Influence of reference tube location on the measured sodium concentrations in calf muscles using a birdcage coil at 3T

To investigate the influence of the sodium (Na) reference tube location in a birdcage coil on the quantification of Na in the calf muscle. Two correction methods were also evaluated.


INTRODUCTION
Sodium (Na) electrolyte homeostasis in the human body plays an important role in the physiology and pathophysiology of many diseases. 1 Na MRI has shown potential to probe these pathologies in the clinical setting. Areas include the brain such as tumors, 2 multiple sclerosis, 3 cartilage of the knee, 4 and kidney. 5 Increased total Na concentration measured in the calf muscle by MRI was found to be related to patients with refractory hypertension 6 and diabetes. 7 In addition, Na MRI of skeletal muscle utilizing an inversion pulse was found to be especially sensitive to the condition of muscular channelopathies. 8 The required sensitivity of the Na measurements in leg muscle will depend on the disease or process being examined. For example, a mean difference of 6 mM 23 Na was found in the leg muscle between a group with diabetes and controls. 7 A mean elevated 23 Na signal in leg muscles of 2.2 mM was found during anaerobic exercise. 9 Most Na MRI imaging studies of the skeletal muscle concentrate on obtaining an as homogeneous as possible B 0 field by shimming on the hydrogen ( 1 H) signals but do not correct for B 1 inhomogeniety. This could be due to increased acquisition time 10 required for B 1 mapping, or because a comparatively homogenous B 1 field was measured in a phantom when using a birdcage coil. 10,11 The birdcage coil design is known to have a highly homogenous B 1 field. 12 Due to the low signal received from Na (3000-20,000 lower 13 ) compared to proton, the smallest possible coil diameter producing a homogeneous B 1 field is desirable. However, B 1 inhomogeniety in a tight-fitting birdcage coil has been implicated for an elevated Na signal when the leg is too close to the active RF coil elements. 14 The aim of this study was to investigate and quantify the influence of the location of the Na reference tubes on the measured Na concentration in the muscles when using a birdcage coil. Additionally, two methods to correct for the coil B 1 inhomogeneity were evaluated.

Na UTE MR imaging
In this study, UTE scans were acquired with a 3D density-adapted radial UTE sequence (DA-UTE) 15 on a Skyra 3T system (Siemens, Erlangen, Germany For signal transmit/receive a dual 23 Na/ 1 H birdcage knee coil (RAPID Biomedical, Rimpar, Germany; inner diameter = 18 cm) was used. For the in vivo scan of the calf muscle, the volunteer was in supine position, with the scanned leg and coil positioned in the center of the bore of the scanner.
Every scan session started with calibrating the reference voltage of the Na signal using an automated nonselective free induction decay B 1 mapping sequence. Then, a dummy single-voxel spectroscopy scan with the adjustment volume containing the whole tissue or phantom region was used to shim on the 1 H signal. The shim settings and reference voltage were then copied to the DA-UTE sequence, and the demodulation frequency of Na was manually adjusted prior to scanning.

FA mapping of coil
To evaluate the homogeneity of the B 1 field within the axial field of the coil, FA maps were acquired in the axial plane of a large spherical (d = 18 cm; 100 mM Na C 2 H 3 O 2 ) quality-assurance phantom ( Figure 1(A)).
The homogenous region for which the FA error = | 45 − 45 • |< 10 • was determined and compared to the position of the leg and reference tubes as acquired with the localizer.

Measured muscle concentration dependence on reference tube position
To evaluate the dependence of the measured muscle concentration on the reference tube location, four tubes (diameter = 25 mm) with 20 mM sodium chloride (NaCl) saline solution were positioned along the left hand side of the coil surface ( Figure 1(C)), and another four tubes with 30 mM NaCl solution on the right side. An additional 30 mM NaCl solution was positioned more centrally in the cavity near the tibia (Figure 1(C)). Two different tube NaCl concentrations were used to compare the results using different Na concentrations with the range expected in calf muscle.
Two volunteers were scanned in total. This work involving human subjects was conducted with informed consent and approval of the institutional review board. First, a localizer was acquired in three orthogonal orientations of the lower leg; then, this was followed by four repeated DA-UTE (FA = 90 • , TR = 120 ms) scans to evaluate the intrascan session reproducibility of the concentration measurements.
For the in vivo study, a lower TR was used than for the phantom experiments in order to reduce the total acquisition time to a more acceptable duration. However, the smaller TR with respect to the Na-T 1 of saline solution of about T 1saline = 54 ms at 20 • C 8 of the reference tubes does imply that T 1 saturation will occur. Given that the Na-T 1 of muscle (T 1muscle ) as measured at 4T and 7T is about 25 ms, 17,18 a simple correction factor (T 1cor ) was applied to the intensity of the reference tubes prior to calculating the concentrations of the muscle: For both volunteers and all four repeated measurements, the mean UTE signal (I muscle ) in the muscles-tibialis anterior (TA), extensor longus, tibialis posterior, fibularis, soleus, and gastrocnemius medialis (GM)-were measured by using the UTE image overlay on the axial localizer and drawing regions of interest (Figure 1(C)) in the muscles groups using 3D slicer 19 (www.slicer.org). Similarly the maximum UTE signal (I max tube ) within each of the nine tubes were measured. The maximum signal was used for the reference tubes to avoid partial volume effects with air. The concentration in one muscle group, using the 20 or 30 mM NaCl reference tube, was then calculated assuming a linear concentration-UTE signal relationship and UTE signal of 0 at 0 mM NaCl as: Where C tube is equal to 20 or 30 mM depending on the tube used for the calibration, and I max tube is the corresponding maximum UTE signal within the tube.
Na MRS measurement was performed additionally purely to illustrate an alternative way to visualize our Na imaging method. It involved 2D chemical shift imaging of an axial slice of 2.5 cm thickness and a FOV of 24 × 24 cm 2 subdivided into 16 × 16 voxels of 15 × 15 × 25 mm 3 each. Free induction decay signals of FA 90 • were acquired at TR/TE = 1500/2.3 ms and Fourier transformed to obtain the spectral map depicted in Figure 1(D).

Correction in a phantom using a normalized FA map
To evaluate the effectiveness of FA correction, the homogenous phantom and FA = 45 • /90 • images described in the section 2.2 were also used for B 1 correction of the FA = 90 • acquisition.
Firstly, given that this was a homogeneous spherical phantom and a hard pulse was used for UTE, the actual FA was assumed to be proportional to the average b + 1 20 : Following the principle of reciprocity in which the transmit and receive fields are assumed to be equal, 21 To evaluate the effectiveness of the correction, similar positions were evaluated as the 30 mM tubes used for the in vivo scans. The intensity percent of these locations with respect to a (6 × 6 pixel) region of interest in the center of the phantom (as measured before the correction) was compared before and after B 1 correction.

Correction using a normalized intensity map
The FA = 90 • UTE scan of the homogeneous Na sphere (see section 2.2) was evaluated for its potential to correct for the coil B 1 inhomogeneity of the in vivo scan for volunteer 1. Firstly, the image of the phantom was normalized with respect to the mean of the central 6 × 6 pixel region assumed not to be affected by coil inhomogeneity.
Because the absolute position of the coil in the scanner with the phantom scanned may be different than the in vivo scan, the phantom image had to be shifted. In our specific case, the in vivo reference tubes were positioned at positions of maximum and minimum B 1 inhomogeneity. Therefore, the corrected image, given by the in vivo scan multiplied by the inversion of the normalized phantom image, was shifted such that the SD of both intensity-corrected 20 mM and 30 mM NaCl reference tube groups were minimized. Two assumptions were made-that the coil inhomogeneity is the same throughout the axial direction of the coil and that there is no coil rotation between the phantom and in vivo scan.
The correction was evaluated for the 30 mM tubes, and given as a percent of the intensity with respect to the 30 mM tube located more centrally, prior to the correction. Figure 1A shows the FA map (FA nom = 45 • ) of one axial slice of the coil region. A homogenous B 1 region within the central circle of 14 cm diameter was found. When compared to the localizer scan of volunteer 1 ( Figure 1B), the leg muscles are entirely in the homogeneous region. All reference tubes along the surface of the coil are mostly outside this region, apart from one reference tube located more centrally in the cavity near the tibia. Table 1 gives the range of Na concentrations measured in the 2 volunteers per muscle group when using reference tubes 1-8. For the central tube, the concentration and SD over the four repeated measurements are also shown. For both volunteers, the measured NaCl concentration in a muscle depended greatly on the position of the reference tube, with a range of up 10 mM (Table 1, GM, volunteer 1). Before correction, the largest concentration was measured in the GM (volunteer 1: 26.3 mM volunteer 2: 23.6 mM) and smallest in the TA muscle (vol 1: 11.1 mM vol 2:11.1 mM). For all 10 tubes, the SD

F I G U R E 2
The measured concentration before correction in GM (orange line) and TA (blue line) muscles versus tube reference number (see Figure 1(C)) for volunteer 1 (solid line) and volunteer 2 (broken line). The solid black and gray lines illustrate the concentration values obtained after correction using a normalized intensity map for the GM and TA muscle group of volunteer 1, respectively. GM, gastrocnemius medialis; TA, tibialis anterior. over the four repeated measurements ranged from 0.2 to 2.2 mM. Figure 2 further illustrates the measured concentration dependence on the reference tube position. As shown in Figure 1(C), tubes 1-4 contained 20 mM NaCl but were shifted in position, that is, at the same distance from the isocenter of the coil with increments of about 25 • , and tubes 5-8; C contained 30 mM NaCl and shifted similarly in position. The GM and TA values alternated up and down from tube to adjacent tube location. The measured concentration using the central tube had a value close (< 1 mM) to the center value of the range measured by the other (nr 1-8) tubes.
The higher Na signals in tubes 2, 4, 6, and 8 are illustrated by the spectral map shown in Figure 1(D). In the shown chemical shift range of six ppm, intense peaks are seen in those voxels that give the best match with the tube positions, compared with weaker signals in voxels suffering from partial volume effects. Note also that in the muscles the Na peaks are broadened and a couple of ppm's shifted downfield relative to the reference tubes.  (Figure 3(B)) appears to reduce the intensity inhomogeneity along the edge of the phantom. This inhomogeneity is further reduced after FA correction (Figure 3(C)) Although the corrected image appears more homogenous around the edge, the center of the phantom appears to have a higher intensity than toward edge of the phantom.

Correction in a phantom using a normalized FA map
For all evaluated points (Figure 4(A)), the correction resulted in an intensity percent closer to 100%, with the exception of reference tube eight. The percent mean (± SD) of the four points before and after correction was 93.0% (±14.9%) and 92.2% (±5.0%), respectively. For the central

F I G U R E 4
Intensity percent before (red line) and after (blue line) correction with respect to the more central tube/or location before correction (C, defined as 100%) (A) Correction in a phantom via FA mapping. (B) Correction of an in vivo scan using a normalized intensity map.
region, assumed not to be influenced by coil B 1 inhomogeniety, the correction resulted in a percent decrease of 1.5%.

3.4
Correction using a normalized intensity map Figure 3(D-F) shows the UTE image before and after correction using a normalized intensity map. Table 1 shows the range of concentration values obtain after correction for volunteer 1. The average reference tube-dependent range over all muscle groups decreased from 7.4 (1.1) mM before correction to 2.8 (0.5) mM after correction. In Figure 2(D), the solid black and gray lines illustrate the correction method applied to the GM and TA muscle group of volunteer 1, respectively. Using the reference tubes containing the 20 mM NaCl resulted in a lower calculated concentration of about 1.5 mM compared to the 30 mM NaCl tubes.
For all reference tubes evaluated (Figure 4(B)), the intensity percentage was closer to 100% after correction. The percent mean (±SD) of the four reference tubes before and after correction was 93.8% (±10.4%) and 96.0% (±2.7%), respectively. For the more central tube, assumed not to be influenced by coil B 1 inhomogeniety, the correction resulted in a percent increase of 2.3%.

DISCUSSION
Our study has shown the importance of considering coil B 1 inhomogeneity for quantitative MR Na mapping of calf muscles, even when using a birdcage coil design. Depending on the reference tube location, we found a potential variation in the muscle measurement of up to 10 mM Na. Having coils as close as possible to the tissue of interest being scanned has SNR advantages, especially useful for Na imaging, but this study has shown that there is potential for large errors if this results in placement of the reference tubes close to the surface of the coil. Our results substantiate a suggestion that an elevated signal may result from the tissue being too close to the active RF coil rather than reflect true pathology. 14 We explored two possible correction methods. The first based on FA mapping. As can be seen in Figure 3(C), this did result in a more homogenous intensity profile along the edge of the phantom. However, there remained a clear intensity offset at the edge region with the respect to the center region of about 8% (Figure 3(A)). This large offset remained, despite the correction being applied to a homogenous spherical phantom.
In addition, we investigated a correction via use of a homogenous phantom scanned, which was applied to the in vivo scans. Similar to the FA correction method, this resulted in less variation in intensity between the tubes (SD from 10.4% to 2.7%); however, a mean offset compared to the central tube still remained of about 4%. Although we used the phantom correction method with the in vivo tubes positioned in a region of maximum and minimum B 1 inhomogeneity, it could be more challenging to do this in practice. It would require reference tubes fixed to the coil-and acquired for both phantom and in vivo scans so that image registration could be used to overlap in vivo and phantom images.
The correction methods had little influence (< 2%) ( Figure 4, tube C) on the intensity value for the reference tube placed more centrally, and away from the surface coil ( Figure 1C). This setup will therefore likely give the best quantification results.
Our study has several limitations. Firstly only two volunteers were scanned. However, these volunteers gave similar results (Figure 2) that were sufficient to show the large impact coil B 1 inhomogeneity may have on Na quantification in the calf muscles. Also, various coil sensitivity correction methods were not investigated. This includes the method based on calculating the coil sensitivity by acquiring an image with the same contrast using body coil and local coil. 22 This was not possible in our case because of RF shielding of the transmit-receive birdcage coil. Also, we did not investigate obtaining sensitivity maps using a low-pass filter, 23 which would be interesting future work. Lastly, a dual-tuned knee coil gives better shimming and 1 H imaging compared with a body coil at the cost of lower SNR in the Na signal as compared with a single tuned coil.

CONCLUSIONS
The main aim of this study was to investigate the reliability of Na quantification in the calf muscle using a birdcage coil at 3T. This is important prior work for future clinical studies that will involve Na quantification of the calf muscle. We found large quantification errors with a range of up to 10 mM Na, and conclude that the more centrally located reference tube gives the most reliable quantification results.