Multi-nuclear MRI and MRS are of great interest to the scientific community because of the ability to probe functional metabolites such as 23Na, 31P, 19F, 7Li, 13C, 129Xe, etc., which are collectively referred to as “x-nuclei.” For example, quantitative 23Na MRI has been shown to be highly specific to the glycosaminoglycan content in cartilage and could therefore be used as a means of detection and assessment of the degree of biochemical degradation of cartilage in the early stages of osteoarthritis. Meanwhile, 31P MRS can quantify metabolites that play important roles in energy consumption in the skeletal muscle, heart, liver, and brain. A dual-nuclei RF coil is preferred for x-nuclei applications; the 1H module provides anatomical reference images and B0 shim settings, while the x-nuclei module provides metabolic information without repositioning the subject or coil hardware. Given that standard RF coils are narrowband devices tuned only to the 1H frequency, specialized techniques must be used to simultaneously provide sensitivity at both the 1H and x-nuclei frequencies of interest Table 1. Gyromagnetic ratio and NMR signal strength in the human brain for common nuclei. Nucleus 1H 31P 7Li 23Na 13C γ/2π (MHz/T) 42.576 17.235 16.546 11.262 10.705 Signal relative to 1H 1 1×10-5 3×10-6 5×10-5 4×10-10 It is important to keep in mind that the main difficulty with x-nuclei MRI is its fundamentally low signal-to-noise ratio (SNR) due primarily to the low concentration of x-nuclei in the body, which is reflected in values in the bottom row of Table 1. This characteristic implies undesirably long acquisition times and large voxel volumes. Over the past several years, the SNR deficit has been somewhat alleviated by the development of efficient pulse sequences and reconstruction techniques along with the proliferation of high field scanners (≥ 3 Tesla). SNR advances have also been achieved with dual-nuclei RF coil designs, which have transitioned from preceding single channel and volume coils to multi-element phased arrays. Multi-element phased arrays are advantageous because they combine the large field-of-view of a volume coil with the improved sensitivity of a surface coil (2,3). An example of a 7 Tesla multi-element 31P/1H brain coil is shown in Figure 1 (4). The coil enables 31P spectroscopy, a saturation transfer technique to calculate the global creatine kinase forward reaction rate, and single-metabolite whole-brain imaging with 1.4 cm nominal isotropic resolution in 15 min, as well as 1 mm isotropic 1H imaging.

Single tuned coil

A coil’s inherent inductive impedance is given by Z_L=jωL. A single resonance is achieved by canceling the inductance with a tuning capacitor Z_T=(jωC)^-1 such that Z=jωL+(jωC)^-1=0. Plots of the coil’s negative inductive reactance and tuning network reactance curves show that resonance occurs at their intersection at the x-nuclei frequency (Figure 2).

Pole insertion

One way to achieve dual resonance is by inserting a pole in the form of a parallel inductor/capacitor pair, or “trap” circuit, in series with the coil (5-7). In this case, the tuning network impedance is Z_T'=(jωC')-1+(jωL_P)(jωC_P)^-1/(jωL_P+(jωC_P)^-1). Inspection of the reactance plot shows two intersections between the coil’s negative inductive reactance and tuning network, which correspond to resonances at both 1H and x frequencies. The low resonance frequency can be modified primarily by the main capacitance C', while the high resonance frequency can be modified primarily by the pole capacitance C_P. In general, dual-nuclei coil techniques involve tradeoffs. In the pole insertion method, flux generated in the trap inductor L_P is not coupled to the sample and therefore generates loss associated with its resistance. The efficiency of the low frequency channel approaches unity (where unity is the baseline efficiency of a single tuned coil) when the value of L_p approaches zero. Of course, dual resonance is not possible when L_p is zero. In practice, the ratio L_p :L is chosen to be ~1:4-5, yielding ~90% efficiency on the low frequency channel and ~45% efficiency on the high frequency channel (5).

Other methods – nested, transformer coupled, etc.

Another method to achieve dual resonance is to use two separate “nested” or explicitly coupled transformer coils, whose individual structures can be semi-independently tuned to the low and high frequencies of interest (8-23). In this case, it is instructive to look at the behavior of each coil at both frequencies. Again, the reactive portion of the coil impedance is given by Z=jωL+(jωC)^-1. Consider a coil that is tuned to the proton frequency: Z(ω=ω_1H)=0. When viewed at the lower x-nucleus frequency, its impedance is dominated by a large capacitive reactance and therefore approximates an open circuit: Z(ω=ω_x)~(jω_XC)^-1»-inf. The degree to which the 1H coil approaches the open circuit condition is proportional to the ratio between the resonant frequencies of interest. Consider next a coil tuned to the x-nuclei frequency Z'(ω=ω_x)=0. When viewed at the proton frequency, its impedance is dominated by its inherent inductive reactance and therefore can be thought of as a shield: Z'(ω=ω_1H)~jω_1HL. This combination of behaviors can be leveraged in a concentric nested dual nuclei strategy; 1) the outer low frequency coil is not significantly affected by the inner high frequency coil, while 2) the low frequency coil shields the high frequency coil to reduce its radiation loss and neighbor coupling (24), albeit at the expense of coverage and penetration due to counter-rotating current induced in the low frequency coil shield. 1H traps can reduce counter-rotating currents in the x-nuclei coil with a small penalty on x-nuclei SNR (21,22). Another method to reduce counter-rotating currents is with a 1H butterfly/x-nuclei loop pair, which generate orthogonal fields and hence experience very little coupling (19,20). This approach can be desirable in proton decoupling applications, where a so-called B2 field is generated to saturate 1H spins concurrent to the x-nuclei MRS experiment to augment the x-nuclei signal. Still other dual-nuclei coil techniques have included modified volume coils with alternating 1H/x legs (25-27) and additional endrings (28-30). Volume coils generally provide a uniform transmit field (B1+), which can simplify x-nuclei quantification methods that may be sensitive to a spatially varying flip angle.

Dual-tuned phased arrays

While early dual-tuned coils primarily consisted of single channel surface or volume coils, recent literature shows a dramatic increase in dual-tuned phased arrays (9,11,13,14,16,17,23,31-33). This can be traced to a general revitalization of x-nuclei research resulting from a greater number of high-field scanners (which inherently improve the x-nuclei SNR), as well as improved pulse sequences and sampling strategies. Ideally, many-element arrays outperform single channel coils in both the periphery as well as in the center of the object (3). However, transitioning from a single channel x-nuclei coil to a many-element array implies a diminishing quality factor (Q=f₀/BW=ωL/R) ratio that coincides with smaller coils and is accentuated at low frequencies. A good rule-of-thumb is to design the quantity and size of the array elements such that the required coverage is provided and each element has a Q ratio ≥ ~3, which is considered to be on the edge of the sample noise dominated regime (an array with a higher channel count but lower Q ratio is unlikely to provide SNR benefit in deep regions). Further, higher channel counts necessitate additional opportunities for unwanted stray currents and noise coupling (i.e. through coaxial cables, interface components, and preamplifiers). Subtle enhancements such as presenting the preamplifier with an impedance mismatch can reduce noise coupling between coils, which can be particularly beneficial in x-nuclei arrays where the loaded Q is high due to low coil-tissue coupling (23,34,35).

Performance characterization

As is the case for single tuned coils, it is important to quantify dual-tuned coil performance. The quality factor is a straightforward way to measure coil efficiency; the unloaded Q_U is an indication of losses associated with the coil itself (namely conductor resistance and radiation) and the loaded Q_L is an indication of losses in the coil plus those induced from the sample. Here, coil Q was measured on 31P/1H coils tuned for operation at 7 Tesla as a means to compare several dual-nuclei strategies in Figure 3.

Several interesting conclusions can be drawn from the Q measurements. Importantly, the Q of the 31P coil is practically unaffected by the presence of the 1H coil in the offset and concentric arrangements. Conversely, the offset 31P coil shields the 1H coil, resulting in an increased unloaded Q value (due to reduced radiation loss) but also a much higher loaded Q due to shielding of the coil from the sample and thus a significantly reduced Q ratio. The concentric arrangement partially restores the Q ratio of the 1H coil, while the trap method results in loss of performance at both frequencies.

The key performance metric in a dual-tuned coil is the SNR of the x-nuclei module. It can be insightful to compare the SNR of a coil developed in-house to that attained with a commercially available coil that serves as a reference standard. When a reference coil is not available, it can be problematic to engage in inter-site SNR comparison owing to the wide variety of specialized pulse sequences and acquisition parameters and the arbitrary nature of SNR units. For this reason, it is preferred to publish SNR measurements acquired with standard gradient echo Cartesian sequences and a well-described phantom such that the measurements can be easily replicated at other institutions. Figure 4 illustrates the SNR advantage of an eight-channel 31P/1H array over a birdcage coil. SNR was measured from data acquired with a 2D gradient echo sequence with the following parameters: voxel size = 8×8×50mm3, TE = 6.5 ms, TR = 10s, FA = 76°, receiver bandwidth = 100 Hz/pixel, and acquisition time = 640s.

A performance metric that is somewhat easier to quantify is transmit efficiency. This quantity stipulates the amount of power or voltage required to generate a given B1+. Various flip angle mapping methods can be applied to determine 1H transmit efficiency. However, x-nuclei flip angle mapping methods are generally not available. One approach, though time-consuming, is to acquire fully relaxed gradient echo images (TR>>T1) over a range of transmit pulse amplitudes V with known duration τ. The signal intensities can then be fit to a sine curve to determine the pulse amplitude required to generate a flip angle α. This value can finally be translated into transmit efficiency: η=B1+/V=(360γτ/α)^-1/V, which is a convenient metric for coil comparisons due to its relative insensitivity to imaging parameters.

Interface

Due to the lack of an x-nuclei transmit coil (the body coil in clinical magnets operates only at the 1H frequency), dual-nuclei coils are typically operated in transmit/receive mode or transmit only/receive only (ToRo) mode, both of which necessitate custom transmit/receive switches and other interface hardware (36). Additionally, coils designed with proton decoupling applications in mind require a low-loss low-pass or band-pass filter at the input of the x-nuclei preamplifier to prevent damage from power leaked from the relatively large concurrent 1H B₂ pulses. Finally, a diplexer circuit may be required for true multi-tuned coils (where both frequencies are available at the same coil port), whereas the circuit is not required for nested coils (where individual ports correspond to a single nucleus).

Cable traps are essential components that reduce common mode currents on the coaxial cable shields in any RF coil (37). In particular, electric fields generated on coaxial cables in close proximity to the subject can pose a safety hazard, while their existence generally deteriorates coil performance. In dual-tuned coils, cable traps are typically required to suppress both 1H and x-nuclei current, regardless of the resonant frequency of the coil connected to a given cable. Dual-tuned cable traps can be formed in a similar manner (i.e. using trap circuits) as a dual-tuned coil is formed; an excellent example of a dual-tuned tri-axial cable trap is detailed in Ref. (13).

Power Limits

Dual-nuclei transmit coils must be carefully regulated in order to restrict tissue heating caused by their electric field in accordance with limits set by the International Electrotechnical Commission (IEC 60601-2-33 2010). The merits of various approaches for determining safe power limits for RF coils are a topic of vigorous discussion in the field. A comprehensive review on procedures for self-developed coils with respect to mechanical and electrical safety is given in Ref. (38). Computer-based specific absorption rate (SAR) prediction models provide excellent insight on the coil’s behavior, though extreme care must be taken to accurately represent the coil, relevant interface components, and subject in the computer model and finally confirm their equivalence (39,40). In the case of dual-nuclei coils, it is important to model and simulate both 1H and x-nuclei coil structures to account for their interaction and to determine power limits for both operating frequencies. An accompanying approach is to measure heating in situ through MR thermometry (41) and/or fluoroptic probes. The main benefit of this approach is that all components of the RF chain are inherently accounted for, although it is critical to recognize experimental subtleties such as the heat diffusivity of the phantom and B0 drift that can reduce accuracy. Given the uncertainties associated with both simulation and thermometry methods, it is generally prudent to install a safety margin beyond the IEC limits.

Dual-nuclei coils are valuable tools for x-nuclei studies whose performance plays a critical role in improving image quality while minimizing acquisition time and spatial resolution. Many of the sound engineering guidelines for single-tuned coils such as minimizing coil loss, improving sensitivity through multi-element receive structures, and eliminating coaxial cable shield currents can be extended to dual-nuclei coils. Dual-resonance can be achieved in a variety of manners, all of which are intended to maximize receive sensitivity on the x-nuclei module while simultaneously providing adequate 1H sensitivity. The popular techniques mentioned above can be considered a starting point for those interested in designing multi-tuned coils.