Creating a clinical platform for carbon‐13 studies using the sodium‐23 and proton resonances

Purpose Calibration of hyperpolarized 13C‐MRI is limited by the low signal from endogenous carbon‐containing molecules and consequently requires 13C‐enriched external phantoms. This study investigated the feasibility of using either 23Na‐MRI or 1H‐MRI to calibrate the 13C excitation. Methods Commercial 13C‐coils were used to estimate the transmit gain and center frequency for 13C and 23Na resonances. Simulations of the transmit B 1 profile of a Helmholtz loop were performed. Noise correlation was measured for both nuclei. A retrospective analysis of human data assessing the use of the 1H resonance to predict [1‐13C]pyruvate center frequency was also performed. In vivo experiments were undertaken in the lower limbs of 6 pigs following injection of hyperpolarized 13C‐pyruvate. Results The difference in center frequencies and transmit gain between tissue 23Na and [1‐13C]pyruvate was reproducible, with a mean scale factor of 1.05179 ± 0.00001 and 10.4 ± 0.2 dB, respectively. Utilizing the 1H water peak, it was possible to retrospectively predict the 13C‐pyruvate center frequency with a standard deviation of only 11 Hz sufficient for spectral–spatial excitation‐based studies. Conclusion We demonstrate the feasibility of using the 23Na and 1H resonances to calibrate the 13C transmit B 1 using commercially available 13C‐coils. The method provides a simple approach for in vivo calibration and could improve clinical workflow.


| INTRODUCTION
Hyperpolarized 13 C MRI is an emerging technique to noninvasively image cellular metabolism in health and disease: the exchange of hyperpolarized 13 C-pyruvate to 13 C-lactate is the most studied in vivo reaction using the technique. [1][2][3] The recent translation of the technology into human studies has demonstrated applications for the method in prostate and brain tumors as well as the normal heart and brain. [4][5][6][7][8] However, there are a number of challenges to be overcome before the technology can be used more routinely. For example, calibration of the RF amplifier gain (here referred to as RF gain as well as transmit gain (TG), coil voltage, and coil reference scale), center frequency (f 0 ), and estimation of transmit-receive B 1 for 13 C can be challenging given the very short time window for hyperpolarized 13 C imaging following a single injection of hyperpolarized 13 C labelled substrate. Calibration is usually undertaken prior to the detection of the transient hyperpolarized 13 C-pyruvate signal in vivo. A number of solutions to this problem have been proposed, including the use of a phantom containing a high concentration of 13 C-enriched molecules for calibration, as well as phantom acquisition prior to patient scanning. 9 Although these methods provide an estimation of RF gain for the field of view (FOV) containing the phantom, there is no current method to establish the transmit B 1 field over the whole FOV, which is particularly relevant because variations in the delivered flip angle are expected throughout the patient. Furthermore, the position and composition of the phantom increase the uncertainty of centre frequency estimation.
A selective excitation approach is frequently employed to acquire high signal to noise ratio images of the metabolic products of [1-13 C]pyruvate. Deviations in the flip angle across the FOV can introduce significant uncertainty in the kinetic parameters that are derived using this spectral-spatial imaging approach. 10,11 A further challenge is the estimation of coil sensitivity maps, which is used to accurately combine the images from individual coils. This absence of significant signal from natural abundance 13 C renders these challenges difficult to solve without the use of a phantom. An interesting calibrationless approach has been reported that uses the pyruvate signal to estimate the sensitivity map for in vivo studies. 12 Here, we propose using the endogenous signal derived from the 1 H and 23 Na nuclei as a reference for the 13 C imaging: 23 Na has a resonant frequency similar to that of 13 C at clinical field strengths (~1 MHz difference at 3 tesla) with a relatively high natural abundance in the body, producing the second highest signal on MRI from the nuclei detectable in biological tissues. The 1 H nucleus is the highest natural abundance NMR active signal in the body and thus represents a further option to confirm center frequency placement prior to 13 C acquisition. A number of clinical studies have demonstrated the biodistribution of sodium using 23 Na-MRI in both health and disease. [13][14][15][16] Previous reports have utilized a variable capacitor custom-built RF coil to enable the coil to be tuned to both the 13 C and 23 Na frequency, allowing accurate RF gain estimation for rodent studies. 17,18 In this study, we have expanded on this work to study the use of commercially available single tuned 13 C coils to acquire transmit B 1 and f 0 information from the 23 Na resonance using a clinical system in large animals, therefore providing the translational leap required for this technique to be incorporated into routine clinical practice. Furthermore, we have incorporated the use of the 1 H nucleus to provide further confidence in the estimated 13 C center frequency derived from the 23 Na measurements.
This approach could improve the workflow of hyperpolarized 13 C-MRI experiments by removing the reliance on external phantoms for the prescan acquisition on clinical systems using the data acquired on commercially available coils.

| METHODS
Experiments were performed at 2 different sites (MR Research Centre, University of Aarhus, Denmark; Department of Radiology, University of Cambridge, UK), which are referred to as sites A and B, respectively.
Human study: Local ethical approval was obtained for this prospective study (NRES Committee East of England, Cambridge South, REC number 15/EE/ 0255).
Porcine study: All porcine imaging was undertaken in accordance with the Danish Animal Welfare Act 2013 following an explicit national ethical review process undertaken by the Danish Animal Experiments Inspectorate.

| Phantom and coil setup
Phantom experiments were performed at site A using a 13 C-labeled urea (8 M, Merck, Darmstadt, Germany) vial and identical 1 L containers filled with saline at varying concentrations (156, 117, 78, 39 mmolL −1 ). The 13 C-urea phantom was placed on top of the saline phantom and secured. The receive coils used in this study were tuned to 13 C and included a simple loop coil (Rapid Biomedical, Rimpar, Germany) and 8-channel paddle coils (GE Healthcare, Waukesha, WI,

| 1819
GRIST eT al. USA). The loop coil was placed on top of the 13 C-urea phantom, and the paddle coils were placed around the right and left side of the saline bottles. A separate 13 C-tuned clamshell volume coil (Rapid Biomedical, Q unloaded = 270, Q loaded = 75, S11 < −150 cB) was used for transmission. 19 Data acquisition was undertaken using a 3 tesla scanner (MR750, GE Healthcare). Phantom and coil positioning can be seen in Supporting Information Figure S1.

| RF gain and f 0 estimation
Using the phantom setup described above, RF gain and f 0 were assessed using a commercially available pulse-acquire sequence (Fidall, GE Healthcare) with 2 off-resonance Bloch-Siegert pulses (excitation pulse width = 0.5 ms, repetition time = 2 s, echo time = 0.5 ms, flip angle = 90°). 20 Estimation of RF gain and f 0 for 13 C and 23 Na were performed in series. Experiments were repeated in triplicate, with the phantom removed and re-sited between each repeat. 1 H, 13 C, and 23 Na acquisitions were acquired for all saline concentrations. Scaling factors to convert between the 1 H f 0 , 23 Na f 0 , and the 13 C f 0 were derived from Equations 1 and 2: where f 1 H 0 , f 23 Na 0 , and f 13 C 0 are the center frequencies of 1 H, 23 Na, and 13 C, respectively.
A further correction for the difference in TG between 23 Na and 13 C was derived using Equation 3. Because RF gain is logarithmically scaled, the subtraction rather than the ratio between 13 C and 23 Na RF gain is used.
where TG 23 Na and TG 13 C are the required TG for 23 Na and 13 C, respectively. The mean scaling factors for frequency and gain were derived by averaging across all experiments.

B 0 mapping
Carbon-13 and sodium-23 transmit B 1 maps were calculated using a cylindrical 8 L saline/pyruvate phantom (150 and 102 mmolL −1 respectively, doped with 80 mL Gadovist to shorten the 13 C T 1 below 1 s; 1 H-MRI image shown in Supporting Information Figure S2A), a 16-channel receive array coil (Rapid Biomedical, Rimpar, Germany), and a clamshell transmit coil, and by employing the double angle method. 21 Acquisition parameters were as follows: 2D-chemical shift imaging (CSI), slice thickness = 60 mm, spectral width = 5000 Hz, spectral resolution = 256 points, FOV = 240 mm, matrix = 8 × 8, flip angles = 40 and 80, 13 C number of averages (NEX) = 32, 23 Na NEX = 64, 13 C repetition time = 2.5s, 23 Na repetition time = 600 ms, RF pulse = partially self-refocusing sinc excitation (1.8 ms, bandwidth 2289 Hz for 13 C) or hard pulse (pulse width = 2 ms, for 23 Na), 23 Na echo time = 1.2 ms, and 13 C echo time = 1.8 ms. The width of the hard pulse is 4 times longer than the default (0.5 ms). Because 23 Na requires approximately 12 dB more power than 13 C, the pulse width for 23 Na was quadrupled, although the amplitude was fixed to remain the same as for the default pulse width. Spectral data were zero-filled in the time domain to 1024 points, Fourier-transformed, zeroorder-phased, and fit with a Lorentzian function prior to calculation of B 0 and B 1 maps. All processing was performed in MatLab (2018b, MathWorks, Natick, MA).
B 0 maps were calculated on a voxel-by-voxel basis by finding the center of the pyruvate or sodium resonance relative to the system center frequency for the inner 6 × 6 voxels of the 2D CSI grid. The mean difference in center frequency for both resonances was calculated over the phantom. The mean difference between 13 C and 23 Na B 0 maps was calculated for the 6 × 6 grid in Hertz, as well as the mean B 0 shift across the FOV for each nucleus in Hertz.
The mean B 1 ratio, as well as the mean absolute percentage difference defined in Equation 4, at and between both frequencies was calculated from the inner 6 × 6 voxels of the 2D CSI grids: where x and y are the spatial locations of each voxel in the 6 × 6 CSI grid.

| Simulations
The B + 1 distribution of the clamshell volume coil was simulated using the frequency solver within Computer Simulation Technology software (CST, CST 2018, Darmstad, Germany). The coil consisted of 2 square loops of 300 mm diameter placed coaxially with the centers separated by 360 mm. This coil design provides a homogenous resonance mode when the signal in its 2 loops is shifted 180°. For the analysis in this study, it was important to include in the simulation a (1) 23 Na, 13 C Frequency scaling factor = f real implementation of the phase shifter used to create the homogenous mode because it is also frequency-dependent. For that purpose, a lumped-element 180° hybrid circuit 22 tuned to the 13 C frequency was included in the simulation using the circuit cosimulation feature within the software. A schematic of the whole simulation setup is shown in Figure 1, including the matching networks (lattice baluns) needed between the 180° hybrid and the loops. The transmit B 1 field distributions for 1 W of accepted power were calculated as per Equation 5 and compared between the 13 C (32.13 MHz) and 23 Na (33.79 MHz) frequencies.
The results are presented in a plane orthogonal to the B 0 direction and averaged over a 100 mm slice.

| Multichannel coil noise correlation
Noise correlation was assessed using the 8-channel paddle receive coils in conjunction with the clamshell transmit. To acquire a noise-only scan, the RF amplifier was disabled, and multichannel receive data was acquired at both 13 C and 23 Na frequencies.

| System magnetic field drift and 1 H center frequency estimation from human studies
A retrospective analysis of previously acquired healthy (N = 8) and patient (N = 9) brain data acquired at site B between March 2016 and October 2018 was performed. Experiments were performed on a 3 T MR750 MR system (GE Healthcare) using a quadrature birdcage 13 C/ 1 H head coil (Rapid, Rimpar, Germany).
A phantom containing either approximately 8 mL of 8 M 13 C-urea or 1 M 13 C-bicarbonate or 2 mL of 4 M [1- 13 C] lactate was placed inside a disposable cover on the superior edge of the ear defenders for use during the calibration of frequency and pulse power, then generally removed prior to the hyperpolarized pyruvate injection.
Slice-selective 13 C-MR spectra and/or images were acquired from the brains of the 17 subjects following injection of 0.4 ml/kg of hyperpolarized [1-13 C]pyruvate, as described previously. 8 Slice-selection was performed using either a spectral-spatial pulse with a pass-band of 85 Hz (22.5 ms duration, or in most cases a partially self-refocusing sinc excitation as described above). 11,23 Individual experimental parameters varied as the protocol developed. In in the majority of subjects, however, 3 axial slices were collected (3 cm thick, 3 mm spacing) using the iterative decomposition using echo asymmetry and least squares estimation spiral CSI technique, 12 with a cycle of 8 steps, including 1 slice-localized spectrum and 7 single-shot spiral images with incremented echo time from which images were reconstructed at the frequency offsets for pyruvate, lactate, bicarbonate, alanine, and pyruvate hydrate. The usual temporal resolution of the dynamic acquisitions was 4 s (sequence repetition time 500 ms), excitation flip angle 15°, image FOV 24 cm, effective true resolution in-plane 12 mm, interpolated to 1.875 mm.
Spectra were analyzed in MatLab to measure the actual frequency of both 13 C-pyruvate from the central brain slice in the time-averaged dynamic series and the reference standard during the preinjection calibration scan. The relationship was characterized between the actual 13 C-pyruvate frequency in vivo and 3 different parameters, which could be used as a predictor of frequency (Temporal Drift, Phantom, and Water 1 H methods, described below). For each of these methods, a Bland-Altman analysis was performed comparing the pyruvate frequency predicted using that method and the true measured value for all subjects to retrospectively determine which method would have performed best.
1. Temporal Drift method. The frequency of pyruvate in vivo was assumed to vary in a slow linear fashion due to drift in the system B 0 . The transmit frequency for a particular subject was therefore calculated from the slope of a linear fit to frequency against the date that the study was performed for all 17 subjects. 2. Phantom method. The frequency difference between pyruvate in vivo and the reference metabolite within the external phantom was tabulated, and the mean offset over all subjects was applied in each individual. 3. Water 1 H method. The frequency of water in the 1 H-MRI series immediately preceding the 13 C experiment was recorded and divided by the ratio of the gyromagnetic ratio (γ) for 1 H/ 13 C (3.97595) to estimate the 13  The pigs were imaged in a supine position, and the 13 C-receive loop was positioned centrally on the biceps femoris muscle of the right lower limb. The receive coil and pig were placed in the central transmit field of the 13 C-transmit coil. Bloch-Siegert experiments were performed prior to the 13 C-pyruvate injection for both the 23 Na calibration acquisitions, with 1 H center frequency taken from the previous series, and the 13 C prescan acquired with 13 C-lactate phantom. Frequency scaling between 1 H/ 23 Na and 1 H/ 13 C pyruvate was calculated from Equations 1 and 2, respectively. Approximately 24 mL of ~250 mM hyperpolarized 13 C-pyruvate was injected in the left femoral vein over 10 s, followed by a 20 mL saline flush. 13 C magnetic resonance spectroscopy was performed at the commencement of the 13 C-pyruvate injection using the following parameters: partially self-refocusing sinc excitation, 23 RF bandwidth = 2000 Hz, spectral acquisition bandwidth = 5000 Hz, number of samples = 2048, repetition time = 1 s, time points = 128, flip angle = 12°, and slice thickness = 40 mm.

| In vivo spectral postprocessing
Hyperpolarized spectra were fit using a matching pursuit algorithm, and apparent kinetic rate constants for the exchange of pyruvate to lactate (k PL ) were calculated by solving the differential form of the modified Bloch equations in the time and frequency domains. 24 Furthermore, spectra were summed in the complex domain over time, and [1- 13

| Statistical analysis
Statistical significance was defined as P < .05. The mean center frequency difference between 13 C-urea and 23 Na/ 1 H at site A was determined by assessing the difference in center frequency between each paired 13 C and 23 Na and the 1 H measurement and averaging the results. Using in vivo data from site A, the ratiometric frequency difference between hyperpolarized 13 C-pyruvate and 1 H/ 23 Na across all porcine experiments was averaged.
Differences in RF gain between different saline loading states were assessed by fitting a linear model to the RF gain data.
Due to the small number of subjects used in this study, differences between time and frequency domain-derived kinetic parameters for the in vivo data were assessed using a Mann-Whitney U test.

| RF gain and f 0 estimation using 23 Na
The difference in 23 Na (NaCl) and 13 C ( 13 C-urea) f 0 at site A was 1664497 ± 12 Hz (mean ± standard deviation [SD]) with a mean scaling factor of 1.05180 ± 0.00001, as derived from Equation 1. The mean correction for the 23 Na and 13 C RF gain was 10.4 ± 0.6 dB, as derived from Equation 2. The correlation between saline loading and RF gain, assessed using a linear model, found no significant results for any of the coil setups (R 2 < 0.1 and P > .05 in all cases; loop and paddle coil results shown in Figure 2A,B, respectively). Because no significant correlation between saline loading and RF gain was observed, data were averaged to estimate a mean RF gain difference between 13 C and 23 Na per coil experiment. Inspection of the calibration files for each coil demonstrated that there was a 1.35 dB difference in the additional requested system RF gain for the 13 C loop and 8-channel paddles. The average RF gain for each coil setup is shown in Table 1, with expanded results in Tables 2 and 3. 13 C and 23 Na B 0 maps showed a mean shift of +1 ± 18 Hz and −6 ± 23 Hz over the 6 × 6 CSI grid, respectively. 13 C and 23 Na B 1 maps showed a similar RF distribution over the FOV ( Figure 3A-C). B 1 maps showed a consistent small overflipping at both 23 Na and 13 C frequencies (1.14 ± 0.06 and 1.18 ± 0.05, respectively). The absolute average difference between the B 1 maps ( Figure 4D) was 2 ± 6% over the FOV. Proton and original flip angle images can be seen in Supporting Information Figure S2.

| Transmit B 1 simulations
The simulated transmit B 1 profiles are shown in Figure 4A,B for the 13 C and 23 Na frequencies, respectively. The difference between the field maps calculated from Equation 5 is shown in Figure 4C, demonstrating that the field distributions are very similar for both frequencies, with the maximum difference throughout the phantom being less than 2 dB. In absolute terms, the difference between the 13 C and 23 Na simulated field over the region of interest is 10.4 ± 0.2 dB, consistent with the experimental results.

| Multichannel coil noise correlation
Noise correlation between the 8 channels in the paddle coil revealed good linearity between coils, with little correlation between channels from the off-diagonal elements  ( Figure 5A). However, when performing at the 23 Na frequency, there was substantial off-diagonal coupling between elements (>0.6), as demonstrated in Figure 5B.

| Temporal drift method
The site B frequencies of both pyruvate in vivo and urea in the phantom drifted slowly downward over the 31-month timescale of the experiments (Figure 6). The rate of drift calculated from a linear fit to the pyruvate frequencies was 0.36 Hz/day. This drift is small in comparison to the scanner specification limits, which allow for drifts of up to 0.1 ppm/h, although such large drifts would only be expected in the case of heating due to running sequences with a high gradient duty cycle. An upgrade to the scanner software but using the existing hardware occurred in December 2017; however, this induced no discernible step change in frequency. Frequency shifts of  (B and C) 13 C and 23 Na transmit B 1 maps, respectively. (D) Ratiometric difference maps between B and C other metabolites in vivo relative to pyruvate appeared very consistent.

| Phantom method
The difference between the frequencies of 13 C-pyruvate in vivo and 13 C-urea in the phantom varied over a wide range (186 ± 43 Hz). The frequency separation was not correlated with date of acquisition (R 2 = 0.05), suggesting it was unlikely to be due to phantom degradation.

| Water 1 H method
The 1 H frequency of water scaled to the 13 C frequency by the respective gyromagnetic ratios, as described above, was on average 2620 ± 11 Hz higher than the pyruvate frequency in vivo.
Frequency prediction using the temporal drift or by referencing to the external phantom both performed poorly (Figure 7): the SD of differences (predicted minus actual) was 39 and 40 Hz, respectively, and 5 or 6 subjects, respectively, would have been outside the bandwidth of spectral-spatial excitation (error > 40 Hz) in the cohort of 17. Frequency prediction based on the water 1 H frequency performed better, with a SD of only 11 Hz, and there were no subjects in whom spectral-spatial excitation would have failed. All results are shown in Figure 7.

| In vivo experiments
Prospectively utilizing the 23 Na and 1 H prescan, hyperpolarized 13 C-magnetic resonance spectroscopy was successfully performed from the musculature of 6 pigs following the injection of hyperpolarized 13 C-pyruvate signal from 13 C-pyruvate, 13 C-lactate, and 13 C-bicarbonate observed in all subjects. The frequency scaling between 23 Na/ 13 C and 13 C/ 1 H calculated using Equations 1 and 2 was 1.05179 ± 0.00001 (mean ± 1 SD) and 3.97630 ± 0.00001 (mean ± 1 SD), respectively. The mean 13 C and 23 Na RF gain was 156 ± 2 and 260 ± 3, respectively. Kinetic analysis revealed a mean k PL of 0.007 ± 0.002 and 0.007 ± 0.002 s −1 in the frequency and time domains, respectively, with no significant difference between methods (P > .05). The correlation (R 2 ) between k PL in the frequency domain and lactate:pyruvate ratio was 0.9 with P = .01. The

| DISCUSSION
Hyperpolarized 13 C-MRI is a powerful technique to noninvasively probe tissue metabolism in many normal and diseased tissues, such as brain, heart, kidneys, and cancer. 4,8,[25][26][27] For example, increased lactate signal has been shown to correlate with more aggressive tumors, and a reduction in this lactate is seen in a wide range of tumor models following treatment. [28][29][30] This work is now being translated into humans, and early clinical research has shown elevated hyperpolarized 13 C-lactate in prostate cancer as well as in brain and breast tumors. Clinical hyperpolarized 13 C studies face a number of technical challenges, including accurate frequency calibration and the requirement for system inhomogeneity correction. This is particularly problematic due to the low natural abundance of 13 C in tissue, which results in poor signal from endogenous 13 C nuclei, and which in turn renders the determination of the center frequency and TG difficult. Therefore, new approaches are needed to increase confidence in 13 C prescan results, estimation of RF gain, transmission of B 1 distribution, and other coil sensitivity parameters.
Here, we show that the center 13 C frequency can be accurately estimated using the water 1 H frequency, which performed better than 2 alternative approaches that we explored: frequency drift and using an external 13 C-urea phantom. In addition, we have recently shown the feasibility of using a 13 C-tuned coil to image the distribution of 23 Na in tissue due to the high natural abundance of the latter and the small frequency difference between the 2 nuclei. 16 Here, we have explored whether this 23 Na signal could also be used to improve 13 C-MRI acquisition. The results show that the RF gain and f 0 for 13 C can be estimated using the endogenous 23 Na resonance acquired using dedicated, commercially available and clinical 13 C-coils.
There are additional benefits in utilizing the 23 Na resonance to calibrate the 13 C experiments: the short T 2 and T 1 of the nucleus allow rapid data averaging to increase signal to noise ratio and thus increase the confidence in the calibration parameters. Conversely, the long T 1 of 13 C-labeled molecules (on the order of several s) can lead to lengthy acquisition times for calibration, which further compound the problems of the low natural abundance of the nucleus.
Here, we have demonstrated the potential for using the 1 H and 23 Na resonances to provide a robust prescan for hyperpolarized 13 C experiments, with center frequency and RF gain, for single and multichannel clinical coils. Simulations showed consistent overflipping at 13 C frequency by the clamshell, which was also experimentally observed. The simulated field 23 Na frequency was highly homogeneous, which was also experimentally observed in the B 1 maps. Therefore, this provides a commercially available solution to the prescan and calibration required for 13 C-MRI and could assist in simplifying hyperpolarized F I G U R E 7 Difference between the predicted and measured frequency (+32130000 Hz) of 13 C-pyruvate in vivo from human brain 13 C-MRI studies at site B using the 3 approaches presented here. Circles: 13 C frequency prediction from a linear fit to the study date, accounting for a drift of 0.36 Hz/day. Triangles: 13 C frequency prediction by adding the mean offset between phantom and pyruvate to the phantom frequency. Squares: 13 C frequency prediction based on the 1 H frequency of water acquired from the anatomic series with ultrashort echo time sequences could be acquired to complement current human imaging protocols, providing a slice-by-slice correction for transmit B 1 for further quantitation. However, this will require further experimental optimization (acquisition of coil sensitivity maps, optimal trajectory design, and eddy current compensation) before clinical implementation is achieved. 31,32 Indeed, bolus tracking methods have been developed to calibrate using the hyperpolarized signal, providing real-time calibration for selective excitation experiments. 33 These techniques are promising and provide an alternative approach to the method presented here. A challenge for the implementation of these methods in vivo is that they commonly require significant scanner modifications to allow for third-party software control of the clinical system. 34 Given that our results have also shown significant changes in acquisition parameters over time, leading to temporal alterations in the center frequency for 1 H and 13 C-pyruvate, it is advisable to utilize the 23 Na or 1 H prescan before each experiment rather than assuming a static center frequency because selective excitation strategies may otherwise fail.
A challenge to our proposed method is the coupling between multichannel 13 C coils, which significantly increased at the 23 Na frequency. This could represent a problem for estimation of the sensitivity maps using array coils, but future 13 C coil design could ensure that this effect is minimized. Future studies could assess this concept in human experiments, including a comparison of k PL values before and after correction with a sodium B 1 map. Uncertainty in transmit B 1 dramatically increases the error in kinetic modeling, which could have significant implications for the interpretation of the results as part of clinical trials. 10 Interestingly, there appeared to be a difference in the RF gain required for the 8-channel paddle coils and the single loop coil used in this study, with an approximate difference of 2 dB. This difference is partially due to the difference in vendor coil files (1.35 dB), and we hypothesize that the remainder is due to differences in coil positioning and volumetric coverage because the transmit clamshell has a nonuniform transmit field (Figure 4). Further differences in TG could be found in variations in coil matching at the 23 Na frequency, leading to differences in TG required for a 90-degree excitation. Reductions in transmit efficiency are expected when operating away from the intended frequency due to degradation in the quality of the tune and match of the coil, although the relatively small difference in TG needed here suggests this degradation is not severe. In the future, the TG could also be used to indirectly inform on the quality of the tune and match. Although we have demonstrated here that 13 C coils can be successfully used to measure the 23 Na resonance, this approach should be applied with caution by assessing the coil response at both frequencies on the bench and also by undertaking studies in phantoms prior to performing these studies in humans. 35

| CONCLUSION
We have demonstrated the feasibility of using the 23 Na and 1 H resonances to calibrate the 13 C transmit B 1 using commercially available 13 C-coils. The method provides a simple approach for in vivo calibration and could improve clinical workflow.