Variability by region and method in human brain sodium concentrations estimated by 23Na magnetic resonance imaging: a meta-analysis

Abstract

Sodium imaging (²³Na-MRI) is of interest in neurological conditions given potential sensitivity to the physiological and metabolic status of tissues. Benchmarks have so far been restricted to parenchyma or grey/white matter (GM/WM). We investigate (1) the availability of evidence, (2) regional pooled estimates and (3) variability attributable to region/methodology. MEDLINE literature search for tissue sodium concentration (TSC) measured in specified ‘healthy’ brain regions returned 127 reports, plus 278 retrieved from bibliographies. 28 studies met inclusion criteria, including 400 individuals. Reporting variability led to nested data structure, so we used multilevel meta-analysis and a random effects model to pool effect sizes. The pooled mean from 141 TSC estimates was 40.51 mM (95% CI 37.59–43.44; p < 0.001, I²Total=99.4%). Tissue as a moderator was significant (F²14 = 65.34, p-val < .01). Six sub-regional pooled means with requisite statistical power were derived. We were unable to consider most methodological and demographic factors sought because of non-reporting, but each factor included beyond tissue improved model fit. Significant residual heterogeneity remained. The current estimates provide an empirical point of departure for better understanding in ²³Na-MRI. Improving on current estimates supports: (1) larger, more representative data collection/sharing, including (2) regional data, and (3) agreement on full reporting standards.

Full text

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Variability by region and method
in human brain sodium
concentrations estimated by 23Na
magnetic resonance imaging:
a meta‑analysis
Ben Ridley
1,4*, Filomena Morsillo
1, Wafaa Zaaraoui
2,3 & Francesco Nonino
1
Sodium imaging (23Na‑MRI) is of interest in neurological conditions given potential sensitivity to the
physiological and metabolic status of tissues. Benchmarks have so far been restricted to parenchyma
or grey/white matter (GM/WM). We investigate (1) the availability of evidence, (2) regional pooled
estimates and (3) variability attributable to region/methodology. MEDLINE literature search for
tissue sodium concentration (TSC) measured in specied ‘healthy’ brain regions returned 127 reports,
plus 278 retrieved from bibliographies. 28 studies met inclusion criteria, including 400 individuals.
Reporting variability led to nested data structure, so we used multilevel meta‑analysis and a random
eects model to pool eect sizes. The pooled mean from 141 TSC estimates was 40.51 mM (95% CI
37.59–43.44; p < 0.001, I2Total=99.4%). Tissue as a moderator was signicant (F214 = 65.34, p‑val < .01).
Six sub‑regional pooled means with requisite statistical power were derived. We were unable to
consider most methodological and demographic factors sought because of non‑reporting, but each
factor included beyond tissue improved model t. Signicant residual heterogeneity remained. The
current estimates provide an empirical point of departure for better understanding in 23Na‑MRI.
Improving on current estimates supports: (1) larger, more representative data collection/sharing,
including (2) regional data, and (3) agreement on full reporting standards.
Sodium magnetic resonance imaging (23Na-MRI) is of interest as a ‘quantitative’ imaging modality. Using a refer-
ence of known concentration (Fig.1a), measured signal (M0) can be converted from arbitrary signal intensity
to a quantitative scale (millimolars, mM). As a candidate for metabolic imaging in particular, the advantages of
23Na-MRI include: (1) it natively produces 3D, whole-brain, voxel-based data and is not restricted to pre-dened
volume-of-interest analyses, and (2) the fact it requires no contrast agents, meaning contraindications are the
same as for conventional proton (1H) MRI. Ionic homeostasis is a pre-requisite for proper cellular functioning,
with sodium in the nervous system being critical in trans-membrane transport, osmotic and electrostatic regula-
tion and the generation/propagation of action potentials1–3. As such, the non-invasive, invivo measurement of
sodium concentration by 23Na-MRI is of interest in the context of neuro-oncological4–6, neurodegenerative7–9,
demyelinating10–19 and cerebrovascular20 conditions, and in both physiological and pathological neuronal
activity21–25.
In practice, assigning a single imaging parameter to a voxel in an MRI image of biological tissue is an over-
simplication. is is the case both for the weighted average referred to as ‘total’ or ‘tissue sodium concentration’
(TSC) in 23Na-MRI, as well as ‘conventional’ MRI contrasts targeting tissue water protons (1H) such as diusion
or T2 measurements26,27. Image sampling/tissue fraction eects are one reason, where diverse tissue types such
as white and grey matter (WM and GM) and cerebrospinal uid (CSF) contribute to measured signal within a
single voxel. Even within a given tissue type MRI cannot resolve the sub-cellular compartments/organelles that,
in the case of 23Na-MRI, can be said to actually have a specic concentration28. e measurement of a given
OPEN
1IRCCS Istituto Delle Scienze Neurologiche di Bologna, Bologna, Italy. 2Aix Marseille Univ, CNRS, CRMBM,
Marseille, France. 3APHM, Hôpital de La Timone, CEMEREM, Marseille, France. 4Ben Ridley, Epidemiologia e
Statistica, IRCCS Istituto Delle Scienze Neurologiche di Bologna, Padiglione G, Via Altura, 3, 40139 Bologna,
Italy. *email: ben.ridley@ausl.bologna.it
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voxel will include, at a minimum, intracellular and extracellular compartments with their own concentrations,
volumes and microstructure (Fig.1b).
Physical behaviour of sodium atoms in biological media and the complexities of measuring them with MRI
present other challenges. Relative to tissue water protons, the lower MR sensitivity and abundance of 23Na result
in lower signal to noise ratios and larger voxel sizes, exacerbating tissue fraction eects29,30. 23Na-MRI pulse
sequences with ultra-fast echo times (TE) that compensate for the short, biexponential transverse relaxation of
23Na nuclei29–32, oen use non-cartesian sampling schemes which can have broader point spread functions (PSF)
and greater inter-voxel spill-over eects in comparison to 1H-MRI. ese partial volume eect (PVE) issues are
the target of growing attempts to develop or import PVE correction techniques, such as those adapted from
positron emission tomography imaging (PET)12,29–32. Correction techniques beg the question of benchmarks
for correction algorithms to target.
A range of tissue volume models to understand and validate 23Na-MRI-derived concentrations have been
proposed. e ‘canonical’ model describes two compartments: a large volume/low concentration (variously
10–15 mM5,6,10,20,33,34) intracellular space and an extracellular space of smaller volume but higher concentration
(140 mM5,6,10,20 or 145 mM33,34). ese gures lead to a general estimate for overall brain tissue (parenchyma) of
about 37–45 mM6,12,20. Model-based estimates beyond a general gure for parenchyma or gross tissue divisions
like GM or WM are largely lacking35, particularly because the cellular data required to elaborate beyond this are
for the most part not available. More broadly, histology is an invaluable tool but should not be naively taken as
the absolute gold-standard for MR features both because it is not necessarily sensitive to the same properties as
Figure1.
23Na magnetic resonance imaging. (a) An exemplar 23Na-MRI brain image, with external calibration
phantoms of diering concentrations visible on the bottom le axial image. Calibration can also be done
relative to internal references such as vitreous humor or cerebrospinal uid in the ventricles. (b) Schematic
Venn diagram (following the nomenclature in Springer28) showing physical domains (Blue) where nuclei share
similar nuclear magnetic resonance properties, and biological compartments (Red) found in brain tissue.
ese are arrayed along two axes to indicate their orthogonality: neither physical domain is unique to any
given biological compartment. 23Na-MRI TSC estimates are a weighted average inuenced by concentrations,
volumes and microstructure in a range of environments including the intracellular (neuronal and glial
cytosol, and organelles), extracellular (interstitial and vascular spaces.) and membranous (cyto/axolemmal)
contributions28. e vast majority of invivo sodium is present in metal-aquo complexes with a tetrahedral
hydration shell surrounding the 23Na ion, with a much smaller population bound to macromolecular loci80.
e domain on the le corresponds to the situation in bulk solution, where magnetic and electric elds average
out to become isotropic. An anisotropic domain (right) pertains at the interface of/with macromolecules
and/or lipid assemblies, where the surface experienced by a diusing ion is not randomly orientated and the
resulting electric eld gradient (EFG) uctuations do not average to zero. 23Na is a quadropolar ion (spin = 3/2)
that, under the inuence of a magnetic eld, exhibits four energy levels with three possible single quantum
transitions, one central and two satellites each contributing to relaxation81. In the context of isotropic domains,
i.e. aqueous environments with rapid motions, quadrupole interactions are minimal and all transitions occur
approximately at the same decay time resulting in a MRI-visible monoexponential decay curve81. In anisotropic
domains, where motions are slowed, the non-spherical distribution of the electric charge of the sodium nucleus
permits interaction with anisotropic electric elds of the charged groups on the macromolecular anions. us,
quadrupole interactions are non-zero and biexponential relaxation is observed66,80–82 with the satellite transitions
showing faster decay than the central transition.
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MR27 and because various techniques suer from their own limitations regarding compartmental concentra-
tions, ecological validity given preparation eects, and limited spatial, temporal and cross-species sampling28.
e positioning of 23Na-MRI as a putative ‘quantitative’ method, implies that concentration measures should
converge toward a ‘true’ estimate for a given sample, modulo statistical and methodological eects. If 23Na-MRI is
sensitive to the physiological state of tissues—a key assumption motivating its use in the context of neurological
conditions—regional variability in measured TSC concentrations should also be expected. Conversely, positing
a single parenchymal concentration as sucient to characterise all regions implies a limit on detectable dier-
ences between individuals with and without neurological conditions, given known variation in factors like uid
fractions36,37, distributions of cellular types and architectures38,39 and macromolecular content40–42.
In this context, meta-analytic approaches are another means to synthesize evidence and identify impediments
and progress towards consensus. Meta-analysis aims to estimate the true eect size (including central tendency
measures like the mean) based on the combination of observed eect sizes taken from several empirical samples,
while trying to account for sample and study variability43. As such, we sought to apply a meta-analytic approach
to investigate the existing literature on estimates of TSC in human brain regions. We aimed to address (1) the
range of available evidence in the form of regional TSC estimates in the literature, (2) the possibility of consensus
estimates of concentration in various brain regions, and (3) the extent to which methodological and anatomical
factors contribute to variation in measured TSC.
Results
Search results. A search (see Methods) of MEDLINE dated 12/7/2021 returned 127 records, and we identi-
ed an additional 278 records by examining the bibliographies of recovered records and the ‘cited by’ function
on the PubMed website. ese records underwent screening of titles and abstracts, and the remaining texts
underwent full text assessment for inclusion (see Preferred Reporting Items for Systematic Reviews and Meta-
Analyses (PRISMA) ow diagram Fig.2, and Supplementary Tables1, 2 for PRISMA checklists). From an overall
total of 405 records, 44 records were screened from further consideration based on title/abstract. 361 records
were sought for full text retrieval, of which 329 were excluded with the main reasons being a focus on non-brain
tissue or the lack of a sodium measurement in the form of a concentration estimate. We were unable to access
four records. See Supplementary Table3 for a full list of records identied and reasons for exclusion. Inclusion
criteria were met by 28 reports.
Included studies. We included 28 reports containing measurements of total sodium concentration in
healthy controls of specied human brain regions or tissue divisions (other than ‘parenchyma’) (Table1). Nomi-
nally, 400 healthy controls in total were included in these reports, the mean number per report being 14.3 indi-
viduals (range: 4–45, S.D: 11.1). All but three included reports were published aer 2010 (Fig.3a).
We used a modied version of the checklists associated with the Committee on Best Practice in Data Analy-
sis and Sharing (COBIDAS)44, appropriate to the context of 23Na-MRI: specically, the sections on descriptive
statistics, image acquisition reporting and pre-processing reporting. A list of reporting domains included in
the modied version can be found in Supplementary Table4, along with the coded results from the included
reports and a summary can be seen in Fig.3b. Information relating to the numbers of included participants,
whether informed consent was given, MRI scanner used, repetition time (TR), echo time (TE), pulse sequence
and nominal resolution was provided by all included studies. No included report provided information of the
distribution of handedness in the included groups. e remaining domains were reported by varying numbers
of included reports.
Figure2. PRISMA ow diagram for search performed 12/7/2021. Generated with the PRISMA 2020 app83.
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Descriptive. From the 28 included studies, a total of 162 eect sizes in the form of means and SD of meas-
ured TSC (mM) in healthy controls were extracted. In addition, relevant information relating to the COBIDAS
domains for which all included studies had relevant data were extracted, except for ‘Scanner’ where the report-
ing was too variable and insucient to permit reclassication. To account for variability in nomenclature, ‘Pulse
sequence’ and ‘Tissue’ were re-coded according to Table1 and Supplementary Table5, respectively. Tissue re-
coding was informed by the wish to maximise the data per region, tissue homogeneity and physiological plausi-
bility and minimise non-independence, and we excluded twenty eect sizes from regions too sparsely sampled
to satisfy these considerations. e remaining 141 eects sizes across 14 updated Tissue regions in were taken
forward for meta-analysis (Fig.3c): 22 eect sizes for both GM and WM regions; 14 in the Brainstem and Pons
combined; 10 each in Central WM, alamus, and ‘GM, Temporal’ regions; eight each in ‘Deep WM’ and WM
in the cerebellum and dentate nucleus (WM, Cb + DN); seven each in ‘GM, Parietal’ and Putamen; six each in
Caudate, Globus Pallidus and ‘GM, Frontal’ and ve in ‘GM, Occipital’.
We also recorded the type of calibration method used—an external phantom, or internal references in the
vitreous humour of the eyes or the ventricles of the brain. Since important demographic factors like age and sex
were not completely reported COBIDAS domains (Fig.3b), we also recorded ‘Comparison group’ in the hopes
that this might capture some of the variability associated with missing demographic information. Where controls
were selected based on matching for age and sex to a patient group, the characteristic range for these factors
in certain patient groups could represent a sampling bias varying between conditions e.g. controls matched to
patients with Huntingdon’s disease versus multiple sclerosis. Reports without a patient-dened comparison group
can oen be technical MR methodology papers, which may tend to sample from a dierent population, such as
for example the authors/students themselves.
Multi‑level meta‑analysis: model‑t. We used a multilevel/multivariable approach with four levels
(participant, eect size, tissue regions and study), and a random eects model to pool eect sizes. e pooled
Table 1. Characteristics of included studies. a Int. internal, Ext. external, CSF cerebrospinal uid, VH vitreous
humour (eyes). b Repetition time. c Echo time, where multiple the shortest TE was used in analysis. d x,y,z
product of nominal resolution, see Supplementary Table7 for specic values. e NR = not reported, other values
are presented as per original reports in ranges (XX-XX), mean ± standard deviation, except for Zaaraoui etal.
2012 and Maarouf etal. 2014 which report median and range and Inglese etal. 2010 and Eisele etal. 2016
which report mean and range.
Paper Ref Tesla Sequence CalibrationaTRb (ms) TEc(ms) Voxel volume (mm3)dN N. Female Age (years)eComparison group
Winkler etal. 1989 45 1.5 GRE Int. VH 98 3 490 4 NR 20–35 None
Ouwerkerk etal. 2003 51.5 TPI External 120 0.37 39.3 9 3 22–63 Tumour
ulborn etal. 2005 87 3TPI External 100 0.3 125 5 NR NR Stroke
Inglese etal. 2010 10 3 Radial External 120 0.05 64 13 10 36.7, 26–60 MS
Lu etal. 2010 33 3 FlexTPI External 160 0.36 125 5 1 32.4 ± 8.9 None
Reetz etal. 2012 84 SPRITE External 10 0.3 64 13 6 44.9 ± 9.9 HD
Qian etal. 2012 71 7 AWSOS Int. CSF 100 0.5 2.9 5 5 20–48 None
Zaaraoui et 2012 11 3 DA radial External 120 0.2 46.6 15 12 30.20–54 MS
Paling etal. 2013 12 3 Radial External 120 0.27 64 27 16 42.9 ± 11.3 MS
Maarouf etal. 2014 13 3 DA radial External 120 0.2 46.6 15 NR 30, 21–54 MS
Mirkes etal. 2015 73 9.4 AWSOS External 150 0.3 5 5 1 29 ± 4 None
Niesporak etal. 2015 88 7 DA radial External 150 0.45 27 4 1 26 ± 2 None
Eisele etal. 2016 15 3 DA radial External 60 0.22 46.6 10 5 33.23–53 MS
Petracca etal. 2016 16 7 GRE External 150 6.8 125 17 8 46.16 ± 11.65 MS
ulborn etal. 2016 34 9.4 FlexTPI External 160 0.26 42.9 45 NR 48 ± 19 None
Maarouf etal. 2017 14 3 DA radial External 120 0.2 46.7 31 15 35.7 ± 12.4 MS
Eisele etal. 2017 17 3 DA radial External 60 0.22 46.7 6 5 42 ± 10 MS
Ridley etal. 2018 63 7 DA radial External 120 0.3 42.9 13 5 23.9 ± 3.6 None
Wortho etal. 2018 46 4 SISTINA Int. VH 150 0.36 216 40 16 19–70 None
Reimer etal. 2019 72 3Cones External 100 0.5 64 11 3 32 ± 6 None
Driver etal. 2019 89 4.7 TPI Int. VH 85 0.11 65.5 9 5 30 ± 6 None
Liao etal. 2019 90 3TPI Int. CSF 160 0.4 40.7 8 3 25–32 None
Meyer etal. 2019a 91 3 DA radial External 120 0.2 46.7 12 8 31 ± 8.3 None
Meyer etal. 2019b 24 3 DA radial External 120 0.2 64 12 12 34.3 ± 10.7 Migraine
Kim etal. 2020 32 7 GRE Int. CSF 100 4 64 8 0 20–35 None
Gerhalter etal. 2021 92 3 FLORET Int. VH 100 0.2 216 19 12 31.4 ± 7.5 TBI
Brownlee etal. 2019 19 3Cones External 120 0.22 27 34 23 35.5 ± 10.1 MS
Schneider etal. 2021 59 7 DA radial Int. CSF 100 0.35 8 5 3 28.4 ± 6.5 None
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mean of TSC across all 141 estimates based on the multilevel meta-analytic model was 40.51mM (95% CI
37.59–43.44; p < 0.001). We identied considerable heterogeneity (I2Tota l=99.4%), with the results of the standard
random-eects model suggesting that most of the total variance is due to between-study heterogeneity (i.e., vari-
ance in the ‘true’ means), while the remaining (0.6%) can be attributed to sampling variance.
Variance components: tissue and study factors. e factors Tissue and Study were included in the
model to account for the nested structure of dependencies within the data: there are multiple eect sizes per
paper and the eect sizes are not independent—a given individual may have contributed to multiple levels of the
factor Tissue, and a given region may be estimated based on dierent numbers of eect sizes from multiple and
varying numbers of papers. e estimated variance components were t = 45.81 for the Study level, 9.93 for Tissue
level and 28.96 for Eect Size level. In terms of the distribution of variance across levels as a percentage of total
variance, 53.75% of the total variation in our data can be attributed to between-study heterogeneity, 11.65% to
between-tissue heterogeneity and 33.99% to the eect size level (i.e. within-factor heterogeneity for Tissue), and
only 0.6% is due to sampling variance. e high heterogeneity both between Studies and within Tissue, suggest
that a subgroup analysis by anatomical region is appropriate.
Model comparison: tissue sub‑group versus reduced model. In Fig.4 we report the forest plots for
anatomical regions with at least ten eect sizes only (following general statistical power guidelines for meta-
analytic sub-analyses43). ese included (pooled mean [95% CI]): GM (45.92mM [42.27; 49.57]), Temporal GM
Figure3. Descriptive plots for identied and included studies. (a) Literature search results 1980–2021 by
year of publication. Chart includes total papers published for a given year (orange), publications identied by
searching bibliographies (cyan), papers identied through the MEDLINE search (red) and number of studies
included (green). (b) Overview of COBIDAS Domains reported in included studies. FOV, Field of view; PSF,
Point spread function; ROIs, regions of interest. (c) Scatterplot of 141 eect sizes used in meta-analysis by
published report in alphabetical order of rst author surname. Error bars correspond to standard deviation,
except for Zaaraoui etal. 2012 who reported range and Driver etal. 2019 who reported standard error. Cb
cerebellum, DN dentate nucleus, GM grey matter, WM white matter. Images created in R84–86.
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(45.48mM [40.92; 50.05]), alamus (42.08mM [36.38; 47.77]), Brainstem + Pons (40.99mM [33.28; 48.70]),
WM (37.29mM [33.04; 41.53]) and ‘Central’ WM (34.67mM [27.89; 41.44]). We found that the subgroup mul-
tilevel model provided a signicantly better t compared to a reduced multilevel model, as indicated by lower
Akaike (AIC) and Bayesian Information Criterion (BIC). e likelihood ratio test (LRT) comparing both models
is signicant (χ213 = 145.50, p < 0.01). A test of the moderators ‘Tissue’ was signicant, F214 = 65.34, p-val < 0.01),
indicating that in this model the mean TSC is dierent between each anatomical region. However, the results
indicate that high heterogeneity remains overall even with the inclusion of ‘Tissue’ level (χ2127 = 9537.26,
p-val < 0.01).
Precision, small study eects and publication bias. We investigated further factors impacting the
distribution of results with respect to pooled means via Egger’s tests and funnel plots (Fig.5). e egger’s test
used standard error, a measure of precision, as predictor. ings being equal, there should an inverse relationship
between standard error and the probability of a given study’s estimate being dierent from the actual value in the
population, with an expected symmetry in over- and under-estimates. Overall, the distribution of all eect sizes
did not show the expected distribution, showing substantial asymmetry (Egger’s test, t = 5.24, p < 0.001) which
remained statistically signicant when outliers (identied by sensitivity analysis eliminating one by one the
extreme points of the distribution) are removed (t = 4.89, p < 0.001). Asymmetry can be evidence for small study
Figure4. Forest plots for anatomical regions with at least ten eect sizes: greymatter;Temporalgreymatter;
thalamus;white matter;central white matter;brainstem + pons. Each forest plot contains the eect size data,
represented by grey squares scaled to their weight in the meta-analytic model and error bars corresponding to
95% condence intervals. e regional pooled estimate for each plot is represented by a grey diamond scaled
in length to the condence interval of the pooled estimates, and a dotted reference line. e pooled overall
mean of all 141 included eect sizes is represented by a solid reference line on each plot. Plots generated in R,
in the metafor package74.
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eects and publication bias, based on the assumption that small studies are at greatest risk of non-signicant
results and biasing the published literature toward the high eect sizes that are most likely to be signicant with
Figure5. Funnel plots comparing eect sizes (mean TSC) with their precision (standard error): All tissues
(141 eect sizes) and with outliers removed (136 eect sizes); GM eect sizes with (22, le) and without
outliers (20, right); WM eect sizes with (22, le) and without outliers (19, right); GM, Temporal; alamus;
Brainstem + Pons, and Central WM. Images created in R74,84.
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small N43. In our case we are investigating a measure of central tendency: mean TSC, as opposed to a standard-
ized mean dierence, compared to standard error. As such, we investigated the possibility that our data does not
show the expected symmetry because it is constituted by sub-groups, and the ’pooled mean’ is not the best refer-
ence given the subgroup analysis, above.
In GM the test of asymmetry was at the threshold of signicance (t = 2.1, p = 0.05), though aer removing
some outliers (60 mM45; 69 mM5) the gures become more symmetrical and the tests become non-signicant
(t = 1.73, p = 0.1) and the remaining regions do not show signicant skewness. Similarly, in WM the presence of
asymmetry is indicated (t = 2.48, p = 0.02), but aer removal of some outliers (19.38 mM10, 25 mM46, 69 mM5)
distribution was no longer signicantly asymmetrical. e remaining regions did not show signicant asymmetry.
Eect of moderators. Papers diered in their methodology across domains. We sought to understand the
eect of additional methodological moderators by adding them individually and exploring their association with
dierent mean TSC estimates. Relative to a reduced model including the factor Tissue, all additional individual
factor added to the model produced a signicantly better t (Table2), in terms of reducing overall heterogeneity.
Moderator eects on mean TSC. Within factors, we explored the levels associated with signicant dier-
ences in mean TSC between levels independent of Tissue (Fig.6). For studies using Sequence Type as “Radial”
or “SISTINA”, the mean TSC is signicantly lower than that of studies using the “DA Radial” type (t118 = −2.95,
p < 0.01 and t118 = −2, p < 0.05 respectively). Field strength of 1.5T is associated with higher concentrations of
Sodium (t122 = 2.54, p = 0.01) relative to 3T. In studies with “Brain Tumour” as the Comparison Group the mean
TSC is higher in controls (t118 = 2.68, p < 0.01) than in studies where there was no comparison group. A single
study is sampled for the SISTINA level of the factor Sequence while another single study was sampled both at
the 1.5 Tesla level of the factor Field Strength and the Brain Tumour level of Comparison Group, which was also
identied as an outlier in the assessment of asymmetry in standard error distribution for both GM and WM5
(Figs.5, 6). Tests for Calibration method, Voxel Volume, TR and TE were non-signicant, indicating no associa-
tion between the level of the two moderators and the mean measured sodium level, regardless of region.
Intra‑regional heterogeneity. Given the high heterogeneity within the factor Tissue, we extended our
analysis to identifying where inclusion of methodological moderators reduces the heterogeneity of estimates
within anatomical regions (with at least 10 eects sizes) suggesting the pooled estimates in the reduced model
are impacted by dierences in a given factor. We compared the specic heterogeneity (tau) of a region in the
reduced model compared to the model with the methodological factor using Hedges’ g, identifying ‘signicant’
reductions in the form of a standardized mean dierence whose 95% CIs did not cross zero (Supplementary
Table6, Supplementary Fig.1).
‘Sequence’ as moderator reduces the heterogeneity for GM, GM-Temporal and WM regions. Adding “Com-
parison Group” reduces heterogeneity in GM, Brainstem + Pons, and WM. “Calibration method” reduces hetero-
geneity within GM. Residual heterogeneity is reduced in “Brainstem + Pons” when “Voxel Volume” is used as a
moderator. “TR” reduced residual heterogeneity when used as a moderator in Temporal GM and the thalamus.
“TE” reduced heterogeneity in Temporal GM and Central WM. Field strength did not contribute to explaining
the variability within anatomical regions. Note that for all methodological factors, the test of residual heteroge-
neity for the model overall remained signicant (Table2).
Discussion
Data from 28 studies, identied by literature search, were explored via meta-analysis—to our knowledge the
rst such attempt in the context of data from 23Na-MRI. e overall pooled estimate from all 141 across all 28
studies was 40.51mM (95% CI 37.59–43.44), well within the ranges suggested by parenchymal volume models
(37–45 mM6,12,20). Meta-analytic estimates were associated with high heterogeneity, which further analysis sug-
gested was largely associated with between-study heterogeneity. is supports the idea that there is underlying
dierences in the ‘true means’ the dierent studies are trying to measure—and that a parenchymal estimate is not
sucient to characterise the range of empirical values obtained from dierent brain regions. Pooled estimates
Table 2. Tests comparing models including each methodological moderator to areduced model. DF degrees
of freedom.
Moderator
Likelihood ratio test Test of residual
heterogeneity
DF χ2pDF χ2p
Sequence 9 78.07 < 0.01 118 4772.90 < 0.01
Comparison group 6 50.73 < 0.01 121 9081.33 < 0.01
Calibration method 2 16.82 < 0.01 125 8636.05 < 0.01
Voxel volume 1 7.93 < 0.01 125 7963.39 < 0.01
Field strength (Tesla) 5 26.81 < 0.01 126 9216.67 < 0.01
Repetition time (TR) 1 29.74 < 0.01 126 8697.18 < 0.01
Echo time (TE) 1 16.01 < 0.01 126 9529.9 < 0.01
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based on the extant literature of TSC estimates in human samples are 45.92mM [42.27; 49.57] for GM and
37.29mM [33.04; 41.53] for WM. is is noticeably higher than tissue volume model-based estimates for both
tissue types, with examples including estimates of 20–33mM in WM and for 30–35 for GM33,47.
A number of potential sources may account for discrepancy between theoretical tissue volume models and
the empirical estimates. One is partial volume eects, and other methodological factors impacting acquisition
of the estimates making up the literature explored here. e models use simplifying assumptions, most notably
that they have adequately captured the relevant inuences on sodium 23Na-MRI measurement with a limited
Figure6. Scatterplot of 141 eect sizes used in meta-analysis ordered by moderators with a mean eect on TSC
between levels independent of Tissue. Error bars correspond to standard deviation, except for Zaaraoui etal.
2012 (DA Radial, 3 Tesla, Multiple Sclerosis) who reported range and Driver etal. 2019 (TPI, 4.7 Tesla, None)
who reported standard error. Cb, cerebellum, DN dentate nucleus, GM grey matter, WM white matter. Images
created in R84–86.
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number of compartmental volume contributions, and that these compartments are internally homogenous. For
example, the extracellular compartment is generally (but not always35) considered to include everything outside
cells membranes, thereby subsuming the interstitial extracellular matrix48 and vascular spaces and attributing
the 23Na concentration of ‘pure’ CSF to the entire compartment20,33,35,49. Similarly, the contribution of mem-
branes, lipids like myelin and other ‘solids’ are assumed to be captured by a single volume contribution with no
sodium contribution (on the basis they exclude sodium and should reduce overall measured signal for a given
volume35,49), and can be summarised by a single fractional variable (e.g. 0.7–0.933,35,37) for a given tissue type. It
would be interesting to see how the modication of any or all these foctors impacts interact to produce expected
values and how this might be applied to regional estimates.
More granular tissue models are currently lacking, as the requisite cellular data is not available. A potentially
relevant factor is regional variation in the ratios of dierent cell types in the context of divergent sodium con-
centrations, for example astrocytes have approximately twice the cytosolic sodium concentration (~ 15–20mM)
compared to neurons (~ 10mM) in rodent samples50–54. Recent automated immunocytochemical techniques
have provided much needed information, including correcting widespread misconceptions about neuronal ver-
sus non-neuronal populations and masses, however precise data on cell volumes and their variation—which
would be relevant for building regionally specic volume models for 23Na-MRI—are not yet available38,39. In the
absence of complete histologic information, another source of insight could come from comparing 23Na-MRI
to other imaging indices that might capture relevant features, with other quantitative imaging modalities being
of particular interest. Parallel changes in 23Na-MRI measures and diusion imaging15,55–57 and proton density58
are suggestive, but extending these to direct evaluations of the redundancy and complementarity with other
quantitative modalities59, especially in healthy controls, in a range of regions and tissue structures would be a
welcome development.
While the empirical values are higher than the model-based estimates for a given tissue, the relative values
of dierent tissue’s concentrations (e.g. GM > WM) is preserved. e dierence in myelin content between grey
and white matter—captured in the dierences in the solid fractions that are usually assigned—may account for
some of this dierence. Indeed, among the subcortical regions we were able to provide pooled estimates for (> 10
eect sizes), it is noticeable that intermediate values were produced. e ostensibly GM nucleus though highly
myelinated alamus has a lower value (42.08mM [36.38; 47.77]) than some other GM estimates (45.48mM
[40.92; 50.05] for Temporal, GM), while ROIs sampling regions that are likely to be predominantly WM but with
contributions from GM nuclei like the brainstem and pons indicate higher values (40.99mM [33.28; 48.70])
than some other regions (34.67mM [27.89; 41.44] for ‘Central WM’). While the overlap between condence
intervals and the remaining heterogeneity limits the certainty of these precise pooled means, which should not
be taken as denitive given the limitations of the available literature as represented in this meta-analysis, the
importance of considering the variation in apparent 23Na associated with regional dierences is reected in the
signicant improvement in the model when including the tissue factor and the nding of signicant dierences
in mean TSC between levels/regions.
Given the remaining unexplained heterogeneity even aer the Tissue factor was involved, we explored addi-
tional methodological factors where full reporting made this possible. e fundamentally most limiting property
of 23Na-MRI is the reduced nuclear MR sensitivity and relative abundance of sodium and other non-1H based
contrasts60, leading to reduced signal to noise ratios and resolution, and consequently to partial volume eects.
A given ‘Sequence’ is an attempt mitigate between trade-os in acquisition parameters with impacts on available
signal and resolution (e.g. TE, TR, Flip angle, Voxel Volume, Field Strength). For example, the ideal sequence
would entail a spin density weighting with a minimum of relaxation eects, however in practice studies will
dier in the degree they are aected by T1 or T2 weighting and thus vary in quantication. Dierent internal
and external calibration methods provide scope for dierent degrees of experimenter error as well as spatial and
physiological variability61. Comparison group may reect demographic factors of potential relevance62 reecting
the target patient group and other variable experimenter/location factors.
We were unable to consider the majority of the methodological and demographic factors sought by the modi-
ed COBIDAS checklist because the information was not reported (Fig.3b). Explicit reference to and information
pertaining to the following COBIDAS domain were not identied for age, handedness, sex, coil information,
acquisition time, processing soware used, ip angle, segmentation and ROI denition, details of normalisa-
tion/registration, eld of view, information pertaining to smoothing or point spread function. Working towards
consensus reporting standards could facilitate comparability of studies in the future. e COBIDAS standards
in general, and the adapted subset used here (Fig.3, Supplementary Table4) could represent a starting point, to
which further 23Na-MRI specic parameters could be added such as relaxation and B1 correction methods, as
well as phantom calibration.
We found each fully-reported methodological factor with included beyond tissue improved the meta-analytic
model t (Table2), but that signicant residual heterogeneity remained regardless. Only Field Strength, Sequence,
and Comparison Group diered in mean TSC between specic levels independently of tissue. Interpretations
of these results should take into consideration the risk of bias due to sampling issues given the limited data for
various levels of these factors. Considered in combination with Tissue, all methodological factors except for Field
Strength reduced heterogeneity in some regions when included (Supplementary Fig.1). Collectively these results
stress the importance of methodological factors but also the limitations of the available literature and underline
the need for more and completely reported data covering multiple acquisition schemes and brain regions.
We analysed estimates of Total/Tissue Sodium Concentration, as the most common measure available. Other
23Na-MRI derived metrics are possible, for example there are approaches that measure63 or lter sodium signal
based on relaxation behaviour (e.g. inversion recovery, IR64), or multiple quantum ltering (MQF)16. In principle,
any specic measurement of invivo sodium by 23Na-MRI—TSC, IR, MQF or other – cannot be said to derive
from a single cellular-level tissue compartment65. However, while attribution to dierent sources is a subject
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of longstanding and ongoing investigation3,66,67, it is legitimate to discuss a dierence or change in measured
parameters (between conditions and across spatial/temporal domains) in terms of changes in concentration or
structure in sub-compartments that may have contributed, even when the latter are below the limit of resolu-
tion. In practice, precisely attributing changes in empirical MR-level estimates to compartmental micro-features
is unlikely to be denitive because these factors rarely alter in isolation. For example, while pathological TSC
alterations may be related to metabolic impairments of transmembrane23Na exchange, they may also reect
changes in cellular death, swelling, proliferation etc68–70. Fundamentally, 23Na-MRI appears to be a more sensitive
than specic measure, and a claim that it is sensitive to variation in a particular structural, functional or patho-/
physiological context is an empirical question to answered by further appropriate data and not modelling nor a
priori arguments from incomplete biophysical data alone.
Some further limitations should be noted and considered in future analysis. Variable reporting required
accommodations to be made in several factors that were included in the analysis. Allocation of a given data point
to a particular level of Tissue was based on explicit textual references in the included studies, but the method of
segmentation, precise anatomic boundaries, use of atlases and precise coordinates were not always clear. is
may be another source of heterogeneity in the results, and again highlights the need for clear reporting. We also
considered only published reports, and not ‘grey literature’ (e.g. dissertations, preprints, government reports,
or conference proceedings)43 which could potentially improve sampling. We produced and examined a central
tendency measure via mean estimates of TSC, but if sucient data were available meta-analytic analysis could be
applied to other 23Na-MRI metrics as well as combined estimates of dierences between groups, structures, and
states. Finally, we considered the impact of methodological parameters in isolation, while to fully characterise
their impact it will likely be necessary to investigate their interactions.
Conclusions
Data from 28 studies, identied by literature search, were explored via meta-analysis—to our knowledge the rst
such attempt in the context of data from 23Na-MRI. e nested nature of the data, due in part to accommoda-
tions made to the variability of reporting in the published studies, lead to the use of a multi-level meta-analytic
approach. We produced pooled meta-analytic estimates of brain TSC, but signicant remaining heterogeneity
limits the certainty and precision associated with the estimates. Consideration of tissue dierences explains part
of that heterogeneity, but not all. Where they were fully reported, methodological moderators were explored.
While their inclusion reduces heterogeneity within certain tissue regions, and eects the measured TSC levels,
substantial residual heterogeneity remains. e current estimates provide an empirical point of departure for
better understanding of variability in 23Na-MRI. Improving on current estimates supports: (1) larger, more rep-
resentative data collection/sharing, including (2) regional data, and (3) agreement on full reporting standards.
Methods
Literature search. e following MEDLINE search was run by BR via pubmed.ncbi.nlm.nih.gov on
12/07/2021: “Brain” [Title/Abstract] AND ((((sodium MRI [Title/Abstract]) OR 23Na MRI [Title/Abstract])
OR sodium imaging [Title/Abstract]) OR 23Na imaging [Title/Abstract])”. Bibliographies of potentially eligible
studies were consulted and studies of potential relevance to 23Na-MRI were included in the screening.
Recovered records were excluded based on the abstract or full text if they were non-experimental, non-
original reports (review/commentary), conference proceedings, phantom-only studies, concerned with cultured
tissue or organs other than the brain, non-human subjects, or did not include estimates of sodium concentrations
determined by quantitative 23Na-MRI in healthy subjects without known neurological conditions. Studies con-
sidering only estimates in overall parenchyma, or where it was not possible to attribute estimates to a specied
anatomical region were also excluded. Screening and full text review were performed by BR with reference to
other authors as necessary.
Data extraction. Initial extraction of data pertaining to 23Na-MRI concentrations and methodological
domains was performed by BR, with verication and consultation with WZ. Data re-coding, as discussed in the
“Descriptive” section in Results, was based on consensus decisions by WZ/BR for “Sequence” and FN/BR for
“Tissue” (See Table1 and Supplementary Table5). Where a given study included multiple potentially relevant
samples a context-based decision was made: where the same individuals were sampled with diering methods
we took the highest eld / highest resolution observation for Qian etal.71; where the same individual was sam-
pled multiple times with the same methods (reproducibility studies) we took the overall mean across samples for
Riemer etal.72 and Meyer etal.24; where PVC-corrected values by dierent methods were used in Kim etal.32 we
used the spill-over and ventricular CSF-based PVC-corrected values. Where multiple TEs were reported45,63,73
we used the acquisition with the fastest TE.
Meta‑analysis. Meta-analyses were conducted in R (R-4.1.2) using the “metafor” package74. e restricted
maximum likelihood estimator75 was used to calculate the heterogeneity variance (τ2) and we used Knapp-
Hartung adjustments76 to calculate the condence interval around the pooled eect. Multi-level models were
investigated to account for any correlations induced by the multi-level structure of the data, whereby a given
individual may have contributed to multiple levels of the factor Tissue, and a given region may be estimated
based on dierent numbers of eect sizes from multiple and varying numbers of papers. To account for cor-
related sampling errors due to dierent eect sizes being based on the same sample of patients we used a Corre-
lated and Hierarchical Eects (CHE) model77: an extension of the multilevel model that considers the correlation
of eect sizes within clusters, in this case the factor ‘Paper’. A robust Sandwich covariate estimator was used to
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estimate condence intervals and relative p-values78. Egger’s tests79 were used to evaluate asymmetry of funnel
plots, based on weighted regression models with multiplicative dispersion, with standard error as the predictor.
Data availability
All data generated or analysed during this study are included in this published article and its Supplementary
Information les.
Received: 4 November 2022; Accepted: 21 February 2023
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Author contributions
B.R. conceived and planned the work, designed, and ran the literature search. B.R., W.Z. and F.N. contributed
to data extraction. B.R. and F.M. designed and ran the analysis and prepared gures. All authors contributed to
interpretation of the results. B.R. draed the manuscript, which was revised by all authors, who agreed to the
nal version.
Competing interests
e authors declare no competing interests.
Additional information
Supplementary Information e online version contains supplementary material available at https:// doi. org/
10. 1038/ s41598- 023- 30363-y.
Correspondence and requests for materials should be addressed to B.R.
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