Kelsey Flanagan
email: kelsey.flanagan@enpc.fr

Philippe Branchu

Lila Boudahmane

Emilie Caupos

Dominique Demare

Steven Deshayes

Philippe Dubois

Laurent Meffray

Chandirane Partibane

Mohamed Saad

Marie- Christine Gromaire

Biofiltration for the on-site management of micropollutants in urban runoff: lessons from a field study

Keywords: Biofiltration, swale, vegetative filter strip, road runoff, micropollutant

Introduction

Urban runoff is contaminated by a number of micropollutants, including trace metals (TM), polycyclic aromatic hyrdocarbons (PAH) and various endocrine disruptors (bisphenol-A or BPA, alkylphenols or AP, phtalates or PAE) (Zgheib et al., 2012). Managing this pollution is important to protecting ecosystems and, when stormwater reuse is intended, human health.

Biofiltration (also referred to as bioretention), wherein runoff water is filtered through a planted filter medium and either drained or exfiltrated into the surrounding soil (Liu et al., 2014), may be useful for managing these pollutant loads close to the source in sponge cities. Numerous studies have demonstrated the potential of this technique for treating traditional pollutants such as total suspended solids (TSS), nutrients and TM. In addition, two previous studies have shown biofiltration to effectively retain PAH from urban stormwater (David et al., 2015;DiBlasi et al., 2009). However, relatively few studies have distinguished the dissolved phase of pollutants (LeFevre et al., 2014) and no previous studies have studied the treatment of BPA, AP and PAE in situ.

The present work focuses on lessons learned from the monitoring of a wide range of micropollutants (TM, PAH, BPA, AP, PAE) in a biofiltration swale (BFS) treating runoff from a suburban highway.

Materials and Methods

Study site

The study site includes a biofiltration swale (BFS), which drains water from the RD 212, a suburban highway with 11,000 vehicles/day/direction traffic located in Compans, France in the Paris region. The system is both drained and lined and was constructed in March 2016. Water is collected from a drain beneath the filter media (a sandy loam) of this device at a depth of 50 cm. Water quality is compared to that of untreated road runoff (RR) collected from a reference catchment on the same road and with identical traffic, located 68 m from the BFS catchment (Fig. 1). Flow is measured in the BFS drain and RR manhole using tipping bucket flow meters; overflow from the BFS is measured using a V-notch weir.

Sampling and analysis

Water was collected at each point in proportion to water flow in order to achieve an event mean concentration (EMC). 15 rain events were sampled between May 2016 (two months after the construction of the BFS) and July 2017. While simultaneous sampling of all points was attempted, due to technical difficulties, not all data is paired. Samples were collected within 24h of each rain event and sent to partner laboratories within 24h of collection where they were immediately filtered to distinguish between dissolved and particulate phases. They were analyzed for pH, conductivity, turbidity, suspended solids (TSS), organic carbon, nutrients, 12 trace metals, 9 major elements, total hydrocarbons (TPH), 19 PAH, BPA, 7 AP and 5 PAE. Results for all pollutants have been discussed thoroughly elsewhere (Flanagan et al., submitted); results for a selection of pollutants are presented here.

In addition, seven composite filter media cores were sampled in the BFS from zones with homogeneous Cu, Pb and Zn surface contaminations, as determined from a cartography produced by soil contamination at 90 points using X-ray fluorescence spectrometry.

Computational methods

Treatment efficiency is considered in terms of concentration reduction (E c ) in BFS compared to RR for each sampled event. In addition, inlet and outlet loads were evaluated at the annual scale using a stochastic approach for a selection of pollutants, as was the evolution in the mass stored in the filter medium over the same period (Flanagan, 2018). This enabled evaluation of annual load reductions in the BFS (E L ) as well as a comparison of intercepted pollutant mass with the mass accumulated in the filter media.

Results

Road runoff quality

Road runoff from the Compans site was found to be quite polluted, with concentration levels (Table 1) situated in the upper range of those previously reported in the scientific literature (Kayhanian et al., 2012). Many pollutants, including TM and PAH, were very particulate, with over 90% found to be associated with the particulate phase.

Treatment efficiency

This study demonstrated the ability of biofiltration to improve runoff quality with respect to micropollutants. The BFS very effectively retained total suspended solids (TSS) for most events (median concentration reduction E C50 >90%, Table 1); as many micropollutants were mainly associated with TSS in RR, this resulted in excellent removals of Zn and PAHs (E C50 >90%) and good removals of Cu, and octylphenol (E C50 >70%). BPA and nonylphenol were moderately well removed (E C50 56-57%), while performance for DEHP was poor (8%). During a winter period when deicing salt was frequently applied, high TSS concentrations were observed at the outlet of the BFS. Particle characterization demonstrated that poor filtration of RR particles rather than soil particle dispersion and erosion was responsible for this phenomenon. This was due to an exceptional abundance of fine (<10µm) TSS particles in RR during this period, combined with filter media cracking. Performance in the dissolved phase tended to be lower, with the highest E c50 observed for octylphenol (59%); dissolved concentration increases were observed for some pollutants (for example, DEHP for which E c50 =-202%).

For Cu and Zn, observed dissolved concentrations frequently exceeded those expected at equilibrium with the filter media, indicating that performance may be limited by the chemical speciation of dissolved metals. For organic pollutants, observed dissolved concentrations were compatible with or sometimes below those expected at equilibrium with the filter media. In the cases of BPA, octylphenol, nonylphenol and DEHP, the mass accumulated in the filter media over the first year of operation significantly exceeded that intercepted from runoff (Figure 3). Batch leaching tests demonstrated that construction materials (asphalt, geomembrane, drain, drain filter fabric) were potential sources of all of these pollutants. These emissions are likely responsible for elevated outlet concentrations of these pollutants during the first months of operation and contamination of the filter media, limiting its ability to sorb dissolved fractions of these contaminants.

Finally, annual load reductions in this study were lower than the total E C50 for most pollutants. This was mainly due to frequent overflow, which accounted for about 38% (34-40%, 95% confidence interval) of water volume, while only about 20% of water volume was retained in the biofilter and lost to evapotranspiration. One exception to this was DEHP, which had very poor total concentration removal (E c50 =8%), most likely due to dissolved-phase emissions from construction materials. In this case, the annual load reduction was higher than E c50 , mainly due to water volume reduction.

Discussion and practical implications

Several practical implications and operational lessons can be taken from these results.

First, as biofiltration is generally effective at particle capture, it is particularly well adapted for treating water from catchments producing high TSS concentrations and thus highly particulate micropollutants. This was the case for the road studied in the present study (median TSS in RR = 291 mg/L) and is likely to be the case for other roads with significant traffic. Concentration reductions in biofilters are likely to be lower in catchments producing less particulate matter (for example, rooftops).

Particle capture was shown to be reduced when particle sizes were smaller, a phenomenon observed in the present study only during winter. Smaller particle sizes in road runoff have also been observed in winter in previous studies (Hilliges et al., 2017;Monrabal-Martinez et al., 2016). Whether this is an effect of deicing salt application, temperature or another factor, it indicates that biofiltration performance may vary seasonally, although further research is required to prove this effect.

Filter media cracking was also seen to reduce filtration efficiency in the present study. Limiting clay content in filter media may reduce the formation of such cracks.

With respect to the dissolved phase of pollutants, the present study demonstrates two different cases where concentration reduction may be difficult to achieve. One such case occurs when chemical speciation (complexation or association with colloidal particles) limits pollutant reactivity, as appears to be the case for Cu and Zn in the present study. Another is when filter media contamination is on the order of that expected at equilibrium with dissolved concentrations in RR, demonstrating the importance of selecting a filter media which is relatively uncontaminated with respect to the pollutants to be treated. On the other hand, achieving dissolved concentrations below those expected at equilibrium with typical soil concentrations in a given region may not be a realistic objective; when dissolved concentrations in runoff are close to this level, concentration reductions are likely to be limited. In this case, loads of dissolved pollutants may be reduced most effectively by optimizing volume reduction in the system.

The study also demonstrated that biofiltration construction materials may be significant sources of organic micropollutants, leading to both degraded water quality improvement performance and filter media contamination. As such, when treatment of organic micropollutants which are ubiquitous in synthetic materials (such as AP and PAE) is an objective, the authors strongly recommend avoiding the use of synthetic materials in system design wherever possible. When these materials are absolutely necessary, the least polluting materials should be selected. Regulatory bodies could facilitate this selection by developing of standard protocols for considering pollutant emissions and by establishing archives of pollutant emission data from various types of materials.

Finally, the excessive overflow observed in the present study, leading to lower annual load reductions compared to concentration reductions highlights the importance of good hydraulic and hydrologic design. In the case of linear devices located beside even slightly sloped roadways, overflow may be minimized by separating the system into sections using check dams. System design may also be improved by using long-term, continuous simulations with a simple hydrologic model to select a configuration for which a desired proportion of water will be treated.

Conclusions

In order to consider the performance of biofiltration for treating road runoff as well as the processes responsible for this performance, a large range of micropollutants (TM, PAHs, BPA, AP, PAE) were monitored in water drained from a biofiltration swale treating road runoff and in untreated road runoff in both the total and dissolved phases. This work demonstrated excellent concentration reductions of particles and highly particulate pollutants. Performance was more limited for the dissolved phase of pollutants and for total concentrations of less particulate pollutants.

A number of operational lessons were drawn from this experience. In particular, biofiltration appears to be particularly well adapted to reducing concentrations from catchments producing large amounts of particles, though its efficiency may be subject to seasonal effects due to variable particle sizes.

Filter media cracking was also seen to degrade filtration performance, underlining the importance of minimizing clay in filter media composition. Removal of the dissolved fraction of some pollutants may be their chemical speciation in road runoff or by background filter media concentrations; when this is the case runoff volume reduction may be the best strategy for reducing pollutant loads. Synthetic construction materials (asphalt, geomembrane, drain, drain filter fabric) were shown to be potential sources of organic micropollutants within the biofiltration swales, capable of contaminating the filter media and degrading water quality performance and should thus be avoided. Finally, high levels of overflow from the present system underlined the importance of good hydraulic and hydrologic design in limiting pollutant loads.

Figure 1 :

 1 Figure 1: The Compans study site

Figure 2 :

 2 Figure 2: Total suspended solid particle size distribution by volume in road runoff. Events with degraded filtration (in Winter 2017) are shown in blue, while events with normal filtration (in Spring 2017) are shown in orange.

Figure 3

 3 Figure 3 (a-d): Net mass balance terms associated with water fluxes (difference between mass entering and exiting the system -Mintercepted) and soil (difference between initial and final masses stored in soil -ΔMsoil) for (a) bisphenol-A, (b) octylphenol, (c) nonylphenol and (e) DEHP. Bars represent medians, while error bars represent the 95% confidence interval.

Table 1 :

 1 Partial presentation of pollutant concentrations in RR and concentration and load reductions in the biofiltration swale (BFS), median (min, max) observed at the event scale for concentrations and concentration reduction, median and 95% confidence interval fromstochastic calculations of annual load reduction.

	Parameter	RR Concentrations Total Dissolved	Concentration reduction (E c ) Total (%) Dissolved (%)	Load reduction (E L ) Total (%)
	Water Volume	.	-	-	-	20 (15, 23)
	TSS

(70, 933) mg/L -92 (11, 95) -

Acknowledgements

This work was supported by funding for the Roulépur research program (AFB and AESN), the Observatory of Urban Pollutants in Paris (OPUR, supported by AESN, SIAAP, CD92, CD93, CD94 and Ville de Paris), and a PhD scholarship from ENPC. We also acknowledge the Seine-et-Marne Departmental Council, and especially Eric Thomas and Tina Ratovelomanana, for their partnership and technical support, as well as Tianran Dong, Delphine Truong, Thi Kim Phung Nguyen, Meriem Kajeiou and Maria Vitart de Abreu Lima for their help with sampling campaigns.

Bibliography

David, N., Leatherbarrow, J.E., Yee, D., McKee, L.J., 2015. Removal Efficiencies of a Bioretention System for Trace Metals, PCBs, PAHs, and Dioxins in a Semiarid Environment. Journal of Environmental Engineering 141, 04014092. https://doi.org/10.1061/(ASCE)EE.1943-7870.0000921 DiBlasi, C.J., Li, H., Davis, A.P., Ghosh, U., 2009. Removal and Fate of Polycyclic Aromatic Hydrocarbon Pollutants in an Urban Stormwater Bioretention Facility. Environmental Science & Technology 43, 494-502. https://doi.org/10.1021/es802090g Flanagan, K., 2018. Evaluation de la rétention et du devenir d'un panel diversifié de micropolluants dans un ouvrage de biofiltration des eaux de ruissellement de voirie. Université de Paris-Est. Flanagan, K., Branchu, P., Deshayes, S., Saad, M., Caupos, E., Boudahmane, L., Partibane, C., Dubois, P., Meffray, L., Gromaire, M.-C., submitted. Field performance of two biofiltration systems treating micropollutants from road runoff. Water Research. Hilliges, R., Endres, M., Tiffert, A., Brenner, E., Marks, T., 2017. Characterization of road runoff with regard to seasonal variations, particle size distribution and the correlation of fine particles and pollutants. Water Science and Technology 75, 1169-1176. https://doi.org/10.2166/wst.2016.576 Kayhanian, M., Fruchtman, B.D., Gulliver, J.S., Montanaro, C., Ranieri, E., Wuertz, S., 2012. Review of highway runoff characteristics: Comparative analysis and universal implications. Water Research 46, 6609-6624. https://doi.org/10.1016/j.watres.2012.07.026 LeFevre, G., Paus, K.H., Natarajan, P., Gulliver, J.S., Novak, P.J., Hozalski, R.M., 2014. Review of Dissolved Pollutants in Urban Storm Water and Their Removal and Fate in Bioretention Cells. Journal of Environmental Engineering 141. Liu, J., Sample, D., Bell, C., Guan, Y., 2014. Review and Research Needs of Bioretention Used for the Treatment of Urban Stormwater. Water 6, 1069-1099. https://doi.org/10.3390/w6041069 Monrabal-Martinez, C., Muthanna, T.M., Meyn, T., 2016. Seasonal variation in pollutant concentrations and particle size distribution in urban stormwater -design implications for BMPs. 9th Novatech conference: Planning & technologies for sustainable urban water management, in: NOVATECH 2016. Presented at the Novatech. Zgheib, S., Moilleron, R., Chebbo, G., 2012. Priority pollutants in urban stormwater: Part 1 -Case of separate storm sewers. Water Research 46, 6683-6692. https://doi.org/10.1016/j.watres.2011.12.012


Sodium ( 23 Na) MRI proffers the possibility of novel information for neurological research but also particular challenges. Uncertainty can arise in in vivo [START_REF] Perman | Methodology of in vivo human sodium MR imaging at 1.5[END_REF] Na estimates from signal losses given the rapidity of T2* decay due to biexponential relaxation with both short (T 2 * short ) and long (T 2 * long ) components. We build on previous work by characterising the decay curve directly via multi-echo imaging at 7 T in 13 controls with the requisite number, distribution and range to assess the distribution of both in vivo T 2 * short and T 2 * long and in variation between grey and white matter, and subregions. By modelling the relationship between signal and reference concentration and applying it to in vivo [START_REF] Perman | Methodology of in vivo human sodium MR imaging at 1.5[END_REF] Na-MRI signal, [START_REF] Perman | Methodology of in vivo human sodium MR imaging at 1.5[END_REF] Na concentrations and apparent transverse relaxation times of different brain regions were measured for the first time. Relaxation components and concentrations differed substantially between regions of differing tissue composition, suggesting sensitivity of multi-echo [START_REF] Perman | Methodology of in vivo human sodium MR imaging at 1.5[END_REF] Na-MRI toward features of tissue composition. As such, these results raise the prospect of multi-echo [START_REF] Perman | Methodology of in vivo human sodium MR imaging at 1.5[END_REF] Na-MRI as an adjunct source of information on biochemical mechanisms in both physiological and pathophysiological states.

In the physiological state, the maintenance of the transmembrane sodium ( 23 Na) concentration gradient (10-15 mM intracellular sodium concentration and ~140 mM extracellular sodium concentration) is a precondition for several critical cellular functions. These include the transport of ions, neurotransmitters and nutrients; regulation of osmotic and electrostatic forces on cells and macromolecules; as well as the transmission of action potentials [START_REF] Chatton | Sodium signaling and astrocyte energy metabolism[END_REF][START_REF] Madelin | Sodium MRI: methods and applications[END_REF][START_REF] Thulborn | Quantitative Sodium MR Imaging: A Review of its Evolving Role in Medicine[END_REF] . In the diseased state, multiple pathological pathways can lead to aberrations of these functions. Such alterations can lead to changes in intra-and extracellular concentrations due to a reduced ability to maintain resting conditions and due to conformational changes in cells themselves as well as the cellular environment in which they are embedded. Thus, [START_REF] Perman | Methodology of in vivo human sodium MR imaging at 1.5[END_REF] Na-MRI is a potential source of more direct and quantitative biochemical information than is generally possible with conventional proton ( 1 H) MRI [START_REF] Madelin | A method for estimating intracellular sodium concentration and extracellular volume fraction in brain in vivo using sodium magnetic resonance imaging[END_REF] . As such, there is substantial interest in [START_REF] Perman | Methodology of in vivo human sodium MR imaging at 1.5[END_REF] Na-MRI regarding a range of neurological conditions despite the additional complications of acquiring [START_REF] Perman | Methodology of in vivo human sodium MR imaging at 1.5[END_REF] Na-MRI signal, including stroke [START_REF] Tsang | Relationship between sodium intensity and perfusion deficits in acute ischemic stroke[END_REF] , epilepsy [START_REF] Ridley | Brain sodium MRI in human epilepsy: Disturbances of ionic homeostasis reflect the organization of pathological regions[END_REF] , tumors [START_REF] Ouwerkerk | Tissue sodium concentration in human brain tumors as measured with 23Na MR imaging[END_REF] and neurodegenerative diseases [START_REF] Maarouf | Topography of brain sodium accumulation in progressive multiple sclerosis[END_REF][START_REF] Mellon | Sodium MR imaging detection of mild Alzheimer disease: preliminary study[END_REF][START_REF] Petracca | Brain intra-and extracellular sodium concentration in multiple sclerosis: a 7 T MRI study[END_REF][START_REF] Reetz | Increased brain tissue sodium concentration in Huntington's Disease -a sodium imaging study at 4 T[END_REF][START_REF] Zaaraoui | Distribution of brain sodium accumulation correlates with disability in multiple sclerosis: a cross-sectional 23Na MR imaging study[END_REF] . The quadrupolar [START_REF] Perman | Methodology of in vivo human sodium MR imaging at 1.5[END_REF] Na nucleus (spin = 3/2) is subject to the influence of fluctuations in neighbouring electric fields due to net positive and non-uniform distribution of charge [START_REF] Thulborn | Quantitative Sodium MR Imaging: A Review of its Evolving Role in Medicine[END_REF][START_REF] Bottomley | Sodium MRI in Man: Technique and Findings[END_REF][START_REF] Madelin | Biomedical applications of sodium MRI in vivo[END_REF][START_REF] Ouwerkerk | Sodium MRI[END_REF] . In the presence of a magnetic field, [START_REF] Perman | Methodology of in vivo human sodium MR imaging at 1.5[END_REF] Na nuclei exhibit four discrete energy states, with three possible (single quantum, SQ) transitions (-1/2, +1/2 "central transition"; -3/2, -1/2 and 1/2, 3/2 "satellite transitions"). In highly motile environments such as plasma or cerebrospinal fluid (CSF), the correlation time (τ C ) is much shorter than the Larmor period (ω 0 -1 ) (ω 0 • τ C ≪ 1), leading to monoexponential longitudinal (T 1 ) and transverse (T 2 ) relaxation. This is in contrast to tissue environments such as within cells and the interstitial spaces between cells where diffusion is restricted by interactions of the [START_REF] Perman | Methodology of in vivo human sodium MR imaging at 1.5[END_REF] Na cation with macromolecular anions. Such interactions modulate decay behaviour in a measurable way: the satellite transitions are subject to additional fast relaxation processes so that both T 1 and T 2 reflect biexponential decay. Literature T 2 estimates in brain parenchyma are in the range ~0.5-5 ms and ~15-30 ms for the short and long components of biexponential decay, respectively [START_REF] Madelin | Sodium MRI: methods and applications[END_REF] .

In the environments that give rise to biexponential behaviour, further transitions beyond SQ coherences (SQC) are possible. Such double and triple quantum coherences (D/TQC) can be selectively detected by appropriate multiple quantum filtering (MQF), and thus provide a source of information regarding short and long components of T 2 * decay. However, there is a strong penalty in terms of signal-to-noise ratio (SNR) and resolution for a given acquisition length [START_REF] Madelin | Sodium MRI: methods and applications[END_REF] . Inversion recovery (IR) methods [START_REF] Stobbe | In vivo sodium magnetic resonance imaging of the human brain using soft inversion recovery fluid attenuation[END_REF][START_REF] Kline | Rapid in vivo monitoring of chemotherapeutic response using weighted sodium magnetic resonance imaging[END_REF][START_REF] Nagel | The potential of relaxation-weighted sodium magnetic resonance imaging as demonstrated on brain tumors[END_REF] can be used to suppress signal arising from unrestricted aqueous environments such as CSF spaces, though interstitial extracellular areas are not 'unrestricted' environments and therefore suppression is incomplete. Furthermore, measurement of concentration remains an unachieved goal for IR methods [START_REF] Thulborn | Quantitative Sodium MR Imaging: A Review of its Evolving Role in Medicine[END_REF][START_REF] Ouwerkerk | Sodium MRI[END_REF] . Both MQF and IR imaging may be argued to provide an unspecified weighting toward intracellular signal beyond the weighted average obtained when measuring the total tissue sodium concentration (TSC). However, all [START_REF] Perman | Methodology of in vivo human sodium MR imaging at 1.5[END_REF] Na-MRI methods continue to receive contributions from intracellular and extracellular spaces [START_REF] Thulborn | Quantitative Sodium MR Imaging: A Review of its Evolving Role in Medicine[END_REF][START_REF] Madelin | Biomedical applications of sodium MRI in vivo[END_REF][START_REF] Ouwerkerk | Sodium MRI[END_REF] .

Crucially, the rapid decay of the short component of T 2 (T 2 * short ) has direct consequences for the accuracy and SNR of [START_REF] Perman | Methodology of in vivo human sodium MR imaging at 1.5[END_REF] Na-MRI [START_REF] Boada | Quantitative in vivo tissue sodium concentration maps: the effects of biexponential relaxation[END_REF] , leading to signal losses of up to 60%. As such, [START_REF] Perman | Methodology of in vivo human sodium MR imaging at 1.5[END_REF] Na-MRI acquisition schemes involving ultra-short echo times (UTE, ~0.2 ms) developed as a strategy that minimises uncertainty in T 2 signal loss due to biexponential relaxation [START_REF] Shah | Imaging of sodium in the brain: a brief review[END_REF][START_REF] Konstandin | Measurement techniques for magnetic resonance imaging of fast relaxing nuclei[END_REF] . However, this does not address variation in T 2 that may be influenced by methodological or physiological factors. The latter in particular may be of interest in the interpretation of [START_REF] Perman | Methodology of in vivo human sodium MR imaging at 1.5[END_REF] Na-MRI signal as a measure of healthy and aberrant biochemical function. Accurate in vivo multi-echo relaxometry techniques may provide an adjunct source of information regarding the contribution and distribution of T 2 * short and T 2 * long . Previous attempts to characterise in vivo brain T 2 decay times have been conducted at lower field strengths with lower sampling rates in the temporal domain without separating multiple T 2 * components [START_REF] Perman | Multiple short-echo (2.5-ms) quantitation of in vivo sodium T2 relaxation[END_REF][START_REF] Perman | Methodology of in vivo human sodium MR imaging at 1.5[END_REF][START_REF] Winkler | Regional T2 and sodium concentration estimates in the normal human brain by sodium-23 MR imaging at 1.5 T[END_REF] , or at higher fields only provide estimates of T 2 * long [START_REF] Bartha | Long component time constant of 23Na T*2 relaxation in healthy human brain[END_REF][START_REF] Fleysher | Sodium long-component T(2)(*) mapping in human brain at 7 Tesla[END_REF] or did not consider variation between tissue types (white matter, WM; grey matter, GM) [START_REF] Nagel | The potential of relaxation-weighted sodium magnetic resonance imaging as demonstrated on brain tumors[END_REF] or between different regions [START_REF] Niesporek | Improved T2* determination in (23)Na, (35)Cl, and (17)O MRI using iterative partial volume correction based on (1)H MRI segmentation[END_REF][START_REF] Blunck | 3D-multi-echo radial imaging of (23) Na (3D-MERINA) for time-efficient multi-parameter tissue compartment mapping[END_REF] .

Here, we designed a novel approach based on the density adapted radial sequence [START_REF] Nagel | Sodium MRI using a density-adapted 3D radial acquisition technique[END_REF] , at 7 T with multiple-echoes (n = 24) (Fig. 1) ensuring echo time (TE) sampling with the requisite number, distribution and range to robustly assess the distribution of both in vivo T 2 * short and T 2 * long through biexponential modelling. Modelling was applied to empirical estimates of sodium signal in healthy volunteers between WM and GM and, for the first time, among several subcortical regions. In addition the fraction of signal or magnetization (M0) at short TEs (M0 SF ) and at long TEs (M0 LF ) was converted to concentrations, by modelling the relationship between [START_REF] Perman | Methodology of in vivo human sodium MR imaging at 1.5[END_REF] Na signal (M0) and concentration (mM) in reference tubes. As such, in vivo [START_REF] Perman | Methodology of in vivo human sodium MR imaging at 1.5[END_REF] Na concentrations (Na SF , Na LF ) corresponding to different signal fractions for the various tissues and regions were provided for the first time (Fig. 2).

Results

Figure 2 provides an overview of the workflow applied to data, including the extraction of decay time components (T 2 * short and T 2 * long ), concentrations (Na SF , Na LF ), total sodium concentration (TSC) and extracellular fraction (EcF). See Table 1 for mean estimates of each parameter for each tissue type and region.

Goodness of fit indicated high performance of the biexponential decay model across the 10 ROIs including complete GM and WM segmentations and eight sub-cortical ROIs (mean r 2 = 0.97 ± 0.01(s.d.)). The mean proportion of the signal fraction (f) associated with the short T 2 * component to total signal estimated by the biexponential model is 57.7% ± 0.07 (s.d.). There was also variation among ROIs (Fig. 3) with the overall highest value obtained for the centrum semiovale (70% ± 0.04 (s.d.)). The caudate nucleus (52% ± 0.06 (s.d.)) and pons (52% ± 0.1 (s.d.)) jointly provide the lowest estimates among subcortical regions, while the lowest mean estimate across all ROIs was for the entire GM segmentation (46% ± 0.03(s.d.)).

T 2 * short and T 2 * long differences between white and grey matter. Table 2a provides results for the whole model (ANOVA, corrected at P < 0.008) and main effects of Tissue Type (GM, WM) for each parameter. Effects of Age and Sex were not found to be significant for any parameter. Significant effects were observed for whole model for T 2 * long (P < 0.0001) and T 2 * short (P = 0.005) as well significant effects of tissue type for T 2 * long (P < 0.0001) and T 2 * short (P = 0.001).

Results of post-hoc Steel-Dwass tests are detailed in Table 3 and represented in Fig. 4. Significantly higher (z = -3.03, P < 0.003) values of T 2 * short were observed in GM ( T 2 * short and T 2 * long differences between sub-cortical regions. ANOVAs revealed significant (P < 0.0001) effects for both the whole model and the effect of Region (Table 2b) on both T 2 * short and T 2 * long . Overall, in terms of the post-hoc analysis (Table 3, Fig. 4b), we observed substantial variation for each parameter between subcortical regions. The shortest mean decay time components were observed in the pons for both T 2 * short (2.43

Concentration differences between white and grey matter.

The whole model and the main effect of tissue type were significant (P < 0.0001) for Na LF , TSC and EcF. Whole model and tissue type effects for Na SF did not survive correction for multiple comparisons. Post-hoc Steel-Dwass tests revealed significantly higher values in GM versus WM for Na LF (25.

Concentration differences between sub-cortical regions. Both NaSF and NaLF, as well as TSC

and EcF, demonstrated significant (P < 0.0001) effects for both the whole model and the effect of Region. A significant effect of Sex was also observed for TSC (P = 0.006). As above, concentrations and derived metrics showed a variety of variations between regions. The thalamus demonstrated the highest mean estimates of Na SF (24.28 mM ± 1.66(s.d.)) and TSC (40.30 mM ± 2.33(s.d.)), with the lowest estimates observed in the pons (Na SF : 13.19 mM ± 3.68(s.d.); TSC: 25.18 mM ± 3.17(s.d.)). The caudate (Na LF : 17.80 mM ± 2.95(s.d.); EcF: 0.13 ± 0.02(s.d.)) and centrum semiovale (Na LF : 8.46 mM ± 1.68(s.d.); EcF: 0.06 ± 0.01 (s.d.)), provided the highest and lowest estimates, respectively, for both Na LF and EcF. Inter-subject variability was especially present for EcF and Na LF in the corpus callosum.

Discussion

Data from a multi-echo [START_REF] Perman | Methodology of in vivo human sodium MR imaging at 1.5[END_REF] Na radial sequence acquired at ultra-high field (UHF) were analysed using a biexponential relaxation model to derive T 2 * short and T 2 * long relaxation times. In addition, [START_REF] Perman | Methodology of in vivo human sodium MR imaging at 1.5[END_REF] Na concentrations apparent at short and long TEs were quantified. As such, to our knowledge, we provide the first [START_REF] Perman | Methodology of in vivo human sodium MR imaging at 1.5[END_REF] Na-MRI data to address regional variation in T 2 * short at UHF, and to quantify the apparent [START_REF] Perman | Methodology of in vivo human sodium MR imaging at 1.5[END_REF] Na concentrations corresponding to short and long signal fractions associated with the respective components of T2* relaxation. Given the interest in [START_REF] Perman | Methodology of in vivo human sodium MR imaging at 1.5[END_REF] Na-MRI particularly for neurological research, quantification of these parameters and characterisation of their variation is necessary as an adjunct to even standard UTE [START_REF] Perman | Methodology of in vivo human sodium MR imaging at 1.5[END_REF] Na-MRI protocols.

The overall contribution of short and long T 2 * components to the measured sodium signal is considered to be ~60% to 40% 2 , respectively, consistent with our mean estimate of 57.7% ± 0.07% (s.d.) for the signal fraction associated with the short T 2 * component (f) across all considered ROIs. In the biexponential relaxation model applied here contributions of different T 2 * components were not fixed. The model revealed that while f was comparable to the general estimate in some regions (eg the entire WM), it varied in others (eg. the lowest signal contributions over the entire GM) (Fig. 3). Additionally, variation was observed across sub-cortical ROIs which are themselves likely to include diverse proportions of grey and white matter. Examples include regions that mainly contain white matter tracts but also grey matter nuclei (eg. Pons), as well as the inverse (eg. thalamus). Deviation from the theoretical ratio of 60:40 may reflect the contribution of additional compartments, for example an increased contribution of highly motile ions pool in CSF where signal decay is monoexponential (eg T 2 * ~ 47 ms) [START_REF] Niesporek | Improved T2* determination in (23)Na, (35)Cl, and (17)O MRI using iterative partial volume correction based on (1)H MRI segmentation[END_REF] . Higher estimates of f may reflect reduced contributions of this type, for example in the centrum semiovale which provided the highest signal fraction associated with the short T 2 * component observed here.

T 2 * relaxation refers to the dephasing of collections of nuclei due to reciprocal interactions of their local magnetic fields (T 2 ) in addition to magnetic field inhomogeneities (T 2 ') [START_REF] Deoni | Quantitative relaxometry of the brain[END_REF] . Attempts to characterize in vivo [START_REF] Perman | Methodology of in vivo human sodium MR imaging at 1.5[END_REF] Na relaxation times in human brain tissue have been made for several decades [START_REF] Perman | Multiple short-echo (2.5-ms) quantitation of in vivo sodium T2 relaxation[END_REF][START_REF] Winkler | Regional T2 and sodium concentration estimates in the normal human brain by sodium-23 MR imaging at 1.5 T[END_REF] . Such applications show variation in terms of applied methods, following developments in sequence design and the availability of higher field strengths. These factors are especially important for [START_REF] Perman | Methodology of in vivo human sodium MR imaging at 1.5[END_REF] Na, given not only the relative rapidity of biexponential relaxation but also due to its lower concentration and intrinsic sensitivity compared to 1 H. This leads to a relatively lower SNR in [START_REF] Perman | Methodology of in vivo human sodium MR imaging at 1.5[END_REF] Na-MRI, which can be partly compensated for by higher fields [START_REF] Thulborn | Quantitative Sodium MR Imaging: A Review of its Evolving Role in Medicine[END_REF][START_REF] Kraff | MRI at 7 Tesla and above: demonstrated and potential capabilities[END_REF] . Consequently, among studies that attempt to quantify either long or short components of T 2 * relaxation in brain tissues (for an overview see Table 4), progressively higher fields have been employed. At 4 T, values of T 2 * long were observed to vary little between cortical GM and WM ROIs, though with some evidence of variation in subcortical regions (thalamus) and higher values in some white matter structures like the corpus callosum (CC) [START_REF] Bartha | Long component time constant of 23Na T*2 relaxation in healthy human brain[END_REF] . In line with theoretical expectations, and as observed in animal experiments [START_REF] Nagel | K and (23) Na relaxation times and MRI of rat head at 21.1[END_REF] , longer relaxation times are observed at the higher field strengths in the current data (Table 1) and more generally at 7 T (Table 4). At 7 T, despite the lack of variation in T 2 * long values between general GM and WM ROIs, variation among other sub-regions comparable to the relative levels of T 2 * long seen in the current work was observed (thalamus > CC > cerebellar WM > putamen) [START_REF] Fleysher | Sodium long-component T(2)(*) mapping in human brain at 7 Tesla[END_REF] . Due to insufficient data points to characterize the initial portion of the decay curve, given that the smallest TEs are > 3 ms, these studies did not attempt to quantify T 2 * short . Thus the possibility of an unknown bias in measurement, relative to studies that model both T 2 * components remains. In a 7 T study in healthy controls of both T 2 * short and T 2 * long in white matter, estimates in excellent agreement with the current data were observed by Nagel et al. [START_REF] Nagel | The potential of relaxation-weighted sodium magnetic resonance imaging as demonstrated on brain tumors[END_REF] . More recent data [START_REF] Niesporek | Improved T2* determination in (23)Na, (35)Cl, and (17)O MRI using iterative partial volume correction based on (1)H MRI segmentation[END_REF] in five subjects provide similarly concordant data for GM, though some disagreement for relative T 2 * short relaxation times between tissues should be noted. Recently, Blunck et al. [START_REF] Blunck | 3D-multi-echo radial imaging of (23) Na (3D-MERINA) for time-efficient multi-parameter tissue compartment mapping[END_REF] validated a multi-echo sequence with a large numbers of TEs, estimating decay components in 4 subjects, and observe T 2 * short relaxation times that are within the range of those seen here, as well as less variation between GM and WM for T 2 * long . The principal methodological differences between this study and the previous studies characterising both T 2 * short and T 2 * long in GM and WM at 7 T, beyond a slightly larger sample, is the distribution of early TEs during the first part of the decay curve thought to be dominated by the short T 2 * component. For example the three shortest TEs correspond to 0.3-0.8-2.3 ms here, versus 0.4-4.5-8.5 ms for Blunck et al. [START_REF] Blunck | 3D-multi-echo radial imaging of (23) Na (3D-MERINA) for time-efficient multi-parameter tissue compartment mapping[END_REF] and 0.35-1-1.5 ms for Niesporek et al. [START_REF] Niesporek | Improved T2* determination in (23)Na, (35)Cl, and (17)O MRI using iterative partial volume correction based on (1)H MRI segmentation[END_REF] . The echo time choices made here are dictated by the minimum inter-echo spacing of about 6 ms. With 3 separate acquisitions there is additional flexibility in the TE choices. The approach adopted was to use logarithmic spacing for the first echoes and equal spacing for later echoes. Logarithmic spacing on the early echoes provides good sensitivity to a range of T 2 * short values. The current data suggest that GM and WM give rise to significantly different time constants of decay, and do so differentially for short and long T 2 * components. These considerations, in addition to the variation among subregions and between T 2 * components for given regions, raise the possibility of the influence of tissue composition on observed relaxation (discussed below). By modelling the relationship between signal (M0) and known reference concentrations, we obtained -from estimates of M0 SF and M0 LF derived from in vivo data -quantitative values for the apparent [START_REF] Perman | Methodology of in vivo human sodium MR imaging at 1.5[END_REF] Na (Na SF , Na LF ) concentrations relating to short (f) and long (1-f) signal fractions (Fig. 2). Na SF was observed to be comparable between GM (21.16 mM ± 0.87(s.d.)) and WM (22.28 mM ± 0.97(s.d.)). These values are higher than the reference intracellular sodium concentration (10-15 mM) commonly cited in the literature [START_REF] Chatton | Sodium signaling and astrocyte energy metabolism[END_REF][START_REF] Madelin | Sodium MRI: methods and applications[END_REF][START_REF] Thulborn | Quantitative Sodium MR Imaging: A Review of its Evolving Role in Medicine[END_REF] , possibly reflecting contributions from extracellular spaces. Various attempts have been made to weight measures of concentration toward the restricted sodium pool. For example, subtraction of only two SQ sodium images as a means of suppressing contributions from the long T 2 * component obtains a concentration of 25.9 ± 1.2 mM for bound sodium in the 'healthy' GM of patients with brain tumours [START_REF] Qian | Short-T2 imaging for quantifying concentration of sodium ((23) Na) of bi-exponential T2 relaxation[END_REF] . This estimate is not dissimilar to our estimates of GM though most similar to the Na LF concentration we observe in WM (Table 1). Recent studies -utilizing IR at 3T [START_REF] Madelin | A method for estimating intracellular sodium concentration and extracellular volume fraction in brain in vivo using sodium magnetic resonance imaging[END_REF][START_REF] Madelin | Repeatability of quantitative sodium magnetic resonance imaging for estimating pseudo-intracellular sodium concentration and pseudo-extracellular volume fraction in brain at 3 T[END_REF] and TQF at UHF [START_REF] Petracca | Brain intra-and extracellular sodium concentration in multiple sclerosis: a 7 T MRI study[END_REF][START_REF] Fleysher | Noninvasive quantification of intracellular sodium in human brain using ultrahigh-field MRI[END_REF] -find little difference in concentration estimates weighted toward the restricted pool between GM and WM in their healthy control comparison samples. This is consistent with the similarity between our estimates of Na SF from whole tissue type segmentation maps for GM (21.16 mM ± 0.87(s.d.) and WM (22.28 mM ± 0.97(s.d.)) (Fig. 4a). Similarly, attempts to measure volume fractions associated with bound sodium (WM > GM) [START_REF] Petracca | Brain intra-and extracellular sodium concentration in multiple sclerosis: a 7 T MRI study[END_REF][START_REF] Fleysher | Noninvasive quantification of intracellular sodium in human brain using ultrahigh-field MRI[END_REF] , are complementary with the current work's estimate of sodium extracellular fraction (GM > WM) derived from Na LF . Indeed, the sodium EcF estimates observed here (0.06-0.18) fall well within the expected overall volume fraction of the extracellular space in healthy adult brains (0.2) derived from a variety of methods [START_REF] Syková | Diffusion in brain extracellular space[END_REF] . Furthermore, they specifically correspond to previous estimates of greater [START_REF] Perman | Methodology of in vivo human sodium MR imaging at 1.5[END_REF] Na extracellular volume fractions in grey versus white matter using [START_REF] Perman | Methodology of in vivo human sodium MR imaging at 1.5[END_REF] Na-MRI [START_REF] Madelin | A method for estimating intracellular sodium concentration and extracellular volume fraction in brain in vivo using sodium magnetic resonance imaging[END_REF][START_REF] Madelin | Repeatability of quantitative sodium magnetic resonance imaging for estimating pseudo-intracellular sodium concentration and pseudo-extracellular volume fraction in brain at 3 T[END_REF] .

Most in vivo studies of brain [START_REF] Perman | Methodology of in vivo human sodium MR imaging at 1.5[END_REF] Na-MRI provide estimates in terms of total sodium concentration (TSC), thus we computed an equivalent metric to permit comparison. Estimates here (GM: 46.92 mM ± 2.83 (s.d.); WM: 38.15 mM ± 1.97 (s.d.)) fall well within the literature range for TSC in GM (30-70 mM) and WM (20-60 mM) [START_REF] Madelin | Sodium MRI: methods and applications[END_REF][START_REF] Madelin | Biomedical applications of sodium MRI in vivo[END_REF] . Specifically, in the majority of studies that report healthy control values in GM, TSC is observed to exhibit higher values compared to WM, including across field strengths and different acquisitions [START_REF] Maarouf | Topography of brain sodium accumulation in progressive multiple sclerosis[END_REF][START_REF] Petracca | Brain intra-and extracellular sodium concentration in multiple sclerosis: a 7 T MRI study[END_REF][START_REF] Zaaraoui | Distribution of brain sodium accumulation correlates with disability in multiple sclerosis: a cross-sectional 23Na MR imaging study[END_REF][START_REF] Inglese | Brain tissue sodium concentration in multiple sclerosis: a sodium imaging study at 3 tesla[END_REF][START_REF] Paling | Sodium accumulation is associated with disability and a progressive course in multiple sclerosis[END_REF][START_REF] Qian | High-resolution sodium imaging of human brain at 7 T[END_REF][START_REF] Eisele | Heterogeneity of acute multiple sclerosis lesions on sodium (23Na) MRI[END_REF] . Niesporek et al. [START_REF] Niesporek | Partial volume correction for in vivo 23Na-MRI data of the human brain[END_REF] , employing a partial volume correction method adapted from PET accounting for both point spread function spreading and resolution issues in [START_REF] Perman | Methodology of in vivo human sodium MR imaging at 1.5[END_REF] Na-MRI, suggest corrected TSC values for GM (48 mM ± 1 (s.d.)) and WM (43 mM ± 3(s.d.)) notably similar to our estimates. Where available, regional TSC estimates in healthy controls are concordant with the current results in terms of finding higher values in the thalamus and caudate compared to putamen and pallidum as well as much lower values in the cerebellum [START_REF] Reetz | Increased brain tissue sodium concentration in Huntington's Disease -a sodium imaging study at 4 T[END_REF] , and specifically its white matter [START_REF] Inglese | Brain tissue sodium concentration in multiple sclerosis: a sodium imaging study at 3 tesla[END_REF] . The correspondence of our observed TSC values (the sum of Na SF and Na LF ) and those in the literature are encouraging, suggesting that the current methods appropriately characterize the overall [START_REF] Perman | Methodology of in vivo human sodium MR imaging at 1.5[END_REF] Na signal with respect to the rest of the literature. This lends further credence to the signal fractions and concentrations associated with the short and long T 2 * components as observed here. Crucially, the current methods achieve this without a high SNR penalty and permit quantification.

F-Values

Dependant variable

Whole Model (3) Tissue Type (1) Sex ( 1 Relaxation is influenced by factors constraining molecular motion as well as the structure and content (tissue density) of the molecular environment experienced by nuclei [START_REF] Deoni | Quantitative relaxometry of the brain[END_REF] . For example, one factor of tissue density is water/ fluid content which can be explored via invasive electrophysiological measures of impedance [START_REF] Koessler | In-vivo measurements of human brain tissue conductivity using focal electrical current injection through intracerebral multicontact electrodes[END_REF] , in vivo MRI estimates of proton density [START_REF] Gelman | Interregional variation of longitudinal relaxation rates in human brain at 3.0 T: relation to estimated iron and water contents[END_REF] and post-mortem wet-to-dry mass ratios [START_REF] Krebs | Assessment of trace elements in human brain using inductively coupled plasma mass spectrometry[END_REF] . Higher water/fluid content is observed in GM tissues versus WM, and particularly in the caudate among sub-cortical regions explored here. This may be reflected here by lower signal fractions associated with the short T 2 * component observed in GM and the caudate in the current data (Fig. 3), and inversely higher values of Na LF and the related metric EcF (Table 1, Fig. 4). Conversely, the white matter ROI in the centrum semiovale provides the highest short signal fraction (f) and the lowest estimates of Na LF and EcF.

The extent and an-/isotropy of the mobility of nuclei also impacts relaxation, with the structure and cellular make-up and the constituents of intracellular and extracellular environments all potentially playing a role. The fluid environment in the interstitium between brain cells differs from the environment of CSF in the ventricles due to the presence of the negatively-charged long-chain molecules of the extracellular matrix [START_REF] Syková | Diffusion in brain extracellular space[END_REF][START_REF] Nicholson | Brain Extracellular Space as a Diffusion Barrier[END_REF] . The extracellular matrix regulates the ionic environment necessary for cellular functions such as synaptic transmission and action potentials, interacts with diffusion through extracellular spaces via viscous drag and the interaction with positive charged ion species such as [START_REF] Perman | Methodology of in vivo human sodium MR imaging at 1.5[END_REF] Na, and varies in composition and density across brain structures [START_REF] Thulborn | Quantitative Sodium MR Imaging: A Review of its Evolving Role in Medicine[END_REF][START_REF] Syková | Diffusion in brain extracellular space[END_REF][START_REF] Nicholson | Brain Extracellular Space as a Diffusion Barrier[END_REF] . The properties of the extracellular space and matrix are in turn influenced by cellular populations of neurons and glia, in terms of the distribution of different subtypes and the manner in which they constrain the structure of their environment via the formation of sheets, extension of processes and size alterations influencing the volume of intra-/extracellular spaces [START_REF] Syková | Diffusion in brain extracellular space[END_REF] .

Estimates from histology, DNA extraction and immunocytochemistry suggest that the human brain contains ~100 billion neurons and an equivalent number of non-neuronal cells including glia (oligodendrocytes > astrocytes > microglia) [START_REF] Pelvig | Neocortical glial cell numbers in human brains[END_REF] and a small proportion of endothelial cells, leading to an approximate overall glia-to-neuron ratio (GNR) of 1:1 [START_REF] Von Bartheld | The search for true numbers of neurons and glial cells in the human brain: A review of 150 years of cell counting[END_REF] . At the same time, GNRs vary widely between brain regions with extremes including the cerebellum (0.23) due to its small, densely packed neurons, while reaching 11.35 in other regions of the brain including brainstem, diencephalon and striatum (i.e. many of the subregions considered here) [START_REF] Von Bartheld | The search for true numbers of neurons and glial cells in the human brain: A review of 150 years of cell counting[END_REF][START_REF] Mota | All brains are made of this: a fundamental building block of brain matter with matching neuronal and glial masses[END_REF][START_REF] Herculano-Houzel | The glia/neuron ratio: how it varies uniformly across brain structures and species and what that means for brain physiology and evolution[END_REF][START_REF] Azevedo | Equal numbers of neuronal and nonneuronal cells make the human brain an isometrically scaled-up primate brain[END_REF] . These variations Table 3. Significant differences between regions. Differences (z) are provided for each significant comparison (P < 0.008), with the corresponding P value provided in italics, and non-significant comparisons indicated by a dash (-). Diagonal elements with asterisks represent borders between the results of different tests, for example in the top row the bottom triangle represents results between regions for T 2 * short , while the upper triangle represents results between regions for T 2 * long . Th, thalamus; Pu, putamen; Pa, pallidum; Ca, caudate; Cc, corpus callosum; Cb, cerebellar WM, Cs, centrum semiovale; Po, pons.

are thought not to reflect differences in glia density, which varies much less between structures, but rather with increasing neuronal density that is itself due to decreasing neuronal cell size (including soma and dendritic and axonal arborisations) [START_REF] Von Bartheld | The search for true numbers of neurons and glial cells in the human brain: A review of 150 years of cell counting[END_REF][START_REF] Herculano-Houzel | The glia/neuron ratio: how it varies uniformly across brain structures and species and what that means for brain physiology and evolution[END_REF] . 500-fold variation in average neuronal cell masses are observed across structures and species versus 1.4-fold for glia [START_REF] Mota | All brains are made of this: a fundamental building block of brain matter with matching neuronal and glial masses[END_REF] . The above evidence suggests that while the WM represents a restrictive environment determined mainly by the anisotropy [START_REF] Assaf | Diffusion tensor imaging (DTI)-based white matter mapping in brain research: a review[END_REF] of axons and small-bodied [START_REF] Pelvig | Neocortical glial cell numbers in human brains[END_REF] myelin-supporting oligodendrocytes, the GM represents a wider variety of cellular environments especially given the range of neuronal sizes. This is a possible explanation for the variation in relaxation times, associated signal fractions and derived metrics observed here. Similarly, these factors may contribute to the variation between regions (Fig. 4) to the extent that they reflect proportions of white and grey matter. It is notable that T 2 * short and T 2 * long, as well as Na LF tend to be lowest in axon/myelin-rich structures. This is most evident across metrics in the pallidum and pons, but also to some extent in centrum semiovale, cerebellar white matter and the corpus callosum. It should be recognized that variability across metrics among these regions suggests additional factors at work as well.

Considering concordance of our results and the available relevant literature, in addition to recent insights into tissue composition, this raises the prospect of multi-echo [START_REF] Perman | Methodology of in vivo human sodium MR imaging at 1.5[END_REF] Na-MRI's sensitivity to microstructural properties of imaged tissues. Future work, including additional measures of microstructure, such as via the measurement of the diffusion properties of 1 H or [START_REF] Perman | Methodology of in vivo human sodium MR imaging at 1.5[END_REF] Na itself [START_REF] Madelin | Biomedical applications of sodium MRI in vivo[END_REF][START_REF] Ouwerkerk | Sodium MRI[END_REF][START_REF] Nagel | The potential of relaxation-weighted sodium magnetic resonance imaging as demonstrated on brain tumors[END_REF][START_REF] Goodman | Sodium ion apparent diffusion coefficient in living rat brain[END_REF] , could confirm and expand the current results, and speak to limitations of the current approach. For example, despite the measures taken to avoid partial volume effects, as is the case for all [START_REF] Perman | Methodology of in vivo human sodium MR imaging at 1.5[END_REF] Na-MRI there is a remaining possibility of an unknown bias due to the influence of higher concentrations of [START_REF] Perman | Methodology of in vivo human sodium MR imaging at 1.5[END_REF] Na in extracellular and cerebrospinal fluid, and the possibility of differences between tissue types in terms of this bias. Further gains in spatial resolution could further ameliorate this issue 3 , as well as the application of partial volume correction methods originally applied in positron emission tomography and recently adapted to [START_REF] Perman | Methodology of in vivo human sodium MR imaging at 1.5[END_REF] Na-MRI [START_REF] Niesporek | Improved T2* determination in (23)Na, (35)Cl, and (17)O MRI using iterative partial volume correction based on (1)H MRI segmentation[END_REF][START_REF] Niesporek | Partial volume correction for in vivo 23Na-MRI data of the human brain[END_REF] . Given the duration of the scan required to characterise the decay curve, there is the possibility of artefacts arising from subject motion. Measures such as the use of foam supports to support subjects' heads and constrain movement were employed; however optimisation of the sequence to shorten overall acquisition times should be pursued. In any case, this will be required for clinically feasible scan times.

In summary, we provide evidence that in the physiological state multi-echo [START_REF] Perman | Methodology of in vivo human sodium MR imaging at 1.5[END_REF] Na-MRI depicts variation in T 2 * relaxation between major distinctions in tissue structure -GM and WM -as well as between diverse brain regions of differing composition and structure. This includes variations in decay times, including the T 2 * short component. Additionally, quantification of [START_REF] Perman | Methodology of in vivo human sodium MR imaging at 1.5[END_REF] Na concentrations apparent at short and long TEs was evaluated via a quantitative multi-echo approach for the first time. This provides a foundation for the examination of the alteration of these properties in pathophysiological populations, as a means of shedding light on both disease processes and the mechanisms underlying normal ionic homeostatic mechanisms as imaged by [START_REF] Perman | Methodology of in vivo human sodium MR imaging at 1.5[END_REF] Na-MRI. Table 4. Examples of literature estimates for short and long component of T 2 * derived using biexponential models, and CSF transverse relaxation rates using monoexponential models. Note that data is attributed to structures as described in the papers concerned, and the details of ROIs likely differ between reports. Brain parenchyma refers to estimates derived from (an) ROI(s) where no specific anatomic attribution was made.

Values reproduced from Bartha and Menon 25 , Fleysher et al. [START_REF] Fleysher | Sodium long-component T(2)(*) mapping in human brain at 7 Tesla[END_REF] , Nagel et al. [START_REF] Nagel | The potential of relaxation-weighted sodium magnetic resonance imaging as demonstrated on brain tumors[END_REF] , Blunck et al. [START_REF] Blunck | 3D-multi-echo radial imaging of (23) Na (3D-MERINA) for time-efficient multi-parameter tissue compartment mapping[END_REF] and Niesporek et al. [START_REF] Niesporek | Improved T2* determination in (23)Na, (35)Cl, and (17)O MRI using iterative partial volume correction based on (1)H MRI segmentation[END_REF] . Abbreviations: Ref, reference; T, Tesla; TE, echo time; GM, grey matter; WM, white matter.

Methods

Subjects. 14

MRI acquisition.

Data were acquired on a whole-body 7 T Magnetom MR system (Siemens, Erlangen, Germany). [START_REF] Perman | Methodology of in vivo human sodium MR imaging at 1.5[END_REF] Na-MRI was acquired using a dual-tuned [START_REF] Perman | Methodology of in vivo human sodium MR imaging at 1.5[END_REF] Na/ 1 H QED birdcage coil and a multi-echo density adapted 3D projection reconstruction pulse sequence (TR = 120 ms, 10000 spokes, 384 radial samples per spoke, radial fraction p of 0.32, 500 us hard RF pulse, bandwidth 200 Hz/pixel, 3.5 mm nominal isotropic resolution, 8 echoes, acquisition time = 20 min). To ensure a sufficient number and distribution of TEs, especially for measuring T 2 * short , while taking into account the 5 ms readout of the sequence, we applied the sequence three times in one exam in order to obtain 24 TEs ranging from 0.3 ms to 100 ms (Run 1: 0. Pre-processing. Sodium images were reconstructed offline in Matlab (Mathworks, Natick, MA) using a Kaiser-Bessel gridding method [START_REF] Nagel | Sodium MRI using a density-adapted 3D radial acquisition technique[END_REF] leading to a full 3D data set for each individual, at each echo time (See Fig. 1 for an example). [START_REF] Perman | Methodology of in vivo human sodium MR imaging at 1.5[END_REF] Na images from all TEs were realigned to the shortest TE (0.3 ms) for each individual. 3D [START_REF] Perman | Methodology of in vivo human sodium MR imaging at 1.5[END_REF] Na images from the shortest TE were then realigned to high resolution 3D-MP2RAGE images obtained from the same individual and the resulting spatial transform was applied to the remaining [START_REF] Perman | Methodology of in vivo human sodium MR imaging at 1.5[END_REF] Na images (SPM12; Wellcome Institute, London, UK). Subsequent analyses using ROIs (see below) were applied to these coregistered [START_REF] Perman | Methodology of in vivo human sodium MR imaging at 1.5[END_REF] Na-MRI images in the native 3D-MP2RAGE space. Figure 2 provides an overview of the workflow applied to data.

Using SPM12, 1 H images were segmented into probability maps of GM, WM and CSF to create masks to be applied to sodium images. A conservative probability threshold of 0.9 for tissue type segmentation was applied to GM and WM prior to the creation of masks. FSL (version 6.0, FMRIB, Oxford, UK) was used to define 8 regional sub-cortical ROIs using 1 H images, thresholded GM and WM maps and [START_REF] Perman | Methodology of in vivo human sodium MR imaging at 1.5[END_REF] Na images of the earliest (high SNR) TE (0.3 ms). Sodium images and thresholded tissue probability maps were projected onto 1 H images to aid expert (S.G.) manual definition of ROIs for each individual. In addition to thresholding of tissue probability maps attempts to limit partial volume effects included the avoidance of tissue boundaries and evident areas of heightened signal due to the proximity of CSF spaces such as the ventricles during manual ROI definition (Fig. 2). In total, 10 ROIs were applied for each individual to derive mean [START_REF] Perman | Methodology of in vivo human sodium MR imaging at 1.5[END_REF] Na signal (MARSBAR toolbox, SPM12) for each ROI for each echo time. ROIs correspond to the entire (thresholded) GM and WM segmentations, in addition to eight sub-cortical manual bilateral ROIs: thalamus, pallidum, putamen, caudate nucleus, corpus callosum, centrum semiovale, cerebellar white matter and pons.

Biexponential model.

Considering the design of the sodium sequence providing a maximum reduction of T1 weighting (TR = 120 ms, around four times longer than the T1 values 7 ), determination of signal fractions and the time constants of short and long T2* components of signal decay in [START_REF] Perman | Methodology of in vivo human sodium MR imaging at 1.5[END_REF] Na images can be modelled by a bi-exponential fitting procedure. For each ROI, we analysed the mean signal intensity across each of the 24 TEs and apply a biexponential model to the obtained curve (Fig. 2a) using the equation:

=            ⋅ + -⋅        +      - - Signal A f f R ic e ( 1 ) e TE T TE T 2 2 2 2 2 short long ⁎ ⁎
where A is an amplitude scaling term, f is the signal fraction associated with the short T 2 * component and Ric refers to a Rician noise-related scaling parameter as described in Gudbjartsson et al. [START_REF] Gudbjartsson | The Rician distribution of noisy MRI data[END_REF] . The best-fit parameters were obtained from nonlinear least-squares (lsqnonlin) fitting. Model performance was measured by goodness of fit (r 2 ). From the model we estimated a signal fraction for short (f) and long (1-f) T 2 * components, as well as estimating the time constants (T2* short and T2* long ). We calculated magnetization (M0) corresponding to the signal fraction estimated by the model in terms of the intercepts of the signal fraction components of the model, obtaining M0 SF = A•f and M0 LF = A•(1-f).

Quantification: Na SF & Na LF . As these signal fraction parameters are expressed in arbitrary units, we attempted to obtain quantitative values to access the same measurement scale across subject in order to explore variations in tissue types and regions, and permit literature comparisons. For each reference tube for each individual, we obtained the value of M0 and the time of transverse relaxation (T 2 *) for a given tube across the 24 TEs, through monoexponential fitting via MATLAB (R2012a, MathWorks) (Fig. 2b). We then model a linear relationship between obtained M0 and known concentrations across all tubes (Fig. 2c), which can be applied to parameters estimated from the biexponential model of in vivo data (M0 SF and M0 LF , Fig. 2a). As such, the apparent concentrations equivalent to a given level of magnetization was obtained, yielding quantitative estimates (Na SF and Na LF ) for each brain ROI. Note that given that we have dynamic information in the form of the curve of signal intensity across TEs, we can hypothesize that at the longest TEs, the major signal contributors will be the slowest relaxing/most motile pools. Accordingly, the magnetization estimated from the intercept of the signal fraction associated with the long T 2 * component may be considered a good approximation of the sodium concentration of extracellular spaces. 'Extracellular fraction' (EcF) was obtained by the division of Na LF by the commonly used value of 140 mM for extracellular Na concentration [START_REF] Ouwerkerk | Tissue sodium concentration in human brain tumors as measured with 23Na MR imaging[END_REF][START_REF] Ouwerkerk | Sodium MRI[END_REF][START_REF] Thulborn | Quantitative tissue sodium concentration mapping of the growth of focal cerebral tumors with sodium magnetic resonance imaging[END_REF] . We also calculated the parameter total sodium concentration (TSC) as the sum of Na SF and Na LF .

Statistical analyses. Six dependant variables of interest were investigated via analysis in JMP v.9 (SAS Institute Inc., Cary, NC). These included T 2 * short and T 2 * long (ms) derived from the biexponential fitting procedure, the quantitative estimates Na SF and Na LF, (mM), as well as TSC (mM) and EcF. An ANOVA was applied separately to the six dependant variables to investigate the factor of interest Tissue Type (2 levels: GM, WM), in addition to factors for Sex and Age. Additionally, an ANOVA was applied to the sub-cortical regional data, with the factor of interest Region (8 levels) as well as Sex and Age. Differences between the levels of factors of interest that were found to be significant were further investigated via non-parametric Steel-Dwass (p < 0.05, adjusted for multiple comparisons between levels) in a pairwise fashion. Based on the possibility of dependence between measures, Bonferroni correction was also applied across tests based on 6 dependant variables yielding a corrected α-level of P = 0.05/6 = 0.008.

  Distribution of brain sodium long and short relaxation times and concentrations: a multi-echo ultra-high field 23Na MRI study Ben Ridley, Armin M Nagel, Mark Bydder, Adil Maarouf, Jan-Patrick Stellmann, Soraya Gherib, Jérémy Verneuil, Patrick Viout, Maxime Guye, Jean-Philippe Ranjeva, et al. To cite this version: Ben Ridley, Armin M Nagel, Mark Bydder, Adil Maarouf, Jan-Patrick Stellmann, et al.. Distribution of brain sodium long and short relaxation times and concentrations: a multi-echo ultra-high field 23Na MRI study. Scientific Reports, 2018, 8 (1), 10.1038/s41598-018-22711-0. hal-02065574 Distribution of brain sodium long and short relaxation times and concentrations: a multi-echo ultrahigh field 23 Na MRI study Ben Ridley 1,2 , Armin M. Nagel 3,4 , Mark Bydder 1,2 , Adil Maarouf 1,2 , Jan-Patrick Stellmann 1,2 , Soraya Gherib 1,2 , Jeremy Verneuil 1,2 , Patrick Viout 1,2 , Maxime Guye 1,2 , Jean-Philippe Ranjeva 1,2 & Wafaa Zaaraoui 1,2

Figure 1 .

 1 Figure 1. Exemplar 23 Na-MRI images from a single subject across echo times. Note the decrease in signal as a function of the length of echo time (TE), and the change in the relative contributions from tissue and cerebrospinal fluid, with the latter providing most signal at long TEs.

  75 mM ± 2.97(s.d.), 15.87 mM ± 1.49(s.d.); z = -4.31, P < 0.0001), extracellular fraction (0.18 ± 0.02(s.d.), 0.11 ± 0.01(s.d.); z = -4.31, P < 0.0001) and TSC (46.92 mM ± 2.83(s.d.), 38.15 mM ± 1.97(s.d.); z = -4.31, P < 0.0001).

Figure 2 .

 2 Figure 2. Schematic workflow of processing procedure applied to data and the six measures obtained. After image post-processing, several fitting procedures were applied to 23 Na-MRI data derived from 10 ROIs (examples shown include the caudate, putamen, pallidum and corpus callosum). Fitting included: (a) a biexponential model to obtain estimates of the magnetization (M0 SF , M0 LF ) apparent from the signal fractions associated with short and long T 2 * components from in vivo ROIs; (b) a monoexponential model to obtain estimates of M0 for each reference tube and (c) a linear model of the relationship between M0 and known reference concentrations. The six output parameters and their derivation are marked: two T 2 * components (dashed outline), a Na concentration for each component (double outline), TSC (solid outline) and EcF (dotted outline) See text for more details. Abbreviations: TE, echo time; mM, millimolar; ms, milliseconds; ROIs, regions of interest.

Figure 3 .

 3 Figure 3. Estimated percentage signal contributions of short (f) and long (1-f) T 2 * components. Mean and standard deviation (s.d) for f are provided at the bottom of the figure, and s.d. is represented as error bars on the stacked chart. Long component percentage contributions are necessarily the inverse (1-f). ROIs: Th, thalamus; Pu, putamen; Pa, pallidum; Ca, caudate; Cc, corpus callosum; Cb, cerebellum, Cs, centrum semiovale; Po, pons.

Figure 4 .

 4 Figure 4.Post-hoc differences (z, Steel-dwass). Note the y-axis scale differs between parameters. Results of tests applied to (a) data from whole GM, WM masks (Significant differences of P < 0.008 marked with a bar and asterisk), and (b) sub-regions. Due to the number of comparisons between subregions, significant differences at Bonferroni-corrected level between a region (circle with dark grey interior) with other regions (full black circles) are indicated below each graph. Abbreviations: EcF, extracellular fraction; GM, grey matter; mM, millimolar; ms, milliseconds; TSC, total sodium concentrations; WM, white matter; Th, thalamus; Pu, putamen; Pa, pallidum; Ca, caudate; Cc, corpus callosum; Cb, cerebellar WM, Cs, centrum semiovale; Po, pons.

1 H

 1 3-6.3-13-19-25-31-54-89 ms; Run 2: 0.8-7-12-17-23-35-45-80 ms; Run 3: 2.3-9.7-15-21-28-40-66-100 ms). The three first subjects underwent an exam of 23 TEs across the same range (Run 1: 0.3-6.3-13-19-25-31-50-100 ms; Run 2: 2-7-12-17-23-40-45-80 ms; Run 3: 3-9-15-22-28-34-70 ms).Six cylinder tubes filled with 2% agar gel doped with a range of sodium concentrations (10-75 mM) were arrayed in the field of view in front of the subject's head as external references for quantitative assessment of brain sodium concentration. Foam cushions were used to immobilize and support the head as well as the external references.1 H-MRI was performed during the same session as[START_REF] Perman | Methodology of in vivo human sodium MR imaging at 1.5[END_REF] Na-MRI after a short pause to permit the changing of head coils. A high-resolution proton MRI 3D-MP2RAGE (TR = 5000 ms/TE = 3 ms/TI1 = 900 ms/TI2 = 2750 ms, 256 slices, 0.6 mm isotropic resolution, acquisition time = 10 min) was obtained using a 32-element (32Rx/1Tx) head coil (Siemens).

  ms ± 0.58(s.d.)) and T 2 * long (31.52 ms ± 11.45(s.d.)), with the longest observed in the centrum semiovale (T 2 * short : 4.37 ms ± 0.43(s.d.); T 2 * long : 54.74 ms ± 14.98(s.d.)). The centrum semiovale also evidenced a wide distribution of T 2 * long estimates between subjects.

T 2 * short (ms) T 2 * long (ms) Na SF (mM) Na LF (mM) TSC (mM) EcF

	GM	Mn s.d	4.99 0.41	31.51 1.78	21.16 0.87	25.75 2.97	46.92 2.83	0.18 0.02
	WM	Mn s.d	4.44 0.34	38.25 2.45	22.28 0.97	15.87 1.49	38.15 1.97	0.11 0.01
	Thalamus	Mn s.d	3.70 0.41	40.13 7.50	24.28 1.66	16.02 2.85	40.30 2.33	0.11 0.02
	Putamen	Mn s.d	3.72 0.61	32.66 7.00	23.04 2.82	13.25 3.19	36.29 1.76	0.09 0.02
	Pallidum	Mn s.d	2.82 0.44	31.62 6.87	21.99 2.08	11.25 2.62	33.24 2.62	0.08 0.02
	Caudate	Mn s.d	4.00 0.61	34.79 6.37	19.26 2.10	17.80 2.95	37.06 2.09	0.13 0.02
	Corpus Callosum	Mn s.d	3.48 0.42	39.82 9.16	19.57 3.30	15.96 4.87	35.52 3.35	0.11 0.03
	Cerebellar WM	Mn s.d	3.57 0.81	35.51 7.26	16.29 2.34	12.31 2.35	28.60 2.88	0.09 0.02
	Centrum Semiovale	Mn s.d	4.37 0.43	54.74 14.98	23.93 2.83	8.46 1.68	32.39 2.74	0.06 0.01
	Pons	Mn s.d	2.43 0.58	31.52 11.45	13.19 3.68	11.99 3.53	25.18 3.17	0.09 0.03

Table 1 .

 1 Mean

(Mn) and standard deviation (s.d) for each dependant variable for each tissue type and region. EcF, extracellular; GM, grey matter; TSC, total sodium concentration. WM, white matter.

Table 2 .

 2 Significant (P < 0.008) main effects (F). Results of ANOVAs applied to a) data from whole GM, WM masks and b) sub-regions. Numbers in brackets indicate degree of freedom. Non-significant main effects indicated by a dash (-). EcF; extracellular fraction; TSC, total sodium concentration.

	)	Age (1)

  healthy subjects with no history of neurological or psychiatric illness provided informed consent and were enrolled in the protocol, as approved by the local Ethics Committee (Comité de Protection des Personnes sud Méditerranée 1). All methods were performed in accordance with the relevant guidelines and regulations. Due to excessive movement in one subject, the final sample consisted of n = 13 subjects (5 female) (mean age: 23.9 ± 3.6 (s.d.) years, range: 20-32).

SCiEnTifiC RepoRTS | (2018) 8:4357 | DOI:10.1038/s41598-018-22711-0 www.nature.com/scientificreports

SCiEnTifiC RepoRTS | (2018) 8:4357 | DOI:10.1038/s41598-018-22711-0

Acknowledgements

This work was supported by the ANR grant JCJC 'NEUROintraSOD-7T' (ANR-15-CE19-0019-01) as well as the Equipex 7T-AMI (ANR-11-EQPX-0001) and A*midex 7T-Amistart (ANR-11-IDEX-0001-02) programs.

Data Availability. Generated datasets are available on reasonable request from the corresponding author.

Author Contributions

B.R., M.B., J-P.R. and W.Z. designed the experiments. A.N. and M.B. implemented the multi-echo sequence in the Siemens scanner. B.R., M.B., S.B., P.V., J.V., J.-P.R. and W.Z. contributed to the acquisition, processing and analysis of data. B.R., A.N., M.B., A.M. J.-P.S., S.G., J.V., P.V., M.G., J.-P.R. and W.Z. interpreted the results and contributed to the final manuscript. All authors reviewed the manuscript.

Additional Information

Competing Interests: The authors declare no competing interests.

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