The authors have declared that no competing interests exist.

Conceived and designed the experiments: GM. Performed the experiments: GM DX. Analyzed the data: GM JB RRR. Contributed reagents/materials/analysis tools: GM JB. Wrote the paper: GM JB DX RRR.

The purpose of this study is to assess the repeatability of the quantification of pseudo-intracellular sodium concentration (C_{1}) and pseudo-extracellular volume fraction (α) estimated in brain in vivo using sodium magnetic resonance (MRI) at 3 T. Eleven healthy subjects were scanned twice, with two sodium MRI acquisitions (with and without fluid suppression by inversion recovery), and two double inversion recovery (DIR) proton MRI. DIR MRIs were used to create masks of gray and white matter (GM, WM), that were subsequently applied to the C_{1} and α maps calculated from sodium MRI and a tissue three-compartment model, in order to measure the distributions of these two parameters in GM, WM or full brain (GM+WM) separately. The mean, median, mode, standard deviation (std), skewness and kurtosis of the C_{1} and α distributions in whole GM, WM and full brain were calculated for each subject, averaged over all data, and used as parameters for the repeatability assessment. The coefficient of variation (CV) was calculated as a measure of reliability for the detection of intra-subject changes in C_{1} and αfor each parameter, while intraclass correlation (ICC) was used as a measure of repeatability. It was found that the CV of most of the parameters was around 10–20% (except for C_{1} kurtosis which is about 40%) for C_{1} and α measurements, and that ICC was moderate to very good (0.4 to 0.9) for C_{1} parameters and for some of the α parameters (mainly skewness and kurtosis). In conclusion, the proposed method could allow to reliably detect changes of 50% and above of the different measurement parameters of C_{1} and αin neuropathologies (multiple sclerosis, tumor, stroke, Alzheimer’s disease) compared to healthy subjects, and that skewness and kurtosis of the distributions of C_{1} and αseem to be the more sensitive parameters to these changes.

Sodium ions (^{23}Na^{+}) are vital components in the human brain, and their homeostasis is a major process in cells through coupled exchange with potassium ions K^{+} between the intra- and extracellular compartments through the Na^{+}/K^{+}-ATPase (sodium-potassium pump) [_{1}) as the gradient cannot be sustained anymore, and furthermore to cell death and subsequent increase of extracellular volume fraction (_{1} and _{1} in brain in vivo could help assess the degree of cell hypometabolism or injury [_{1} and

Sodium magnetic resonance imaging (MRI) [_{1} and _{1} and _{1} and _{1} and _{1} and _{1} and _{1} and

The brains of eleven healthy volunteers (6 men, 5 women, mean age = 32.1 ± 7.9 years) were scanned twice within a month (on average) with exactly the same proton/sodium protocol. This study was approved by the institutional review board (IRB) of New York University Langone Medical Center and all volunteers signed informed consent form (#11783, Technical Development of up to 7T Magnetic Field Level) prior to the scans.

All scans were performed at 3 T on a Tim Trio system (Siemens, Erlangen, Germany) using a dual-tuned ^{1}H/^{23}Na birdcage radiofrequency (RF) coil tuned at 128/33 MHz (Stark Contrast, Erlangen, Germany).

Two double inversion recovery (DIR) MRI acquisitions were performed. The first DIR image was acquired in order to suppress both CSF and WM using the DIR Turbo Spin Echo SPACE sequence [^{3} isocenter, resolution = 2.5 mm isotropic, inversion times TI_{1} = 2650 ms and TI_{2} = 550 ms, time of acquisition (TA) = 4:00 min. The second DIR image was acquired in order to suppress both CSF and GM with the same parameters as the first DIR except TI_{1} = 2800 ms and TI_{2} = 800 ms.

Sodium acquisitions were performed using the 3D ultrashort echo time (UTE) non-Cartesian FLORET sequence [

Sequence 1—without fluid suppression: TR = 80 ms, TE = 0.2 ms, flip angle (FA) = 80°/0.5 ms, 3 hubs at 45°, 200 interleaves/hub, 745 data points / interleaf, dwell time 10

Sequence 2—with fluid suppression by inversion recovery (IR): a ‘soft’ rectangular inversion pulse [

All sodium images were reconstructed offline in Matlab (MathWorks, Natick, MA, USA) with standard 3D regridding [

The data processing (in Matlab) for calculating the final pseudo-intracellular sodium concentration (C_{1}) and pseudo-extracellular volume fraction (

^{2} ⩾ 0.99 and adjusted

_{short}∼5 ms, T2_{long}∼25 ms, in parenchyma), correction factors of the sodium maps (0.85 for aTSC and 0.5 for aISC) were calculated using full density operator simulation of the sodium spin dynamics [

^{1}H DIR acquisitions using SPM8 [_{1} and

_{1} and _{1}) and pseudo-extracellular volume fraction (_{2}∼140 mM [_{WM} = 0.7, w_{GM} = 0.85 and w_{brain} = 0.775 (mean value from WM and GM)[_{1}×V_{1}+C_{2}×V_{2})/V_{t} (with V_{t} = total volume of the voxel). The value of each voxel of the aISC map is by definition equal to the intracellular sodium concentration only: aISC=(C_{1}×V_{1})/V_{t}. From these assumptions and equations, we can calculate the unknown parameters C_{1} and _{WM}, w_{GM} and w_{brain} depending on the masked aTSC and aISC maps used: α = (aTSC−aISC)/C_{2} and C_{1} = (C_{2}×aISC)/(w×C_{2}−aTSC+aISC). This calculation is performed for each voxel. All voxels are then recombined in maps of C_{1} and _{1} and

_{1} and sodium concentration C_{1}; compartment 2 = extracellular space of volume V_{2}, sodium concentration C_{2} and extracellular volume fraction _{s} and no sodium. Total volume is V_{t} = V_{1}+ V_{2} +V_{s}. Water volume fraction is denoted w. _{1} and _{1} and

Note that no RF (B_{1}) map was acquired in this preliminary study, as it was not deemed necessary from preliminary data acquired while testing this technique. We used a birdcage coil with homogeneous transmit and receive B_{1} fields, no improvement in the quality of the images, nor in the sodium data quantification was observed when B_{1} correction was applied. Moreover, B_{1} correction for the fluid suppressed images (from inversion recovery) is not trivial, as the effect of B_{1} inhomogeneities on the images depends not only on the pulses (inversion and excitation) but also on the T1 of the tissues and the relaxation of their magnetization during the inversion time, which varies in different compartments of the brain.

Simulations of ‘fluid’ (cystic-like) and ‘solid’ (tumor-like) lesions, either compact (10×10×10 voxels) or randomly distributed over the whole brain (1000 voxels over 86571, which correspond to about 1.15% of all voxels in brain) were also performed and are presented in Supporting Information (

Restricted maximum likelihood estimation of the variance components in a random effects model was used to estimate the intra-subject variance (i.e., the variance between results from replicate scans of the same subject) and inter-subject variance (the variance between results from different subjects) of each measure (i.e., mean, median, mode, std, skewness and kurtosis) within each tissue. The estimated variance components were used to compute the coefficient of variance (CV, in %) as the square root of the intra-subject variance expressed as a percentage of the mean, and the intra-class correlation (ICC) as the inter-subject variance divided by the sum of the intra- and inter-subject variances. By expressing the intra-subject variance relative to the overall mean of a given measure, the CV is considered an indicator of the utility of a measure for detecting within-subject changes over time; temporal changes that are not substantively greater in magnitude than the CV would be difficult to distinguish from changes attributable to random noise. It is noted that the CV is not appropriate for measures (e.g., skewness) that can be both positive and negative since the mean of such a measure does not represent the magnitude of a typical observed value of the measure. The ICC is a measure of the repeatability (or test-retest reliability) of the method [

_{1} and _{1} and _{1} and ^{st} scan vs. 2^{nd} scan), in GM, WM and full brain. Data from the histogram statistics for all volunteers and all scans can be seen in Supporting Information (_{1} values from scan/re-scan are in the range 5–20 mM. The mean, median and mode _{1} values are all regrouped around 5 mM, while std _{1} are all regrouped around 0, while they are in the range 1–3 for _{1} are tightly regrouped in the range 3–5, while they are more spread out for

_{1} and _{1} and _{1} and _{1} and

_{1}. _{1}.

_{1} and _{1} and

Tables _{all}, std_{all}, CV and ICC of the C_{1} and _{all} and std_{all} to avoid confusion with the mean and std of the measurements of C_{1} and

_{1} (mM) |
_{all} |
_{all} |
||||||
---|---|---|---|---|---|---|---|---|

Mean | 1.49 | 1.48 | 1.53 | 10.8 | • | 0.492 | ∘ | |

Median | 1.55 | 1.60 | 1.66 | 11.0 | • | 0.491 | ∘ | |

Mode | 3.11 | 9.02 | 2.13 | 13.0 | • | 0.809 | •• | |

Std | 0.64 | 0.28 | 0.27 | 11.9 | • | 0.517 | ∘ | |

Skewness | 0.29 | 0.07 | 0.03 | NA | 0.732 | • | ||

Kurtosis | 0.51 | 0.26 | 0.05 | 6.4 | •• | 0.846 | •• | |

Mean | 2.02 | 2.80 | 2.67 | 12.0 | • | 0.511 | ∘ | |

Median | 2.20 | 3.37 | 3.10 | 12.8 | • | 0.520 | ∘ | |

Mode | 3.39 | 9.18 | 5.23 | 19.2 | • | 0.637 | • | |

Std | 0.87 | 0.51 | 0.52 | 15.5 | • | 0.493 | ∘ | |

Skewness | 0.27 | 0.06 | 0.03 | NA | 0.681 | • | ||

Kurtosis | 1.68 | 1.51 | 2.62 | 40.4 | ◊ | 0.365 | ◊ | |

Mean | 1.69 | 1.98 | 1.90 | 11.0 | • | 0.510 | ∘ | |

Median | 1.80 | 2.26 | 2.09 | 11.3 | • | 0.520 | ∘ | |

Mode | 3.41 | 7.89 | 7.85 | 22.8 | ∘ | 0.501 | ∘ | |

Std | 0.73 | 0.36 | 0.36 | 12.9 | • | 0.497 | ∘ | |

Skewness | 0.29 | 0.07 | 0.03 | NA | 0.728 | • | ||

Kurtosis | 0.66 | 0.44 | 0.04 | 5.6 | •• | 0.916 | •• |

Mean and standard deviation (two first columns) of mean, median, mode, standard deviation (std), skewness and kurtosis of C_{1} were calculated over all data (n = 22, from 11 volunteers scanned twice). Note that the mean and std over all data were labeled mean_{all} and std_{all} to avoid confusion with the mean and std of the measurements of C_{1} and

_{all} |
_{all} |
|||||||
---|---|---|---|---|---|---|---|---|

Mean | 0.017 | 0.0001 | 0.0003 | 8.9 | •• | 0.217 | ◊ | |

Median | 0.016 | 0.00007 | 0.0004 | 9.7 | •• | 0.169 | ◊ | |

Mode | 0.235 | 0.0002 | 0.0007 | 15.3 | • | 0.181 | ◊ | |

Std | 0.011 | 0.00009 | 0.00005 | 8.8 | •• | 0.657 | • | |

Skewness | 0.38 | 0.10 | 0.08 | NA | 0.549 | ∘ | ||

Kurtosis | 1.82 | 2.19 | 2.32 | 26.6 | ∘ | 0.485 | ∘ | |

Mean | 0.017 | 0.00007 | 0.0004 | 11.8 | • | 0.155 | ◊ | |

Median | 0.017 | 0.00005 | 0.0005 | 13.3 | • | 0.104 | ◊ | |

Mode | 0.022 | 0.0001 | 0.0008 | 18.1 | • | 0.108 | ◊ | |

Std | 0.011 | 0.0001 | 0.00005 | 10.9 | • | 0.702 | • | |

Skewness | 0.43 | 0.10 | 0.16 | NA | 0.387 | ◊ | ||

Kurtosis | 2.44 | 3.50 | 5.02 | 21.8 | ∘ | 0.411 | ∘ | |

Mean | 0.013 | 0.00003 | 0.0003 | 8.4 | •• | 0.097 | ◊ | |

Median | 0.013 | 0.00001 | 0.0003 | 9.6 | •• | 0.042 | ◊ | |

Mode | 0.020 | 0.00008 | 0.0006 | 14.9 | • | 0.120 | ◊ | |

Std | 0.010 | 0.00008 | 0.00005 | 9.3 | •• | 0.613 | • | |

Skewness | 0.24 | 0.06 | 0.004 | NA | 0.938 | •• | ||

Kurtosis | 1.17 | 1.38 | 0.12 | 5.4 | •• | 0.922 | •• |

Mean and standard deviation (two first columns) of mean, median, mode, standard deviation (std), skewness and kurtosis of _{all} and std_{all} to avoid confusion with the mean and std of the measurements of C_{1} and

_{1}_{1} over the 22 scans had a mean_{all}±std_{all} of 11.4±1.5 mM in GM and slightly higher 13.6±2 mM in WM, std was 4.5±0.7 mM in both GM and WM, skewness was 0±0.3 in both GM and WM, kurtosis was 3.4±0.5 in GM and slightly higher 4.0±1.7 in WM (but with higher variability). Median and mode values were in the same range as the mean value, in GM and WM respectively. For full brain, all the measures were of the same order of magnitude than in GM and WM.

_{all}±std_{all} of 0.21±0.02 in GM and lower 0.17±0.02 in WM, std was 0.08±0.01 mM in GM and slightly lower 0.06±0.01 in WM, skewness was 1.2±0.4 in GM and higher 1.9±0.4 in WM, kurtosis was 5.7±1.8 in GM and almost doubled 10.3±2.4 in WM. Due to the positive skewness of the

_{1}

_{1}

Mean, median, mode and std values of C_{1} were all in good agreement with values from the literature for intracellular sodium concentrations in healthy brain tissues, which are generally in the range 5–15 mM [_{1} distribution over whole GM, WM or full brain was very close to the normal (Gaussian) distribution (skewness = 0, kurtosis = 3), while the ^{23}Na and ^{1}H images, both C_{1} and _{1} distributions don’t differ significantly between GM and WM.

The skewness and kurtosis of both the C_{1} and ^{1}H DIR images (2.5 mm resolution), the ^{23}Na aTSC images (5 mm resolution for the data acquisition) and the ^{23}Na aISC images (6.7 mm resolution). Because of all these limitations, it can be difficult with the present method to assign a relevant biological or clinical meaning to the skewness and kurtosis of the distributions. As we are more interested in changes in these variables from healthy to non-healthy tissues, and because the exact same protocol is applied to all subjects, this lack of accurate biological interpretation should not impair the ability of the method to assess changes in C_{1} and

Except for C_{1} kurtosis where the CV > 40%, all measures of C_{1} and _{1} and _{2}) approximations. Taking CV and uncertainties into account, it is therefore reasonable to estimate that in general the proposed method would be able to detect changes in C_{1} and _{1} > 20–25 mM and mean _{1} and _{1} and

For example, in stroke, it is generally estimated that an apparent total tissue sodium concentration (aTSC) of 65–70 mM is a marker of irreversible tissue damage (cell death). This would correspond to an intracellular sodium concentration of about 40–50 mM (see for example Ref. [_{1} < 50 mM would correspond to loss of homeostasis that might be reversible, and C_{1} > 50 mM would correspond to irreversible loss of cell viability. For cancer, tumor cells have altered physiology, such as evasion of apoptosis, limitless replicative potential, tissue invasion [_{1} and

As ICC for skewness and kurtosis in full brain are very good, these two variables seem to be the best features for detecting differences between subjects. From the simulations of different lesions (see _{1} maps, but random lesions cannot be detected on either _{1} maps. However, these lesions (compact and random) can be detected on the C_{1} and

As a first approximation in this study, we assume that all extracellular sodium is either completely suppressed by IR (with TI optimized to suppress fluids) or reduced within noise level (for ‘bound’ extracellular sodium, which can be expected to have intermediate T1 between fluid sodium T1 and bound sodium T1 from within the cells). Future studies will take this into account by using a more complex tissue model (more compartments) which will include the presence of sodium with restricted motion within the interstitial space, that is different from extracellular CSF or plasma space.

Due to time constraints for the subjects (we try to keep scans of the volunteers in about 45–60 min maximum) and for scanner availability, the sodium scans were optimized to last 11 min and 17 min by using shorter TRs (80 ms and 100 ms). Although these TRs are not optimized for full recovery of the longitudinal magnetization, we found that the parameters used were a good compromise between SNR and total acquisition time for this pilot study. Relaxation times in pathologies are unknown and might affect the quantification, but we expect these relaxation times within and outside pathological cells to be still quite similar to the relaxation times within and outside normal cells, respectively. For example, assuming an average T1 ∼30 ms in parenchyma [_{1} and

Partial volume effect is a real concern for this data and was already partially discussed in Ref. [

No sodium signal from zero concentration in reference phantoms was measured for the linear regression, as it is hidden in the noise of the images. As sodium images have low SNR, we observed that adding measurements of [Na] = 0 mM (therefore noise) can induce large errors in the quantifications, which are very sensitive to the slopes of the linear regressions. Future increases of the SNR of the images, as already described above, will improve the robustness of the method to noise.

In conclusion, estimating the pseudo-intracellular sodium concentration (C_{1}) and pseudo-extracellular volume fraction (_{1} maps and the development of B_{1} inhomogeneities correction for the calculation of C_{1} and _{1} and/or _{1} and/or

(XLSX)

_{1}) maps of the brain of a healthy volunteer (1 axial slice) with artificial ‘fluid’ and ‘solid’ inclusions.

_{1}) values in full brain (GM+WM, black), GM (blue), WM (red) from a volunteer, with artificial ‘fluid’ and ‘solid’ inclusions.

(PDF)