Introduction

Sodium MRI proves challenging due to the ~10000 times weaker signal strength compared to proton imaging. For translation, however, not only the development of signal efficient methods is crucial, but also biexponential transverse relaxation, resulting from the spin-3/2 characteristics of the 23Na nucleus, needs to be taken into account. While the fast component plays no role in fluids due to rapid molecular movement, it is the dominating process in tissue making up approximately 60% of the T₂ decay. Currently, the gold standard for sodium MRI is the use of twisted projection imaging (TPI)⁽¹⁾. The major downside of this method are the extremely long dead times within TR intervals (TR $$$\approx$$$ 160ms) to ensure complete T₁ recovery for quantification of tissue sodium concentration (TSC). In contrast, balanced steady-state free precession (bSSFP) imaging is performed with much shorter TR and offers the highest signal-to-noise ratio (SNR) among fast imaging methods⁽²⁾. This, in principle, makes bSSFP the perfect candidate for sodium MRI. Furthermore, Kharrazian et. al.⁽³⁾ found out in the context of bSSFP that the spin-3/2 system of 23Na can be treated as a spin-1/2 system in some limits, such as long TR and small flip angles. In this work the feasibility of quantitative sodium imaging with classical bSSFP theory is explored.

Methods

Configuration-based bSSFP: One of the major issues of proton-based bSSFP are off-resonances leading to prominent signal modulations. Evidentially, also with sodium, bSSFP shows a periodic frequency response. This, in good approximation, can be approached by the Freeman-Hill equation for spin-1/2 particles⁽⁴⁾⁽⁵⁾. Generally, due to the periodic modulation with the phase θ, accumulated within any TR-period, the sodium magnetization can be expressed in the configuration space that can be explored by the acquisition of multiple phase-cycled bSSFP scans and a subsequent N-point Fourier transform⁽⁶⁾. Heuristically, considering the modes to follow the theoretical framework developed for protons for a pure spin-1/2 ensemble (i.e., mono-exponential decay), this can be used to compute longitudinal (T₁) and transverse (T₂) relaxation times⁽⁷⁾, as well as the relative TSC from the zeroth-order mode, using⁽⁸⁾
$$\mathrm{SSFP}_{\mathrm{FID}} = \tan\left(\frac{\alpha}{2}\right) \left(1- \frac{(E_1 - \cos\alpha)\left(1-E_2^2\right)}{\sqrt{p^2-q^2}}\right) \tag{1}$$
where
$$E_i = \exp(-\mathrm{TR}/T_i) \hspace{1cm}\mbox{for } i=1,2$$
$$p = 1-E_1\cos\alpha - E_2^2(E_1 - \cos\alpha)$$
$$q = E_2(1-E_1)(1 + \cos\alpha)$$
MRI: Sodium MRI was performed on two highly concentrated (4mol/l with and without 4% agar) sodium phantoms⁽⁵⁾ and in the brain of a healthy volunteer. For transmission and reception a dual-tuned 1H/23Na birdcage coil was used. For TSC estimation, the birdcage coil sensitivity was assumed to be constant. The RF reference amplitude was estimated by maximizing the free induction decay. Subsequently, a set with N = 8 phase-cycled 3D isotropic bSSFP scans were acquired with RF phase increments of {0, 45, 90, 135, 180, 225, 270, 315}°, using TR = 5ms, TE = 2.5ms, flip angle α = {30, 40, 50}° for the phantoms, α = 40° for the brain, isotropic resolution: 8mm. For the phantoms a total of 24 averages per measurement were used, yielding 2:55 minutes per bSSFP scan and 23:20 minutes in total. For the brain imaging 60 averages were used, yielding 7:15 minutes per scan, resulting in a total scan time of 58 minutes.

Results/Discussion

Fig.1 shows magnitude and phase data of a representative coronal slice of both fluid and agar phantoms for all eight phase cycles as well as their computed modes F_p. From the three most dominant modes F_-1, F₀ and F₁, T₁ and T₂ maps were heuristically computed together with the relative TSC according to equation (1) (Fig.2). As expected, the T₁ and T₂ values are of the same order for the fluid but markedly different in agar due to spin-3/2 effects. Notably, a slight dependency of the relaxation times on the flip angle α was observed in agar.
In analogy, F_-1, F₀ and F₁, as well as maps for T₁, T₂ and the relative TSC are shown for the brain scan in Figs. 3 & 4. Mean T₁ and T₂ values for the phantom as well as gray matter/white matter (GM/WM) and cerebral spinal fluid (CSF) are summarized in Tab. 1. Overall, T₁ values for brain tissue and CSF agree with expectations^(9)(10). T₂ values appear predominantly lower than the literature values⁽¹⁰⁾ in tissues and fluids. For tissues, this is most likely due to the fast T₂ decaying component that can not be resolved, whereas for CSF, partial volume effects might affect T2 estimates. While the absolute TSC can not be computed in this experiment, the calculated ratio of 3.1$$$\pm$$$0.9 between WM/GM tissue and CSF is in accordance with the literature ⁽¹¹⁾.

Conclusion

The presented heuristic treatment of 23Na using a spin-1/2 based configuration analysis for subsequent quantification yields results that are in agreement with literature. Further investigations, however, are required to corroborate and validate our findings.

Acknowledgements

This work was supported by the Swiss National Science Foundation (SNF grant No. 325230_182008).