Combined imaging of potassium and sodium in human skeletal muscle tissue at 7 T

To validate the feasibility of quantitative combined potassium (39K) and sodium (23Na) MRI in human calf muscle tissue, as well as to evaluate the reproducibility of the apparent tissue potassium concentration (aTPC) and apparent tissue sodium concentration (aTSC) determination in healthy muscle tissue.


| INTRODUCTION
Sodium (Na + ) and potassium (K + ) ions play a vital role in many cellular processes. In healthy tissue, Na + exhibits an approximately eightfold to 10-fold higher concentration in the extracellular space than in the intracellular space. An inverse concentration gradient can be observed for 39 K. For example, in human skeletal muscle cells, intracellular ion concentrations in the range of [Na + int ] = 10-25 mM 1 and [K + int ] = 150-165 mM can be found, [2][3][4] whereas the extracellular concentrations-measured as the serum Na + and K + concentrations-are normally in the range of [Na + ext ] = 130-145 mM and [K + ext ] = 3.5-5.5 mM. 5,6 This concentration gradient between the intra-and the extracellular space contributes to the cell membrane potential and is maintained by the Na + -K + -ATPase, often referred to as the Na + -K + -pump. In skeletal muscle cells, the ATPase activity and resulting maintenance of the Na + and K + concentration gradient are essential for the muscle contractility. 7 Various diseases, such as diabetes and muscular dystrophies, as well as exercise have been reported to alter the ATPase activity and consequently the ion distribution in human skeletal muscle. Further, skeletal muscle cells are supposed to be an important storage for Na + and K + to handle an overload or depletion of these ions. 8,9 Thus, a noninvasive determination of the muscular Na + and K + tissue concentrations using 23 Na and 39 K MRI might help elucidate the physiological mechanisms underlying various pathologies.
Using 23 Na MRI, it is possible to gain information about the tissue sodium concentration (TSC), which represents the mean of the intra-and extracellular sodium concentrations weighted by their respective volume fractions. Changed TSC in skeletal muscle tissue has been observed in the context of various diseases, for example, in muscular dystrophies, 10,11 muscular channelopathies, 12 hypertensive patients 13 and patients with acute kidney injury. 14 Additionally, efforts are made to enhance the sensitivity toward intracellular sodium by suppressing signal from the extracellular space, for example, using inversion recovery 12 and multiple quantum filtration 15 approaches. However, it is still an open question to what extent these techniques are able to differentiate between sodium ions within the intracellular and extracellular space. 16 In particular for multiple quantum filtration, it has been shown that a significant amount of the detected signal arises from the extracellular space. 17,18 Because K + ions are mainly located in the intracellular space (around 98% of the total potassium content 19 ), a noninvasive determination of the tissue potassium concentration (TPC) using 39 K MRI might help gaining deeper insights into pathological processes connected to the intracellular space.
In clinical practice, alterations of the K + concentration in ion homeostasis are currently only analyzed in extracellular body fluids, for example, blood samples. However, increases in extracellular K + concentrations are initially buffered by moving K + into the intracellular space until it is excreted by the kidneys. 8 Moreover, declines in extracellular K + concentrations can be balanced by reducing the intracellular stores in skeletal muscle cells. This ensures that blood serum K + concentrations are usually tightly regulated. In many diseases, however, either too low (hypokalemia) or too high (hyperkalemia) blood serum K + concentrations lead to life-threatening conditions that are often associated with ventricular arrhythmias and sudden cardiac arrest. The underlying pathophysiological mechanisms can be depletion (in hypokalemia) or overload (in hyperkalemia) of the total body potassium and/or internal redistributions between extra-and intracellular space. 19 A determination of the TPC might help to elucidate these underlying disease mechanisms. Because skeletal muscle is the most important storage of potassium within the human body, containing approximately 75% of the total potassium content, 2 a noninvasive K + concentration determination in human skeletal muscle tissue is desirable. However, because it has not yet been examined if the total potassium content in muscle tissue is MR visible and how the nonzero residual quadrupolar interaction of 39 K ions in muscle tissue 20 influences the signal intensity, we will use the term apparent tissue potassium concentration (aTPC)-and equivalently apparent tissue sodium concentration (aTSC) instead, as suggested by Stobbe and Beaulieu. 21 The major challenge of 39 K MRI is the low SNR due to low in vivo K + concentrations and the low gyromagnetic ratio (γ K = 1.99 MHz/T). For similar Na + and K + concentrations as well as similar relaxation times, the SNR of 39 K MRI is expected to be 34 to 126 times lower than the SNR of 23 Na MRI, depending on the noise model (dominated either by inductive losses in the sample or by resistive losses in the coil). 22,23 In addition, technical restrictions did not allow the application of 39 K MRI on clinical MRI systems thus far. Therefore, in vivo 39 K MRI was performed only on preclinical systems 24,25 or using experimental, custom-built setups in humans. 20,26,27 Recently, the first | 241 GAST eT Al. MRI in humans did not examine the quantitative capability and especially not the reproducibility of 39 K imaging. The aim of this work was to validate the feasibility of combined Na + and K + concentration quantification in skeletal muscle tissue using 23 Na/ 39 K MRI on a clinical 7T MR system. In addition, the reproducibility of Na + and K + quantification in healthy skeletal muscle tissue was examined.

| Image acquisition
All measurements were performed on a whole-body 7T MR system (Magnetom Terra, Siemens Healthcare GmbH, Erlangen, Germany) using a dual-tuned, circular polarized 23 Na/ 39 K calf coil with an inner diameter of 20 cm (Rapid Biomedical, Rimpar, Germany). A 5-compartment reference tube holder included in the coil design was used for quantification such that the leg can be positioned directly on the reference holder. The reference tubes were filled with different combinations of NaCl and K 2 HPO 4 solution, resulting in Na + and K + concentrations of [Na + ]/[K + ] = 10/240, 20/210, 25/180, 30/150, and 40/120 mM. K 2 HPO 4 solution possesses a lower electrical conductivity than KCl solution and is therefore expected to arise less image artifacts. Because the measurement setup does not contain a hydrogen ( 1 H) channel, B 0 shimming was performed based on B 0 maps calculated from 23 Na MRI data in combination with a constrained regularized algorithm. 29 23 Na and 39 K images were acquired using a 3D acquisition-weighted density-adapted stack-of-stars scheme. [30][31][32] This acquisition scheme allows anisotropic sampling of the k-space, which is beneficial for muscle measurements due to possible higher in-plane resolution. 33 Moreover, it was found to provide a higher SNR compared with a density-adapted radial acquisition with cuboid k-space sampling scheme. 32 23 Na and 39 K data sets were reconstructed offline using a custom-written MatLab tool (2017b, MathWorks, Natick, MA) and interpolated to the same matrix size (240 × 240 × 120), corresponding to an interpolated resolution of 1 × 1 × 2 mm 3 .

| Concentration determination
Na + and K + concentration calibration was performed by a linear regression of the signal intensities within the reference compartments to their nominal concentrations. The effect of different corrections on the 23 Na and 39 K signal intensities on the quantification accuracy was evaluated. The workflows for signal postprocessing and correction of in vivo data are illustrated in Figure 1.

| B 0 correction
Offresonances can cause signal blurring and therefore may induce quantification errors. This is of special importance if external references are used because the large susceptibility differences at the transition between reference tubes and muscle tissue might lead to strong B 0 inhomogeneities. 34 To correct for these inhomogeneities, offresonance maps were calculated using 2 echoes of both 23 Na and 39 K MR acquisitions according to with the phase unwrapped phase images ϕ 1,unwrapped and ϕ 2,unwrapped , the TEs of the double echo acquisition (TE 1 and TE 2 ), and the gyromagnetic ratios of 23 Na and 39 K, respectively (γ Na = 11.27 MHz/T, γ K = 1.99 MHz/T). B 0 correction was performed using a frequency-segmented approach, 35 in which the measured raw data are first multiplied by phases resulting from the offresonance frequencies found in the B 0 map. Then, these new k-space data are Fourier-transformed into the image space, and a voxel-wise combination is performed to create the B 0 corrected image. Because this B 0 correction approach does not require additional acquisition time, it was performed for all quantitative measurements in this work.

| Partial volume correction
For quantification in X-nuclei MRI, the signal intensities of the tissue and reference compartments are commonly determined within manually drawn regions of interest. However, especially for 39 K MRI, the low nominal resolution in combination with fast T * 2 relaxation lead to strong partial volume effects. These partial volume effects result in a strong dependence of the calculated tissue ion concentration on the positioning of the regions of interest. To enhance the reproducibility of the quantification approach while mitigating partial volume effects, a binary-mask based partial volume correction (PVC) as described by Niesporek et al 36 was applied to the data. Using this approach, a constant ion concentration is calculated for each tissue compartment. The mask for the reference tube regions was calculated based on a high-resolution 1 H image by thresholding. This mask was then coregistered onto the 23 Na images using SPM12 (Wellcome Trust Centre for Neuroimaging, London, UK). Because coregistration of muscle tissue is challenging due to the varying positioning of the leg using different coil setups that would be necessary due to the lack of a 1 H channel in the used 23 Na/ 39 K calf coil, no 1 H images were used for muscle mask calculation. Instead, the mask for the muscle area was calculated based on the 23 Na images using a combination of manual segmentation and thresholding. For subjects exhibiting a significant subcutaneous fat layer (thickness > approx. 5 mm), a binary mask for fat tissue also was extracted from the corresponding 23 Na image. The central 20 slices (interpolated slice thickness = 2 mm) were evaluated both for phantom and in vivo measurements in the quantification process. After PVC, a corrected signal intensity is obtained for each compartment. Using these signal intensities in combination with the region-spread-functions describing the signal blurring of each individual compartment, 36 an artificial partial volume corrected image was created.

| B 1 correction
Beause the transmit-and-receive fields for both the 23 Na and the 39 K channel of the used calf coil were found to be not identical, no conventional B 1 correction using flip angle (FA) maps and assuming B − 1 = B + 1 could be performed. Instead, constant B 1 correction factors were determined for the reference compartments because B 1 inhomogeneities were highest on the edges of the FOV (compare maps of effective FAs shown in Supporting Information Figure  S1). Therefore, a phantom measurement was performed in which all compartments of the reference holder, as well as the phantom itself, were filled with the same solution (15 mM NaCl + 60 mM K 2 HPO 4 ). After PVC, the signal intensities within all compartments and the phantom should be equal. The B 1 correction factors for the reference compartments were therefore calculated as the inverse signal intensities within these compartments normalized to the phantom signal intensity.

F I G U R E 1
Postprocessing workflows for correction of in vivo 23 Na and 39 K MRI data sets. B 0 correction is performed using the individual B 0 maps calculated from the 2 echoes of the 23 Na and 39 K acquisitions. Moreover, the muscle mask used for the PVC of the data sets is extracted from the 23 Na data set. The corresponding segmentation mask for the reference compartments is extracted from a high-resolution 1 H acquisition and coregistered to the 23 Na images. Individual 39 K T * 2 decay curves were acquired for each volunteer. The resulting relaxation times are used for both the PSF simulation and relaxation correction. For the PSF simulation and relaxation correction of the 23 Na data sets, T 1 and T * 2 values as found in the literature are used (c.f. Table 1). By combining the PSF with the individual structural information of each compartment, a so-called RSF can be created that is used in the geometric transfer matrix approach to correct for partial volume effects. 36 In the last correction step, B 1 correction factors as determined in a phantom measurement are applied to the reference compartment signal intensities. Finally, concentration calibration is performed by a linear regression of the corrected reference compartment signal intensities, and artificial corrected 39 K and 23 Na images are transformed to concentration maps. 23 Na, sodium; 39 K, potassium; PSF, point-spread-function; PVC, partial volume correction; RSF, region-spreadfunction | 243 GAST eT Al.

| Relaxation correction
For quantitative MRI measurements, a short TE (<<T * 2 ) and long TR (>5T 1 ) are needed. However, for in vivo measurements, a slight T 1 weighting by reducing TR was accepted to reduce measurement time and to increase SNR by increasing the number of averages for 39 K MRI acquisitions. As the solutions used for the concentration calibration exhibit considerably longer relaxation times than muscle tissue (c.f. Table 1) a relaxation correction was performed. Assuming a homogeneous FA of 90°, the relaxation coefficients for solutions containing both contributions from T 1 and (monoexponential) T * 2 can be calculated according to For muscle tissue, the biexponential transverse relaxation has to be taken into account, 37,38 resulting in a relaxation correction coefficient of Here, f denotes the fraction of the fast component fraction of T * 2 , and q describes the time-averaged, so-called residual, quadrupole interaction of the nuclei with their environment. For 39 K, the individually measured relaxation behavior for each subject was used for relaxation correction (compare Section 2.4.2). For 23 Na ions in muscle tissue, relaxation times as summarized in Table 1 were used. Further, q ≈ 0 was assumed for 23 Na and f was fixed to its theoretical value (f = 0.6) because sodium ions in healthy calf muscle tissue were reported to exhibit a fast component fraction close to 60%. 39 Finally, the signal was corrected by dividing the uncorrected signal by the relaxation coefficients.

| Simulations
To evaluate the implemented quantification workflow, 23 Na and 39 K MRI data sets both of a phantom and a lower leg model were simulated (see Utzschneider et al 40 for detailed description of the simulation approach). The phantom was modeled as a cylinder with diameter 14 cm and height 12 cm. Two cylindrical tubes were included (diameter 2/4 cm) containing 0 mM ion concentration representing the tibia and fibula. For the muscle simulations, high-resolution 1 H images of both a female and a male lower leg were manually segmented into 6 different muscle regions (gastrocnemius medialis/lateralis, soleus, tibialis anterior/posterior, fibularis), as well as subcutaneous fat tissue and vessels using the Medical Interaction Toolkit. Moreover, the reference compartments were extracted from a 1 H image by thresholding and included into the simulation.
All phantom and muscle compartments were assigned specific Na + and K + concentrations (c.f. Table 1). The resulting simulation ground truth for 23 Na and 39 K MRI of lower leg can be found in Supporting Information Figure S2. They were then Fourier-transformed and regridded onto a radial trajectory by a nonuniform fast Fourier transform. The different compartments were added up to form the simulated k-space. Finally, Gaussian noise was added to yield a noise level close to actual measurements. Moreover, T * 2 and T 1 decay was included into the simulated raw data of each compartment. For 23 Na phantom and muscle simulations, relaxation times from literature were used (c.f. Table 1). For 39 K muscle simulations, T * 2 and T 1 relaxation times as determined in the phantom and volunteer measurements were used. Moreover, the same acquisition parameters as for the phantom/in vivo measurements were used for the simulations.

| T * 2 and T 1 mapping
The knowledge of the T * 2 relaxation times is indispensable both for partial volume correction as well as for relaxation correction of the 39 K signal intensities. Therefore, 39 K T * 2 maps were acquired for both phantom solutions and muscle tissue using a multi-echo acquisition-weighted densityadapted stack-of-stars scheme. Average signal intensities (3) T A B L E 1 Parameters used for the simulation of 23 Na and 39 K MRI data of the phantom and lower leg muscles. Relaxation times and concentrations-except for 39 K relaxation times in K 2 HPO 4 solution and muscle tissue-were taken from literature. For 23 Na ions in fatty tissue, the same relaxation properties as for muscle tissue were assumed due to a lack of references. Relaxation times were also used for PVC and relaxation correction of the measured data sets 52 within a region of interest were determined, and a fit of the theoretical signal decay was performed. For NaCl and K 2 HPO 4 solution, a monoexponential T * 2 decay was assumed For muscle tissue, a biexponential fit was performed 26,38 with n describing a noise factor. In a homogeneous environment possessing a constant quadrupolar interaction between the nuclei and the surrounding molecules, a fraction of f = 0.6 is observed. 37 However, in biological tissues such as muscle tissue, a distribution of quadrupolar interactions and consequently a varying relaxation behavior can be expected. 38 Thus, the fast component fraction was chosen as a free fit parameter. Because 39 K ions in muscle tissue are expected to experience a residual quadrupolar interaction, 20 the time-averaged quadrupolar interaction q was included in the fit.
Moreover, 39 K T 1 maps were acquired using an inversion recovery acquisition-weighted density-adapted stack-of-stars scheme by varying the TI. Fitting was performed according to

| Phantom measurements
To verify the quantification process under practical measurement conditions, a phantom representing the structure of the lower leg as described in the simulations section was used. It was filled with a solution containing 15 mM Na + and 120 mM K + (15 mM NaCl, 60 mM K 2 HPO 4 ). Both T 1 and T * 2 time of 39  both ions were performed twice to assess the quantification accuracy of the implemented PVC approach. No relaxation correction was applied to the phantom data because the solutions within the phantom and the reference tubes were assumed to possess the same relaxation behavior. 23 Na and 39 K images of the lower leg were acquired in 10 healthy volunteers (5 male, 5 female, age 27.4 ± 4.6 years). The study was approved by the local ethical review board, and all volunteers provided informed consent prior to the examination. Healthy subjects did not take any regular medication, did not suffer from any preexisting or acute illness, and had routine laboratory parameters (including blood pressure) within the normal range. For each volunteer, a 39 K T * 2 map was acquired (TR = 35 ms, TE = 0.4-20 ms, 15 acquisitions with 2 echoes each, T RO = 3 ms, nominal spatial resolution 8 × 8 × 30 mm 3 , 6 averages, TA = 32:15 min). The sequence parameters used for quantitative 23 Na/ 39 K MRI were the same as those in the phantom measurements. Around 65% to 70% of the maximum admissible specific absorption rate in the normal operation mode was reached for 39 K MRI using a 90° RF pulse of 500 µs duration and a TR of 40 ms. The minimum RF pulse duration was restricted by the maximum RF voltage of the MR system (339 V). To reduce motion effects during the acquisition, several cushions were used to fix the position of the leg in the RF coil.

| In vivo measurements
Postprocessing of the data sets was performed as described in Figure 1. For PVC and relaxation correction of the 39 K data sets, the individual 39 K T * 2 times were used. To assess the variation in the calculated ion concentrations, the 23 Na and 39 K quantification measurements were repeated for each subject after a short break (30-45 min). For comparison, Na + and K + concentrations in blood serum were determined. Moreover, 39 K T 1 maps of muscle tissue were acquired for 2 male healthy subjects (TR = 100 ms, TE = 0.4 ms, TI = 2-40 ms, 11 acquisitions, T RO = 3 ms, nominal spatial resolution 10 × 10 × 30 mm 3 , TA = 42:10 min).

| Data analysis
A paired sample t test was performed to compare the concentrations determined in the first and second measurement (M1 and M2) of the same subject. To assess the variability of the concentration determination, Bland-Altman graphs were created by plotting the difference between the aTSC and aTPC values of M1 and M2 against the mean values of the 2 measurements. Moreover, the coefficient of variation was calculated as the ratio of the SD to the mean concentration of the measurements, as well as the coefficient of repeatability

| 245
GAST eT Al. as 1.96 multiplied by the SD of the differences between M1 and M2. 41

| Simulations
Simulated 23 Na and 39 K data phantom sets, together with concentration calibration curves and resulting calculated Na + and K + concentration maps after PVC, are shown in Figure 2. Before correction, partial volume effects led to an underestimation of the signal intensity within the reference compartments, especially for the smaller reference compartments in the 39 K acquisition. After PVC, calibration curves were in good accordance with the theoretical expectations both for 23 Na and 39 K. To determine the quantification variation due to random noise, data sets were simulated and evaluated 5 times each for phantom and muscle. For the simulated phantom, ion concentrations of [Na + ] = (16.5 ± 0.02) mM and [K + ] = (134.2 ± 0.8) mM before correction were determined. After PVC using the simulation ground truth as binary masks, concentrations of [Na + ] = (15.2 ± 0.02) mM and [K + ] = (120.0 ± 0.7) mM were determined. The deviation from the ground truth concentrations of [Na + ] = 15 mM and [K + ] = 120 mM were therefore reduced from (10 ± 1)% to (1 ± 1)% for Na + and from (12 ± 1)% to (0 ± 1)% for K + by applying a PVC. For the simulated muscle data sets, the effect of the relaxation correction and an imperfect binary mask extracted from the simulated 23 Na data sets also were examined. Therefore, PVC was performed using both the simulation ground truth and a muscle/fat mask calculated based on the 23 Na image for the simulated female calf (c.f. Figure 3; see Supporting Information Figure S2 for evaluation including all 3 tissue compartments). Before correction, Na + and K + concentrations were overestimated (deviation from ground truth concentrations > 10%) (see Figure 4). For 23 Na measurements, both PVC and relaxation correction reduced the deviation from the nominal concentrations ( Figure 4A). In contrast, for 39 K measurements the effect of relaxation weighting on the quantification accuracy was stronger such that both PVC and relaxation correction were needed to effectively reduce absolute quantification deviations ( Figure 4B). Calculation of the segmentation mask based on the 23 Na image led to an additional quantification error. Here, the total area of the calculated muscle mask showed a deviation of 9% from the area of the ground truth mask in the evaluated slice range (deviation of fat mask: 20%).
F I G U R E 2 Simulated 23 Na (A) and 39 K (B) phantom images, together with calculated Na + and K + concentration maps. Concentration maps were created based on the artificial images calculated using the RSF and corrected signal intensities for each compartment. The corresponding concentration calibration curves are shown on the right. Here, the signal intensities were normalized to the reference compartment containing the lowest ion concentration (compartment 5 for 23 Na; compartment 1 for 39 K). The calibration fit was performed before (red line) and after correction of partial volume effects (green line). The calibration curve after PVC for both ions is in good accordance with the theoretically expected relation for both nuclei (dashed line). K + , potassium ion; Na + , sodium ion (A)

(B)
However, the concentration deviation from the ground truth increased only by approximately 2% after using the calculated segmentation mask.
As for in vivo lower leg data sets with thin subcutaneous fat layer it is often difficult to extract a fat mask based on the 23 Na image, the simulated male calf images were F I G U R E 3 Simulated 23 Na (A) and 39 K (B) images of human lower leg, together with Na + and K + concentration maps after PVC. Concentration maps were created based on the artificial images calculated using the RSF and corrected signal intensities for each compartment. As segmentation mask for PVC, both the simulation ground truth (middle column) and a muscle/fat mask calculated based on the 23 Na image (right column) were used to evaluate the influence of an imperfect binary mask as found in in vivo measurements. For the evaluation of 39 K images, only the muscle area was considered because a negligible K + concentration is expected in fatty tissue (A) (B) F I G U R E 4 Deviation from ground truth concentrations of calculated ion concentrations for simulated muscle data sets before and after correction of partial volume effects and relaxation weighting. Moreover, the effect of an imperfect binary mask extracted from the simulated 23 Na muscle image overestimating the muscle area compared with the ground truth was examined. For 23 Na, both concentrations in muscle and fat tissue were determined. Absolute deviations can be strongly reduced by applying both a PVC and relaxation correction. An evaluation including all simulated tissue types (muscle, fat, and blood vessels) can be found in Supporting Information Figure S2  additionally evaluated using only a muscle mask but no fat mask (see Supporting Information Figure S3). This muscle mask partially included the fatty tissue so that the area of the calculated muscle mask deviated from the area of the ground truth mask by 15%. In this case of strong overestimation of the segmentation mask, the concentration deviation increased by approximately 5% compared with the PVC based on the ground truth mask to a total deviation of −11% for K + concentration determination.

| Phantom measurements
For K 2 HPO 4 solution, 39 K relaxation times of T 1 = (47.5 ± 0.5) ms and T * 2 = (43.2 ± 0.7) ms were determined. Measured 23 Na and 39 K phantom images, together with concentration calibration curves before and after PVC as well as B 1 correction and resulting Na + and K + concentration maps, are shown in Figure 5. Mean ion concentrations of [Na + ] = (13.9 ± 0.1) mM and [K + ] = (121.0 ± 0.6) mM after corrections could be determined for the phantom. This corresponds to a deviation of (−7.3 ± 0.7)% for Na + and (0.8 ± 0.5)% for K + from the nominal concentrations of [Na + ] = 15 mM and [K + ] = 120 mM.

| In vivo measurements
Exemplary 39 K T 1 and T * 2 decay curves for human lower leg muscle tissue can be found in Figure 6. The resulting T * 2 times for all volunteers, together with the measured Na + and K + concentrations in blood serum, are summarized in Table 2. Mean T * 2 components of T * 2f = (1.2 ± 0.2) ms and T * 2s = (7.9 ± 0.9) ms, as well as a mean quadrupolar interaction of q = (143 ± 17) Hz for 39 K ions in muscle tissue, were determined. The fraction of the fast component was f = 58 ± 4%. Because this is close to the theoretically expected value (f = 60%), the T * 2 decay was additionally evaluated with a fixed fraction of 60% to enhance the fit stability. The resulting values were T * 2f = (1.2 ± 0.1) ms, T * 2s = (8.1 ± 0.2) ms, and q = (142 ± 12) Hz. Moreover, a mean T 1 of (8.8 ± 1.3) ms for 39 K in healthy lower leg muscle tissue was determined. 23 Na and 39 K images of human lower leg acquired in measurement M1 and M2, as well as the corresponding aTSC and aTPC maps including all signal corrections, were found to be in good accordance (see Figure 7). The effect of the different correction steps on the aTSC and aTPC calculated for the first measurement in lower leg muscle tissue is shown in Figure 8A,B. For both 23 Na and 39 K measurements, B 0 F I G U R E 5 Measured 23 Na (A) and 39 K (B) phantom images, together with Na + and K + concentration maps after PVC. Concentration maps were created based on the artificial images calculated using the RSF and corrected signal intensities for each compartment. The corresponding 23 Na and 39 K concentration calibration data and fit curves are shown on the right. The signal of the reference compartments was normalized to the compartment with the lowest nominal Na + and K + concentration (compartment 5 and 1). Moreover, B 1 correction factors were applied to the measured signal intensities of the reference compartments. The calibration fit was performed before (red line) and after correction of partial volume effects (green line). For 23 Na, the deviation of the calculated calibration curve from the theoretically expected relation (dashed line) can be decreased by applying both PVC and B 1 correction. However, some deviations still can be found after correction. For 39 K, the calibration curve after PVC and B 1 correction is in good accordance with the theoretically expected relation correction did not result in an alteration of the measured ion concentrations. In future aTSC and aTPC measurements, a B 0 correction could therefore be omitted. PVC and B 1 correction reduced the measured Na + concentration, whereas they led to an increase in the measured K + concentration. The relaxation correction had a higher impact on the 39 K data sets, resulting in a strong reduction of the measured ion concentration in muscle tissue. Bland-Altman plots indicate a good agreement between the ion concentrations calculated from the corrected data sets of the 2 measurements performed for each subject ( Figure  8C,D). Including all corrections, mean aTSC values for muscle and fat tissue of aTSC m = (16.9 ± 1.0) mM and aTSC f = (7.0 ± 1.3) mM in the first measurement (M1) and aTSC m = (17.0 ± 1.1) mM and aTSC f = (6.7 ± 1.2) mM in the second measurement (M2) were determined. For K + , muscle concentrations of aTPC = (83.4 ± 6.1) mM in M1 and aTPC = (87.2 ± 4.9) mM in M2 were calculated. No significant differences between the apparent muscle tissue ion concentrations determined in M1 and M2 were observed (P = .82 for 23 Na measurements and P = .06 for 39 K measurements). Moreover, the coefficient of variation was similar for aTSC and aTPC (coefficient of variation = 5.7%). A coefficient of repeatability of 1.73 mM (10.2%) and 10.7 mM (12.6%) were determined for 23 Na and 39 K measurements, respectively. No correlations between the measured Na + and K + blood serum F I G U R E 6 Exemplary 39 K T * 2 (A) and T 1 decay curves (B) for human lower leg muscle tissue. For the shown subject, a biexponential fit revealed T * 2 components of T * 2f = (1.0 ± 0.2) ms and T * 2s = (7.7 ± 1.6) ms. Moreover, the influence of the residual quadrupolar interaction with frequency q = (112 ± 19) Hz can be clearly observed in the decay curve. The T 1 was determined by a monoexponential fit to T 1 = (9.5 ± 1.1) ms aTPC and aTSC values are given as mean and SD of the 2 measurements per subject. Correlation plots between the ion concentration measures are shown in Supporting Information Figure S4. 39  concentrations and the mean aTSC and aTPC in muscle tissue were found for the healthy subjects (see Supporting Information Figure S4 for correlation plots between measured ion concentrations in muscle and blood serum, as well as hematocrit content).

| DISCUSSION
In this work, combined imaging of sodium and potassium in human skeletal muscle at 7T was performed for the first time using the same RF coil. Moreover, the repeatability of the quantification of Na + and K + concentrations using 23 Na/ 39 K MRI in muscle tissue was examined in 10 healthy subjects. Mean apparent tissue concentrations of aTSC = (17 ± 1) mM and aTPC = (85 ± 5) mM for healthy lower leg tissue were determined in this study. For both apparent Na + and K + concentrations, we found a good agreement between the 2 measurements performed in the same subject. A low coefficient of variation (5.7% for both nuclei) was determined. Moreover, no significant differences between the mean measured ion concentrations in the 2 measurements were found.
Recent studies examined the reliability and repeatability of quantitative 23 Na MRI in healthy calf muscle tissue at 3T. 34,42 Both found a high degree of agreement between scan and re-scan, with a lower coefficient of repeatability (also referred to as smallest real difference) for measurements performed on the same day than for measurements performed within 1 to several weeks. Because measured Na + concentrations in muscle tissue are highly sensitive to exercise and postural changes, a higher variation is expected when performing quantification measurements at different time points, and therefore under different physiological conditions. The results of our 23 Na MRI measurements performed at 7T are in good accordance with these studies, even showing a slightly lower coefficient of repeatability (1.79 mM) than the same-day measurements performed by Dyke et al (1.71-5.89 mM, depending on the evaluated muscle area). 42 This indicates a high reproducibility of our quantification approach. In contrast to the evaluations performed by Dyke et al 42 and Gerhalter et al, 34 the region-based quantification method proposed in this work does not depend on a manual positioning of the regions of interest, which we assume to be a reason for the observed higher degree of reproducibility.
The determined muscle aTSC values lie within the range of values that can be found in the literature for healthy calf muscle tissue (approx. 15-28 mM). 11,14,[43][44][45] Only 1 study measured the K + content in thigh muscle tissue using 39 K MRI so far, observing aTPC values significantly higher than the values observed in our study (aTPC between 112 and 125 mM for 3 healthy volunteers). 26 However, this study corrected for neither partial volume effects nor inhomogeneities in the B 1 or B 0 field. From muscle biopsy, K + concentrations in the range of 75 to 105 mmol per kg wet weight were derived. 2 Assuming a muscle density of 1.056 kg/L, 46 this corresponds to a range of 79 to 110 mmol/L. In our work, we measured a range of 74-94 mmol/L, which is close to the range observed in muscle biopsy. Overall, a direct comparison between muscle biopsy and MRI-as performed by Kopp et al for 23 Na measurements of human calf 47 -might be a promising approach to assess the deviation of the aTPC value from the real K + concentration in skeletal muscle tissue.
Nevertheless, the aTPC values measured in our study might be slightly underestimated. For the simulated muscle data sets, we found an underestimation of the K + concentration in muscle tissue of approximately 10% compared with the ground truth concentration in case of a strong overestimation of the muscle segmentation mask. In addition, 39 K nuclei in muscular tissue experience a strong quadrupole interaction with a mean quadrupolar interaction frequency q ≠ 0. 20 Over the entire lower leg muscle area, we found a mean quadrupolar interaction frequency of q = (143 ± 17) Hz using T * 2 decay fits. Roesler et al even observed a quadrupolar splitting of up to q = 200 Hz in unlocalized spectroscopic 39 K measurements of human thigh and calf muscle. 20 The so-called flip angle effect states that in case of large q , only the central transition might be excited leading to an effective flip rate up to twice the value prescribed, and therefore a loss in measured signal intensity. 48 Thus, in case q ≠ 0, it might be beneficial to use FAs lower than 90° to mitigate this effect. 21 Kordzadeh et al recently observed a mild flip-angle effect in the head of the gastrocnemius muscle using 23 Na MRI measurements of the knee. 49 However, the examination of the flip-angle effect is challenging because the additional influences on the signal intensity corrected in this work-for example, caused by T 1 weighting-also vary with the effective FA. In addition, particularly for the 39 K channel, an inhomogeneous distribution of the effective FA was found (compare Supporting Information Figure S1). These B 1 inhomogeneities would have a higher impact on the signal intensity at lower FAs.
Generally, B 1 correction of the 23 Na and 39 K MRI data sets was challenging because the transmit and receive profiles of the 23 Na/ 39 K calf coil were not identical. Thus, a 90° pulse-which is quite robust with respect to slightly deviating effective FAs-was chosen for quantitative 23 Na and 39 K MRI measurements to reduce the influence of B 1 inhomogeneities. Further, the applied B 1 correction approach is only valid in case the coil loading is the same for the quantitative in vivo measurements and the phantom measurements used to determine the B 1 correction factors. A different loading of the RF coil might result in a deviating B + 1 /B − 1 profile and correspondingly varying B 1 correction factors. Although this condition was fulfilled for the 39 K MR measurements, the coil loading was slightly lower in the phantom measurement than in the human lower leg measurements for 23 Na MRI. This might be a reason for the better agreement between the determined concentration calibration curves and the theoretical expectation for the 39 K MRI data sets than for the 23 Na MRI data sets.
The quantification accuracy in this work was mainly limited by the segmentation approach based on 23 Na data sets. For example, the determination of Na + concentrations in muscle tissue could be improved by including the vessels in the PVC process due to the high Na + concentration in blood. An inclusion of the vessels into the muscle mask-as it was done in this work-leads to an overestimation of the muscle Na + concentration (compare Supporting Information Figure S2). However, the segmentation of vessels as well as determination of muscle-specific aTSC and aTPC values that would be interesting in the context of muscle specific pathologies would require high-resolution 1 H images, which could not be acquired using the given coil setup. Thus, to improve the quantification accuracy, dual-tuned 1 H/ 23 Na or 1 H/ 39 K RF coils might be advantageous compared with the used dual-tuned 23 Na/ 39 K RF coil. However, this would require a repositioning of the subjects and thus would complicate translation into clinical studies. In addition, further examinations-for example, using the proposed simulation approach-would be required to evaluate if a muscle-specific aTPC determination might even result in reasonable values given the low nominal spatial resolution of the 39 K acquisitions.
In this work, PVC of 39 K data sets were performed using individually determined T * 2 relaxation times for each subject. Mean T * 2 components of T * 2f = (1.2 ± 0.2) ms and T * 2s = (7.9 ± 0.9) ms were determined. Furthermore, the fraction of the fast component was close to the theoretical expectation (f = 58 ± 4%). The measured T * 2 times are in good accordance with the values reported by Umathum et al 26 and Roesler et al 20 for human thigh and calf muscle tissue. Because the variation in determined fast and slow components of T * 2 in healthy lower leg tissue between the 10 volunteers examined in this work was quite small, a PVC based on the mean relaxation time values instead of the individual values in future work is supposed to be reasonable. In patients, altered T * 2 might be found due to edema or fatty infiltration, resulting in quantification errors. Therefore, relaxation times should also be measured in pathological muscle tissue before applying the PVC workflow, as described in this work to patient data. However, because T * 2 mapping is highly time consuming (~30 min), a general inclusion in clinical studies might not be feasible.
Overall, the noninvasive determination of tissue potassium concentrations using 39 K MRI offers a great potential for the application in various diseases. Due to the high reproducibility of the aTPC determination in healthy muscle tissue, this technique should be able to detect alteration in the ion concentration, for example, in patients with renal impairment or muscular channelopathies. Moreover, a higher variation can be expected in the measured muscle aTPC values than in the blood K + concentrations, which are tightly regulated. Therefore, quantitative 39 K MRI could help gaining additional insights into the underlying physiological processes of various diseases.

| CONCLUSION
We showed that using the presented measurement setup and image postprocessing approach, a reproducible aTSC and aTPC determination using 23 Na and 39 K MRI at 7T in human skeletal muscle tissue is feasible in clinically acceptable acquisition times.