Synopsis

· Dual-tuned coils provide metabolic information (x-nuclei module) and co-registered anatomical images and B0 shim settings (1H module) without repositioning the subject or coil

· X-nuclei signal strength is typically less than 1/1,000× that of 1H (1). Therefore it is important to maximize x-nuclei receive sensitivity while simultaneously providing adequate 1H sensitivity

· We will discuss prevalent dual-tuning techniques and considerations for performance characterization and interfacing dual-tuned coils

Background

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 to detect biochemical degradation in the early stages of osteoarthritis (2). Meanwhile, 31P MRS and 17O can quantify metabolites that play important roles in energy consumption and delivery, thus providing a means to probe oxidative phosphorylation and the metabolic rate of oxygen (3).

A dual-nuclei RF coil is preferred for x-nuclei applications; the 1H module provides anatomical reference images and phase images to determine B0 shim settings, while the x-nuclei module provides metabolic information without repositioning the subject. Given that standard RF coils are narrowband devices tuned only to the 1H frequency, specialized techniques must be used to simultaneously detect 1H and x-nuclei signals. Popular techniques for achieving dual resonance will be reviewed in the following section.

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 and low gyromagnetic ratio (Table 1). These characteristics imply undesirably long acquisition times and large voxel volumes to sufficiently average signals in time and space. Over the past several years, the SNR deficit has been somewhat alleviated by efficient pulse sequences (4) and reconstruction techniques along with the proliferation of high field scanners (≥ 3 Tesla) that boost the baseline SNR. Coil hardware also has a significant influence on SNR, which will be the focus of this text.

Dual-nuclei RF coil designs have recently transitioned from 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 (5,6). An example of a 7 Tesla multi-element 31P/1H brain coil is shown in Figure 1 (7). 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.

Dual-tuned coil methods

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 parallel inductor/capacitor pair (i.e. a pole or “trap” circuit) in series with the coil (8-10). 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 reactance, which give rise 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, the dual resonance property vanishes when Lp is zero rendering it irrelevant. 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 (8).

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 (11-25). In this case, it is instructive to model the coils as a mutually coupled system (14,23,24). The resonant frequencies of the coupled coils can be written as: 1-(ω⁄ω_1H )²-(ω⁄ω_x )²+(1-k² )(ω⁴ ω_1H^-2 ω_x^-2 )=0, where k is the coupling coefficient, and ω_1H and ω_x the resonance frequencies of each coil in isolation, and ω the resonance frequency of the coupled system (23). In the coupled system, two modes are formed: high-frequency mode is created at a frequency while the low-frequency mode is created at a frequency . The high-frequency mode is “counter-rotating” because the current induced in the x-nuclei coil flows 180° out-of-phase with that in the 1H coil. This out-of-phase current shields the 1H coil by compressing its flux pattern and reducing its effective inductance, which can reduce B1 sensitivity, increase resistive loss, and potentially reduce radiation loss. In contrast, the low-frequency co-rotating mode is generally unperturbed by the presence of the 1H coil.

This combination of behaviors can be leveraged in a concentric nested dual nuclei strategy; 1) the low frequency coil is not significantly affected by the high frequency coil, while 2) the low frequency coil shields the high frequency coil to reduce its radiation loss and neighbor coupling (26), albeit at the expense of coverage and penetration due to counter-rotating current induced in the low frequency coil shield. If radiation loss is not significant, it may be desirable to install filters in the x-nuclei coils that are tuned to block counter-rotating 1H currents. Note that the filters come with a small x-nuclei SNR penalty (23,24,27).

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 (21,22). 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 (28-30) and additional endrings (31-33). Volume coils generally provide a uniform transmit field (B1+), which can simplify x-nuclei quantification methods that may be undesirably 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 (12,15,16,18,19,25,34-38). This can be traced to a general revitalization of x-nuclei research resulting from the new prevalence 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 (6). 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 an array such that the quantity and size of the individual coils provide the required coverage and a Q ratio ≥ ~3, which is considered to be on the edge of the sample noise dominated regime. Note that an array with a smaller coils and therefore lower Q ratio is unlikely to provide SNR benefit at the center of the object compared to a simpler array with fewer, larger coils. 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 (25,39,40).

Performance characterization It is important to quantify dual-tuned coil performance as a function of its environment. The quality factor is a straightforward way to measure coil efficiency; the unloaded QU is an indication of losses associated with the coil itself (namely conductor resistance and radiation) and the loaded QL 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 increased loaded Q due to shielding of the coil from the sample and thus a significantly reduced Q ratio and B1 sensitivity. 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 tissue-equivalent phantom (41,42) along with the processing method such that the measurements can be easily replicated at other institutions. Figure 4 (37) illustrates the SNR advantage of an eight-channel 31P/1H array over a birdcage coil processed using the algorithm described by Kellman and McVeigh (43). 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+. The high 1H signal level allows for a variety of 1H flip angle-mapping methods (44-49) that are difficult to translate to x-nuclei (50). 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=(360/α γτ)^-1/V, which is a convenient metric for coil comparisons due to its relative insensitivity to imaging parameters.

Interface – front end Due to the lack of a system integrated x-nuclei transmit coil (the body coil in clinical systems operates only at the 1H frequency, while high field 7 Tesla systems do not include a body coil for any nucleus), 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 (51). 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 large concurrent 1H B2 pulses (52). Finally, a diplexer circuit may be required for true multi-tuned coils (where both frequencies are available at the same coil port). A diplexer is a passive three-port device with high-pass, low-pass, and combined ports in order to allow frequency multiplexing. This is required to separate signals prior to narrowband amplification.

Cable traps are essential components that reduce common mode currents on the coaxial cable shields in any RF coil (53). 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 through parasitic current pathways. 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. (15).

Interface – back end Most clinical systems are designed only for 1H-MRI and require modifications to the RF architecture in order to process or generate signals at heteronuclear frequencies (51,54). In the receive chain, signals are sampled at a predetermined “intermediate frequency (IF)” that is set by the manufacturer and created by down-converting the 1H signal via frequency mixing with a local oscillator signal (LO). In order to process heteronuclear receive signals, one can pre-mix the x-signal with an auxiliary LO set to the difference between the 1H and x frequencies. In this way, the x-signal is disguised as 1H, allowing the system to process the signal as usual. On the transmit side, one needs a dedicated broadband amplifier that is fed by a pre-modified waveform generated originally at the 1H frequency by the system (to synchronize timing) and down-converted to the desired x frequency. Lee, et al. provides details of such a system in (51).

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. (55). 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 in situ (56,57). 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 (58) 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, phase SNR, 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.

Summary

Acknowledgements

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