In ¹H MRI, steady-state free precession (SSFP) techniques are widely applied due to their acquisition speed, high SNR and clinically useful contrast properties. The SSFP dynamics of ²³Na are expected to be fundamentally different from spin-1/2 nuclei (such as ¹H) [1]. ²³Na has a spin of 3/2 and possesses a quadrupolar moment which dominates its relaxation characteristics [2]. The objective of this work was the investigation of phantoms with high NaCl concentrations which are suited to explore SSFP contrast mechanisms and signal properties with sodium MRI at 3 Tesla.

Phantom specifications.

Sodium probes were created containing either saline solution or 4 % agar gel with a NaCl concentration of 4 mol/l in each (close to the solubility limit to generate a high ²³Na signal). While in the NaCl solution, the time-averaged quadrupolar interaction of ²³Na is generally assumed to be zero, in the agar gel, biexponential relaxation is expected to occur [2]. The phantoms were constructed using two different approaches. For the first, rather conventional approach, the saline solution and agar gel were filled into empty cylindrical containers of a diameter of about 9 cm (cf. Fig. 1a). For the second, novel approach, cylindrical phantom containers filled with small insulating tubes each of a diameter of about 7 mm were used (cf. Fig. 1b).

MR imaging protocol.

The sodium phantoms were evaluated using 3D balanced SSFP (bSSFP) protocols with both ²³Na MRI as well as ¹H MRI for comparison. Imaging was performed with the following main sequence parameters (²³Na / ¹H): TR = 12.03 ms / 3.18 ms, TE = 6.02 ms / 1.59 ms, flip angle = 90°, 30° / 20°, in-plane resolution = (4 x 2) mm² / (0.5 x 0.5) mm², slice thickness = 10 mm, 12 slices were acquired. For the ²³Na scans, 300 averages were used yielding a total acquisition time of 32 min.

Frequency profile measurements.

The dynamics of ²³Na MRI were studied by measuring the frequency profile of the bSSFP signal. To this end, first, B₀ shimming was applied. Then, the shim gradient along the z-axis was offset manually and the phase of the RF pulse adjusted to produce two bands across the phantom. To gain sufficient SNR, the measurements specified above were repeated three times and the acquired signal amplitudes were averaged, resulting in a total scan time of 1 h 37 min. The projection of the acquired profile onto the frequency encoding axis was fitted to the bSSFP signal model [3] by assuming monoexponential relaxation and treating T₁, T₂, and the proton density as free variables. The Levenberg-Marquardt algorithm for nonlinear least squares fitting was used.

Skin effect.

The bSSFP images displayed in Figure 2a were obtained by measuring the agar gel phantom constructed as specified in Figure 1a with both ¹H (Fig. 2a, left) and ²³Na (Fig. 2a, right) MRI. The observable signal attenuation towards the center of the phantom is likely to be caused by the relatively high conductivity of the measured NaCl phantom – a phenomenon known as skin effect. In good conductors, the electromagnetic field associated with the RF pulse decays exponentially with the characteristic distance $$$\delta$$$, the skin depth, [4]

$$\delta\approx\frac{1}{\sqrt{\pi\mu_0\sigma\nu}}$$

where $$$\mu_0$$$ is the permeability of vacuum, $$$\sigma$$$ the electrical conductivity and $$$\nu$$$ the carrier frequency of the RF pulse. Based on this formula and an estimate of 222 mS/cm for $$$\sigma$$$ [5], the skin depth in NaCl solutions can be approximated by about 1 cm for ¹H MRI and about 2 cm for ²³Na MRI (cf. Fig. 2a). By placing insulating tubes with a diameter of d < $$$\delta$$$ in the phantom containers (cf. Fig. 1b), the skin effect can successfully be circumvented as illustrated in Figure 2b.

Frequency profile.

The derived novel phantoms proved ability to analyze the frequency profile of ²³Na bSSFP (cf. Fig. 3). The profiles of both, the saline solution and the agar gel phantom, seem to follow the characteristics of the spin-1/2 bSSFP signal model. From the fit, a rough estimate for the ²³Na relaxation times of about T₁ ≈ T₂ ≈ 49 ms is obtained for the saline solution and of about T₁ ≈ 49 ms, T₂ ≈ 18 ms for the agar gel in good agreement with reported literature values [2]. Deviations from the assumed signal model may be caused by flip angle miscalibrations or biexponential relaxation in the case of the agar gel.

A novel type of sodium phantoms was presented that is not prone to the skin effect. As a result, it allows to use high NaCl concentrations and is ideally suited to study the SSFP dynamics of ²³Na at 3 Tesla.