometric decoupling alone from a planar receive array to using active detuning [25]. A tuned active trap was added on each capacitor of one end ring of the 1 H coil. Te active trap was constructed using variable inductors (165 Series, Coil Craft) and active pin diodes (MA4P7006F-1072-T, MACOM). Alternatively, the sodium coil was detuned with a diferent network by adding an active PIN diode in parallel with the variable tune capacitor and a distributed capacitor on another leg 80 degrees ofset from the feed port to fully detune the coil. Tis simpler network was shown to shift the resonant frequency of the coil to efectively detune the coil, given the larger distributed capacitors on the sodium birdcage as compared to the hydrogen coil. Schematics for the multinuclear coil with active detuning networks are shown for 1 H in Figure 1(a) and 23 Na in Figure 1(b). A custom PIN diode driver was designed to integrate the active detuning into the control logic of the scanner following the designs of White [26]. Te driver was designed to output 1.6 A of current to detune the birdcage and 48 V to reverse bias during transmit.
To test the ability of the birdcage to decouple from planar receive elements, two loops were constructed out of 24AWG wire with a 4 cm diameter, one for sodium (53 MHz) and one for hydrogen (200 MHz) matched and tuned with variable capacitors (SGC3S, Sprague Goodman). Tese loops were then moved into each of the six positions in the volume coil based on where they potentially would be located in a sixelement array in order to test geometric decoupling and fnd the "worst-case scenario" for comparison to active detuning. A dedicated phantom former was designed (Figure 2(a)) and 3D printed out of polyamide (HP PA 12) on an MJF (Material Jet Fusion) printer. Te former also provided a platform for positioning of the receive coils ( Figure 2(b)) and to maintain the orthogonal felds ( Figure 3(a)) between the loops and birdcages for a consistent decoupling angle. Te phantom was composed of a single homogeneous food region of NaCl (σ � 0.73 S/m, ε r � 78). Ramps were added for slice localization and a pin cushion structure was added for quantifying resolution. Te lid of the phantom was etched to accommodate a six-element receive array, or in this case, to indicate where to place the single loop to test coupling at the various relevant positions.
Finally, to further demonstrate the utility of the parallel felds generated by this architecture, a phosphorous saddle coil insert was constructed to create a triple-tuned volume coil. Tis coil was positioned within the birdcage such that it created net linear felds orthogonal to the net birdcage felds, resulting in a purely geometrically decoupled triple-tuned volume coil ( Figure 3(b)). Te saddle coil was created using adhesive copper tape on a 12.7 cm diameter acrylic tube with a length of 17 cm. Te saddle coil was then coarsely tuned with distributed capacitors (1111C, Passive Plus) and fnely matched and tuned with variable capacitors (NMAT 40HVE, Voltronics). Bench measurement characterizations were performed to demonstrate the matching and decoupling capabilities of the saddle from the birdcage.

Benchtop Measurements.
Bench measurements were used to characterize coil performance and the decoupling abilities of the diferent coil confgurations presented here. All bench measurements were taken on a vector network analyzer (E5071C, Agilent). S 11 and Q were measured and compared between the single-tuned birdcages and doubletuned birdcage confgurations with and without active detuning. Active detuning was verifed using a crossed probe to show no resonant peak at the frequencies of interest. An S 21 measurement was used to note any coupling between the two birdcage ports, and a feld probe was used to map the homogeneity of the birdcage using an in-house feld mapping system. Te decoupling between the birdcage and loop elements in the six diferent locations was assessed with an S 21 measurement taken between the birdcage port and the loop. Although this measurement does not defne absolute sufcient decoupling given the large diferences in coil sensitivity between the large transmit birdcage and the smaller receive loops, it allowed for quantifcation and comparison of decoupling at diferent positions within the birdcage. In this way, the worst case was found for the fairest comparison to active detuning. Similarly, S 11 and S 21 measurements were acquired with the 31 P saddle coil to verify sensitivity and coupling measurements on the bench.

Results and Discussion
3.1. Volume Coil Construction. Te interleaved coil design allowed for a straightforward decoupling mechanism to create aligned felds without the complex and lossy limitations typical of other double-tuned designs. Te main modes of the single-tuned nine-leg lowpass (Figure 4(a)) and bandpass (Figure 4(b)) birdcages are shown with the homogeneous birdcage mode, and the main degenerate modes are measured with a single probe centered in the coil. Te fnal double-tuned coil is shown in the shield in Figure 5(a). Te concentric saddle insert is shown partially inserted in Figure 5(b), and side-by-side with dimensions to show relative longitudinal coil positioning in Figure 5(c). Table 2 summarize the sensitivity and decoupling behavior of the birdcage with loaded measurements. While all coil confgurations were shown to be well matched (better than −29.7 dB), the double-tuned confgurations did show a 5% loss in Q for 1 H and 3% for sodium when compared to the single-tuned designs. Tis loss in Q was compounded by the addition of active detuning circuitry, resulting in a 32% loss for 1 H and 16% for sodium, thus signifcantly reducing transmit coil efciency. Q ratios were taken for the single-tuned coil confgurations and were shown to be 1.67 for 1 H and 1.35 for 23 Na. Additionally, coupling between the two birdcage ports was shown to be 4.6 dB worse at 200 MHz with the addition of active detuning suggesting some coupling through the detuning circuitry itself at that frequency. Axial feld maps for the 1 H coil (Figure 6(a)) and sodium coil ( Figure 6(b)) show the homogeneity of the coil to be within 1.5 dB of variation over the food region of the phantom with phase maps shown for 1 H (Figure 6(c)) and sodium ( Figure 6(d)). Similarly, the triple-tuned volume coil confguration further demonstrated the geometric decoupling benefts of the interleaved birdcage design. Te matching and tuning data (Table 4) demonstrated that all coil confgurations could be easily matched to better than −21.7 dB. Quantifcations of decoupling between the birdcage and saddle insert ( Table 5) showed that port-to-port coupling was no worse than −14.6 dB and up to −30.2 dB depending on the frequency. Tis coil architecture benefts from the low-complexity approach of changing coil inserts to add or remove sensitivity to specifc (or additional) nuclei and adjusting the coil to suit the required application. Tis particular nine-leg interleaved birdcage design was originally intended to be used as a double-tuned 1 H-23 Na transmit coil with planar receive elements, and the 31 P insert coil was added to further demonstrate the utility of the parallel linear felds [27,28]. Tis design could (and should) easily be modifed for a given study to optimize sensitivity by arranging the coils such that the lowest-sensitivity nuclei are the insert, making it the most sensitive to the sample. It is worth noting that oddlegged birdcages cannot straightforwardly operate in a standard quadrature mode with conventional 90-degree-separated ports. Te least complicated approach to making a single nucleus quadrature (presumably the less sensitive non-1 H one) is the addition of an insert coil positioned orthogonally within the main coil. For example, in this case, the third-nucleus saddle coil could instead be tuned to the less sensitive 23 Na frequency to provide quadrature operation. In summary, the straightforward decoupling and fexibility/modularity provided by the design are signifcant benefts of odd-leg birdcages.

Imaging Studies.
To demonstrate the homogeneity of the birdcage an image was frst acquired using the birdcage in the T/R mode (Figure 7). Tis showed no visible distortions to the homogeneity of the feld with a loop in place, suggesting sufcient decoupling during transmit between the birdcage and the receive array due simply to geometric decoupling. Due to the low sensitivity of the sodium birdcage, a T/R image was only acquired for 1 H. However, given the similar sizes of the coils and comparable benchtop coupling measurements and feld maps, it is expected that the same efect would be seen for sodium. 1 H images were acquired both with (Figure 8(a)) and without (Figure 8(b)) active detuning to demonstrate the efects of the additional decoupling of the active detuning circuitry. Te average SNR was quantifed for two regions as shown in Figure 8: a region highlighted in a blue box directly under the loop and a region highlighted in a red box within the phantom but not directly below the loop. Te average SNR of these two regions was calculated by taking the average intensity of the regions within the two boxes and the average intensity of the same regions in a separate noise image acquired without the transmit power amplifer active. For consistency, SNR calculations were scripted to take the exact same regions in all four images (with and without active detuning at both nuclei). Raw SNR data is available in the supplementary table (available here) to show the infuence of active detuning on both the average signal and noise levels in these regions. Te region within the blue box was found to have an average SNR of 391 with active detuning compared to 388 with purely geometric decoupling. Similarly, the average SNR of the region within the red box was found to be 34.4 with active detuning compared to 48.6 with purely geometric decoupling. Tis suggests that roughly 41% more signal was detected with purely geometric decoupling compared to an actively detuned network in this region away from the loop, presumably through coupling between the birdcage and receive loop. ® tape is also visible, electrically isolating the hydrogen birdcage end rings from the sodium birdcage legs.      Te coupling between the loop coils and birdcage (Table 3) was no worse than −28 dB with a range of 1.4 dB for sodium. Te 1 H coils coupled no worse than −26.5 dB with a range of 4.7 dB. Given that the variation was more signifcant for the 1 H frequency and the higher sensitivity of this nuclei, the element in position six was used for imaging studies to demonstrate the worst-case coupling to validate the purely geometric decoupling design.
Similarly, images were taken for sodium using the same experimental setup with and without active detuning. Given the lower sensitivity of these coils the background signal was not as visible either with (Figure 9(a)) or without (Figure 9(b)) active detuning. Quantifcations of average SNR were made using the same regions of the phantom as with 1 H with a region highlighted with a blue box directly under the loop and a region highlighted with a red box within the phantom but not directly below the loop. Directly under the loop, the average SNR was found to be 46.3 with active detuning versus 44.2 without. Outside the loop, the average SNR was found to be 3.26 with active detuning compared to 3.74 without, a roughly 15% increase in signal with purely geometric decoupling as compared to active detuning.
While imaging experiments did show active detuning leads to a decrease in coupling, the application must be considered in the decision of whether the added complexity and loss are needed. Certain applications of spectroscopy for low-sensitivity X-nuclei using receive element reception and requiring the absolute highest SNR achievable or those requiring the use of nonplanar arrays will make purely geometric decoupling as described inappropriate. Other applications where a slight reduction in SNR using a receive element is acceptable and will still yield the necessary results or where the coil will be used in the volume T/R confguration, this simple and adaptable hardware may be sufcient. In the end, the needs of a given study must be taken into consideration when designing the appropriate hardware.

Conclusions
Odd-numbered leg interleaved birdcages can generate parallel felds at two frequencies, creating a straightforward geometric decoupling mechanism from either planar receive elements or any additional insert with an orthogonal feld. Tis was demonstrated with a set of nineleg birdcages tuned to 1 H and 23 Na and reception loops at both frequencies, and the addition of a 31 P saddle coil insert to create a triple-tuned coil. While the application of a purely geometrically detuned coil is limited to planar arrays or a T/R volume coil, a simple active detuning network can be easily added if the application requires further decoupling either due to geometric constraints or if the geometric decoupling is deemed insufcient for a given experiment. Given the simplicity and adaptability of the interleaved nine-leg design for multinuclear NMR spectroscopy and the additional decoupling provided by the geometric decoupling even with the addition of active detuning, this design ofers a straightforward alternative to the many complex and lossy designs currently available for multinuclear birdcages and volume coils.

Data Availability
Te data used to support the fndings of this study are included within the article.

Conflicts of Interest
Te authors declare that there are no conficts of interest.