Lisa Leroi^{1}, Arthur Coste^{1}, Ludovic de Rochefort^{2}, Mathieu Santin^{3}, Romain Valabrègue^{3}, Franck Mauconduit^{4}, Marie-France Hang^{1}, Edouard Chazel^{1}, Jérémy Bernard^{1}, Michel Luong^{5}, Eric Giacomini^{1}, Denis Le Bihan^{1}, Cyril Poupon^{1}, Fawzi Boumezbeur^{1}, Cécile Rabrait-Lerman^{1}, and Alexandre Vignaud^{1}

Quantifying
physical properties of sodium could be of benefit to assess more specifically changes
in cellular homeostasis accompanying neuroinflammatory or neurodegenerative diseases.
This work aimed at adapting for ^{23}Na MRI at 7 Tesla the Quantitative
Imaging using Configuration States (QuICS) method, primarily developped for ^{1}H MRI. We demonstrate the possibility to not only estimate
accurately the T_{1}, T_{2}, FA, M_{0} and ADC simultaneously
for ^{23}Na at physiological concentration at UHF, but to acquire 3D
maps for all of them.

Given the hemi-cylindrical geometry of the coil (Fig.1.), a region-of-interest
(ROI) was defined over the top of the phantom as shown in Fig.2. In this ROI,
mean R_{1} was 17.3±1.43s^{-1} (T_{1}=58ms), R_{2}
19.9±2.13s^{-1 }(T2=50ms),
ADC 1.11±0.50x10^{-9}m².s^{-1} and flip angle 51.5±10.9° (Fig.
2).

For saline solutions of 140-150mM mimicking the physiological
CSF, T_{1} values of 50-55ms and T_{2} values of 55-65ms are
reported in the literature^{7,8} for in
vivo conditions. Diffusion coefficient were estimated for sodium in the rat
brain at 25°C to be 1.15x10^{-9}m².s^{-1} ^{9} and in sodium fluorine in aqueous solution at
25°C to be 1.3x10^{-9}m².s^{-1} ^{10}. Overall, our results were in good agreement
with these data, with an error of 5% for T_{1}, 9% for T_{2}
and 8% for ADC.

In this preliminary in vitro study,
we have demonstrated the possibility to use the QuICS method, not only to
estimate accurately the T_{1}, T_{2}, FA, M_{0} and ADC
simultaneously for ^{23}Na at physiological concentration at UHF, but
to acquire 3D maps for all of them. This is particularly exciting considering the difficulty of
conventional approaches to estimate parameters such as the ADC for nuclei with
short T_{2} relaxation times. To the knowledge of the authors, this is
the first time that such multi-parametric extraction is reported in the context
of X-nuclei imaging.

Diffusion was the most complicated parameter to estimate and required the
full range of RF spoiling increments described above. However, the estimation
of M_{0}, R_{1} and R_{2} was achieved with good
precision in less than an hour. For now, the long acquisition time remains a
significant hurdle to translate this method to clinical or preclinical MRI. We
are aiming at accelerating our method by using shorter TE, non-Cartesian
sampling trajectories^{11}, a better coil configuration^{12} and eventually less FA, RF and gradient
spoiling steps. An optimization algorithm based on Fisher information and
Cramér-Rao lower bound will be used for this purpose^{13,14}.

1. D. Ma et al., “Magnetic resonance fingerprinting,” Nature, vol. 495, no. 7440, pp. 187–192, Mar. 2013.

2. J. b. m. Warntjes et al., “Novel method for rapid, simultaneous T1, T*2, and proton density quantification,” Magn. Reson. Med., vol. 57, no. 3, pp. 528–537, Mar. 2007.

3. J. b. m. Warntjes, et al., “Rapid magnetic resonance quantification on the brain: Optimization for clinical usage,” Magn. Reson. Med., vol. 60, no. 2, pp. 320–329, Aug. 2008.

4. R. Heule et al., “Triple echo steady-state (TESS) relaxometry,” Magn. Reson. Med., vol. 71, no. 1, pp. 230–237, Jan. 2014.

5. P. Schmitt et al., “Inversion recovery TrueFISP: Quantification of T1, T2, and spin density,” Magn. Reson. Med., vol. 51, no. 4, pp. 661–667, Apr. 2004.

6. L. de Rochefort, “Encoding with Radiofrequency Spoiling, Equilibrium States and Inverse Problem for Parametric Mapping,” Proc. Intl. Soc. Mag. Reson. Med., 2015, p. 445.

7. G. Madelin and R. R. Regatte, “Biomedical applications of sodium MRI in vivo,” J. Magn. Reson. Imaging, vol. 38, no. 3, pp. 511–529, Sep. 2013.

8. N. J. Shah et al., “Imaging of sodium in the brain: a brief review,” NMR Biomed., vol. 29, no. 2, pp. 162–174, Feb. 2016.

9. J. A. Goodman, C. D. Kroenke, G. L. Bretthorst, J. J. H. Ackerman, and J. J. Neil, “Sodium ion apparent diffusion coefficient in living rat brain,” Magn. Reson. Med., vol. 53, no. 5, pp. 1040–1045, May 2005.

10. A. C. F. Ribeiro et al., “Diffusion Coefficients of Sodium Fluoride in Aqueous Solutions at 298.15 K and 310.15 K,” ResearchGate, vol. 57, no. 2, pp. 410–4, Jun. 2010.

11. A. Coste et al., “Assessment of benefit to use a non-Cartesian trajectory and nonlinear reconstruction method compared to a Cartesian strategy for fast 31P MRI,” Proc. Intl. Soc. Mag. Reson. Med. 24, 2016, p. 3940.

12. G. Shajan et al., “Three-layered radio frequency coil arrangement for sodium MRI of the human brain at 9.4 Tesla,” Magn. Reson. Med., vol. 75, no. 2, pp. 906–916, Feb. 2016.

13. L. de Rochefort et al., “In Vivo Feasibility of Multi-Parametric Mapping Based on Fast Steady-State Sequences,” Proc. Intl. Soc. Mag. Reson. Med., 2016, p. 1823.

14. R. Valabrègue and L. de Rochefort, “Fisher Information Matrix for Optimizing the Acquisition Parameters in Multi-Parametric Mapping Based on Fast Steady-State Sequences,” Proc. Intl. Soc. Mag. Reson. Med., 2016, p. 1569.

Fig. 1 : Schematic
of our hemi-cylindrical non-human primate ^{23}Na RF coil and NaCl phantom
positioning

Fig. 2 : Multi-parametric
maps: (a) M_{0}, (b) FA in degrees, (c, d) R_{1} and R_{2}
in s^{-1}, (e) diffusion map in 10^{-9}m².s^{-1}. Average
physical parameters detailed in the text were calculated over the ROI (in red)