Triple-Tuned Birdcage and Single-Tuned Dipole Array for Quadri-Nuclear Head MRI at 7 T

Abstract

Purpose:

The purpose of this work was to design and build a coil for quadri-nuclear magnetic resonance imaging (MRI) of the human brain at 7 T.

Methods:

We built a transmit/receive triple-tuned (45.6 MHz for ²H, 78.6 MHz for ²³Na, and 120.3 MHz for ³¹P) quadrature four-rod birdcage that was geometrically interleaved with a transmit/receive four-channel dipole array (297.2 MHz for ¹H). The birdcage rods contained passive, two-pole resonant circuits that emulated capacitors required for single-tuning at three frequencies. The birdcage assembly also included triple-tuned matching networks, triple-tuned baluns, and triple-tuned transmit/receive switches. We assessed the performance of the coil with quality factor (Q) and signal-to-noise ratio (SNR) measurements, and performed in vivo multi-nuclear MRI and MR spectroscopic imaging (MRSI).

Results:

Q measurements showed that the triple-tuned birdcage efficiency was within 33 % of that of single-tuned baseline birdcages at all three frequencies. The quadri-tuned coil SNR was 78, 59, 44, and 48 % lower than that of single or dual-tuned reference coils for ¹H, ²H, ²³Na, and ³¹P, respectively. Quadri-nuclear MRI and MRSI was demonstrated in brain in vivo in about 30 min.

Conclusion:

While the SNR of the quadruple tuned coil was significantly lower than dual- and single-tuned reference coils, it represents a step toward future truly simultaneous quadri-nuclear measurements.

Introduction

The brain is a highly aerobic organ that relies on glucose and oxygen as fuel for adenosine triphosphate (ATP) production, mainly through oxidative phosphorylation in mitochondria. ATP is then used to drive ionic transporters which maintain ion homeostasis responsible for cell viability in healthy tissues [1, 2]. Many neuropathologic processes spanning cerebral ischemia, Alzheimer’s disease (AD), traumatic brain injury (TBI), or malignant tumors, can be related to the disruption of one or many mechanisms involved in cell energy homeostasis [3–7]. Therapeutic interventions may target these mechanisms, either by re-establishing a normal pipeline of ATP production and consumption in cells [2, 8, 9], or by disrupting metabolic pathways to promote cell death in tumors [10–12].

Direct and concurrent quantitation of multiple energetic parameters and metabolites in the brain, such as glucose uptake and lactate generation [13], levels of ATP and phosphocreatine (PCr) [14], or intracellular sodium (Na⁺) concentration [15, 16], can provide fundamental insights on individual cellular processes and their interconnection. Multi-nuclear MRI can play a role in this endeavor by non-invasively probing, for example, deuterium-²H labeled glucose to depict the Warburg effect [13], sodium-²³Na to track ion concentration gradients [15], and phosphorus-³¹P to measure energy storage or utilization and membrane synthesis and breakdown [17, 18].

While measurements of individual nuclei provide unique insight into a narrow window of cellular function, the literature on the complex interplay among metabolites is sparse despite their important physiological connection. For example, in cancer, oxidative phosphorylation gives way to anaerobic phosphorylation, which affects ATP and lactate production and appears to alter ion pumps as evidenced by increased intracellular sodium. However, multi-nuclear MRI measurements are challenging due to inherently low signal-to-noise ratio (SNR) stemming from low NMR receptivity and low concentration in the body. Signal averaging can alleviate the issue but at the cost of acquisition time, which compounds when attempting to measure multiple nuclei in a traditional sequential manner.

One way to address this issue is to simultaneously acquire multi-nuclear signals. Our group and others have recently developed novel pulse sequences to simultaneously image various nuclear pairs such as sodium/proton [19, 20], phosphorus/proton [21], and deuterium/proton [22] to reduce scan time or observe interplay between multi-nuclear metabolic parameters.

In addition to a custom pulse sequence, a radiofrequency coil that is resonant at multiple frequencies is required to carry out multi-nuclear MRI. While dual-resonant coils are abundant in the literature [23], coils with three or more resonances are rare [24–26]. In this work, our goal was to explore the possibility of creating a quadruple-resonant coil to allow simultaneous ¹H, ²H, ²³Na, and ³¹P MRI in the human brain at 7 T.

Diodes or microelectromechanical system (MEMS) switches can be used to set up unique current paths in the coil that allows the user to toggle between resonances [27], [28], [29]. While this approach provides a straightforward means to perform sequential multi-nuclear imaging, simultaneous multi-nuclear imaging is not allowed because the selected coil resonance precludes the others. Alternatively, we built a quadruple-tuned coil that included a quadrature birdcage that was tuned using passive circuitry to generate three resonances at the same time for ²H, ²³Na, and ³¹P imaging. A separate sub-coil consisting of four dipoles was added for ¹H imaging. Herein, we describe the quadruple-tuned coil architecture and circuitry used to interface the coil and scanner. We also compare the coil to available single- and dual-tuned coils and show first in vivo measurements.

Methods

Triple-Tuned Birdcage

We begin by describing the triple-tuned birdcage sub-coil (20 cm diameter, 26.7 cm length) (Figure 1). To trade off simplicity and B1 field uniformity we designed the simplest possible quadrature birdcage with the least amount of conductor breakpoints; a low-pass topology with four rods. The first step to tune the birdcage was to populate the four breakpoints (one per rod) with the capacitor required for a single resonance at each of the three desired frequencies at 7 T: 46 pF for ²H at 45.6 MHz, 15 pF for ²³Na at 78.6 MHz, and 5.7 pF for ³¹P at 120.3 MHz. The breakpoints were subsequently populated by two-pole parallel resonant networks $\left({\mathrm{Z}}_T\right)$, that were designed to emulate the respective capacitors at each frequency (Figure 2). To compare loading, Q measurements were performed while the breakpoints were populated with a capacitor or ${\mathrm{Z}}_T$. For simplicity, the measurements were perfomed while only one of the quadrature birdcage modes was active. In other words, two opposing rungs were populated, while the other two rungs were open circuited. The phantom was a cylinder filled with saline to mimic human head loading (volume = 5.1 L, diameter = 15 cm, and dielectric properties ${ϵ}_r=78$ and $\sigma =0.4\mathrm{S}/\mathrm{m}$ at 100 MHz).

Figure 1:

The quadri-nuclear coil. (a) Coil model with the triple-tuned ²H/²³Na/³¹P birdcage in gray and single-tuned ¹H dipole array in green. (b) Photograph of the constructed coil without protective shell. (c) Photograph of the constructed coil connected to the triple-tuned and ¹H interfaces.

Figure 2:

Triple-tuned ²H/²³Na/³¹P birdcage. (top) Triple-tuned birdcage schematic with detailed tuning impedance ${\mathrm{Z}}_T$ and feeding network for one of the two modes. The feeding network is comprised of a triple-tuned balun and the matching impedances ${\mathrm{Z}}_{p,d}$ and ${\mathrm{Z}}_{p,s}$. (bottom) Photographs of the constructed tuning impedance and the feeding network circuits. Lumped element values are shown in Figure S1.

The two birdcage modes were excited at feed ports on two neighboring rods that were matched to 50 Ω using two parallel impedances: one on the differential side of a triple-tuned balun ${\mathrm{Z}}_{p,d}$ and one on the single ended side ${\mathrm{Z}}_{p,s}$. The balun included parallel resonant networks with one pole, extending upon the double-tuned design in [30]. The insertion loss of the triple-tuned balun was estimated by simulating a system comprised of back-to-back baluns connected at the differential side and measuring S21 between the single-ended ports. To facilitate reproducibility, circuit board and mechanical files are available at https://github.com/NYU-Radiology-Hardware/Triple-Tuned-Birdcage-and-Single-Tuned-Dipole-Array.

Triple-Tuned Interface

We built a custom transmit/receive (TR) interface to drive the triple-tuned birdcage in quadrature mode and to receive (Rx) signals from the two birdcage ports with two broadband preamplifiers (Figure 3). Our MRI system (Siemens Healthcare, Erlangen, Germany) uses a single broadband amplifier to generate excitation pulses for non-proton nuclei. To achieve quadrature at all three frequencies, the amplifier was connected to a triplexer to separate its signal into frequency specific lines. Each line was connected to a single-tuned quadrature hybrid circuit to divide the signal into two parts with equal amplitude and a 90 deg phase offset for quadrature, resulting in a total of six lines. Triplets with the same phase offset were fed into a pair of triplexers whose outputs contained all three signals with either 0° or 90° offset, resulting in a total of two lines. Each was fed through a triple-tuned TR switch described below to the two quadrature feed ports of the birdcage.

Figure 3:

Triple-tuned TR interface and switch. (a) Triple-tuned TR interface schematic. (b) Triple-tuned TR switch schematic. Lumped element values are shown in Figure S2. (c) Photograph of the constructed triple-tuned TR interface.

The triple-tuned TR switch (see Figure 3b) is based on the single-tuned design described in [31]. The pi-network in the Rx arm was optimized to achieve low insertion loss between the coil and Rx ports and low reflection looking into the Rx arm with the diodes reverse biased (Rx mode). However, this network resulted in parasitic reactance looking into the transmit (Tx) port with the diodes forward biased (Tx mode). The parasitic reactance was cancelled with a parallel resonant network with two poles $Z_c$ in the Tx path. To improve isolation in Tx mode we inserted a 6-component LC network ${\mathrm{Z}}_s$ in series to the shunt diode in the Rx arm to create an RF-short at the X-nuclei frequencies. A broadband preamplifier was used to amplify signals from all three nuclei (optimal noise impedance = 50 Ω and noise figure between 0.5 and 0.6 dB at the frequencies of interest, model WBA0001B, WanTcom Inc., Chanhassen, MN, USA).

Dipole Array

We built a ¹H four-channel dipole sub-coil whose elements bisected the triple-tuned birdcage apertures (Figure 1 a). The sub-coil consists of two dipoles with 14.5 cm length that were mounted on the left and right sides of the same cylindrical surface as the birdcage coil, along with two dipoles with 22 cm length that were mounted on the anterior and posterior sides of the coil (Figure 4). The latter were offset by 5 cm from the cylinder to reduce local specific absorption rate (SAR). Each of the dipoles were fed through single-tuned lattice baluns to reduce cable currents. The dipoles were electrically lengthened with appropriate inductors to fine tune their resonant frequency to 297.2 MHz. Matching to 50 Ω was achieved with two capacitors in parallel, one before the balun and one after the balun. The dipoles were matched while loaded with a head-shaped phantom filled with tissue simulating liquid (volume = 4.5 L, ${ϵ}_r=65,\sigma =0.45\mathrm{S}/\mathrm{m}$ at 300 MHz)[32].

Figure 4:

¹H dipole array. (a) the 145 mm dipoles positioned on the left and right of the coil; (b) the 220 mm dipoles positioned on the top and bottom.

The dipole sub-coil was driven through a single-tuned interface. The Tx signal was divided into four parts with equal amplitude and 90° phase offsets. The power divider outputs were connected to the dipoles via four TR switches (Stark Contrast, Erlangen, Germany). Quadrature drive was adjusted with individual coaxial cables that ensured constructive interference of the individual dipole ${\mathrm{B}}_1^{+}$ fields in the center of the phantom.

Safety Assessment

Electromagnetic simulations and experiments were performed to ensure the coil operated within IEC SAR limits [33, 34]. In simulation, we modeled the birdcage and dipoles together in finite element software (HFSS, ANSYS Inc., Canonsburg, PA). The six coil ports were matched to 50 Ω while loaded with a male body model. We calculated whole head and 10 g local SAR at each frequency by processing simulated E-fields in MATLAB (The MathWorks, Natick, MA).

Whole head SAR was also estimated experimentally by measuring the temperature difference $\mathrm{\Delta }T$ before and after a high power pulse sequence was applied for 10 min while the coil was loaded by a saline phantom with mass m and conductivity similar to the human head. We then computed power loss due to heat deposition in the phantom $P_{\mathrm{\Delta }T}$ using:

$$P_{\mathrm{\Delta }T}=\frac{m\cdot \left(\mathrm{\Delta }T+\mathrm{\Delta }{T}_{ϵ}\right)\cdot c}{t}$$ [1]

where $c$ is the heat capacity of water and $t$ the duration of the sequence. Thermal power dissipated from the phantom into its surroundings during the experiment was neglected. We added $\mathrm{\Delta }{T}_{ϵ}=0.2\mathrm{K}$ to the measured temperature difference $\mathrm{\Delta }T$ to account for measurement uncertainty of the temperature probe. Whole head SAR was then computed with:

$$SAR=\frac{P}{m}\text{with}P=min\left(P_{\mathrm{\Delta }T},P_{in}\right)$$ [2]

where $\mathrm{P}$ is the minimum of $P_{\mathrm{\Delta }T}$ and the power delivered to the coil $P_{in}$ as measured by the scanner monitoring system. The final power limit $P_{limit}$ for each frequency was set to the experimentally derived power limit, unless the local 10 g SAR was the limiting factor as derived in the simulations. When the simulated local 10 g SAR was used as a power limit, we further reduced by a conservative safety factor of two.

Imaging

We compared SNR of the developed quadruple-tuned coil to that of available single- or dual-tuned reference coils at our Center. The reference coils were: 1) single-tuned ¹H 24-channel Rx coil with a Tx birdcage (Duyn Array, Nova Medical, Wilmington, MA); 2) for a lack of an existing ²H coil we built a single-channel rectangular loop (10 cm × 20 cm); 3) dual-tuned ²³Na/¹H 8-channel head coil (length = 19 cm and diameter = 27.9 cm) [35]; and 4) dual-tuned ³¹P/¹H 8-channel head coil (length = 20 cm and diameter = 28 cm)[36]. The phantoms used for SNR measurements were: 1) head-shaped container filled with tissue simulating liquid listed above for ¹H; 2) cylinder filled with with 99.8% deuterium oxide for ²H (volume = 100 ml, diameter = 5 cm); and 3) cylinder filled with distilled water, 40 g phosphate buffered saline, and 20 g potassium phosphate monobasic for ²³Na and ³¹P (volume = 4 L, diameter = 17 cm).

Since ²H MRI is not directly supported by our system, we used the method described by Roig et al. [37] in which an external local oscillator signal is provided to the scanner to enable excitation and detection at the desired frequency. The SNR was measured using a gradient echo sequence with a 60 V excitation pulse for the X-nuclei and 20 V for proton, along with a separate measurement in which the excitation pulse was deactivated to measure noise (see Table 1 for imaging parameters). The SNR maps were calculated using the method described by Kellman and McVeigh [38]. To demonstrate metabolic imaging in vivo, we scanned one human subject after obtaining their informed written consent and approval from the New York University Institutional Review Board.

Table 1:

Imaging parameters. The phantom data for SNR comparison was acquired in 2D (1 slice). The in vivo brain data was acquired in 3D. Sequences: GRE, Gradient Echo; FLORET, Fermat Looped Orthogonally Encoded Trajectories; CSI, Chemical Shift Imaging.

	SNR comparison in phantoms				Brain imaging in vivo
	2H	23Na	31p	1H	2H	23Na	31p	1H
Sequence	GRE	GRE	GRE	GRE	FLORET	FLORET	CSI	GRE
Voxel size [mm]	3.1	6.3	25	7.8	30	5.8	30	1.5
Slice thickness [mm]	20	100	50	6	30	5.8	30	1.5
TR [ms]	30	29	2000	2000	19	25	300	18
TE [ms]	3.7	7.5	3.2	4.5	1.0	0.2	1.3	3.1
Pulse voltage [V]	60	60	60	20	60	60	60	181
Number of averages	1	16	32	1	335	300	64	1
Bandwidth [Hz/pixel]	500	260	260	300	390	390	4000	320
Acquisition time	2.5 s	31 s	17:06 min	2:10 min	3:11 min	12:45 min	7:41 min	6:01 min

Results

Measurements showed that the triple-tuned birdcage had $\mathrm{Q}$-ratios between 1.6 and 1.9, compared to ratios of 4.2 to 6.3 for the single-tuned birdcages (Table 2). Note that ${\mathrm{Q}}_0$ for ³¹P in the triple-tuned configuration was greater than that in the single-tuned configuration. This counterintuitive result can be due to efficient energy storage in the tuning network $\left({\mathrm{Z}}_T\right)$, whose components are assumed to have higher $\mathrm{Q}$ values than the birdcage itself [39]. For this reason, the $\mathrm{Q}$-ratio is more relevant than ${\mathrm{Q}}_0$ for assessing coil performance since it describes power delivered to the phantom.

Table 2:

Measured $\mathrm{Q}$-values, efficiency, and relative efficiency for single- and triple-tuned birdcages. Efficiency is calculated as ${(1-\frac{Q_L}{Q_0})}^{1/2}$ and the relative efficiency is normalized to that of single-tuned birdcages. ${\mathrm{Q}}_0$: $\mathrm{Q}$ unloaded. ${\mathrm{Q}}_{\mathrm{L}}$: $\mathrm{Q}$ loaded.

	${\mathbf{Q}}_0$			${\mathbf{Q}}_{\mathbf{L}}$			Efficiency			Relative Efficiency
	2H	23Na	31p	2H	23Na	31p	2H	23Na	31p	2H	23Na	31p
Single-tuned	530	420	160	125	67	27	0.87	0.92	0.91	1	1	1
Triple-tuned	260	200	210	145	125	110	0.67	0.61	0.69	0.76	0.67	0.76

The insertion loss of the triple-tuned balun was −0.1, −0.4, and −0.1 dB at the three frequencies. The reflection coefficient plots show that the triple-tuned birdcage ports and dipoles were matched to below −25 and −15 dB, respectively (Figure 5 a,b). The scattering matrices show that coupling between birdcage ports was less than −20 dB at 45.6 MHz, 78.6 MHz, and 120.3 MHz, while the maximum coupling between dipole ports at 297.2 MHz was −13 dB (Figure 5 c). Cross-coupling between the birdcage and dipole ports was less than −30 dB at all four frequencies. Adding the dipole array to the triple-tuned birdcage had a negligible effect on the ${\mathrm{B}}_1^{+}$ field distribution (Figure S3) and caused only a minimal shift in resonance frequency at the X-nuclei, see Table S1. Adding the birdcage to the dipole array resulted in a 5.5 MHz shift in resonance frequency. This caused an attenuation of the EM-fields due to the mismatch, which was simply resolved by matching the dipole array in the presence of the birdcage (Figure S3). The noise coefficient matrices show that the maximum coefficient was 4.2 %, 6.7 %, and 37 % between birdcage channels at 45.6 MHz, 78.6 MHz, and 120.3 MHz, respectively, and 35 % between dipole channels at 297.2 MHz (Figure 5 d). Assymetries in the ¹H scattering and noise correlation matrices are due to assymetric loading by the head phantom and different offsets between the dipoles and phantom.

Figure 5:

Coil characteristics. (a,b) Reflection coefficients ($\mathrm{\Gamma }$, in dB) versus frequency (freq, in MHz) for the channels of the triple-tuned birdcage (a) and dipoles (b). (c) Six-element scattering matrices at the four Larmor frequencies in which the active birdcage or dipole sub-coils are highlighted with a white dotted rectangle. (d) Measured noise coefficient matrices at the 4 Larmor frequencies for the relevant sub-coils.

With the triple-tuned TR switch in Rx mode, the reflection coefficient looking into the Rx port was below −20 dB and the insertion loss between the coil and Rx ports was below −0.2 dB at 45.6 MHz, 78.6 MHz, and 120.3 MHz. In Tx mode, the isolation between the Rx and Tx ports was below −37 dB. Due to the 15 dBm input power limit of the broadband preamplifier, the multi-nuclear Tx pulse voltage was limited to 60 V while the ¹H Tx pulse was limited to 200 V due to dipole arcing. Power limits are listed in Table 3. Power deposition can be a concern for simultaneous multi-nuclear excitation. Table 3 shows that the time-averaged power delivered by the system during the in vivo protocol was well below the power limit for ²H, ²³Na, and ³¹P, indicating headroom is available to excite multiple nuclei within the same TR.

Table 3:

Simulations: Power limits based on global and maximal 10 g local SAR (${\mathrm{P}}_{\mathit{local}}$ and ${\mathrm{P}}_{\mathit{global}}$, respectively). Measurements: Measured parameters for experimentally estimated power limit based on global SAR. $\mathrm{\Delta }\mathrm{T}$: Temperature difference before and after a high power pulse sequence was applied while the coil was loaded by a saline phantom with mass m. ${\mathrm{P}}_{\mathrm{\Delta }T}$: Power loss due to heat deposition in the phantom. ${\mathrm{P}}_{in}$: Power delivered to the coil as measured by the scanner monitoring system. Power limit $\left({\mathrm{P}}_{\mathit{limit}}\right)$: the experimentally derived power limit, unless the local 10 g SAR was the limiting factor as derived in the simulations. When the simulated local 10 g SAR was used as a power limit, we further reduced it by a conservative safety factor of two. Applied power $\left({\mathrm{P}}_{\mathit{applied}}\right)$: the time-averaged power applied during in vivo scans listed in Table 1.

	2H	23Na	31p	1H
Simulations
${\mathrm{P}}_{\mathit{local}}\left[\mathrm{W}\right]$	22.1	22.7	23.1	14.6
${\mathrm{P}}_{\mathit{global}}\left[\mathrm{W}\right]$	18.5	18.5	18.6	22.7
Measurements
$\mathrm{\Delta }\mathrm{T}\left[\mathrm{K}\right]$	0.2	0.2	0.2	0.2
m [kg]	3.9	4.2	3.9	3.4
${\mathrm{P}}_{\mathrm{\Delta }T}\left[\mathrm{W}\right]$	10.9	11.8	10.9	9.3
${\mathrm{P}}_{\mathit{in}}\left[\mathrm{W}\right]$	4.2	11.1	5.7	18
${\mathrm{P}}_{\mathit{global}}\left[\mathrm{W}\right]$	12.5	13.4	12.5	21.1
Power limit
${\mathrm{P}}_{\mathit{limit}}\left[\mathrm{W}\right]$	12.5	13.4	12.5	7.3
Applied power
${\mathrm{P}}_{\mathit{applied}}\left[\mathrm{W}\right]$	3.5	2.5	0.1	7.0

In the center of the phantom, the quadruple-tuned coil SNR was 78, 59, 44, and 48 % lower than that of single- or dual-tuned reference coils for ¹H, ²H, ²³Na, and ³¹P respectively (Figure 6). Note that the quadruple-tuned coil operates in the linear flip angle regime due to the pulse amplitude limits, therefore no estimation of flip angle can be given, and SNR measurements were influenced by both Tx and Rx efficiency. The quadruple-tuned coil demonstrated sufficient sensitivity for proof-of-concept in vivo multi-nuclear imaging and spectroscopy (Figure 7).

Figure 6:

Comparison of SNR maps for ¹H, ²H, ²³Na, and ³¹P measured with the quadri-nuclear coil and with single- or dual-tuned reference coils in the central transversal plane in phantoms. The central and slice-averaged SNR values are overlaid in the center and lower-right corner of each panel.

Figure 7:

Quadri-nuclear MRI in brain in vivo at 7 T. (Columns 1–3) Three plane ¹H, ²H, and ²³Na images. (Columns 4–5) ³¹P spectral maps and single-voxel spectra. Single-voxel spectra locations are indicated by axis color that corresponds to colored ROIs overlaid in the transverse ¹H image and ³¹P map.

Discussion and Conclusion

We designed and constructed a triple-tuned birdcage and four-channel dipole coil along with a customized interface for head imaging at 7 T. We used the coil to acquire ¹H, ²H, and ²³Na images, along with ³¹P spectra. The triple-tuned birdcage showed whole-brain coverage and sufficient sensivity for in vivo imaging. While not demonstrated here due to ongoing pulse sequence development, the coil enables truly simultaneous multi-nuclear excitation and signal detection because passive components were used for coil tuning, matching, and signal routing. Active switching diodes were used only to toggle between Tx and Rx modes. Our approach relied upon multi-pole circuits to create multiple resonances in the triple-tuned birdcage. Such circuits necessarily involve efficiency trade-offs [40] that we attempted to balance by empirically selecting component values that resulted in similar unloaded-to-loaded $\mathrm{Q}$-ratios at all three frequencies (see Table 2). The triple-tuned balun and TR switch were designed with the same goal of balancing loss roughly equally at all three frequencies. Due to the large component value search space, gradient optimization in modeling software was used to guide the design of all triple-tuned circuits (PathWave Advanced Design System, Keysight Technologies, Santa Rosa, CA, USA).

The efficiencies $\sqrt{1-Q_L/Q_0}$, that are provided in Table 2 provide a means for relative comparison with respect to a lossless coil with identical geometry [41, 42]. Using single-tuned birdcage coils as reference points, the $\mathrm{Q}$-measurements indicated that the triple-tuned network resulted in an efficiency penalty of 24 – 33%. To give a rough sense of how this would impact image SNR measured with a given Tx pulse amplitude in the linear flip angle regime, we can use the relationship: SNR $\propto \left|B_1^{+}\cdot B_1^{-}\right|={\left|B_1^{-}\right|}^2$ (with $B_1^{-}\approx B_1^{+}$ at low frequencies), and therefore $\propto 1-Q_L/Q_0$. Given this framework, the triple-tuned network is expected to result in an image SNR penalty of 42 – 55%. This is in the same ballpark as actual SNR comparisons between the triple-tuned birdcage and single- and dual-tuned coils in the center of the phantom (Figure 6). However, we point out that the single- and dual-tuned coils varied in terms of efficiency, number of Rx channels, and Rx chain loss, which make it difficult to breakdown the sources of SNR disparity. Another confounding factor is that quadruple-tuned coil pulse amplitude limit restricted the flip angle to the linear regime, which prevented flip angle estimation. Therefore, SNR measurements were influenced by Tx chain loss as well.

Approaches for multiple frequency coil tuning using passive components can be roughly classified into three classes: (1) dependent structures in which sub-coils tuned to different frequencies are allowed to interact [35, 36, 43–46], (2) independent structures in which interaction between sub-coils tuned to different frequencies is minimized by filtering or geometric arrangement [47–51], or (3) integrated structures in which all resonances are present on a single structure [40, 52–54]. We utilized dependent structures for ¹H and the group of ²H, ²³Na, and ³¹P because of their large disparity in resonant frequencies. The 4-channel ¹H dipole sub-coil was selected because its minimal copper footprint, geometric symmetry with the 4-rod birdcage, and small electrical size at the X-nuclei frequencies allowed straightforward combination with negligible disturbance to the birdcage. On the other hand, the 4-channel dipole sub-coil was far from optimal in terms of SNR and B1 uniformity (Figure 6). Other drawbacks such as relatively low power and pulse voltage limits could be remedied by expanding the number of dipoles from 4 to 8 or more, while keeping interaction with the birdcage to a minimum.

We utilized an integrated triple-tuned birdcage for ²H, ²³Na, and ³¹P. Compared to dependent and independent structures, the integrated triple-tuned birdcage can be considered more elegant due to fewer ports, preamplifiers, and coaxial cable connections, as well as the inherent decoupling and efficiency gain associated with quadrature mode orthogonality. On the other hand, the triple-tuned birdcage approach required precise tuning circuitry. For this reason, we used a four-rung birdcage to reduce the number of approximately identical tuning circuits at the cost of homogeneity compared to a birdcage with larger numbers of rungs [55]. We also point out that the triple-tuned balun and TR switch circuits have higher loss and can be simplified in dependent and independent structures because of the opportunity to optimize each frequency separately [23]. One specific example is a linear birdcage tuned to one frequency combined with a orthogonal linear saddle coil tuned to a second frequency [56]. In this case, quadrature operation is sacrificed in favor of simplified linear operation and more efficient single-tuned circuitry. Detailed analysis is required to determine which approach provides more SNR. Of course, quadrature or linear volume coil designs are expected to be outperformed in receive mode by phased-arrays [23], although at the cost of complexity. Therefore the preferred coil design may be dependent upon the specific application including SNR, B1+, and SAR considerations for each nucleus. Another limitation of the integrated triple-tuned approach was the sparse selection of commercially available broadband preamplifiers. Despite reasonable TR switch isolation (−37 dB), the low input power limit of the preamplifier (15 dBm) restricted ²H, and ²³Na, and ³¹P excitation pulse amplitude to 60 V. One could potentially remedy this issue at the cost of sensitivity by inserting low loss MEMS circuits into the Rx path to increase isolation from the Tx pulse or by filtering the Rx signal into frequency-specific components that could be inputted to standard narrowband preamplifiers that typically have higher power limits.

While the original incentive to build this quadri-nuclear RF coil was to acquire simultaneous data from ¹H, ²H, ²³Na, and ³¹P, this proof-of-concept work was only performed with independent acquisitions in phantom and one brain in vivo because sequences for simultaneous MRI or MRS of ²H and ³¹P are not available in our Center yet. Furthermore, we point out that modifications to the system RF chain, similar to those described in [19–22, 57], may be necessary to carry out simultaneous multi-nuclear measurements.

In conclusion, we designed and built a proof-of-concept triple-tuned birdcage (²H, ²³Na, and ³¹P) and single-tuned dipole array (¹H) for quadri-nuclear MRI of the head at 7 T. Simultaneous MR acquisitions of pairs (or more) of nuclei are now under development for further applications in healthy brain and in pathologies such as neurovascular diseases and brain tumors.