Assessing muscle-specific potassium concentrations in human lower leg using potassium magnetic resonance imaging

2.1 Determination of ω_q for individual muscles

To assess muscle-specific ³⁹K residual quadrupolar interactions and T₂^* relaxation times, ³⁹K multiecho datasets of 10 healthy subjects of a previous study³ were re-evaluated. These datasets were acquired using a 3D acquisition-weighted density-adapted stack-of-stars (AW-SOSt) sequence¹⁰ using the following parameters: TR = 35 ms, TE = 0.4–20 ms, 15 acquisitions with two echoes each, T_RO = 3 ms, nominal spatial resolution = 8 x 8 x 30 mm³, six averages, and total acquisition duration T_Acq = 32 min 15 s. Regions of interest (ROIs) in soleus muscle (SOL) and tibialis anterior muscle (TA) as well as a combined ROI for gastrocnemius muscle, medial head (GM) and gastrocnemius muscle, lateral head (GL) were evaluated. An individual evaluation of the T₂^* decay within GL was not possible because of the low image resolution and low SNR, resulting in low fit stability. However, while the two heads of gastrocnemius muscle generally possess varying architecture, their average PAs reported in the literature differ only by some degrees,¹¹ resulting in similar expected effective residual quadrupolar interaction values.

2.2 Simulations

To assess the achievable accuracy of a muscle-specific TPC determination, ³⁹K MRI datasets of lower leg were simulated as described in Utzschneider et al.¹⁰ The simulation was based on a high-resolution ¹H MRI dataset of a female calf that was manually segmented into six different muscle regions (gastrocnemius medialis/lateralis, soleus, tibialis anterior/posterior, peroneus longus et brevis), subcutaneous fat tissue and blood vessels using the Medical Imaging Interaction Toolkit (MITK).^{3, 10} Additionally, the five reference compartments used for quantification calibration (section 7) were extracted from a ¹H acquisition by thresholding and combined with the tissue compartments to form the simulation ground truth.

After assigning individual K⁺ concentrations (Table 1), the compartments were Fourier transformed as well as regridded onto a radial trajectory using a nonuniform fast Fourier Transform (NUFFT).¹² Tissue-specific T₂^* and T₁ decay (Table 1) were included and the different compartments were summed up to form the simulated k-space. Finally, Gaussian noise was added to match the SNR of actual in vivo measurements. Simulation parameters were chosen identical to measurement parameters (Table 2). Each simulation was performed 15 times to assess the influence of noise.

In the first simulation experiment, TPC was fixed to 100 mM for all muscle compartments. Two scenarios were investigated: (1) a constant quadrupolar splitting in all muscles corresponding to the mean value reported for calf muscle tissue (ω_q = 142 Hz)³; (2) a varying quadrupolar splitting between individual muscles according to the values derived from ³⁹K T₂^* decay curves (GM/GL = 150 Hz, SOL = 100 Hz, TA = 200 Hz; compare section 10). For the remaining muscles, ω_q was set to the mean value for muscle tissue (ω_q = 142 Hz). Additionally, ω_q within each SOL and GM was varied by up to ±50% to assess the influence of a varying effective residual quadrupolar interaction (e.g., because of variations in fiber angles relative to B₀).

In the second simulation experiment, altered ion concentrations (40–160 mM in 20-mM steps) for each GM, SOL, and TA were simulated while TPC was kept constant at 100 mM for all other muscles. In this part, varying ω_q values of 150, 100, and 200 Hz for GM/GL, SOL, and TA were applied.

2.3 MRI of the lower leg

Overall, MRI datasets of the lower leg of 14 healthy subjects (seven males, seven females; mean age 25.0 ± 2.8 years) were acquired. The study was approved by the local institutional ethics committee and all volunteers provided informed consent prior to the examination.

²³Na/³⁹K MRI measurements were performed on a whole-body 7-T MR system (Magnetom Terra, Siemens Healthcare GmbH, Erlangen, Germany) using a dual-tuned, circular polarized ²³Na/³⁹K birdcage coil with an inner diameter of 20 cm (Rapid Biomedical, Rimpar, Germany). The ²³Na/³⁹K resonator was fixed on a mounting, which also included a container for reference solutions. The complete coil setup was placed within the center of the patient table parallel to the bore of the scanner with the aid of specifically manufactured spacers. Therefore, the lower leg was lying approximately parallel to the main magnetic field (Figure S1). The largest circumference of the calf was marked before examination and placed within the isocenter of the measurement. Moreover, to reduce motion effects during the acquisition, several cushions were used to fix the position of the leg in the RF coil. B₀ shimming was performed based on ²³Na MRI data in combination with a constrained regularized algorithm.¹³ Quantitative ²³Na and ³⁹K images were acquired using an AW-SOSt sequence applying nonselective excitation pulses.^14-16 Sequence parameters are summarized in Table 2.

An acquisition of corresponding high-resolution ¹H MRI datasets with sufficiently large field of view and homogeneity was not possible at 7 T because of the lack of suitable hardware. Thus ¹H MRI datasets were acquired on a whole-body 3-T MR system (Magnetom Prisma Fit, Siemens Healthcare GmbH, Erlangen, Germany) using an 18-channel body array coil (Siemens Healthcare GmbH, Erlangen, Germany). To obtain a comparable leg positioning and muscle deformation to the 7-T acquisitions, the reference container was removed from the ³⁹K/²³Na RF coil and fixed on the patient table of the 3-T scanner using sandbags, so that the leg was again lying approximately parallel to B₀ on top of the references during the ¹H acquisitions. T₁-weighted turbo spin echo (TSE) ¹H MR images as well as time-of-flight (TOF) MR angiography data were collected for muscle and blood vessel segmentation (Table 2).

2.4 Image postprocessing

Radial ²³Na and ³⁹K datasets were reconstructed offline using a NUFFT in Matlab (MathWorks, Natick, MA, USA).¹² A Hamming filter was applied to reduce Gibb's ringing artifacts as well as to enhance the SNR. Moreover, a correction for gradient nonlinearity was performed¹⁷ on the reconstructed ²³Na and ³⁹K images. Corrected ²³Na data were interpolated to match the ¹H image resolution and coregistered to the T₁-weighted ¹H images using the Elastix toolbox¹⁸ by a nonrigid (b-spline) approach. Because of the low image resolution, coregistration of the ³⁹K MRI data to the ¹H MRI data was not feasible. Thus the transformation parameters obtained from the ²³Na MR image coregistration were applied to the ³⁹K MRI datasets.

Muscle tissue, subcutaneous adipose tissue (SAT), and bones (tibia/fibula) were segmented based on the T₁-weighted images using a semiautomatic approach originally developed for segmentation of thigh data.¹⁹ Moreover, individual muscles (GM/GL/SOL/TA) were extracted manually from the same acquisitions using MITK.²⁰ Further, TOF ¹H MR images were coregistered to the T₁-weighted ¹H acquisition using an affine image registration. Blood vessels were extracted from the coregistered TOF acquisition using a Frangi-filter²¹ with the following parameters: Gaussian kernel sigma = 0.4/0.8 (summed up) with each using thresholds to control sensitivity alpha = 0.4, beta = 0.3, and c = 40.²² Finally, binary masks for the five reference compartments were calculated based on one ¹H T₁-weighted acquisition by thresholding and then coregistered to each ²³Na MRI dataset. The workflow for binary mask creation is visualized in Figure 1.

2.5 Partial volume correction

Segmentation masks for muscles, SAT, blood vessels, and reference compartments were used. After PVC, a constant corrected signal intensity was obtained for each compartment.

2.6 Concentration determination

²³Na and ³⁹K concentrations in calf muscles were determined using five external reference tubes filled with different combinations of NaCl and KCl solution ([Na⁺]/[K⁺] = 10/240, 20/210, 25/180, 30/150, 40/120 mM). Concentration calibration was performed by a linear regression of the signal intensities within the reference compartments to their nominal concentrations. To obtain a pure spin density weighting, generally long repetition times (TR > 5·T₁) and short echo times (TE < < T₂*) are required. As such values could not be realized because of technical restrictions (e.g., switching time of the transmit-receive coils) or limited acquisition duration, corrections for T₁ and T₂^* relaxation effects were performed on the partial volume corrected signal intensities.³ Typical ²³Na and ³⁹K T₁ and T₂^* relaxation times for muscle tissue and NaCl/KCl solution were assumed (Table 1).

2.7 Data analysis

TPC/TSC values were expressed as mean ± standard deviation. For simulated data, differences between TPC/TSC values of individual muscles were assessed using a one-way analysis of variance (ANOVA). For volunteer measurements, mean TPC values between different muscle regions were compared using a nonparametric Friedman test combined with a Bonferroni-corrected post hoc test. Correlation between TSC and TPC was examined using Pearson's correlation coefficient; p values less than 0.05 were considered significant for all statistical tests.

3.1 Determination of muscle-specific ω_q

Figure 2 shows ³⁹K T₂^* decay curves determined for GM/GL, SOL, and TA. A biexponential fit revealed a significantly higher residual quadrupolar interaction in TA (ω_q = 194 ± 28 Hz) compared with GM/GL (ω_q = 151 ± 25 Hz) and SOL (ω_q = 102 ± 32 Hz). No significant differences were found for the short T₂^* components (T_2s^* = 1.5 ± 0.3 ms for both SOL and GM/GL, T_2s^* = 1.4 ± 0.3 ms for TA). Long T₂^* components slightly varied between the individual muscles (T_2l^* = 11.5 ± 2.5 ms in TA, T_2l^* = 8.8 ± 2.0 ms in GM/GL, T_2l^* = 9.3 ± 2.0 ms in SOL), with a significantly higher T_2l^* in TA than GM/GL (p = 0.03).

3.2 Simulations

Figure 3 shows simulated ³⁹K MR images assuming a constant TPC (100 mM) together with either a constant ω_q of 142 Hz in all muscles (Figure 3A) or a varying ω_q between muscles (Figure 3C). Overall, a higher simulated ω_q led to a reduced signal intensity, while a lower value for ω_q corresponded to an apparently higher signal intensity. For both scenarios, the deviation of the measured TPC from the ground truth concentration was determined before and after PVC (compare Figure 3B,D). A correction for relaxation effects was performed in all cases. For both constant and varying ω_q, the TPC in SOL was strongly overestimated before PVC, while concentrations in other muscles were underestimated. After PVC using the correct ω_q values, the variations between the individual muscles strongly decreased and TPC values were close to the ground truth. However, if a constant ω_q was assumed for PSF calculation in the case of varying ω_q, an overestimation of the TPC in SOL and underestimation of the TPC in the other muscles remained after PVC. Overall, overestimating ω_q resulted in an overestimated TPC, while underestimating ω_q led to an underestimated TPC.

According to Equation 2, variations in the muscle fiber orientation relative to B₀ (e.g., due to varying leg positioning or subject-specific variations in muscle architecture) result in changes in the effective ω_q following a $\left(3{\cos }^2\theta -1\right)$-dependence. The corresponding uncertainty in ω_q is smaller for muscles that are aligned more parallel to B₀ (e.g., TA⁷) than for muscles with a larger angle relative to B₀ (e.g., SOL; see Figure 4A). To assess the influence of such variations on the TPC determination, ω_q in SOL/GM was varied by ±50%, while using a fixed ω_q of 100/150 Hz in the PVC (Figure 4B,C). The resulting deviations in TPC from the ground truth value of 100 mM were below ±5% for all Δω_q values but +50%. By contrast, deviations in GM were larger (ΔTPC > 10% for Δω_q > 25%).

In the case of concentration variations between individual muscles, the impact of applying a PVC further increased (Figure 5). Without PVC, an elevated ground truth TPC in one muscle resulted in an underestimation of the measured TPC in the muscle itself together with an overestimation in adjacent muscles. Similarly, a reduced ground truth TPC resulted in an overestimation of the measured TPC in this muscle together with an underestimation in adjacent muscles. This effect was particularly strong for SOL, which is completely surrounded by other muscles, so that the measured ion concentration in SOL was overestimated by more than 50% if no PVC was applied. PVC strongly reduced concentration deviations and dependence on varying concentrations.

3.3 MRI of the lower leg

²³Na and ³⁹K MR images together with corresponding ¹H T₁-weighted and TOF images are shown in Figure 6. Nonrigid coregistration of the ²³Na/³⁹K data to the ¹H T₁-weighted data resulted in a good spatial agreement of the images. ³⁹K datasets were evaluated using constant ω_q and T₂^* values for muscle tissue (ω_q = 142 Hz, T_2s* = 1.2 ms, T_2l^* = 8.1 ms) as well as the mean values determined for GM/GL, SOL, and TA given above (Figure 7). If a constant residual quadrupolar interaction was assumed for all muscles, TPC was significantly higher in SOL than in all other three examined muscles, even after PVC (p < 0.01 for SOL-GL and SOL-TA, p = 0.02 for SOL-GM). By contrast, if muscle-specific ω_q values were used for PVC, differences in TPC between the four muscles were no longer significant. Mean resulting TPC values were close to 100 mM for all four muscle regions. Overall, the inclusion of blood vessels in PVC of ³⁹K MRI data had no significant influence on the resulting TPC values.

For PVC of ²³Na data, constant relaxation properties (Table 1) and a constant ω_q of 0 Hz were assumed (Figure 7E). The resulting TSC after PVC was significantly higher in SOL than in GL and TA (p < 0.01 and p = 0.01, respectively). To evaluate if these differences could be caused by a varying residual quadrupolar interaction, PVC of ²³Na data was additionally performed using a muscle-specific ω_q. The corresponding values were chosen based on observations made by double quantum-filtered ²³Na and ³⁹K MRI with magic angle excitation (DQF-MA)^{4, 23}: as the reported DQF-MA signal of ²³Na was approximately half of the DQF-MA signal of ³⁹K in lower leg, we also assumed half the strength of residual quadrupolar interaction for ²³Na than for ³⁹K for each muscle (Figure 7F). As a result, differences in TSC between SOL and TA became nonsignificant (p = 0.08), but remained significant between SOL and GL (p = 0.02). All TSC and TPC values before and after PVC are summarized in Table 3.

Comparing the individual TSC and TPC values, a significantly negative correlation was found for GM/GL (p = 0.02; see Figure 8A). For SOL and TA, no significant correlations between TSC and TPC were observed (p = 0.23 for SOL, p = 0.24 for TA).