Andreea Hertanu

Lucas Soustelle

Julie Buron

Julie Le Priellec

Myriam Cayre

Arnaud Le Troter

Gopal Varma

David C Alsop

Pascale Durbec

Olivier M Girard

Guillaume Duhamel
email: guillaume.duhamel@univ-amu.fr

T 1D -weighted ihMT imaging -Part II. Investigating the long and short T 1D components correlation with myelin content. Comparison with R 1 and the macromolecular proton fraction (MPF)

Keywords: ihMT T 1D -filtering, long T 1D components, short T 1D components, myelin specificity, myelin microscopy imaging

de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

INTRODUCTION

Myelination and demyelination mechanisms in the central nervous system (CNS) are a hallmark of aging and pathology. High specificity and sensitivity imaging tools are essential for an early detection of the variations in myelin content. The versatility of MRI has endowed the neuroscience community with numerous non-invasive MR markers sensitive to a variety of biophysical mechanisms and tissue microstructural features. In particular, the myelin sheath, composed of 40% of water and 60% of dry mass containing a high proportion of lipids [START_REF] Morell | Characteristic Composition of Myelin[END_REF], can be characterized by quantitative MRI measures probing both the water and the macromolecular components [START_REF] Mancini | The quest for measuring myelin with MRI -An interactive meta-analysis of quantitative comparisons with histology[END_REF][START_REF] Piredda | Probing myelin content of the human brain with MRI: A review[END_REF][START_REF] Van Der Weijden | Myelin quantification with MRI: A systematic review of accuracy and reproducibility[END_REF][START_REF] Lazari | Can MRI measure myelin? Systematic review, qualitative assessment, and metaanalysis of studies validating microstructural imaging with myelin histology[END_REF][START_REF] Weiger | Advances in MRI of the myelin bilayer[END_REF].

While the issue of sensitivity has been addressed in multiple studies, the specificity to myelination of various quantitative and semi-quantitative MR metrics remains an open question.

The macromolecular proton fraction (MPF) [START_REF] Yarnykh | Pulsed Z-spectroscopic imaging of cross-relaxation parameters in tissues for human MRI: Theory and clinical applications[END_REF] is a quantitative metric derived from the binary spin-bath model for MT [START_REF] Yeung | Transient Decay of Longitudinal Magnetization in Heterogeneous Spin Systems under Selective Saturation. IV. Reformulation of the Spin-Bath-Model Equations by the Redfield-Provotorov Theory[END_REF][START_REF] Morrison | Modeling magnetization transfer for biological-like systems using a semi-solid pool with a super-Lorentzian lineshape and dipolar reservoir[END_REF], exhibiting a higher sensitivity to pathologically induced variations than the classical MT ratio according to preclinical [START_REF] Rausch | Characterization of white matter damage in animal models of multiple sclerosis by magnetization transfer ratio and quantitative mapping of the apparent bound proton fraction f[END_REF][START_REF] Underhill | Fast bound pool fraction imaging of the in vivo rat brain: Association with myelin content and validation in the C6 glioma model[END_REF][START_REF] Khodanovich | Histological validation of fast macromolecular proton fraction mapping as a quantitative myelin imaging method in the cuprizone demyelination model[END_REF] and clinical Multiple Sclerosis (MS) [START_REF] Yarnykh | Fast Whole-Brain Three-dimensional Macromolecular Proton Fraction Mapping in Multiple Sclerosis[END_REF] measurement involves the acquisition of multiple MT-weighted images sampling a large number of offset frequencies and powers with regards to the preparation pulse in spoiled gradient echo (SPGR) sequences. However, the latest techniques for quantitative MT (qMT) allow the estimation of 3D MPF maps in a relatively short acquisition time (single-point qMT) [START_REF] Yarnykh | Fast Whole-Brain Three-dimensional Macromolecular Proton Fraction Mapping in Multiple Sclerosis[END_REF][START_REF] Yarnykh | Fast macromolecular proton fraction mapping from a single off-resonance magnetization transfer measurement[END_REF][START_REF] Yarnykh | Scan-Rescan Repeatability and Impact of B 0 and B 1 Field Nonuniformity Corrections in Single-Point Whole-Brain Macromolecular Proton Fraction Mapping[END_REF][START_REF] Soustelle | Correlations of quantitative MRI metrics with myelin basic protein (MBP) staining in a murine model of demyelination[END_REF][START_REF] Soustelle | Determination of optimal parameters for 3D single-point macromolecular proton fraction mapping at 7T in healthy and demyelinated mouse brain[END_REF].

The longitudinal relaxation rate (R 1 ) provides the basis for the most common contrast used in clinical routine. Besides the high dependence of in vivo R 1 quantification on the employed measurement technique [START_REF] Stikov | On the accuracy of T1 mapping: Searching for common ground[END_REF], additional controversies are linked to the dominant factor influencing the R 1 contrast. While some publications show a clear relationship between iron deposition and R 1 [START_REF] Ogg | Age-related changes in Brain T1 are correlated with iron concentration[END_REF][START_REF] Vymazal | The quantitative Relation Between T1-Weighted and T2-Weighted MRI of Normal gray Matter and iron concentration[END_REF], other studies suggest a greater and more significant contribution from macromolecules [START_REF] Stüber | Myelin and iron concentration in the human brain: A quantitative study of MRI contrast[END_REF][START_REF] Rooney | Magnetic field and tissue dependencies of human brain longitudinal 1H2O relaxation in vivo[END_REF]. Nonetheless, R 1 is shown to be a good predictor of the macromolecular tissue volume of the in vivo brain throughout the whole lifespan [START_REF] Yeatman | Lifespan maturation and degeneration of human brain white matter[END_REF] and allows differentiation between cortical layers [START_REF] Lutti | Using high-resolution quantitative mapping of R1 as an index of cortical myelination[END_REF]. In addition to macromolecules [START_REF] Manning | Understanding aqueous and non-aqueous proton T1 relaxation in brain[END_REF] and paramagnetic ions [START_REF] Lauffer | Paramagnetic metal complexes as water proton relaxation agents for NMR imaging: theory and design[END_REF], R 1 is also sensitive to tissue hydration [START_REF] Filo | Disentangling molecular alterations from water-content changes in the aging human brain using quantitative MRI[END_REF] and protein content [START_REF] Zhong | Quantitative studies of hydrodynamic effects and cross-relaxation in protein solutions and tissues with proton and deuteron longitudinal relaxation times[END_REF].

Inhomogeneous magnetization transfer (ihMT) [START_REF] Varma | Magnetization transfer from inhomogeneously broadened lines: A potential marker for myelin: Magnetization Transfer from Inhomogeneously Broadened Lines[END_REF] is an MRI technique, weighted by T 1D, the dipolar order relaxation time [START_REF] Varma | Dynamics of phosphate head groups in biomembranes. Comprehensive analysis using phosphorus-31 nuclear magnetic resonance lineshape and relaxation time measurements[END_REF], an endogenous source of contrast driven by slow molecular dynamics and tissue microstructure (31,[START_REF] Annabestani | Dipolar Relaxation Mechanism of Long Lived States in Methyl Groups[END_REF]. The sensitivity of ihMT to myelinated tissues [START_REF] Girard | Magnetization transfer from inhomogeneously broadened lines (ihMT): Experimental optimization of saturation parameters for human brain imaging at 1.5 Tesla: Optimizing Saturation Parameters for ihMT Brain Imaging at 1.5T[END_REF][START_REF] Girard | Magnetization transfer from inhomogeneously broadened lines (ihMT): Improved imaging strategy for spinal cord applications: ihMT for Spinal Cord Applications[END_REF][START_REF] Mchinda | Whole brain inhomogeneous magnetization transfer (ihMT) imaging: Sensitivity enhancement within a steady-state gradient echo sequence: Whole Brain Inhomogeneous Magnetization Transfer (ihMT)[END_REF][START_REF] Ercan | Microstructural correlates of 3D steady-state inhomogeneous magnetization transfer (ihMT) in the human brain white matter assessed by myelin water imaging and diffusion tensor imaging: Ercan et al[END_REF][START_REF] Geeraert | A multiparametric analysis of white matter maturation during late childhood and adolescence[END_REF] and myeloarchitectonic mapping [START_REF] Munsch | Characterization of the cortical myeloarchitecture with inhomogeneous magnetization transfer imaging (ihMT)[END_REF] was validated in studies on healthy subjects, and for the characterization of myelin pathology in MS patients [START_REF] Van Obberghen | Evaluation of the Sensitivity of Inhomogeneous Magnetization Transfer (ihMT) MRI for Multiple Sclerosis[END_REF][START_REF] Rasoanandrianina | Region-specific impairment of the cervical spinal cord (SC) in amyotrophic lateral sclerosis: A preliminary study using SC templates and quantitative MRI (diffusion tensor imaging/inhomogeneous magnetization transfer)[END_REF]. A previous study comparing ihMT with histology [START_REF] Duhamel | Validating the sensitivity of inhomogeneous magnetization transfer (ihMT) MRI to myelin with fluorescence microscopy[END_REF] on genetically modified plp-GFP (proteolipid protein -Green Fluorescence Protein) mice highlighted the impact of distinct T 1D -filtering strategies on the sensitivity and the specificity of ihMT to healthy myelinated tissues. As shown in Part I, high RF power and low duty-cycle ihMT preparations are sensitive to at least two T 1D components. While high-pass T 1Dfilters can be used to adjust the signal contribution of long T 1D components (> 1 ms) to the total ihMT signal, sensitivity to the short component is achieved by linear combinations of data with different switching times, e.g., to produce an ihMT bandpass T 1D -filter in the 100 µs to 1 ms range. These filtering strategies inform on studies of microstructural correlates in healthy myelinated tissues using the corresponding ihMT images.

The aim of this work was thus to evaluate the specificity of ihMT high-pass and bandpass T 1D -filters to myelination and compare it to that of MPF and R 1 . In addition to ihMTR, ihMTsat metrics compensated for R 1 relaxation effects and B 1 + inhomogeneity effects arising from the excitation pulses were computed. The specificity to myelination was evaluated based on the estimated intercept and slope values [START_REF] Duhamel | Validating the sensitivity of inhomogeneous magnetization transfer (ihMT) MRI to myelin with fluorescence microscopy[END_REF] from linear regressions between the MR metrics and myelin quantifications using two microscopy measurements: plp-GFP fluorescence intensity signal and the LFB (Luxol Fast Blue) optical density.

METHODS

Animal experiments

Animal studies were conducted in agreement with the French guidelines for animal care from the French Department of Agriculture (Animal Rights Division), the directive Sixteen C57Bl/6J control mice were scanned in vivo at 10 weeks of age. Among them, 6 genetically modified mice expressing the green fluorescent protein (GFP) under the control of the Plp promoter which drives the expression of a major myelin component in the CNS -the proteolipid protein (PLP) [START_REF] Greer | Myelin proteolipid protein-the first 50 years[END_REF] were sacrificed after the MR scans and analyzed by microscopy.

During scans under isoflurane anesthesia (1.5%, constant flow, 300 mL/min; Univentor 400 anesthesia unit, Zejtun, Malta), animal respiratory rate and temperature were monitored (SA Instruments, Stony Brook, NY, USA). Respiration was maintained at 100 ± 10 breaths-per-minute using minor adjustments to the isoflurane concentration.

Temperature was maintained at 37.5 ± 0.5 °C using a heating blanket connected to a water bath system.

Quantitative MR protocol and image processing

MR experiments were performed on a preclinical 7T scanner (Bruker PharmaScan, Ettlingen, Germany), using a 72-mm body volume coil and a four-channel phased array receive-only MRI CryoProbe (Bruker, Ettlingen, Germany) for RF transmission and RF reception, respectively.

R 1 maps

Variable Flip Angle VFA-SPGR sequences (TE/TR = 2.2/30.0 ms, TA = 9 mins 30 s) for R 1 quantification were acquired using FAs of 6°, 10°, and 25°. Data were fit to the Ernst equation [START_REF] Chang | Linear least-squares method for unbiased estimation of T 1 from SPGR signals[END_REF] to estimate voxel-wise the R 1 values corrected for B 1 + deviations.

Single-point MPF maps

An MT-prepared SPGR sequence (TE/TR = 2.2/30.0 ms, TA = 3 mins 10 s) was performed using a 10.25 ms off-resonance gaussian pulse for saturation with an offset frequency of 6 kHz and a flip angle of 600° (corresponding B 1peak = 9.1 µT and B 1rms = 5.0 µT) [START_REF] Soustelle | Determination of optimal parameters for 3D single-point macromolecular proton fraction mapping at 7T in healthy and demyelinated mouse brain[END_REF]. According to the single-point strategy, the two-pool model for MT with optimal constrained parameters (17) was used to estimate MPF maps with B 1 + correction. The VFA-SPGR acquisition at FA = 10° was used as a reference image. 3 , cartesian centric-out in the RAGE partition). IhMT images were calculated from the difference between the single and the dual-frequency offset MT images. The latter were obtained either with cosine-modulated pulses (dual-frequency switching time virtually corresponding to t = 0.0 ms and referenced hereafter as t 0.0 ), either with frequency-alternating pulses and t = 0.8 ms, and t = 3.2 ms (referenced hereafter as t 0.8 and t 3.2 , respectively). Based upon the results of Part I, the selected t values led to ihMT high-pass T 1D -filters with increasing T 1D cutoff values. In addition, an ihMT bandpass T 1D -filter, isolating components within the 100 µs to 1 ms range, was obtained by subtracting ihMT images derived from the t 0.0 and t 0.8 configurations ( t 0.0 -t 0.8 ). For each configuration, a reference image with zero power saturation, MT 0 , was also acquired. IhMTR maps were calculated:

IhMTR maps

equation 1 𝑖ℎ𝑀𝑇𝑅 = (𝑀𝑇 + + 𝑀𝑇 -) -(𝑀𝑇 ± + 𝑀𝑇 ∓ ) 𝑀𝑇 0 F o r P e e r R e v i e

w

For SNR consideration, a total number of 6, 12, and 18 repetitions of MT + and MT ± images were acquired for the t 0.0 , t 0.8 , and t 3.2 respectively, leading to acquisition times of 8 mins 40 s, 11 mins 20 s, and 22 mins.

IhMTsat maps

IhMT metrics corrected for R 1 relaxation and B 1 + inhomogeneity effects on the readout excitation pulses (ihMTsat) were derived based on a strategy initially proposed for MT imaging [START_REF] Helms | High-resolution maps of magnetization transfer with inherent correction for RF inhomogeneity and T1 relaxation obtained from 3D FLASH MRI[END_REF], and more recently customized to the ihMTRAGE framework [START_REF] Munsch | Characterization of the cortical myeloarchitecture with inhomogeneous magnetization transfer imaging (ihMT)[END_REF].

Equations (A10) from Munsch et al. [START_REF] Munsch | Characterization of the cortical myeloarchitecture with inhomogeneous magnetization transfer imaging (ihMT)[END_REF] were used to derive the longitudinal magnetization at the first RAGE segment, taking into account all the events in the sequence (i.e., saturation and free precession periods, and readout pulses). The attenuation factor ( ), described under the hypothesis of a single instantaneous saturation (6.4 ms burst), was estimated using the Brent's root finding method for both single-and dual-offset saturations to derive ihMTsat.

Python-based wrappers are made available: 1) for R 1 and MPF maps calculation at: https://github.com/lsoustelle/SP_qMT_proc (hash cc210c2); 2) for ihMTsat maps calculation at: https://github.com/lsoustelle/ihmt_proc (hash 34bd8b3).

A diagram summarizing the acquired raw images and the processing steps required to build the R 1 , MPF, ihMTR and ihMTsat metrics is provided in Figure 1.

MR images quantification

ROI-wise analyses (MRI vs. microscopy)

ROI-wise analyses on each of the 6 plp-GFP mice at 3 bregma levels (+ 0.7 mm, -1.0 mm and -3.2 mm from bregma), corresponding to the microscopy slices, were performed for comparison between MR and microscopy metrics. ROI-based quantification was performed from the averaged values in seven structures (mCCmedial corpus callosum, INT -internal capsules, OPT -optical tract, TH -thalamus, CP -caudoputamen, CTX-cerebral cortex, and HIP -hippocampal region) for all MR and microscopy metrics.

Voxel-wise analyses (MPF vs. ihMT T 1D -filters)

A brain mask was generated from a hard thresholding procedure based on the MPF template image, and applied to all co-registered templates (ihMTR, ihMTsat, MPF and T 2 w). In order to eliminate the CSF contribution in view of whole-brain voxel-wise analyses, a 3-classes k-means clustering was performed using Atropos [START_REF] Avants | An Open Source Multivariate Framework for n-Tissue Segmentation with Evaluation on Public Data[END_REF] from ANTs based on the skull-stripped T 2 w template image. Voxels were then retrieved for each common slice of the ihMTR, ihMTsat and MPF templates. Analyses between MPF and ihMT metrics were done on the voxel-wise averaged metrics of the 16 mice. After in vivo MR experiments, the 6 plp-GFP mice were sacrificed (ketamine 150 mg/kg with xylazine 15 mg/kg) and intracardially perfused with a fixative of (4% paraformaldehyde). Mouse brains were then extracted, post-fixed for 2 h in 4% paraformaldehyde and cryopreserved overnight in 20% sucrose. Frozen brains were sectioned into 20 µm thick histological slices (Cryostat Leica CM305S) in the rostrocaudal direction at 3 different levels (+ 0.7 mm, -1.0 mm and -3.2 mm from bregma) for plp-GFP fluorescence and LFB optical density analyses. ROIs were manually placed on the microscopy images by two different observers (J.B. and M.C.) in the seven brain structures chosen for the ROI-wise MRI quantification, using a mouse brain atlas as reference.

Microscopy images quantification

Plp-GFP fluorescence

Six mouse brains were used for the plp-GFP fluorescence analysis. For each level, three slices were acquired using a Zeiss fluorescence microscope with a 5x objective and a fixed exposure time. Background noise was measured in the ventricles and subtracted. Analyses were performed using the ImageJ software (National Institutes of Health, Bethesda, MD) and the mean value in each of the seven structures was computed. The resulting signal was normalized, taking as a reference the signal in the internal capsules.

LFB optical density

Three mouse brains were used for the LFB staining analysis. Brain sections were postfixed in methanol for 2 mins at -20°C, then rinsed in ethanol/acetic acid (96/4) for 5 mins. Sections were then stained in LFB (Sigma-Aldrich) 0.1% diluted in ethanol/acetic acid during 3 h at 60°C. After a short rinse in ethanol 96%, sections were decolorized in lithium carbonate 0.05% for 1 min and rinsed in ethanol 70%. Finally, sections were dehydrated through increasing ethanol gradients (from 70% to 100%) and mounted in Eukitt (VWR). Pictures were taken with a Zeiss AxioImager microscope with a 5x objective and optical density was measured using ImageJ, as described by Khodanovich et al. [START_REF] Khodanovich | Histological validation of fast macromolecular proton fraction mapping as a quantitative myelin imaging method in the cuprizone demyelination model[END_REF]. Briefly, the mean intensity of the red channel was measured in RGB images as a quantity characterizing the complementary blue channel saturation. Background signal was also measured in the ventricle, and LFB optical density was calculated as follows: (1 -red mean intensity / background intensity).

Signals were normalized to the signal of the internal capsules.

Analyses and Statistics

MRI vs. microscopy

Mean and standard deviation values in the seven averaged ROIs from the three bregma levels of the 6 plp-GFP mice were used to evaluate the specificity of each MR metric and the sensitivity of ihMTR and ihMTsat configurations. The normality of data and that of residuals in regression analyses was assessed in JMP (v.16.0.0; SAS Institute, Cary, NC) using the Shapiro-Wilk test. Pearson's correlations and linear regressions were performed for a total of ten response variables (ihMT high-pass and bandpass T 1D -filters, MPF and R 1 ) and two predictor variables (normalized plp-GFP and LFB signal intensities).

Comparisons between the linear regression analyses

A one-way analysis of covariance (ANCOVA) with interaction in JMP was used to test for significance in differences between pairs of slopes and intercepts. Steiger's modification of Dunn and Clark's z approach [START_REF] Steiger | Tests for Comparing Elements of a Correlation Matrix[END_REF] and the Zou's confidence interval [START_REF] Zou | Toward using confidence intervals to compare correlations[END_REF] from the cocor package ( 52) for overlapping correlations based on dependent groups in R (v.1.4.1106; RStudio, PBC, Boston, MA, US) was used to test for significance in differences between pairs of correlation coefficients.

Two types of comparison analyses were performed. First, by considering the MR metrics as the common variable, we investigated whether the MR metrics behave significantly different when associated with plp-GFP or LFB signals. Second, by considering one of the microscopy metrics as the common variable, we investigated whether there is an MR metric that associates significantly better with each of the two microscopy references.

Specificity assessment

The specificity to myelin of all MR metrics (41) when referenced to either plp-GFP or LFB measurements was assessed as the fraction of MRI signal associated with myelin over the total signal, calculated as:

equation 2 𝑆𝑝𝑒𝑐𝑖𝑓𝑖𝑐𝑖𝑡𝑦 = 𝑠𝑙𝑜𝑝𝑒 * 𝑋 𝑚𝑎𝑥 𝑠𝑙𝑜𝑝𝑒 * 𝑋 𝑚𝑎𝑥 + 𝑌 𝑖 𝑡𝑒 𝑐𝑒𝑝𝑡
Where slope and Y_intercept are defined as the coefficients of the affine functions derived from the linear regression analyses. The Y_intercept is by definition the MRI signal measured in the absence of microscopy signal (i.e., for X = 0), and hence in the absence of myelin. The product slope*X max represents the maximum MRI signal corresponding to X max , the maximum of microscopy signal (and hence the maximum of myelin content). The product slope*X max thus corresponds to the fraction of ihMT signal associated to myelin. The specificity, as defined here, is thus relative to a reference anatomical structure, in this case, the internal capsules. Note that for the specificity calculation, the Y_intercept values were corrected for the offset corresponding to the values of MR metrics in pure water: 0.3 Hz for R 1 [START_REF] Taylor | Comparison of spin-lattice relaxation measurements made in the presence of strong radiation damping[END_REF] and 0.0% for the MT-based metrics.

Sensitivity assessment

Sensitivities were evaluated for ihMTR and ihMTsat metrics, respectively based on the slope values resulting from linear regression analyses with plp-GFP and LFB.

MPF vs. ihMT T 1D -filters

Pearson's correlations and linear regression analyses were performed between MPF and ihMT T 1D -filters (ihMTR and ihMTsat) voxel-wise quantifications for a total of 51 common slices in the template space. Pairs of correlation coefficients and intercepts for the ihMTR and ihMTsat configurations were tested for significant differences using a Kruskal-Wallis test with post-hoc pairwise comparisons.

RESULTS

MR templates for R 1 , MPF, ihMTR and ihMTsat at +0.7 mm, -1.0 mm, and -3.2 mm from bregma are presented in Figure 2 along with the corresponding plp-GFP intensity images. Qualitatively, R 1 showed a lower contrast between White Matter (WM) and Grey Matter (GM) tissues compared to ihMTR, ihMTsat and MPF. In addition, WM/GM contrast was qualitatively improved in the ihMTsat images as compared to ihMTR.

Quantification of all metrics in each of the segmented structures are reported in Supporting Information Table S1.

Plp-GFP vs. LFB

Linear regression and Pearson's correlation analyses between LFB and plp-GFP normalized signals (Figure 3) revealed a strong and significant correlation (r 2 = 0.83, p < 0.001) with a positive significant slope (1.12 ± 0.12, p < 0.001) and a non-significant intercept (-0.16 ± 0.09, p = 0.11).

MRI vs. microscopy analyses

Outcomes of the linear regressions between the MR metrics and the plp-GFP and LFB signals are shown in Table 1, along with the corresponding scatter plots in Figure 4.

Residuals followed a normal distribution according to the Shapiro Wilk test (p > 0.05).

Strong and significant correlation coefficients were obtained for ihMT high-pass T 1Dfilters (ihMTR ( t 0.0 , t 0.8, t 3.2 ) and ihMTsat ( t 0.0 , t 0.8, t 3.2 )) and MPF with regards to plp-GFP (r 2 0.79, p < 0.001) and LFB (r 2 0.87, p < 0.001). Lower but significant correlation coefficients corresponded to R 1 and the ihMT bandpass T 1D -filter. Estimated Y_intercept values were generally significantly different than zero (p < 0.05), except for the intercept of ihMTR ( t 3.2 ) and ihMTsat ( t 0.8 , t 3.2 ) when compared to plp-GFP. Globally, the specificity to myelination for the investigated MR metrics was higher for associations with plp-GFP than for associations with LFB except for the ihMT bandpass T 1D -filter, for which similar specificity was found when plp-GFP or LFB was used for association. The specificity of the ihMT high-pass T 1D -filters exhibited an increasing trend with increasing t, while ihMTsat specificity values were superior to those of ihMTR for all t values.

Comparisons between the linear regression analyses: MR metrics as the common variable

No significant differences were found between pairs of correlation coefficients and pairs of slopes when MR metrics were considered as the common variable, suggesting similar sensitivities of each MR metric to the two microscopy references. However, significant differences (p < 0.05) were found between pairs of intercept values for all the MR metrics, except for the ihMT bandpass T 1D -filter and R 1 (Supporting Information Table S2).

Comparisons between the linear regression analyses: microscopy metrics as the common variable

The significance of differences between pairs of overlapping correlation coefficients with either plp-GFP or LFB as the common variable are presented in Table 2.

Significant differences were generally found when comparing ihMT bandpass T 1D -filter or R 1 correlation coefficients with ihMT high-pass T 1D -filters or MPF correlation coefficients. For ihMT metrics, the significance of differences between pairs of intercepts and pairs of slopes with either plp-GFP or LFB as the common variable are presented in Table 3. Significant differences were noticed for comparisons between all F o r P e e r R e v i e w pairs of intercepts, except for comparisons between t 0.0 with t 0.0 -t 0.8 (ihMTR and ihMTsat) and t 0.8 with t 3.2 (ihMTR and ihMTsat) for associations with plp-GFP, and between t 0.8 and t 0.0 -t 0.8 (ihMTR and ihMTsat) for associations with LFB.

Differences between pairs of slopes were significantly different for all ihMTR and ihMTsat metrics (p < 0.05), except for comparisons between ihMTR ( t 0.0 -t 0.8 ) and ihMTR ( t 3.2 ) for associations with LFB or ihMTsat ( t 0.0 -t 0.8 ) with ihMTsat ( t 3.2 ) for associations with plp-GFP and LFB. Correlations of MPF with ihMT high-pass T 1D -filters (Figure 7a) were significant and strong (r 2 > 0.64, p < 0.001 for ihMTR, and r 2 > 0.72, p < 0.001 for ihMTsat) for all slices. Significant (p < 0.001) but lower and more dispersed correlations were obtained for the ihMT bandpass T 1D -filter. All estimated slope and intercept values were significantly different from zero (p < 0.001). Intercepts increased for increasing t, for ihMT high-pass T 1D -filters. Lowest intercept values were obtained for ihMT high-pass T 1D -filters with the lowest cutoff ( t 0.0 ) and for the ihMT bandpass T 1D -filter (Figure 7b).

MPF vs. ihMT T 1D -filters analyses

Examples of linear regression analyses are given in Supporting Information, figures S1 and S2.

DISCUSSION

Increasing the fraction of ihMT signal corresponding to long T 1D s enhances the specificity to myelination.

The assessment of the specificity was based on the evaluation of the intercept and slope values resulting from linear regression analyses between the MR metrics and the normalized signals of two microscopy references. In this approach, the intercept and slope values are competitive estimates. For the specificity to increase with the lengthening of t, the decrease in the intercept must be more important than the decrease in the slope. According to the results in Part 1, this is due to the disproportionate attenuation of long and short T 1D signals as t increases. High-pass T 1D -filters increase the fraction of ihMT signal corresponding to long T 1D s and reduce that of short T 1D s (Part I, Table 2), leading to an enhanced specificity to myelination.

The specificity dependence on t observed in this study for ihMT high-pass T 1D -filters is in agreement with previously reported results [START_REF] Duhamel | Validating the sensitivity of inhomogeneous magnetization transfer (ihMT) MRI to myelin with fluorescence microscopy[END_REF]. However, specificity values corresponding to the plp-GFP reference obtained here are generally higher compared to those reported by Duhamel et al. [START_REF] Duhamel | Validating the sensitivity of inhomogeneous magnetization transfer (ihMT) MRI to myelin with fluorescence microscopy[END_REF]. While a discrepancy arising from a calibration bias of the plp-GFP signal may not be excluded, several differences regarding the RF saturation parameters with a direct influence on the T 1D filtering mechanisms might [START_REF] Varma | In vivo measurement of a new source of contrast, the dipolar relaxation time, T 1 D , using a modified inhomogeneous magnetization transfer (ihMT) sequence: In Vivo Measurement of T 1D Using ihMT[END_REF] allowing us to maintain constant pulse power throughout all ihMT acquisitions. Thus, the sole effects of the switching time were consistently isolated, and the specificity was more accurately assessed and compared across ihMT variants. Furthermore, partial volume effects were approximately 13 times lower per voxel in the current work, and the mouse cohort investigated here was larger.

Short T 1D components are poorly correlated with myelin.

Since the intercept designates the value of a specific MR metric obtained for a null plp-GFP or LFB signal, it actually relates to the part of the MR signal corresponding to a non-myelin source. Interestingly, for associations with the plp-GFP signal, the t 0.0 configuration containing a high amount of signal originating from the short T 1D s (Part I, Table 2) had a slightly higher, but not significantly different intercept as compared to the band-pass T 1D -filter which mainly isolates the short T 1D s. As t increased, the fraction of signal corresponding to the short T 1D s diminished as compared to the fraction of signal corresponding to long T 1D s, and the intercept decreased as well. For example, the intercept of the t 3.2 configuration which had a higher signal contribution from the long T 1D s, was significantly different from the intercept of both of the t 0.0 and t 0.0 -t 0.8 configurations for associations with both plp-GFP and LFB signals. In addition, the r 2 correlation coefficient of the band-pass T 1D -filter was significantly lower than that of any of the high-pass T 1D -filters containing long T 1D s in various amounts. This allowed us to conclude that the non-myelin part of the ihMT signal is preferentially associated to the signal of short T 1D components. However, the source of the various T 1D s in in vivo tissues has still to be determined.

While some short T 1D s could also be present in myelin tissue, another important possible source could be the non-myelin macromolecules with a restrained movement, presumably associated with glial cells. For example, the fibrous astrocytes with elongated morphology and processes aligned with the myelinated fibers present in WM [START_REF] Lundgaard | White matter astrocytes in health and disease[END_REF], are a potential candidate for the short T 1D component. Further dedicated studies will however be required to confirm the precise nature of short T 1D non-myelin molecules revealed by the ihMT bandpass T 1D -filter.

IhMTsat improves the specificity of ihMT to myelination.

The correction for confounding B 1 + inhomogeneity and R 1 relaxation effects in the ihMT signal is vital for proper clinical studies, reproducibility, and multi-site comparisons.

Moreover, as shown in this study, the relative WM/GM contrast is qualitatively enhanced for ihMTsat and the specificity to myelination is considerably improved.

While various available approaches [START_REF] Helms | High-resolution maps of magnetization transfer with inherent correction for RF inhomogeneity and T1 relaxation obtained from 3D FLASH MRI[END_REF][START_REF] Helms | Modeling the influence of TR and excitation flip angle on the magnetization transfer ratio (MTR) in human brain obtained from 3D spoiled gradient echo MRI[END_REF][START_REF] Rowley | A model-based framework for correcting inhomogeneity effects in magnetization transfer saturation and inhomogeneous magnetization transfer saturation maps[END_REF] demonstrated their utility, the ihMTsat approach presented by Munsch et al. [START_REF] Munsch | Characterization of the cortical myeloarchitecture with inhomogeneous magnetization transfer imaging (ihMT)[END_REF] and implemented here has the advantage of a minimum number of assumptions.

MR metrics specificity is higher for associations with plp-GFP, than with LFB.

The two microscopy references investigated in this study led to non-identical specificity values for MR metrics and generally higher values for associations with plp-GFP (7% higher for MPF and higher than 11% for ihMT high-pass T 1D -filters). For R 1 and the ihMT bandpass T 1D -filter the difference in the absolute specificity values calculated with either plp-GFP or LFB was inferior to 5%. Additionally, for these metrics, linear regression analyses presented non-significant differences in the intercept and slope values for associations with plp-GFP and LFB, potentially suggesting a non-significant difference between specificities.

The distinct underlying sources of signal for the two microscopy references may explain the discrepancies between specificity values for MPF and ihMT high-pass T 1Dfilters. Lipids and proteins alike contribute to the MRI contrast [START_REF] Kucharczyk | The effect of phospholipid vesicles on the NMR relaxation of water: an explanation for the MR appearance of the neurohypophysis?[END_REF][START_REF] Mäkelä | Proton Exchange as a Relaxation Mechanism for T1 in the Rotating Frame in Native and Immobilized Protein Solutions[END_REF]), but disparate MT effects have been observed depending on the molecules. Increased MT effects were obtained for cerebrosides as a result of a higher number of exchangeable protons and greater accessibility to free water [START_REF] Yang | Magnetization transfer in liposome and proteoliposome samples that mimic the protein and lipid composition of myelin[END_REF]. Conversely, phospholipids with fewer exchangeable protons such as dimyristoylphosphatidylcholine (DMPC) and phosphatidylcholine (PC) were found to have reduced MT effects [START_REF] Yang | Magnetization transfer in liposome and proteoliposome samples that mimic the protein and lipid composition of myelin[END_REF][START_REF] Kucharczyk | Relaxivity and magnetization transfer of white matter lipids at MR imaging: importance of cerebrosides and pH[END_REF]. Although such studies only considered a limited number of myelin components, the lower specificity obtained for associations between the MT-derived metrics (ihMTR, ihMTsat, and MPF) and LFB might be explained by a lower sensitivity of MT effects to the presence of certain phospholipids, as opposed to the LFB quantifications [START_REF] Salthouse | Luxol Fast Blue Arn: A New Solvent Azo Dye with Improved Staining Qualities for Myelin and Phospholipids[END_REF][START_REF] Lycette | The Binding of Luxol Fast Blue Arn by Various Biological Lipids[END_REF]. For example, PC is a major lipid of biological membranes accounting for 12% of the myelin lipids in rodents [START_REF] Norton | Myelination in Rat Brain: Changes in Myelin Composition During Brain Maturation1[END_REF]. In addition, phospholipids present in the membrane of other neural cells, such as astrocytes [START_REF] Ansell | Functional Metabolism of Brain Phospholipids[END_REF], are also stained by LFB, thereby reducing the specificity of LFB for the myelin membrane.

On the other hand, transgenic mice expressing the green fluorescent protein driven by the proteolipid protein gene promoter have been developed to investigate cells in the [START_REF] Spassky | The Early Steps of Oligodendrogenesis: Insights from the Study of the plp Lineage in the Brain of Chicks and Rodents[END_REF][START_REF] Bras | Oligodendrocyte development in the embryonic brain: the contribution of the plp lineage[END_REF], offering a high specificity to mature oligodendrocytes in the adult brain [START_REF] Ferent | Investigation of the proteolipid protein promoter activity during demyelination and repair[END_REF] and thus a more specific biomarker for the myelin membrane.

MPF is weighted toward short T 1D components.

MPF quantifications in the various ROIs are consistent with previously reported results using the single-point method [START_REF] Soustelle | Determination of optimal parameters for 3D single-point macromolecular proton fraction mapping at 7T in healthy and demyelinated mouse brain[END_REF]. The extrapolated specificity of MPF calculated with the slope and intercept values reported by Khodanovich et al. [START_REF] Khodanovich | Histological validation of fast macromolecular proton fraction mapping as a quantitative myelin imaging method in the cuprizone demyelination model[END_REF] for associations with LFB on C57BL/6 healthy mice is higher by 15% as compared to the specificity in our study (66% vs. 51%). Both intercept and slope values are lower in our study. A lower number of data points for the linear regression analyses in this study combined with microscope calibration biases and a different staining and storage procedure of the brain slices might explain this difference.

Generally, the lower specificity of MPF to myelination can be explained by the underlying sensitivity of the saturation efficacy in z-spectrum analyses. Although dipolar order effects were shown to have moderate to significant impact on the accuracy of MT data fitting depending on the investigated tissue [START_REF] Morrison | Modeling magnetization transfer for biological-like systems using a semi-solid pool with a super-Lorentzian lineshape and dipolar reservoir[END_REF][START_REF] Sled | Quantitative Interpretation of Magnetization Transfer in Spoiled Gradient Echo MRI Sequences[END_REF], the binary spinbath model used for MPF estimation does not consider any dipolar order contribution. This has particularly problematic consequences. Long RF pulses with low instantaneous power as used in MT-prepared SPGR sequences are inefficient in creating dipolar order effects with regards to the short T 1D components. The saturation of the corresponding Zeeman pools is therefore not altered, and the MT effects of the short T 1D components are well modeled by the two-pool model. Conversely, for longer These observations are further confirmed by the voxel-wise regression analyses between MPF and ihMT. The lowest intercept values and thus the ihMT configurations the closest to being in a direct proportionality relationship with MPF correspond to ihMT ( t 0.0 ), the signal of which is weighted by short T 1D components and ihMT ( t 0.0 -t 0.8 ), which specifically isolates short T 1D s.

Thereupon, the effects of dipolar interactions on the MPF estimations in in vivo brain tissues and for the experimental scenarios used here should be considered in the future. Alternatively, cosine-modulated RF saturation pulses, which decouple Zeeman and dipolar order pools, should be employed for MPF estimations when using the classical binary-spin bath model. In terms of sensitivity, R 1 , MPF, and to a lesser extent the t 0.0 ihMT configuration offer the best SNR performance and are also moderately to strongly correlated to myelination (r 2 = 0.67 for R 1 and > 0.8 for MPF and ihMT). Unfortunately, these are also the least specific metrics due to a non-negligible contribution from non-myelin tissue to their signal, reflected by the high Y_intercept values. Almost all the investigated MR metrics have non-zero Y_intercept, which is not surprising since macromolecules other than myelin contribute to T 1 relaxation, the MPF size, and the dipolar order exists in other macromolecules as well. An accurate estimation of each metric in non-myelin neuronal tissue would allow compensating for the non-zero Y_intercept, but this is not an easy task and could be further complicated in the case of pathology.

In this context, a great advantage of ihMT over the other metrics is that there is no need to accurately quantify and correct for the signal of non-myelin neuronal tissue to improve the specificity. A better myelin selectivity can be achieved through the lengthening of t, and hence for specificity purpose, ihMT high-pass T 1D -filters ( t 0.8 ms) are very good candidates although they have lower SNR. The group standard deviation of ihMTR values in the seven investigated ROIs (Table S1) represents in average less than 7% of the mean ihMTR value for t 0.0 but more than 17% for t 3.2 .

Lengthening t over 3.2 ms would probably induce a prohibitive SNR for accurate specificity measurements. Here, the minimum SNR obtained for t 3.2 (isolating mainly long T 1D s) and the bandpass T 1D -filter (isolating mainly short T 1D s) was high enough to accurately demonstrate a higher specificity of t 3.2 than that of the bandpass T 1D -filter by more than 1.5 standard errors.

Regarding the computational simplicity (Figure 1), ihMTR is the only metric derived from a simple combination of the raw images. Other metrics require a more advanced knowledge of their respective model, hence complicating their derivation. In terms of acquisition time, ihMTR ( t < 3.2 ms) and R 1 required less than 12 minutes, while ihMTR ( t 3.2 ) and MPF required more than 15 minutes. These acquisition times might appear too long from a clinical perspective, but they are in line with typical preclinical acquisition times for parametric imaging with a 100 µm in-plane resolution. Moreover, in clinical applications, the nominal resolution is lower (~1.5 -2 mm), and the degree of myelination is higher (leading to higher ihMTR values), thus the ihMT high-pass T 1D filters strategies are routinely feasible ( t = 0.0 ms (47) and t > 0.0 ms [START_REF] Mchinda | Whole brain inhomogeneous magnetization transfer (ihMT) imaging: Sensitivity enhancement within a steady-state gradient echo sequence: Whole Brain Inhomogeneous Magnetization Transfer (ihMT)[END_REF]).

To summarize, the higher sensitivity of R 1 , MPF and the t 0.0 high-pass T 1D -filter (ihMTR/ihMTsat) can be advantageously used for the general characterization of diseases for which myelin alterations are part of the pathological processes. On the other hand, high-pass T 1D -filters with long t values should be preferred to investigate whether myelin is specifically altered in pathologies.

Limitations

First, an important limitation in the assessment of the specificity in the current study was the lower spatial resolution of the MR slices (750 µm) as compared to that of the microscopy slices (20 µm). To partially overcome this issue, three slices of 20 µm were sampled inside the corresponding MR slice thickness of 750 µm and the resulting signals were averaged. Second, the specificity as defined here is not an absolute measure, but rather a relative estimation referenced to the signal of a known highly myelinated structure (internal capsules). Normalization to another structure with a higher degree of myelination may yield slightly different specificity values. Finally, for a more comprehensive qualitative and quantitative analysis on the specificity of different MR metrics, future studies should comprise a larger number of microscopy markers including antibodies for other myelin specific proteins, lipid dyes or even more advanced techniques such as Coherent Anti-Stokes Raman Spectroscopy (CARS) [START_REF] Yu | Shedding new light on lipid functions with CARS and SRS microscopy[END_REF] which can be tuned to the specific vibrational frequency of methylene groups present along the lipid chains. Comparison with other MR metrics putatively sensitive to myelin but whose contrast rely on different mechanisms, e.g., Myelin Water Fraction, should also be performed [START_REF] Mackay | Magnetic Resonance of Myelin Water: An in vivo Marker for Myelin Zalc B[END_REF].

CONCLUSIONS

The specificity to myelination of ihMT high-pass and bandpass T 1D -filters, MPF and R 1 was assessed using two histological reference techniques for myelin imaging.

Lengthening of the t leads to an increase in the fraction of signal corresponding to long T 1D s and thus provided higher specificities to myelination for ihMT high-pass T 1Dfilters, albeit at the cost of lower sensitivity. The correction for T 1 /B 1 effects allowed us to further enhance the specificity of ihMT to myelination and generate images with higher WM/GM contrast. The ihMT bandpass T 1D -filter, which isolates the short T 1D components (< 1 ms) whose nature will require future dedicated studies, provided lower specificity values.

Additionally, an important contribution of short T 1D components to the MPF estimation can explain the lower specificity of MPF to myelination as compared to the ihMT highpass T 1D -filters.

Future studies with ihMT T 1D -filters would be of particular interest when analyzing ihMT signal variations in pathological brain conditions. As T 1D is sensitive to membrane organization (31), the myelin structural transformation occurring in some diseases (e.g., loss of the normal compact multilamellar structure observed in MS ( 72)) might induce changes on the short and long T 1D components, and hence modify the ihMT signal in the brain. Thus, ihMT bandpass and high-pass T 1D -filters with properly adjusted T 1D cutoff values could determine the ranges of T 1D components affected by the pathological processes. Coefficients significantly different than zero (p-value < 0.05) are represented by the asterisk symbol (*). The specificity estimation of R 1 ( † ), for which the Y_intercept was corrected with the value of the metric in pure water measured at room temperature [START_REF] Taylor | Comparison of spin-lattice relaxation measurements made in the presence of strong radiation damping[END_REF] might be slightly overestimated due to the higher in vivo temperature. for ihMTsat (left) and ihMTR (right) when either plp-GFP (above the main diagonal) and LFB (below the main diagonal) was considered as the common variable. The acquisition time for each MR sequence was: 4 mins 32 s for qMT; 9 mins 30 s for VFA; 1 min 59 s for AFI and 1 min 40 s for ihMTR. In the context of this study, the acquisition time necessary for the derivation of each metric was: 11 mins 29 s for R 1 , 16 mins 01s for MPF, 8 mins 40 s for ihMTR ( t 0.0 ) and 20 mins 9s for ihMTsat ( t 0.0 ), 11 mins 20 s for ihMTR ( t 0.8 ) and 22 mins 49 s for ihMTsat ( t 0.8 ), 22 mins for ihMTR ( t 3.2 ) and 33 mins 29 s for ihMTsat ( t 3.2 ). The increasing time of ihMTR/ihMTsat as t is lengthened is due to an increasing number of averages of the raw MTw images.

F

Figure Captions

Main document

IhMTR and B 1 maps were generated by direct computation, whereas R 1 , ihMTsat and MPF maps were generated via model fitting. The corresponding t 0.0 , t 0.8 , MPF, and t 0.0 -t 0.8 images in the signal ranges [0%, 23%], [0%, 15%], [0%, 10%], and [0%, 10%] respectively, are illustrated.

Supporting Information Figure S2: Example of linear regression analyses between

MPF and ihMTsat voxel-wise quantifications (MPF signal = Y_intercept + ihMTsat signal * slope) on six different slices from the caudal to the rostral part of the brain (a to f). The corresponding t 0.0 , t 0.8 , MPF, and t 0.0 -t 0.8 images in the signal ranges [0%, 23%], [0%, 15%], [0%, 10%], and [0%, 10%] respectively, are illustrated.

F o r P e e r R e v i e w

  /EU of the European Parliament and of the Council of 22 September 2010 and approved by our institutional committee on Ethics in animal research (Comité d'Ethique de Marseille n°14, project authorization APAFIS#1747-2015062215062372v6).

  After positioning in the magnet isocenter, a field map-based shimming (acquisition time 1 min 22 s) was performed to optimize B 0 field homogeneity over the entire mouse brain.Structural T 2 -weighted (T 2 w) images were acquired using a 2D multi-slice RARE sequence (RARE factor = 8, TE/TR = 32/5030 ms, matrix size 256x256, in-plane voxel size 78x78 µm 2 , slice thickness 300 µm, 49 slices covering the whole brain, acquisition time TA = 5 mins 22 s). B 1 + mapping was performed with the Actual Flip Angle imaging (AFI) method[START_REF] Yarnykh | Actual flip-angle imaging in the pulsed steady state: A method for rapid threedimensional mapping of the transmitted radiofrequency field[END_REF][START_REF] Nehrke | On the steady-state properties of actual flip angle imaging (AFI): Steady-State Properties of AFI[END_REF] (TE/TR 1 /TR 2 = 2/15/60 ms, matrix size 48x48x44, 400x400x750 µm 3 , FA = 60°, TA = 1 min 59 s) on the whole mouse brain.

  weighted ihMT images were acquired with the sequence presented in Part 1 and the protocol described in Part I. In brief, slab-selective 3D low duty-cycle[START_REF] Mchinda | Whole brain inhomogeneous magnetization transfer (ihMT) imaging: Sensitivity enhancement within a steady-state gradient echo sequence: Whole Brain Inhomogeneous Magnetization Transfer (ihMT)[END_REF][START_REF] Varma | Low duty-cycle pulsed irradiation reduces magnetization transfer and increases the inhomogeneous magnetization transfer effect[END_REF] ihMTRAGE (47) sequences were acquired with different dual-frequency offset switching times ( t) (Saturation: 15 bursts of N p = 8 Hann-shaped pulses, pulse duration pw = 0.5 ms, B 1peak =42.4 µT, offset frequency f = 10 kHz, burst repetition time BTR = 60 ms, total saturation time = 900 ms, corresponding root-mean-squared saturation power calculated over the total saturation time B 1RMS SAT = 6.7 µT and RF duty-cycle DC = 6.7%. Readout: TE/TR = 2.1/2200.0 ms, matrix size 192x192x8, voxel size 100x100x750 µm

  of ihMTR, ihMTsat, MPF and R 1 were constructed and registered in the same reference as the T 2 w templates. A comprehensive description of the template construction from the individual images of the 16 mice, and the segmentation of Regions-of-Interest (ROIs) is provided in the appendix of Part I.

Figure 5 and

 5 Figure 5 and Figure 6 represent the distribution of ihMT high-pass and bandpass T 1D -

  in our results. The main advantage of this work consisted of the use of a modified version of ihMT

T

  1D components, the RF pulses generate dipolar order effects, which alter the corresponding Zeeman pool saturation, but are not considered by the two-pool model.The MT effects of long T 1D components are thus not appropriately modeled. The estimated MPF derived from the classical binary spin-bath model is therefore preferably weighted toward short T 1D components, associated with a low specificity to myelination.

R 1 ,

 1 MPF and ihMT: practical considerations for myelin imaging.

From a clinical point

  of view, the ideal technique for myelin imaging should be highly sensitive and specific, have a straightforward computation and relatively short acquisition time. None of the techniques investigated in this work meets all the criteria.

Table 1 :

 1 Results of linear regression analyses between the MR metrics with the two microscopy references (MR signal = Y_intercept + Normalized plp-GFP Signal * slope and MR signal = Y_intercept + Normalized LFB Signal * slope). The values of the Yintercept, slope and specificity are presented as estimated value ± standard error.

  Significant p-values (p-value < 0.001 and p-value < 0.05) are accompanied by the asterisk symbol (*).

Figure 1 :

 1 Figure 1: Diagram summarizing the acquisition and processing steps from the raw

Figure 2 :

 2 Figure 2: Templates of MR metrics and the corresponding fluorescence images at

Figure 3 :

 3 Figure 3: Linear regression analysis between the LFB and plp-GFP normalized signals.

Figure 4 :

 4 Figure 4: Linear regression analyses between the MR metrics with the plp-GFP

Figure 5 :

 5 Figure 5: Bivariate histograms for MPF and ihMTR t 0.0 (a, f, k), MPF and ihMTR t 0.8

Figure 6 :

 6 Figure 6: Bivariate histograms for MPF and ihMTsat t 0.0 (a, f, k), MPF and ihMTsat

Figure 7 :

 7 Figure 7: Plots of (a) r 2 correlation coefficients and (b) intercepts for the linear

Table 1 :Figure 1 :

 11 Figure 1: Diagram summarizing the acquisition and processing steps from the raw images to the final quantitative and semi-quantitative metrics investigated in this study. The acquisition time for each MR sequence was: 4 mins 32 s for qMT; 9 mins 30 s for VFA; 1 min 59 s for AFI and 1 min 40 s for ihMTR. In the context of this study, the acquisition time necessary for the derivation of each metric was: 11 mins 29 s for R 1 , 16 mins 01 s for MPF, 8 mins 40 s for ihMTR ( t 0.0 ) and 20 mins 9 s for ihMTsat ( t 0.0 ), 11 mins 20 s for ihMTR ( t 0.8 ) and 22 mins 49 s for ihMTsat ( t 0.8 ), 22 mins for ihMTR ( t 3.2 ) and 33 mins 29 s for ihMTsat ( t 3.2 ). The increasing time of ihMTR/ihMTsat as t is lengthened is due to an increasing number of averages of the raw MT w images. IhMTR and B 1 maps were generated by direct computation, whereas R 1 , ihMTsat and MPF maps were generated via model fitting. 175x102mm (300 x 300 DPI)

Figure 2 :

 2 Figure 2: Templates of MR metrics and the corresponding fluorescence images at three levels of bregma (+ 0.7 mm, -1.0 mm, and -3.2 mm from bregma). The seven segmented ROIs are indicated by red arrows on the plp-GFP and the T 2 -weighted images. 146x241mm (600 x 600 DPI)

Figure 3 :

 3 Figure 3: Linear regression analysis between the LFB and plp-GFP normalized signals. 86x67mm (600 x 600 DPI)

Figure 4 :

 4 Figure 4: Linear regression analyses between the MR metrics with the plp-GFP normalized signal (a -d) and the LFB normalized signal (e-h). One data point corresponds to the ROI average of one structure from one mouse.130x241mm (300 x 300 DPI)

Figure 5 :

 5 Figure 5: Bivariate histograms for MPF and ihMTR Δt 0.0 (a, f, k), MPF and ihMTR Δt 0.8 (b, g, l), MPF and ihMTR Δt 3.2 (c, h, m), MPF and Δt 0.0 -Δt 0.8 (d, i, n) for three different slices from the caudal to the rostral part of the brain (e, j, o). The bins were calculated with the Freedman-Diaconis rule. 120x240mm (300 x 300 DPI)

Figure 6 :

 6 Figure 6: Bivariate histograms for MPF and ihMTsat Δt 0.0 (a, f, k), MPF and ihMTsat Δt 0.8 (b, g, l), MPF and ihMTsat Δt 3.2 (c, h, m), MPF and Δt 0.0 -Δt 0.8 (d, i, n) for three different slices from the caudal to the rostral part of the brain (e, j, o). The bins were calculated with the Freedman-Diaconis rule. 119x240mm (300 x 300 DPI)

Figure 7 :

 7 Figure 7: Plots of (a) r 2 correlation coefficients and (b) intercepts for the linear regression analyses between voxel-wise MPF and ihMT metrics on the 51 common template slices. The mean value of the distribution of each coefficient in all investigated slices is represented by a black line, and the median value by a red line.The wider sections of the violin plot (73) represent a higher probability of the coefficients to take on the corresponding values represented on the x-axis. All the tested pairs were significantly different (p < 0.05), except for the comparisons accompanied by the corresponding non-significant p-values.165x241mm (600 x 600 DPI)

  studies. Standard methodology for MPF

	F
	o r
	P
	e e r
	R e v
	i e w

  73. Hoffmann H. Violin Plot. https://www.mathworks.com/matlabcentral/fileexchange/45134-violinplot. Published 2021. Accessed May 1, 2021.

	effect within motion restricted molecules. J. Magn. Reson. 2015;260:67-76 doi:
	10.1016/j.jmr.2015.08.024.
	F F F F F
	o r o r o r o r o r o r
	P P P P P P
	e e r e e r e e r e e r e e r e e r
	R e v R e v R e v R e v R e v R e v
	i e w i e w i e w i e w i e w i e w

Table 2 :

 2 Results of comparisons between pairs of overlapping correlation coefficientsresulted from associations between the MR metrics with the two microscopy references. Plp-GFP (top) and LFB (bottom) are considered as the common variable.

	Significant p-values (p-value < 0.001 and p-value < 0.05) are accompanied by the
	asterisk symbol (*) and the 95% confidence intervals are reported. Pairs not indicated
	in this table were not significantly different.

Table 3 :

 3 Results of comparisons between pairs of slopes (top) and intercepts (bottom)

Acknowledgements

This work was funded by ANR 17 CE18 0030, VERISMO project and partly funded by France Life Imaging (grant ANR-11-INBS-0006), ARSEP 2021 and CARNOT STAR 2020. Authors thank Nathalie Cuge for animal handling.

Magnetic Resonance in Medicine

Magnetic Resonance in Medicine F o r P e e r R e v i e w


Laurent Plasseraud
email: laurent.plasseraud@u-bourgogne.fr

Organotin(IV) Complexes Containing Sn-O-Se Moieties: A Structural Inventory

Keywords: X-ray crystallography, Structures, Organotin(IV), Oxoanions, Chalcogenites, Selenium, Coordination chemistry

This review focuses on organotin compounds exhibiting SnOSe moieties and whose the molecular structures were previously resolved by single-crystal X-ray diffraction analysis. Three distinct classes of compounds have been identified. Thus, the various modes of coordination of selenite, selenate and organoseleninate anions with tin atoms of organtin(IV) fragments are illustrated and detailed. 1 Introduction 2 Organotin(IV) Selenite Complexes 3 Organotin(IV) Selenate Complexes 4 Organotin(IV) Organoseleninate Complexes

Introduction

It is known for a long time that organotin(IV) compounds exhibit an interesting reactivity towards oxoacids (HnEOx). As early as 1924, Labourne reported on it, exploring the action of several protic acids on methylstannonic acid. 1 At the end of the 1980s, under the leadership of Holmes and his coworkers, this area of research generated a renewed interest. 2 Since then, this has led to the isolation of countless new organooxotin compounds, containing SnOE moieties and highlighting various modes of coordination of oxoanions to tin. The literature on organotin compounds is therefore very abundant of examples reporting such reactions and involving in particular carboxylic acids, sulphonic acids, arsenic acid, phosphinic acids and phosphonic acids as reactants. Organotin(IV) precursors employed are generally halide, hydroxide or oxide types. SnC bond cleavage reactions have also been considered as a possible access route for the synthesis of new organo-oxotins. 3 From a structural point of view, these synthetic approaches have provided to an exceptional diversity of architectures, ranging from discrete mononuclear compounds to polynuclear clusters and more complex edifices (classified as: ladder, O-capped, cube, prismanes, butterfly drum, football cage, and cyclic trimer). 4 This aspect has already been the subject of several articles and reviews, listing and discussing the fascinating shapes isolated in the solid state. Thus, for example, the resulting assemblies of di-organotin sulfonates [START_REF] Chandrasekhar | Tin Chemistry: Fundamentals, Frontiers, and Applications[END_REF] and monorganotin(IV) phosphonates 6 were intensively studied by the Chandrasekhar's group while the reactivity of aryl arsenic acids towards organotin(IV) compounds was investigated by Ma and coworkers. 7 The chemistry of organotin triflates was also reviewed by Beckmann. 8 More recently, the structural aspects of organotin(IV) dithiocarboxylates and carboxylates were the subject of a new contribution. 9 Moreover, the study of the behavior of some of these species in solution, based on NMR studies, has also attracted much interest. This was particularly the case for the Sn12-oxo cluster entity. 10 Considering more specifically the elements of the chalcogens group (group 16), most published studies concern mainly sulfur-based derivatives and were achieved to extend the structural possibilities and also to confer potential catalytic and biological properties to the resulting compounds. However and to our knowledge, structural examples combining organotin compounds with selenium and tellurium derivatives, through SnOSe,Te coordination, are much less common. Yet, there is a perceptible renewal of interest in this field and in general for the preparation of heterobimetallic oxides 11 which are admitted to be suitable precursors in materials science for the preparation of inorganic-organic hybrid materials 12 and oxide nanomaterials. 13 Herein, only compounds containing SnOSe moieties characterized by X-ray crystallographic analysis will be considered. Tellurium-containing organo-oxotin derivatives and which also arouse a growing interest, are not included in this inventory. However, to date twenty-six X-ray crystallographic structures have been identified in the Cambridge Structural Data Base and which are mostly attributed to the four distinct research groups of Beckmman 14 , Ma 15 , Merzweiler 16 and Vij 17 .

Regarding the selenium oxoanions, two types are known, (i) selenites (SeO3 2-) and (ii) selenates (SeO4 2-), which are differentiated by the oxidation state of selenium, +IV and +VI, respectively. The corresponding oxoacids are selenic (H2SeO4) and selenous acids (H2SeO3), respectively. These acids are the main source of selenium for the preparation of selenites and selenates of organotin(IV) compounds. In some cases, selenium dioxide, SeO2, is also used. Se oxoanions and parent acids related to this review are shown in Scheme 1. The scheme 2 summarizes the possible bonding modes leading to SnOSe moieties.

The first two sections of this review deal with organotin derivatives of these oxoanions, while the last one is devoted to the structures of organotin organoseleninate complexes. These latter derivatives are prepared from organoseleninic acids, RSeO2H, where R, organic, can be easily modified and functionalized (in general it is an arene group), thus offering a larger modularity in synthesis and of structures. Therefore, this family is currently the most represented in terms of crystallographic reports.

Organotin(IV) Selenite Complexes

These compounds are rather rare since to date there are only five X-ray crystallographic structures relating to this type of complex. Interestingly, in 2011, Diop and Molloy reported a unique example of an organotin hydrogen selenite complex by reacting SnMe2Cl2 with H2SeO3 (1:2 ratio) in ethanol. 18 HSeO3SnMe2Cl (1), obtained in 60% yield, consists of a one-dimensional polymeric chain in which the tin atoms describe a distorted octahedral geometry. The methyl groups are trans-arranged and the [HSeO3]  anions are tridentate. The skeleton of the chains can be viewed as composed of two types of rings, (i) four-atoms Sn2O2 ring and (ii) eight-atoms [SeO2Sn]2 ring, which are adjacent (Figure 1). From a supramolecular point of view, the OH group of each [HSeO3]  anion is involved in OH•••Cl hydrogen bonds which brings the chains together and leads to the formation of sheets. To the best of our knowledge this is the only example of organotin hydrogen selenite complex characterized up to now by X-ray crystallography. The reaction of (Me4N)2SeO3•2H2O with SnMe3Cl in ethanol leads to the formation of (Me3Sn)2SeO3•H2O (2) which crystallized by slow evaporation of an acetonitrile solution (Eq. 1). 19 The structure of 2 can be described as a polymeric zig-zag chain consisting of SnMe3 moieties bridged by selenite anions. Pendant SnMe3(H2O) groups are also connected to the chain, according to a syndiotactic modes, and via SnOSe bonds (Figure 2). All tin atoms adopt a trigonal bipyramidal geometry and selenito ligands are triply-bridging. In solution (CDCl3), the 119 Sn NMR spectrum exhibits only one resonance located at 23.4 ppm. A comparable framework was obtained for SeO3(SnPh3)2 (3) prepared from triphenyltin hydroxide and selenous acid. 20 Single crystals suitable for an X-ray crystallographic analysis were grown in ethanol in the presence of Et4NI. In agreement with the 119 therefore there are no interactions between adjacent zig-zag chains (Figure 3). As part of their work on the NSn intramolecularly coordinated organotin(IV) compounds, Dostál and Jambor reported a dinuclear organotin(IV) selenite derivative, [L(Ph)SnSeO3]2 (4) (L = 2,6-(Me2NCH2)2C6H3  ), by reacting L(Ph)SnCO3 with SeO2 (89% yield, Eq. 2). 21 The release of CO2 leads to an unusual structure which consists of two [L(Ph)Sn] moieties bridged by two selenito -O,O' groups generating the formation of an eight-membered inorganic ring. The two tin atoms are hexacoordinated (Figure 4). The authors argue that the coordination around the tin atoms is maintained in solution, supported in particular on the chemical shift measured by 119 Sn NMR spectroscopy, in CDCl3 ( = 270.7 ppm), which corroborates the crystallographic data. Recently Qin and Liu reported an unusual dimethylfunctionalized polyoxotungstate polyanion, characterized [{Sn(Me)2}10{Sn(Me)2(H2O)}6Se11W56O211(OH)8] 18 (5) and incorporating organotin(IV) selenito moieties. 22 Negative charges are compensated by [C2H8N] + and Na + cations. In an unpredictable and remarkable way, the SnOSe moieties can be considered as the keystones of a tetrameric "closed" ringshaped architecture (Figure 5). According to the authors, 5 can be considered as the first example of dimethyltin-functionalized organic-inorganic hybrid selenotungstate.

By way of comparison, the Table 1 summarizes the lengths of the SnO and SeO bonds and the SnOSe angles recorded in the organotin(IV) selenite complexes previously listed. It appears that the SnO(Se) and SeO(Sn) bonds show significant variability from one compound to another, ranging almost from 2.0-2.6 A and 1.6-1.80 Å, reflecting the impact of the coordination mode of the selenite anion (doubly-or triplybridging) and the nature of the tin-connected substituents. The values of the SnOSe angles also exhibit significant variations in this class of compounds. 23 Both derivatives describe a comparable framework which can be described as a main zig-zag polymer chain alternating [SnPh3] + and [SeO4] 2 fragments (Figure 6). Pendant SnPh3X fragments are positioned along the chain. The tin atoms are in a pentacoordination geometry environment. In solution, the 119 Sn NMR spectra reveal two resonances at 115 ppm and 69 (6) or 65 ppm (7). Selenium atoms are tetrahedrally coordinated and involved in three SeOSn bonds. One oxygen atom of each selenates is not coordinating. A similar polymeric structure was solved for {[(Ph3Sn)2O4Se]•1.5H2O}n (8) prepared from H2SeO4 and triphenyltin hydroxide in ethanol. 24 In this case, the pendant organotin fragments are SnPh3(H2O). This results in the propagation of hydrogen interactions between adjacent chains, involving the free oxygen of the selenates and the water molecules, and leading to a three-dimensional network, consisting of cavities.

Under the same conditions, interestingly, when SnMe3Cl is used as precursor of tin, a discrete complex is preferentially formed, characterized as [(Me3Sn)2O4Se](H2O)2 (9). 24 Two Me3Sn moieties are bridged by a bidendate SeO4 unit which exhibits a nearly tetrahedral geometry (Figure 7). The two tin atoms have a trigonal bipyramidal geometry. The apical positions are occupied by two oxygen atoms, from the selenate ligand and a water molecule, respectively. The two uncoordinated oxygen atoms of each SeO4 unit are involved in hydrogen interactions with aqua ligands of surrounding complexes of 9 leading to a supramolecular three-dimensional network.

In solution, respectively in CD3OD and CDCl3, compounds 8 and 9 are characterized by 119 Sn resonances located at  = 213 and 27.5 ppm. More recently the reaction of H2SeO4 and SnPh3OH, in ethanol and in the presence of n-Bu2NH, led to the isolation of [n-Bu2NH2]3[SnPh3(SeO4)] (10) (Figure 8). 25 The synthetic route requires two steps, first with the in situ preparation of

Organotin(IV) Organoseleninate complexes

This type of derivatives also exhibiting SnOSe moieties, is the most represented by the number of structures identified on the Cambridge Structural Database. To date, thirty five X-ray structures have been reported. The presence of an organic substituent linked to the selenium atom significantly increases the range of available reagents. However, most of them are areneseleninate derivatives.

To the best of our knowledge, the first crystallographic report of organotin(IV) organoseleninate complexes dates from 1978, 26 in which Lindner reported the resolution of the structure of [Me3Sn(O2SeMe)]n (11). Synthetically, 11 was prepared from Me3SnCl and MeSeO2Na (65% yield, Eq. 3) and suitable crystals were obtained in a chloroform solution.

Compound 11 consists to a polymeric seleninato-O,O' complex describing an organization of zig-zag chains. The unit cell contains two symmetrical independent chains (Figure 9). More than a decade later, Chandraskehar and Tiekink published the isolation and X-ray structure of [Ph3Sn(O2SePh)]n ( 12), described as the first example of an organotin ester of phenylseleninic acid. 27 Prepared from bis(triphenyltin)oxide and phenylseleninic acid (Eq. 4), 12 is also organized according to a zig-zag chain-type polymer structure in which PhSeO2 units act as bridging ligands. Tin atoms display a trigonal bipyramidal geometry. The apical positions are occupied by two oxygen atoms from two distinct phenylseleninate ligands. Three phenyl ligands complete the coordination by defining the basal plane (Figure 10). In 2009, a comparable chain structure was obtained for [Ph3Sn(O2SeOCH2CH3)]n (13) synthesized from [(C6H5)3SnCl, selenium oxide (SeO2) and ethanol (Eq. 5). 28 To our knowledge, this is only the second example of organotin (IV) organoseleninate complexes for which the organic group R linked to Se is not of the arene type (the first being the Lindner's Template for SYNTHESIS © Thieme Stuttgart • New York 2022-01-17 page 6 of 8 complex). The chain displays a more rectilinear character compare to areneseleninate derivatives (Figure 11). Since then, numerous X-ray structures of triorganotin(IV) organoseleninate compounds exhibiting a comparable organization in one-dimensional zig-zag chain, have been solved and published. They varies according to the nature of organic ligands bound to tin (exclusively phenyl and methyl derivatives) and also to selenium (mainly arene derivatives): [Ph3Sn(O2SeC6H4-2-Me)]n, 29 [Ph3Sn(O2SeC6H4-4-Me)]n, 30 [Ph3Sn(O2SeC6H4-4-t-Bu)]n, 30 [Ph3Sn(O2SeC6H4-4-i-Pr)]n, 31 [Ph3Sn(O2SeC6H4-4-Cl)]n, 30 [Ph3Sn(O2SeC6H4-4-Et)]n, 32 [Ph3Sn(O2SeC6H4-2-Et)]n, 32 [Ph3Sn(O2SeC6H4-4-OMe)]n, 31 [Ph3Sn(O2SeC6H4-4-F)]n, 33 [Ph3Sn(O2SeC6H4-2-CF3)]n, 34 [Me3Sn(O2SeC6H5)]n, 35 [Me3Sn(O2SeC6H4-4-Me)]n, 30 [Me3Sn(O2SeC6H4-4-Me)]n, 31 [Me3Sn(O2SeC6H4-4-Et)]n, 32 [Me3Sn(O2SeC6H4-4-i-Pr)]n, 31 [Me3Sn(O2SeC6H4-4-t-Bu)]n, 30 [Me3Sn(O2SeC6H4-4-Cl)]n, 30 [Me3Sn(O2SeC6H4-4-OMe)]n, 31 [Me3Sn(O2SeC6H4-4-F)]n, 33 [Me3Sn(O2SeC6H3-3,4-F2)]n, 36 .

Interestingly, two triorganotin(IV) organoseleninate complexes exhibit a tetranuclear macrocyclic geometry instead of an infinite one-dimensional chain: [Me3Sn(O2SeC6H4-4-Et)]4 (14) and [Me3Sn(O2SeC6H4-2-CF3)]4 (15) (Figure 12). 32 , 34 Both complexes were prepared from trimethyltinchloride used as triorganotin precursor, and 4-ethylbenzeneseleninic acid and 2trifluoromethylbenzeneseleninic, respectively. The structure of these derivatives can be described as 16-membered Sn4Se4O8 tetranuclear macrocycles formed by trimethyltin and organoseleninate fragments alternately linked. The resulting cavities size is reported in the range of 6-8 Å. Moreover, the presence of intermolecular interactions (CH•••O and CH•••π) leads to the propagation of supramolecular networks.

In solution, and based on 119 Sn NMR data recorded in CDCl3 for 14 and 15 ( = 92.6 and 23.3 ppm, respectively), fourcoordinate geometries are suggested for tin atoms, thereby inconsistent with the macrocyclic structures isolated in the solid state. Examples of diorganotin (IV) organoseleninate complexes are less common. To date, only five X-ray crystallographic structures have been resolved: [n-Bu2Sn(O2SeC6H4-2-CF3)2]n ( 16), 34 [n-Bu2Sn(O2SeC6H5-2-OMe)2]n (17), 37 [Me2Sn(O2SeC6H4-2-CF3)2]n (18), 34 [Me2Sn(O2SeC6H4-4-i-Pr)2]n (19), 37 [Me2Sn(O2SeC6H4-4-Et)2]n (20), 37 . These compound were synthesized from n-Bu2SnCl2 and Me2SnCl2, respectively, by reacting with four distinct areneselenic acids: 2trifluoromethylbenzeneseleninic, 2-methoxybenzeneseleninic, 4-isopropylbenzeneseleninic, and 4-ethylbenzeneseleninic acid, respectively, and in the presence of sodium ethoxide. All describe a comparable polymeric structure which can be viewed as the linear propagation of Sn2O4Se2 eight-membered rings describing an infinite 1D-helical double-chain structure. Tin atoms systematically display a six-coordination geometry environment, linked through SnOSe connections to four distinct bridging areneseleninate ligands (Figure 13). In solution in CDCl3, the 119 Sn NMR spectra of 17, 19, and 20 reveals only one resonance located between 220 and 282 ppm which is consistent with the crystallographic data. For 16 and 18, on the other hand, 119 Sn NMR chemical shifts of less than 200 ppm are recorded, which would tend to suggest a pentacoordination geometry in solution for the tin atoms. In summary, this structural inventory of organotin(IV) complexes containing SnOSe groups revealed an interesting diversity of architectures, as well as various coordination modes. Three distinct classes of compounds have been highlighted, ranging from discrete complexes to polymeric edifices. From a supramolecular point of view, organotin(IV) selenite and selenate derivatives preferentially generate one-dimensional chain-based organizations while organoseleninate complexes lead to the formation of macrocyclic derived structures. Thus, these successive examples show and confirm that seleniumbased oxoanions exhibit also a significant reactivity toward organotin(IV) precursors. The reaction conditions, the number and the nature of the ligands bound to the tin atom (but also to the selenium atom in the case of organoseleninate derivatives) play significant structural roles. To date, the published work has focused mainly on structural characterization, but these compounds would certainly be of interest to consider for their chemical, catalytic and biological properties.

Scheme 1

 1 Scheme 1 Molecular representations of Se oxoanions and parent acids

Figure 1

 1 Figure 1 Molecular structure of 1 (MERCURY view) [Sn dark grey, O red, Se orange, Cl green, C grey, H white]. Hydrogen atoms of methyl groups are omitted for clarity.

Figure 2

 2 Figure 2 Molecular structure of 2 (MERCURY view) [Sn dark grey, O red, Se orange, C grey]. Hydrogen atoms are omitted for clarity.

  SnNMR spectrum measured in the solid state (two resonances given at  = 69 and 99 ppm), two distinct geometries are also observed for the tin atoms: (i) trigonal bipyramidal and (ii) tetrahedral. In comparison to the methylated compound 2, the tin atoms of the pendant moieties in 3 are not terminally coordinated by a water molecule of and Template for SYNTHESIS © Thieme Stuttgart • New York 2022-01-17 page 3 of 8

Figure 3

 3 Figure 3 Molecular structure of 3 (MERCURY view) [Sn steel blue, O red, Se orange]. Phenyl groups are omitted for clarity.

Equation 2

 2 Synthesis of 4.21

Figure 4

 4 Figure 4 Molecular structure of 4 (MERCURY view) [Sn steel blue, O red, Se

Figure 5

 5 Figure 5 Molecular structure of 5 (MERCURY view) [W blue, Sn steel blue, O red, Se orange, Na violet, C grey]. Hydrogen atoms and [C2H8N] + are omitted for clarity.

  Like the previous one, this family consists only of five compounds, isolated in the solid state as single-crystals. Four of which contain a triphenyltin(IV) moiety and one, a trimethyltin(IV) moiety. They result mainly from studies carried out in Senegal (Dakar) within the Diop's group, in collaboration with various European teams. Initially, in 2001, they shown that the reactions of [(Ph3Sn)2O4Se•H2O] with tetraphenylphosphonium bromide or chloride led to the formation of polymeric complexes {Ph4P[(SeO4)(SnPh3)(SnPh3X)]}n [X = Br (6) or Cl (7)].

Figure 6

 6 Figure 6 Molecular structure of 7 (MERCURY view) [Sn steel blue, O red, Se orange, Cl green]. Phenyl groups are omitted for clarity.

Figure 7

 7 Figure 7 Molecular structure of 9 (MERCURY view) [Sn steel blue, O red, Se orange, C grey, H white].

  [n-Bu2NH2][HSeO4]. (Ph3Sn)2O is co-produced with the complex 10. Its structure consists to a SnPh3 moiety trans-coordinated by two SeO4 2 . The negative charges of [SnPh3(SeO4)] 3 are compensated by the presence of three surrounding [n-Bu2NH2] + cations. From a supramolecular point of view, the uncoordinated O atoms [SnPh3(SeO4)] 3 participate to NH•••O interactions leading to a three-dimensional network. An astonishing organization based on trinuclear macrocyclic rings has thus been highlighted. In solution in CD3OD, the 119 Sn NMR spectrum of 10 reveals one resonance at  = 232 ppm which corroborates with the trans trigonal bipyramidal geometry environment, recorded in the solid state for 10.

Figure 8

 8 Figure 8 Molecular structure of 10 [Sn steel blue, O red, Se orange, C grey]. Hydrogen atoms and [n-Bu2NH2] cations are omitted for clarity (MERCURY view).

Equation 3

 3 Synthesis of 11.26

Figure 9

 9 Figure 9 Molecular structure of 11 (MERCURY view) [Sn dark grey, O red, Se orange, C grey].

Equation 4

 4 Synthesis of 12.27

Figure 10

 10 Figure 10 Molecular structure of 12 [Sn dark grey, O red, Se orange, C grey]. Hydrogen atoms are omitted for clarity (MERCURY view).

Equation 5 28 Figure 11

 52811 Figure 11 Molecular structure of 13 [Sn dark grey, O red, Se orange, C grey]. Hydrogen atoms are omitted for clarity (MERCURY view).

Figure 12

 12 Figure 12 Molecular structure of 15 [Sn dark grey, O red, Se orange, C grey, F green]. Hydrogen atoms are omitted for clarity (MERCURY view).

Figure 13

 13 Figure 13 Molecular structure of 19 [Sn dark grey, O red, Se orange, C grey]. Hydrogen atoms are omitted for clarity (MERCURY view). Sn-O and Se-O bond lengths (Å), and Sn-O-Se angles (deg) recorded in organotin(IV) organoseleninate complexes are listed in Table 3. In general, for all these compounds, few variations in distances are observed from one complex to another, leading to the following mean values: Sn-O(Se) = 2.24 Å, Se-O(Sn) = 1.68 Å and Se-C = 1.96 Å. With regard to SnOSe angles, the values are between 120 and 135° for diorganotin derivatives (compounds 11-15), and between 125 and 140° for triorganotin derivatives (compounds 16-20).

Table 1

 1 Comparison of Sn-O and Se-O bond lengths (Å), and Sn-O-Se angles (deg) in organotin(IV) selenite complexes.

	Compounds	Sn-O(Se)	Se-O(Sn)	Se-O	SeO(H)	Sn-O-Se	CSD Entry	Ref.
							Deposition Number
	HSeO3SnMe2Cl (1)	2.235(5)	1.677(5)		1.767(6)	110.4(3)	BOFBEF	18
		2.546(5) 2.285(6)	1.645(6)			134.5(3) 174.2(4)	782622
	(Me3Sn)2SeO3•H2O (2)	2.263(6)	1.655(6)			128.0(3)	NIVXIZ	19
		2.293(6) 2.139(6)	1.675(6) 1.707(6)			140.4(4) 124.3(3)	1221026
	SeO3(SnPh3)2 (3)	2.193(3)	1.681(3)			128.76(18)	HIBLOU	20
		2.252(3) 2.030(3)	1.678(3) 1.724(3)			121.71(17) 126.10(19	622160
	[L(Ph)SnSeO3]2 (4)	2.052(3)	1.731(3)	1.633(3)		121.80(2)	TELGOI
		2.069(3)	1.721(3)			130.16(3)	903804

Table 2

 2 Comparison of Sn-O and Se-O bond lengths (Å), and Sn-O-Se angles (deg) in organotin(IV) selenate complexes.

	Compounds	Sn-O(Se)	Se-O(Sn)	Se-O	Sn-O-Se	CSD Entry	Ref.
						Deposition
						Number
	{Ph4P[(SeO4)(SnPh3)(SnPh3Br)]}	2.215(3)	1.640(3)	1.603(3)	139.0(2)	QENRUW	23
	(6)	2.276(3) 2.284(5)	1.630(3) 1.644(3)		142.2(2) 149.7(2)	146133
	{Ph4P[(SeO4)(SnPh3)(SnPh3Cl)]}	2.208(7)	1.611(7)	1.582(7)	138.6(4)	QENQUV	23
	(7)	2.276(6) 2.313(7)	1.648(6) 1.658(6)		141.2(4) 149.7(4)	146132
	{[(Ph3Sn)2O4Se]•1.5H2O}n (8)	2.2032(18)	1.6386	1.6106	133.40(9)	QOTCIM	24
		2.2169(17) 2.2457(17)	1.6388 1.6390	1.6207	135.2(1) 140.2(1)	241567
		2.2505(17)	1.6436		141.2(1)
		2.2793(17)	1.6488		143.7(1)
		2.3095(17)	1.6601		146.9(1)
	[(Me3Sn)2O4Se](H2O)2 (9)	2.252(2)	1.644(2)	1.631(2)	129.2(1)	QOTCOS	24
		2.300(3)				283468
	[n-Bu2NH2]3[SnPh3(SeO4)] (10)	2.152(9)	1.599(9)	1.598(8)	170.7(9)	UDOMOR	25
		2.182(8)	1.632(8)	1.603(10) 1.618(8)	170.8(6)	933485
				1.627(8)
				1.632(8)
				1.639(9)

a Insert table footnotes here.

Table 3

 3 Comparison of Sn-O and Se-O bond lengths (Å), and Sn-O-Se angles (deg) in organotin(IV) organoseleninate complexes.

	Compounds	Sn-O(Se)	Se-O(Sn)	Se-OR	Se-C	Sn-O-Se	CSD Entry	Ref.
							Deposition number
	[Me3Sn(O2SeMe)]n (11)	2.23(2)	1.67(2)		1.91(4)	120.4(3)	MSNSEL	26
		2.24(2)	1.68(2)		1.92(3)	122.7(1)	1214525
		2.26(2)	1.76(2)			129.6(10)
		2.28(2)
	[Ph3Sn(O2SePh)]n (12)	2.223(4)	1.682(5)		1.929(8)	128.8(3)	KUTRAS	27
		2.225(5)	1.696(5)			133.7(3)	1201626
	[Ph3Sn(O2SeOCH2CH3)]n (13)	2.147(9)	1.599(10)	1.721(12)		131.3(6)	VUQXUB	28
		2.262(10)	1.684(11)			134.6(6)	698175
	[Me3Sn(O2SeC6H4-4-Et)]4 (14)	2.269(19)	1.683(19)		1.95(3)	126(2)	POHZOD	32
		2.28(2)	1.70(2)		2.04(3)	131(2)	928636
			1.71(2)
	[Me3Sn(O2SeC6H4-2-CF3)]4 (15)	2.235(6)	1.661(7)		1.95(1)	126.7(3)	ADEFEX	34
		2.236(6)	1.666(6)		1.96(1)		1061825
		2.246(6)	1.668(6)
		2.243(6)	1.675(8)
		2.256(6)
		2.284(6)
		2.290(6)
	[n-Bu2Sn(O2SeC6H4-2-CF3)2]n (16)	2.226(4)	1.676(4)		1.985(5)	127.0	ADEFUN	34
		2.231(3)	1.681(4)			139.6	1061828
	[n-Bu2Sn(O2SeC6H5-2-OMe)2]n (17)	2.217(3)	1.686(3)		1.958(5)	140.40(17)	XEHVOX	37
		2.225(3)	1.687(3)				837259
	[Me2Sn(O2SeC6H4-2-CF3)2]n (18)	2.206(4)	1.668(4)		1.987(6)	126.5	ADEFOH	34
		2.219(4)	1.689(4)			139.6	1061827
	[Me2Sn(O2SeC6H4-4-i-Pr)2]n (19)	2.232(7)	1.692(7)		1.953(10)	138.9	XEHVUD	37
		2.239(7)	1.723(7)				841668
	[Me2Sn(O2SeC6H4-4-Et)2]n (20)	2.235(13)	1.665(13)		1.94(1)	123.2	XEHWAK	37
		2.237(14)	1.708(14)			124.6	841669

Acknowledgment

The University of Bourgogne Franche-Comté (UBFC) and the Centre de la Recherche Scientifique (CNRS) are thanked for their supports. LP also wishes to thank the anonymous reviewers for their pertinent suggestions that contributed to improving the content of this article.

Biosketches

Laurent Plasseraud (47 years old) is CNRS researcher as Chargé de Recherche at the University of Burgundy (Dijon-France). His main research results concern original structures of transition metal and main group metal complexes with relevance to sustainability, homogenous catalysis, supramolecular chemistry, and molecular materials fields. Since he joined the CNRS (2001-present), he devoted his research activities on sustainable chemistry projects using CO2 as a C1 synthon, and more recently he focuses on the transformation of biobased molecules into chemicals and materials with a higher added value.