Repeatability assessment of sodium (²³Na) MRI at 7.0 T in healthy human calf muscle and preliminary results on tissue sodium concentrations in subjects with Addison’s disease

MRI was performed on a whole-body 7.0 T MR scanner with a 70 mT/m gradient amplitude and a 200 mT/m/ms slew rate (Magnetom, Siemens Healthcare, Erlangen, Germany). Study participants were scanned in the supine, feet-first position. A dual-tuned sodium and proton knee coil (14 ²³Na channels and a single ¹H channel; Stark Contrast, Germany) was used.

A cylindrical phantom made of poly methyl methacrylate (PMMA) filling completely the knee coil was filled with a mixture of agarose (4%) (Agarose, Sigma-Aldrich, USA) and a saline solution of 61.6 mmol/L, and was used for field mapping and corrections.

A set of calibration phantoms was made of 4% agarose and saline solution with four different sodium concentrations: 15.4, 30.8, 46.2, and 61.6 mmol/L, doped with 1% nickel sulfate. Concentration phantoms were attached to the inner side of the coil and were used for calibration curve derivation. To match the T₁ value of the phantom and muscle tissue, we added 2.9 g/L copper sulfate to the mixture.

All ²³Na multi-channel data sets were acquired using a density-adapted, isotropic three-dimensional radial projection reconstruction pulse sequence (DA-3DPR) [16]. For T₁ relaxation time measurements, a modified DA-3DPR with an inversion recovery (IR) pulse was included and five different inversion times (TI) were used. T₂^* mapping was performed employing the same DA-3DPR sequence with 20 different echo times (TE).

A proton (¹H) double echo steady state (DESS) sequence was acquired for partial volume effect (PVE) correction. Sodium imaging was performed using DA-3DPR followed by noise-only scans (no radio frequency [RF] power). More details on the sequences used can be found in Table 1.

Ten healthy subjects were recruited. In four of ten participants, relaxation time measurements were performed. Repeatability tests were performed in all ten participants and planned in such a way that subjects underwent three lower leg muscle MRI examinations organized as two separate visits. Between the two scans (M1, M2), during one visit, the subject left the scanner for a five-minute-long break. Seven to eight days after the first visit, the same subject was scanned third time (M3). Volunteers were placed in a similar position according to anatomic landmarks from proton (¹H) morphological imaging for the next scan. In addition, five participants with a diagnosis of Addison’s disease were scanned. Demographic data on study participants are shown in Table 2.

Healthy subjects with no contraindications for MRI exam, such as cardiac implantable electronic devices, metallic intraocular foreign bodies, drug infusion pumps, implantable neurostimulation systems, cochlear/ear implant, drug infusion pumps, orthodontic braces, metallic particles, or items in or on the subject’s body, piercing and/or tattoo, and tendency towards claustrophobia were included in this study. The additional inclusion criteria for patients were that they had biochemically confirmed primary adrenal insufficiency and were on a stable hormone replacement therapy for at least three months prior the study according to routine clinical practice guidelines.

Sodium images were reconstructed using an adaptive combining method (ADC) implemented in three dimensions to combine the complex images of the individual coils, with an interpolation factor of two and an overlap of eight pixels [17, 18]. SNR maps were calculated using a multiple replica approach [19]. The cylindrical homogeneous phantom which filled the knee coil and was used for B₀ and B₁⁺ maps generation, and it was scanned with the same geometry as subjects. The local transmitter B₁⁺ field was mapped with a phase-sensitive method that applies a pulse combination of nominal flip angles of α_x = 180° about the x-axis and α_y = 90° about the y-axis [20]. External B₀ field inhomogeneity correction was achieved by generating a data set with two different TEs; the first data set was acquired for off-resonance map calculations due to the resultant phase differences of two different echo times, and, in a second step, the data set was reconstructed multiple times with the corresponding off-resonance for each pixel to correct for B₀ inhomogeneity. Sequence parameters are presented in Table 1. The correction factors derived from the cylindrical phantom were applied on in vivo data similar to previous work [21]. The feasibility of the applied method was evaluated on a set of agarose phantoms with different sodium concentrations comparing prepared sodium concentrations of calibration phantoms with the concentrations calculated after image corrections were applied [22] (supplementary material).

T₁ and T₂^* relaxation time maps were derived by fitting the ²³Na signal evolution to a mono-exponential function (T₁) or a bi-exponential function (fast T₂^* and slow T₂^* components) using IDL software (version 6.3, Research Systems, Boulder, CO, USA) with mpfit function [23]. For T₁ calculation five different TIs were used: 3, 15, 30, 60, 120 ms and for T₂^* 20 different TEs were taken: 0.4, 0.6, 1.0, 2.0, 5.0, 10.0, 12.0, 14.0, 16.0, 18.0. 20.0, 22.0, 24.0, 26.0, 29.0, 32.0, 36.0, 40.0, 45.0 and 50.0 ms. For T₂^*, bi-exponential fitting procedure was performed on all MR data sets on a ROI-by-ROI basis ROI has been selected on the image acquired at the lowest TE (0.4 ms) and subsequently transferred to the rest of images. Mean sodium signal intensity has been stored for each ROI.

For bi-exponential fitting, a five-parametric function was used to fit the signal intensity:

where T_2s^* corresponds to the short component of T₂^*, T_2l^* corresponds to the long component of T₂^* C_0s and C_0l are the component ratios expressed further as a percentage value of C_0s + C_0l: F_s = 100* C_0s /( C_0s + C_0l) and F_l = 100* C_0l /( C_0s + C_0l). Offset is again determined primarily by the noise in the image.

For T₁ mapping, the following formula has been used:

where M_m is the maximum magnetization at full recovery, TI is the set of inversion times, and the offset reflects the noise.

Segmentation masks were created on morphological images acquired with DESS sequence with the parameters mentioned above and using a combination of automatic and manual segmentation (Functional Magnetic Resonance Imaging of the Brain (FMRIB) Software Library (v6.0, Analysis Group, FMRIB, Oxford, UK, the FMRIB's Automated Segmentation Tool (FAST) [24]) and ITK-SNAP, v3.8.0, Penn Image Computing and Science Laboratory (PICSL), University of Pennsylvania, Scientific Computing and Imaging Institute (SCI), University of Utah). Three different tissue compartments (delineated as regions of interests, ROIs) covering the certain muscle type (GM, S, TA) were used for PVE correction. The segmentation masks derived for three muscles and were co-registered with sodium images previously corrected for B₀ and B₁⁺ inhomogeneity. PVE calculation was performed according to a method proposed by Niesporek et al. [25], based on the geometric transfer matrix (GTM) method for PVE correction. The structural information was used in combination with a simulated point spread function (PSF) to calculate the corresponding region-spread functions (RSF) via convolution. For the PSF simulation and relaxation correction of the ²³Na data sets, we used values that we obtained in healthy subjects.

Sodium data sets from every volunteer were reconstructed using an in-house-written MATLAB (R2020b, MathWorks Inc., Natick, MA) script. Values for ²³Na-concentration in millimoles per liter (mmol/L) were calculated according to the formula (3) taking sodium signal intensities from selected ROIs and including them in the following formula:

where \(\left[{Na}_{in\;vivo}\right]and\left[{Na}_{ref}\right]\) are sodium concentrations in muscle of interest and reference concentration of 25 mmol/l [13, 26]. \(I_{in\;vivo}^{corr}\) is signal intensity derived from ²³Na images previously corrected for PVE, and B₀ and B₁⁺ inhomogeneity and \({I}_{phan}^{corr}\) is corrected signal derived form a calibration curve (supplementary material, Table 1). Additionally, \(I_{in\;vivo}^{corr}\) and \({I}_{phan}^{corr}\) were corrected for relaxation time differences between muscle tissue and phantoms.

The repeatability of measurements was estimated with an intra-class correlation coefficient (ICC) in test–retest analysis using a two-way mixed, absolute agreement model [27]. Based on the 95% confident interval of the ICC estimate, values less than 0.5, between 0.5 and 0.75, between 0.75 and 0.9, and greater than 0.90 were indicative of poor, moderate, good, and excellent repeatability, respectively [27]. Agreements between three measurements (M1, M2, M3) were assessed using Bland–Altman plots.

In the subgroup of four healthy volunteers (age: 25 ± 4 years), the mean T₁ and T₂^* relaxation times were measured, calculated, and summarized in Table 3. The mean T₁ in GM, TA, and S were: 25.9 ± 2.0 ms, 28.2 ± 2.0 ms, and 27.6 ± 2.0 ms, respectively. The mean short component of T₂^*, T₂^*_short were GM: 3.6 ± 2.0 ms; TA: 3.2 ± 0.5 ms; and S: 3.0 ± 1.0 ms, and the mean long component of T₂^*, T₂^*_long, were GM: 12.9 ± 0.9 ms; TA: 12.8 ± 0.7 ms; and S: 12.9 ± 2.0 ms, respectively (Fig. 1).

Flowchart showing the image correction procedure is provided in Fig. 2. For the first measurement, the mean TSC values for GM, TA, and S were: 19.9 ± 0.5 mmol/L, 14.0 ± 0.5 mmol/L, and 12.7 ± 0.7 mmol/L, respectively. For the second scan, we found TSC of 19.9 ± 0.6 mmol/ for GM, 13.8 ± 0.6 mmol/L for TA, and 12.7 ± 0.5 mmol/L for S. The third exam for GM, TA, and S found TSC values of 19.8 ± 0.5 mmol/L, 13.7 ± 0.5, mmol/L and 12.4 ± 0.8 mmol/L, respectively. ICC test–retest analysis showed a good repeatability for each group of muscles individually. The ICC for the gastrocnemius medialis was 0.784 (CI 95%, lower bound = 0.468, upper bound = 0.951), for the tibialis anterior, the ICC was 0.818 (CI 95%, lower bound = 0.435, upper bound = 0.948), and, for the soleus, the ICC was 0.807 (CI 95%, lower bound = 0.435, upper bound = 0.948). Bland–Altman diagrams of reproducibility tests show that majority of points are scattered between the limits of agreement, except for the comparison of M1 with M3 in tibialis anterior, M2 with M3 in tibialis anterior, and M2 with M3 soleus muscle. There is no apparent pattern in the Bland–Altman plot – the difference between measurements does not change as the average of measurements increases and indicates a good agreement between the three measurements performed in the same subject (Fig. 3).

Ten healthy subjects, five men and five women (age: 30 ± 6 years, body mass index (BMI), 21.1 ± 1.0 kg/m²) were involved in repeatability tests. The mean SNR of sodium images of the healthy human calf was 16 ± 3. In subjects with Addison’s disease the mean SNR was 13 ± 5. Before corrections were applied, the mean TSC values for GM, TA, and S were 22.7 ± 0.7 mmmol/L, 17.8 ± 1.0 mmol/L, and 16.4 ± 0.9 mmol/L and, respectively. After all corrections were applied, the mean TSC of three measurements were: gastrocnemius medialis: 19.9 ± 0.1 mmol/L; tibialis anterior: 13.8 ± 0.2 mmol/L; and soleus: 12.6 ± 0.2 mmol/L (Table 4).

Nonparametric Friedman test showed a significant difference between TSC values for all three types of muscles (P = 0.0005). There was a difference between gastrocnemius medialis and soleus muscle (P = 0.018) and between gastrocnemius medialis and tibialis anterior (P = 0.018). A difference between the soleus and tibialis was found as well (P = 0.018).

In participants with Addison’s disease (age: 41 ± 10 years, BMI: 22.5 ± 1.0 kg/m²) the mean TSC measured in the gastrocnemius medialis was 10.2 ± 1.0 mmol/L. In the tibialis anterior and soleus, measured TSC values were 8.4 ± 0.6 mmol/L and 7.2 ± 0.1 mmol/L, respectively (Table 4).

A significant difference in TSC values was found between healthy volunteers and patients for all three muscles: P = 0.0007, P = 0.0027 and P = 0.0007 for GM, TA and S, respectively (Fig. 4).