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Proof of concept for the separation of free and bound sodium in human brain through two-TE acquisitions at 3T

Yongxian Qian¹, Tiejun Zhao², Karthik Lakshmanan¹, Yulin Ge¹, Yvonne Lui¹, Timothy Shepherd¹, and Fernando E. Boada¹

¹Radiology, New York University, New York, NY, United States, ²Siemens Medical Solutions USA, New York, NY, United States

Synopsis

In human brain, intracellular sodium ions (Na⁺) are in slow and restricted motion due to their binding to negatively-charged macromolecules while their extracellular counterparts are in fast and unrestricted motion. This difference in motion properties leads to changes in bi-exponential transverse decay of free and bound sodium ions, which have been explored previously as a means to separate free and bound sodium. In this study, a new approach is proposed to separate free and bound sodium using single-quantum sodium images, without the SNR and SAR limitations as encountered in the triple-quantum filtering approach.

INTRODUCTION

In human brain, intracellular sodium ions (Na⁺) exhibit slow and restricted motion due to their binding to negatively-charged macromolecules while the vast majority of their extracellular counterparts experience fast and unrestricted motion.¹ This difference in motion properties for intra/extracellular sodium ions leads to changes in their bi-exponential transverse decay, which have been explored previously as a means to separate intra and extracellular components of brain sodium signal.² Separation of free and bound sodium signal is, therefore, a key technical hurdle for the quantification of intracellular sodium concentration and its application for the study of cell ion homeostasis during pathologies such as brain tumors, multiple sclerosis (MS), epilepsy, bipolar disorder, and mild traumatic brain injury (mTBI). Current approaches, such as triple-quantum filtering (TQF),³ inversion recovery (IR),⁴ and short-T2 imaging (sT2),⁵ are challenging in a clinical setting because of their low signal-to-noise ratio (SNR), large specific absorption rate (SAR), and/or incomplete suppression of free sodium signal. In this study, we demonstrate a new approach for the separation of free and bound sodium through the use of a robust, of pixel-wise relaxographic analysis. Our initial results demonstrate good concordance with the results obtained using TQF techniques, albeit without their SNR and SAR limitations.

METHODS

Bound sodium nuclei have a bi-exponential T2 decay in tissue with 60% of the signal decaying through a short component (T_2bs ~3ms) and 40% through a long component (T_2bl ~25ms). Free sodium, on the other hand, exhibits a mono-exponential T2 decay (T_2fr ≥ T_2bl) (Eq. 1).¹ We hypothesize that this distinct behavior in T2 decay may be used to separate free and bound sodium using single-quantum sodium (²³Na) images of multiple echo times (TE). Eq. 2 details our approach for two TEs, where α and β are signal intensities of free and bound sodium at a voxel, which are to be determined using SQ images acquired at "pre-optimized" echo times TE1 and TE2. In our implementation, T2 decay is replaced with T2* decay and the values of (T2*_fr, T2*_bs, T2*_bl) are estimated from a separate FID acquisition on whole brain. After separation, α and β are converted voxel-by-voxel into volume-fraction-weighted sodium concentrations, v_frC_fr and v_bdC_bd, where v_fr+v_bd=1, through an integrated calibration.⁵ In addition, total sodium concentration, C_Total, is calculated from total signal intensity at a voxel, namely α+β.

Eq. [1a] $$$Y_{bd}(t)=0.6exp(-t/T_{2bs})+0.4exp(-t/T_{2bl})$$$

Eq. [1b] $$$Y_{fr}(t)=1.0exp(-t/T_{2fr})$$$.

Eq. [2a] $$$y(r,t)=\alpha(r)Y_{fr}(t)+\beta(r)Y_{bd}(t)$$$.

Eq. [2b] $$$\bf \it y=Fx$$$, with $$$\alpha\geq0$$$, $$$\beta\geq0$$$.

Eq. [2c] $$$\bf \it y\equiv\left(\begin{array}{c}y(TE1)\\y(TE2)\end{array}\right)$$$, $$$\bf \it x\equiv\left(\begin{array}{c}\alpha\\\beta\end{array}\right)$$$, $$$\bf \it F\equiv\left(\begin{array}{c}Y_{fr}(TE1),\ Y_{bd}(TE1) \\Y_{fr}(TE2),\ Y_{bd}(TE2)\end{array}\right)$$$.

EXPERIMENTS

Sodium MRI scans were performed on phantoms and human subjects on clinical scanners at 3T; a Magnetom Prisma (Siemens Healthcare) using a custom-built 8-channel dual-tuned ¹H-²³Na Tx/Rx head coil,⁶ and a Magnetom Tim Trio (Siemens Healthcare) using a commercial dual-tuned ¹H-²³Na volume head coil (Advanced Imaging Research Inc., Cleveland)). In the phantom study, three 10% w/w agar tubes of sodium concentrations 90-150mM and one saline water tube of 150mM sodium were used. In the human study, seven patients (2 bipolar, 3 epilepsy, 1 MS, and 1 mTBI; age 33±16yr in 18-59yr; 3/4 M/F) were scanned, with an approved IRB. The twisted projection imaging (TPI) sequence ⁷ was used for maximizing SNR, with FOV=220mm, matrix size=64, 3D isotropic, TR=100ms, TE1/TE2=0.5/5ms, θ=90°, averages=8 (subjects) or 4 (phantoms), and TA=99sec (1 TE-image at 1 average). The images were reconstructed offline with custom-developed programs in C++. The separation was performed in MATLAB (R2015b, The MathWorks) using the non-negative least squares (NNLS) algorithm.⁸ After corrections for B1+/- inhomogeneity associated with the array coil, a calibration factor was determined using an internal marker of vitreous fluid at 145mM.⁹

RESULTS AND DISCUSSION

Fig. 1 shows the FID signal and T2* spectrum from a subject’s brain, and demonstrates the feasibility of estimating values of (T2*fr, T2*bs, T2*bl) in human brain. Fig. 2 shows the images of free and bound sodium in the phantoms. These demonstrated that high separation accuracy can be achieved for the free (99.9%) and bound (99.8%) sodium components. Figs. 3 and 4 are two representative results from the patient study, that provide further evidence of the accurate separation of free sodium in the vitreous fluid (99.5±0.9%) and ventricle CSF (96.9±2.4%) in the free sodium images, in contrast to 0.5±0.9% and 3.1±2.3% in the bound sodium images. These results collectively demonstrated evidence for the feasibility of our approach for the separation of free and bound sodium in human brain.

Acknowledgements

This work was financially supported in part by NIH grants R01 MH088370, R01 CA111996 and R01NS082436.

References

1. Jaccard G, Wimperis S, Bodenhausen G. Multiple-quantum NMR spectroscopy of S=3/2 spins in isotropic phase: A new probe for multiexponential relaxation. J Chem Phys 1986; 85: 6282-6293.

2. Winter PM, Bansal N. Triple-quantum-filtered 23Na NMR spectroscopy of subcutaneously implanted 9L gliosarcoma in the rat in the presence of TmDOTP5-. J Magn Reson 2001; 152:70-78.

3. Hancu I, Boada FE, Shen GX. Three-dimensional triple-quantum-filtered (23)Na imaging of in vivo human brain . Magn Reson Med. 1999 Dec;42(6):1146-54.

4. Kline RP, Wu EX, Petrylak DP, Szabolcs M, Alderson PO, Weisfidt ML, Cannon P, Katz J. Rapid in vivo monitoring of chemotherapeutic response using weighted sodium magnetic resonance imaging. Clin Cancer Res 2000; 6:2146-2156.

5. Qian Y, Panigrahy A, Laymon CM, Lee VK, Drappatz J, Lieberman FS, Boada FE, Mountz JM. Short-T2 imaging for quantifying concentration of sodium (23 Na) of bi-exponential T2 relaxation. Magn Reson Med 2015; 74:162-174.

6. Wiggins GC, Brown R, Lakshmanan K. High-performance radiofrequency coils for (23)Na MRI: brain and musculoskeletal applications NMR Biomed 2016; 29(2):96-106.

7. Boada FE, Gillen JS, Shen GX, Chang SY, Thulborn KR. Fast three dimensional sodium imaging. Magn Reson Med 1997; 37:706–715.

8. Lawson CL, Hanson RJ. Solving least squares problems. Prentice-Hall, 1974, Chapter 23, p. 161.

9. Kokavec J, Min SH, Tan MH, et al. Biochemical analysis of the living human vitreous. Clin Exp Ophthalmol 2016; 44(7):597-609.

Figures

Fig. 1. Sodium FID (a) and T2* spectrum (b) at 3T from a subject brain (59 years, male), showing the feasibility to use the FID and estimate T2* values for (T2*fr, T2*bs, T2*bl) in human. In a: AdjXFre, TE/TR=1/200ms, averages =1, TA=0.2sec, SNR= 104 at the 1st data point. In b: 0.5ms interval, 200 points. (8-channel Tx/Rx array coil)

Fig. 2. Phantom study. (a) Agar and water tube phantoms. (b, c) SQ images. (d-f) The two-TE separations. (g) Signal intensity after the separation. Signal recovery is 99.8±0.1% for the bound sodium and 99.9% for the saline water. Note: All the images have the same window/level. (volume coil)

Fig. 3. Patient study (bipolar, 59 years, male): (a) low and (b) high brain slices. The ventricle CSF and vitreous fluid in (a) are well separated into the free sodium at 98.7% and 99.9% of total sodium, respectively. All the images are at the same scale, except for the red-bordered images (top right) which are at a two-fold large scale for better display of bound sodium. (8-channel Tx/Rx array coil)

Fig. 4. Patient study (MS, 21 years, female): (a) low and (b) high brain slices. The vitreous fluid in (a) and ventricle CSF in (b) are well separated into the free sodium at 99.9% and 98.5% of total sodium, respectively. All the images are at the same scale, except for the red-bordered images (top right) which are at a two-fold large scale for better display of bound sodium. (8-channel Tx/Rx array coil)

Proc. Intl. Soc. Mag. Reson. Med. 25 (2017)

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