Aurélie Benoit

Sandra Guérard
email: sandra.guerard@ensam.eu

Brigitte Gillet

Geneviève Guillot

François Hild

David Mitton

Jean-Noël Périé

Stéphane Roux

3D analysis from micro-MRI during in situ compression on cancellous bone

Keywords: 3D digital image correlation, Mechanical characterization, Cancellous bone Word count: 2992

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Introduction

Mechanical properties of cancellous bone have been investigated for many years using different methods and it has been proven that they depend upon their apparent density [START_REF] Carter | Bone compressive strength: the influence of density and strain rate[END_REF][START_REF] Rice | On the dependence of the elasticity and strength of cancellous bone on apparent density[END_REF]. Moreover the contribution of the microstructure to the mechanical properties is widely accepted [START_REF] Mosekilde | Age-related changes in vertebral trabecular bone architecture--assessed by a new method[END_REF][START_REF] Parfitt | Trabecular bone architecture in the pathogenesis and prevention of fracture[END_REF]. In order to take into account these different parameters, finite element models of cancellous bone specimens have been proposed [START_REF] Hollister | A homogenization sampling procedure for calculating trabecular bone effective stiffness and tissue level stress[END_REF][START_REF] Van Rietbergen | A new method to determine trabecular bone elastic properties and loading using micromechanical finiteelement models[END_REF]. Model validations are often based on global measurements. Local measurements thanks to the digital image correlation (DIC) that is based on textured surfaces were used to measure local strains with cortical bone images [START_REF] Duchemin | Prediction of mechanical properties of cortical bone by quantitative computed tomography[END_REF][START_REF] Liu | Accuracy and precision of digital volume correlation in quantifying displacements and strains in trabecular bone[END_REF][START_REF] Nicolella | Machine vision photogrammetry: a technique for measurement of microstructural strain in cortical bone[END_REF]. This technique was also developed in 3D and applied to bone [START_REF] Bay | Measurement of strain distributions within vertebral body sections by texture correlation[END_REF][START_REF] Nazarian | Time-lapsed microstructural imaging of bone failure behavior[END_REF] or to solid foam to estimate 3D displacement fields [START_REF] Verhulp | A three-dimensional digital image correlation technique for strain measurements in microstructures[END_REF][START_REF] Roux | Three-dimensional image correlation from X-ray computed tomography of solid foam[END_REF]. Such data are extremely useful in particular for extensive finite element model validation [START_REF] Zauel | Comparison of the linear finite element prediction of deformation and strain of human cancellous bone to 3D digital volume correlation measurements[END_REF]. Moreover 3D displacement fields may also be used to determine material properties.

We propose in this study to apply such measurement technique on cancellous bone by using a non irradiating imaging method such as micro-MRI. The resolution can be less than the trabecular thickness so that the trabecular network is used as a random texture for the correlation technique. Moreover micro-MRI limits temperature rise within the tested specimen and allows for future (similar) works on ligaments, muscles or cartilage.

Displacement mapping at subvoxel accuracy in soft tissues (e.g., muscle, cartilage) has been already demonstrated by different MR techniques [START_REF] Neu | Displacement encoding for the measurement of cartilage deformation[END_REF]. Among these, MR elastography directly maps the shear stiffness in different tissues by visualizing the propagation velocity of shear waves [START_REF] Glaser | Stiffness-weighted magnetic resonance imaging[END_REF]). However such approaches would fail with trabecular bone, due to the complexity of the bone marrow interface, namely, local field heterogeneities due to magnetic susceptibility mismatch would make phase encoding displacement unreliable, and shear wave propagation would not be exploitable due to the strong difference in mechanical response between the stiff matrix and the soft marrow. For these reasons, we resorted to a direct method to obtain 3D-displacement fields in trabecular bone.

In the present study, a 3D 'finite element based' digital image correlation method is used to determine displacement and strain fields of trabecular bone based on the real microstructure imaged with micro-MRI. The aim of the study is to show the feasibility of the technique, and to evaluate measurement uncertainties in order to assess displacements in a compression test of cancellous bone taken from bovine femoral head.

Materials and methods

Specimen preparation

A (16-mm long, 100-mm 2 square cross-section) parallelepiped was extracted from a frozen bovine femoral head; its axis was parallel to that of the femoral neck. The dimensions were limited by the MRI antenna and the achievable field of view, which was 40 mm × 20 mm × 20 mm. A 20-mm thick slice was first cut with a band saw, perpendicular to the axis of the femoral neck. Then, the parallelepiped was extracted from this slice with a diamond saw and kept frozen until the MR experiment is performed. The marrow could be kept intact inside the sample thus providing an MR signal from the trabecular cavities.

Compression device

A mini-compression jig (Figure 1) was built from a glass fiber reinforced PEEK (polyethyletherketone) to be MRI-compatible. The specimen was held in a threaded pipe (wall thickness of 2 mm) between two compression platen, a calibrated washer (acting as a load cell, which is not used herein) and two outer screws. It was glued with cyanoacrylate to one surface of the platen to place it at the center of the device without touching the inner wall. The container was entirely filled with water so that the washer load cell deformation could be monitored. A silicone cap was encapsulated around the lower end of the pipe to make it watertight. The load was prescribed by rotating the screw in contact with the washer so that the ball joint between the platen and the washer limited the rotation of the specimen with the screw. Two steps of loading were applied corresponding to a translation of the screw equal to 0.25 mm and 0.5 mm. The tested specimen was allowed to relax 20 minutes prior to image acquisition, so that the specimen reaches an equilibrium stress (as suggested by many studies from the literature [START_REF] Nazarian | Time-lapsed microstructural imaging of bone failure behavior[END_REF][START_REF] Nagaraja | Trabecular bone microdamage and microstructural stresses under uniaxial compression[END_REF][START_REF] Thurner | Time-lapsed investigation of three-dimensional failure and damage accumulation in trabecular bone using synchrotron light[END_REF]).

The compression device was put in the MRI coil. Its position was reproducible thanks to markers indicating the position in rotation and translation of the device inside the coil. The uncertainty of the positioning was about ± 5° in rotation and ± 0.5 mm in translation. The translation has been easily calculated as a rigid body motion thanks to the correlation algorithm, but the images had to be rotated in order to decrease the rotation gap.

Image acquisition (micro-MRI)

MRI was performed on a vertical 9.4 T magnet with a 3D SE sequence and the following parameters: FOV 40 mm × 20 mm × 20 mm, matrix 512 × 256 × 256 voxels, TE/TR 8/1000 ms, BW 120 kHz, scan time 9h (RARE factor 2), to get an isotropic resolution of 78 µm per voxel. A (37-mm in diameter) birdcage coil provided by the manufacturer was used. It created a B 1 radio-frequency field uniform over a cylindrical region of dimensions of about 20 mm in diameter and 20 mm in height.

The noise level of the 3D pictures was assessed in background areas in the images (out of signal areas). The noise distribution is known to follow a Rayleigh distribution, since MR images are obtained as the magnitude of a complex data set, after 3D Fourier transform of the measured signal. In signal areas, the signal distribution around the mean due to noise is expected to be Gaussian, with a standard deviation equal to the noise level n. The expected relationship between the mean m and the standard deviation  n in the noise areas

( ) 2 / 2 )( 2 / (      n m
), see [START_REF] Gudbjartsson | The Rician distribution of noisy MRI data[END_REF]) was confirmed, and the noise level n was computed as

) 2 / 2 (     n n
(1)

Displacement measurement by image correlation

An in-house 'finite element based' digital image correlation software was used [START_REF] Roux | Three-dimensional image correlation from X-ray computed tomography of solid foam[END_REF] to measure displacement fields. The spirit is to register as well as possible two gray level volumes, a first one, ) (x f , called reference image, which corresponds to the unloaded stage, and a second one, ) (x g , called deformed image, under load by using displacement bases associated with finite element discretizations. They are assumed to be related through the brightness conservation hypothesis

)) ( ( ) ( x u x x   f g (2)
The displacement field, ) (x u , is decomposed over a set of finite-element shape functions

  ) ( ) ( x x u n n a 
. Here 8-node cubic elements with polynomial functions of order 1 (C8-P1) are used. A weak form of the brightness conservation (Galerkin approach) is implemented through the minimization of the domain integral over the whole considered domain of the

quadratic difference   2 2 )) ( ( ) ( ) ( x u x x x    f g r
. After an initial rigid body translation correction, a multiscale linearization procedure allowing for good convergence properties is used. Details on the algorithm can be found in [START_REF] Roux | Three-dimensional image correlation from X-ray computed tomography of solid foam[END_REF]). This implementation is a major difference with "local" approaches [START_REF] Bay | Measurement of strain distributions within vertebral body sections by texture correlation[END_REF], or such as the ones compared in [START_REF] Liu | Accuracy and precision of digital volume correlation in quantifying displacements and strains in trabecular bone[END_REF]) that consist in registering small and independent volumes.

A priori performances

To give confidence in the following results, a performance analysis is first performed. The performance of the correlation depends on the quality of the texture of the images to be analyzed. An image that has large gradients, with an almost random texture will be a good choice. Hence, the uncertainty of the displacement measurement is first assessed a priori on the reference image, when the specimen is not loaded. This was performed over a volume of 96 × 96 × 96 voxels or 7.5 mm × 7.5 mm × 7.5 mm. An artificial displacement of 0.5 voxel in each direction is artificially prescribed to the volume, creating a new (and artificially)

"deformed" image. This displacement corresponds to a critical situation where the information contained in the reference and deformed images is the most biased [START_REF] Roux | Three-dimensional image correlation from X-ray computed tomography of solid foam[END_REF]. Then, the two images are registered and the artificial translation is subtracted from the measured displacement. The mean error thus corresponds to the average of the difference between the measured and prescribed displacements, and the standard uncertainty to the corresponding standard deviation.

To assess a posteriori the quality of the displacement measurement a distance criterion (or dimensionless correlation residual) between the two images f and g is used

) min( ) max( f f r R   ( 3
)
where  is the average value over the considered ROI, max(.) and min(.) are the maximum and minimum values of the gray levels present in the image. This dimensionless indicator is equal to 0 when the two images are identical, or when no correlation error occurs.

Strain evaluations

From the measured displacement fields, the mean strain per element is assessed by using the C8 interpolation functions. Further, when the displacement field is interpolated over a gauge volume by using a single trilinear polynomial, macroscopic principal strains are assessed by using the mean transformation gradient.

Results

A priori performances

Figure 2 shows the mean displacement error and the standard uncertainty as functions of the element size used for the volume correlation calculation. The mean error is always less than the standard uncertainty, the results of the correlation were therefore considered as unbiased.

Its level is very low, and is independent of the element size. Moreover the standard displacement uncertainty decreases when the element size increases. From these values, it is concluded that the displacements are assessed with subvoxel resolution.

Strain uncertainties are also evaluated by using the previously measured displacement field.

Very small standard uncertainties are obtained yielding strain resolutions less than 3 × 10 -2 for element sizes greater than or equal to 12 voxels.

Displacement measurement

The quality of the displacement measurement is analyzed for both loading steps on a Region

Of Interest (ROI) of 96 × 192 × 96 voxels (or 7.5 mm × 15 mm × 7.5 mm). The initial value of R between the reference image and the image of the specimen after the first loading step is equal to 11.3 % when only the ROI was considered. As a starting point, rigid body translations (corresponding to an isometric transformation) are corrected for, and this leads to a reduction of R to 4.2 %. With optical images of good quality, the correlation algorithm enables one to reach a final value of about 1 % [START_REF] Besnard | Finite-element displacement fields analysis from digital images: Application to Portevin-Le Châtelier bands[END_REF]. In the present case, the correlation residuals are about 1.4 % for the first step of loading with an element size of 12 voxels at the end of the correlation procedure. For the second loading step, the initial value of R is 10.8 %. After removal of the rigid body translation, it reduces to 5.7 %, and after convergence it reached 1.6 % for 12-voxel elements. The quality of the correlation was very satisfactory although it varied slightly with the element size. Table 1 summarizes the final gaps as functions of the element size.

The residual maps (Figure 4) show that correlation residuals are not only very small on average, but also locally for the two loading steps. The gray level histograms of Figure 4 can be compared to that of the reference picture (Figure 3). The residual level is very small. Furthermore, the standard deviation of the residual can be compared to the noise level that was estimated. The noise level is about 2.4 gray levels when the image data is limited to an 8bit range. It changes by less than 10% along the long specimen axis (also the probe axis) over the region of interest. From the standard deviation of the correlation residual (respectively equal to 4 and 4.3 gray levels), the standard deviation associated with each volume is equal to the former divided by 2 (namely, 2.8 and 3 gray levels). The two values are very close to the noise level. The measurement results are therefore deemed trustworthy.

Strain fields

In the present case, the mean strain levels per element are determined by using the (trilinear) interpolation functions associated with the discretization. The values of the latter are assigned to the center of the element, and linearly interpolated between these points to obtain 3D maps whose cuts by two perpendicular planes containing the longitudinal axis of the ROI are shown in Figure 5 for the two load levels when 12-voxel elements are used. The strain field is not uniform for the first and second load levels.

To quantify even more this result, a gauge volume of size 96 × 96 × 96 voxels (or 7.5 mm × 7.5 mm × 7.5 mm) is moved along the specimen axis by increments equal to the element size. The displacement field is interpolated trilinearly and the mean transformation gradient estimated. The nominal strain tensor is computed and its eigen values extracted. The change of the three eigen strains is shown in Figure 6 for the two load levels for 12-voxel elements. As one moves from the top to the bottom of the longitudinal axis, it is observed that the mean strain state varies significantly. When compared to the previous results, the use of 16, 24 and 32-voxel elements in the gauge volume changes the results by  2  10 -4 at most.

Discussion

This article presents a mechanical compression device and a three dimensional DIC technique that uses micro-MRI images of bovine cancellous bone that allows for the measurement of displacement and strain fields. The overall aim of this study is to demonstrate the feasibility of using 3D digital image correlation on compressed bovine cancellous bone monitored by micro-MRI.

The standard displacement and strain uncertainties decrease when the element size increases.

This result is explained by the fact that there are more data (voxels) in large size elements to make the correlation between the reference and deformed images more secure. However, if the element size is too large, the number of measurement points in the specimen will be limited and the displacement will be prone to interpolation errors, in particular in the presence of localized phenomena.

The map and histogram of correlation residuals (Figure 4) show that the errors are very small, and very close to the noise levels due to the acquisition device. This result fully validates not only the a priori analysis on artificial displacement, but also the whole experimental procedure developed to measure accurately displacement fields when using MRI.

From the measured strain fields, it is concluded that for the two analyzed load levels, no uniformity is achieved in terms of mesoscopic strains (i.e., on the scale of each finite element), and macroscopic strains (i.e., at the level of the gauge volume). This phenomenon is related to the coarse microstructure (at the scale of micro-MRI) of trabecular bone. Even though a compressive load is applied, the material response is not that expected from a homogeneous medium. This observation shows that even if elasticity can be assumed (since the first mean strain level is equal to 0.6 %), the elastic properties (e.g., Poisson's ratio) cannot be inferred from the present observations. This is not a drawback of the experimental procedure, or of the measurement technique, but an effect of the microstructure at hand. This result shows that more advanced identification procedures are called for to evaluate the microscopic properties.

Conclusion

Volume correlation was used on a loaded bovine cancellous bone monitored by micro-MRI leading to 3D-displacement fields of subvoxel uncertainty less than 0.1 voxel (or 8 µm) for element sizes greater than 12 voxels. The mean correlation residuals remain less than 1.4% of the image dynamic range for 12-voxel elements, and the displacement fields were stable for each tested element size. The corresponding standard deviation is very close to the noise level, thereby proving that the registration was successful, and the measured displacements are trustworthy.

From the measured displacements, macroscopic and mesoscopic strain fields were evaluated.

The latter show that the local strain field is not uniform in the present experiment. This phenomenon is due to the coarseness of the studied microstructure. Furthermore, the variation of the macroscopic principal strains along the height of the sample shows that a classical identification procedure to evaluate Poisson's ratio would lead to erroneous results. More advanced identification tools are needed to determine the elastic parameters at a microscopic (at the level of trabeculae), mesoscopic (at the level of the elements considered herein) or even macroscopic scale (i.e., the studied sample). This analysis shows that the representative volume element is significantly larger than the volume tested herein. Such methodology opens the way for in-depth validation of micro-finite element models of cancellous bone.

Last, MRI has a wide field of application to other types of biological tissues. By means of some adaptations, it could be possible to measure macroscopic damage on soft tissues such as cartilages or ligaments.

List of figures:

1. Compression device.

2.

  Mean error (a), standard uncertainty (b) of the displacement measurement and standard strain uncertainty (c) as functions of the element size. 3. Reference region of interest (a) in gray levels (size: 96 × 192 × 96 voxels or 7.5 × 15 × 7.5 mm 3 ) and corresponding histogram of gray levels (b) (dynamic range: 8 bits). 4. Correlation residual measured in gray levels and corresponding histogram with the same dynamic range as Figure 3(b) for a ROI of 96 × 192 × 96 voxels and an element size of 12 voxels, for the first loading step (a) and for the second loading step (b). 5. Cuts along two planes containing the longitudinal axis of the region of interest. The gray level picture and the longitudinal strain fields corresponding to the two loading steps are shown. 6. Macroscopic principal strains as functions of the longitudinal position of the gauge volume for the first loading step (a) and for the second loading step (b).

FigureFigure 2 :Figure 3 :Figure 4 :Figure 5 :Figure 6 :

 23456 Figure Legend(s)

Acknowledgements

The authors would like to acknowledge Claude Verliac and Joachim Magnier for technical advice on the manufacturing process of the mechanical loading system.

Conflict of interest

There are no conflicts of interest related to the work submitted in this manuscript.


Tatiana Munteanu

Valérie Mazan

Mourad Elhabiri

Camil Benbouziyane

Gabriel Canard

Denis Jacquemin

Olivier Siri

Simon Pascal
email: simon.pascal@cnrs.fr

A Strategy to Design Substituted Tetraamino-Phenazine Dyes and Access to an NIR-Absorbing Benzoquinonediimine-Fused Quinoxaline

The straightforward access to N-or C-substituted dinitrotetraamino-phenazines (P1-P5) is enabled in oxidative conditions via two intermolecular C-N bonds formation from accessible 5-nitrobenzene-1,2,4-triamine precursors. The photophysical studies revealed green absorbing and orange-red emitting dyes, with enhanced fluorescence in the solid state. Further reduction of the nitro functions led to the isolation of a benzoquinonediimine-fused quinoxaline (P6), which undergoes diprotonation to form a dicationic coupled trimethine dye absorbing beyond 800 nm Phenazines are tricyclic dibenzannulated heterocycles containing a central pyrazine core, well-known as naturally occurring substances, biologically active species and dyestuffs (e.g. safranine, neutral red). [START_REF] Turner | Occurrence, Biochemistry and Physiology of Phenazine Pigment Production[END_REF][START_REF] Beifuss | Methanophenazine and Other Natural Biologically Active Phenazines[END_REF][START_REF] Schiessl | Phenazine Production Promotes Antibiotic Tolerance and Metabolic Heterogeneity in Pseudomonas Aeruginosa Biofilms[END_REF][START_REF] Kohatsu | Total Syntheses of Pyocyanin, Lavanducyanin, and Marinocyanins A and B[END_REF][START_REF] Lee | Isolation, Structure Determination, and Semisynthesis of Diphenazine Compounds from a Deep-Sea-Derived Strain of the Fungus Cystobasidium Laryngis and Their Biological Activities[END_REF][START_REF] Che | Design Strategies and Applications of Novel Functionalized Phenazine Derivatives: A Review[END_REF] Beyond being popular chromophores, their unique optical and electrochemical properties allowed for their use as chemosensors [START_REF] Banerjee | Phenazines as Chemosensors of Solution Analytes and as Sensitizers in Organic Photovoltaics[END_REF][START_REF] Xiao-Ni | Phenazine Derivatives for Optical Sensing: A Review[END_REF] or photocatalysts for photopolymerization or cross-coupling reactions. [START_REF] Cole | Photoinduced Organocatalyzed Atom Transfer Radical Polymerization Using Low Ppm Catalyst Loading[END_REF][START_REF] Deol | Phenazine-Based Donor Acceptor Systems as Organic Photocatalysts for "Metal-Free" C-N/C-C Cross-Coupling[END_REF][START_REF] Bobo | Recent Advancements in the Development of Molecular Organic Photocatalysts[END_REF] In organic electronics, phenazines have demonstrated their potential as low bandgap semiconductors in solar cells, [START_REF] Mastalerz | Conjugated Oligothienyl Dendrimers Based on a Pyrazino[2,3-g]Quinoxaline Core[END_REF][START_REF] Li | A Chlorinated Phenazine-Based Donor-Acceptor Copolymer with Enhanced Photovoltaic Performance[END_REF] and as electro-active compounds in batteries. [START_REF] Pang | Biomimetic Amino Acid Functionalized Phenazine Flow Batteries with Long Lifetime at Near-Neutral PH[END_REF][START_REF] Tie | A Symmetric All-Organic Proton Battery in Mild Electrolyte[END_REF] They have also found a particular interest for the elaboration of organic light-emitting diodes (OLEDs), notably due to the rigidity and electron-withdrawing character of the phenazine core, which is beneficial for designing thermally activated delayed fluorescent dyes, [START_REF] Xiao | NIR TADF Emitters and OLEDs: Challenges, Progress, and Perspectives[END_REF] as exemplified with the recent report of sterically hindered tetrabenzophenazinephenoxazines that afforded efficient orange-red OLEDs. [START_REF] Balijapalli | Phenazine Backbone for Highly Efficient Orange-Red Thermally Activated Delayed Fluorescence with Completely Horizontal Molecular Orientation[END_REF] Furthermore, the straightforward synthesis of simple phenazines through polycondensation reactions enables the preparation of various π-extended planar chromophores derived from azaacenes, and this motif can be found in many polyaromatic heterocyclic nanographenes, [START_REF] Borissov | Recent Advances in Heterocyclic Nanographenes and Other Polycyclic Heteroaromatic Compounds[END_REF] two-dimensional conjugated macrocycles, [START_REF] Marco | Twisted Aromatic Frameworks: Readily Exfoliable and Solution-Processable Two-Dimensional Conjugated Microporous Polymers[END_REF] 3D porous architectures, [START_REF] Kohl | Rigid π-Extended Triptycenes via a Hexaketone Precursor[END_REF][START_REF] Hu | Three-Dimensional Pyrene-Fused N-Heteroacenes[END_REF][START_REF] Lauer | A Hexagonal Shape-Persistent Nanobelt of Elongated Rhombic Symmetry with Orthogonal π-Planes by a One-Pot Reaction[END_REF] as well as helicoidal derivatives. [START_REF] Jakubec | Photochemical Oxidation Specific to Distorted Aromatic Amines Providing Ortho-Diketones[END_REF][START_REF] Chen | Planar and Helical Dinaphthophenazines[END_REF] Seminal strategies to access phenazine dyes are based on the condensation of nitrobenzene and aniline derivatives at high temperature in the presence of base (Wohl-Aue procedure), the ring enlargement of benzofuran-1-oxide (Beirut reaction) and the condensation of 1,2-diaminobenzenes with various diones or o-benzoquinones. [START_REF] Chaudhary | Synthetic Routes for Phenazines: An Overview[END_REF] Other notable approaches rely on the reaction of o-aminobenzophenones and cyclohexanones, [START_REF] Xiao | Recent Advances in the Synthesis of Acridines and Phenazines[END_REF] or on several catalytic processes including straightforward metal-catalyzed intramolecular cyclization or N-arylation. [START_REF] Emoto | A New Route to Phenazines[END_REF] Interestingly, a handful of works report the formation of phenazines via the intermolecular formation of C-N bonds in ortho position between two electron-rich aromatic amines. [START_REF] Hiroto | Synthesis of π-Functional Molecules through Oxidation of Aromatic Amines[END_REF] Such reaction, particularly relevant for the present contribution, can occur in the presence of an oxidant such as dioxygen, potassium dioxide or 2,3-dichloro-5,6-dicyano-p-benzoquinone (DDQ) to form extended phenazines from amino-derivatives of naphthalene, carbazole or anthracene. [START_REF] Crank | Organic Chemistry of Superoxide. II Oxidation of β-Naphthylamine -Possible Involvement of the Hydroxyl Radical[END_REF][START_REF] Piechowska | Excited State Intramolecular Proton Transfer in π-Expanded Phenazine-Derived Phenols[END_REF][START_REF] Kosugi | Unexpected Formation of Dibenzo[a,h]Phenazine in the Reaction between 1-Naphthyliminodimagnesium Dibromide and 1-Nitronaphthalene[END_REF][START_REF] Nagasaki | π-Extended Dihydrophenazines with Three-State NIR Electrochromism Involving Large Conformational Changes[END_REF] These protocols principally afford mono-to tetrasubstituted phenazines, the principal examples of per-substituted derivatives being the tetrabenzo[a,c,h,j]phenazines. [START_REF] Che | Design Strategies and Applications of Novel Functionalized Phenazine Derivatives: A Review[END_REF][START_REF] Chaudhary | Synthetic Routes for Phenazines: An Overview[END_REF] Herein we describe a straightforward synthetic approach to access N-or C-substituted dinitro-tetraamino-phenazines via the intermolecular C-N bonds formation between two 5nitrobenzene-1,2,4-triamine precursors (self-condensation), obtained through a controlled mono-reduction protocol. The new phenazines P1-P5 (Scheme 1) feature four amine moieties (positions 1,3,6,8) and two nitro groups (positions 4,9), and their structures were varied via the introduction of N-substituents or ethynyl functions (positions 2,7). We investigated the impact of such modifications on their redox and optical properties, including their solid-state enhanced emission. Moreover, the reduction of the nitro functions borne by the phenazine P5 led to a unique benzoquinonediimine-fused quinoxaline P6 absorbing in the near-infrared (NIR) upon diprotonation, due to the generation of two cationic coupled trimethines. [START_REF] Dähne | Coupling Principles in Organic Dyes[END_REF]

Scheme 1. Synthesis of Phenazines P1-P5

The three-step synthesis of phenazines P1-P3 starts from 1,5-difluoro-2,4-dinitrobenzene that undergoes nucleophilic aromatic substitution with primary aryl-or alkylamines to readily afford 1a-c (≥95%). Compound 1d is prepared in aqueous ammonia and its halogenation using N-iodosuccinimide provides compound 2 with 90% yield. The Sonogashira cross-coupling between 2 and ethynyltriisopropylsilane is carried out in the presence of catalytic amounts of Pd(II) and Cu(I) complexes, to give the intermediate 3a with 81% yield. Prior to this synthesis, conditions were optimized with the less costly ethynyltrimethylsilane and showed that the reaction at room temperature using N,N-dimethylformamide as solvent leads to the highest yield of 3b (Table S1). Interestingly, the selective reduction of only one nitro function of 1ac or 3a is efficiently performed with hydrazine in the presence of 5 mol% of Pd/C in up to 2 hours in tetrahydrofuran (THF). Such reaction was previously reported using Raney-Nickel but provided inextricable mixtures of mono-and di-reduced products. [START_REF] Gampe | Stable and Easily Accessible Functional Dyes: Dihydrotetraazaanthracenes as Versatile Precursors for Higher Acenes[END_REF] Molecules 4a-d are obtained in excellent yields (87-98%), without forming the totally reduced tetraaminobenzene species that are commonly obtained under similar conditions when ethanol is used as solvent instead of THF, [START_REF] Pascal | Controlling the Canonical/Zwitterionic Balance through Intramolecular Proton Transfer: A Strategy for Vapochromism[END_REF] or when other reducing agents such as tin chloride or iron are used. [START_REF] Lavaud | Tetra-Substituted Quinonediimines: A Drastic Effect on Coordination Chemistry[END_REF][START_REF] Lavaud | Fused Bis-Azacalixphyrin That Reaches NIR-II Absorptions[END_REF] Compound 4b was used to screen the conditions to form P2 and designated p-chloranil (2 equiv.) as the best oxidizing agent to achieve the highest yield (see Table S2). Increasing the amount of oxidant or changing it to DDQ, magic blue or ferrocenium salt decreases the yield of P2 formation. For P3, the reaction process is complicated by the lower solubility of the starting compound 4c. While the use of highly polar solvents is ineffective to improve the formation of P3, it was possible to increase the yield from 5 to 20% by changing the solvent from dichloromethane (DCM) to chloroform and performing the reaction at 50 °C. Surprisingly, when using more equivalents of oxidant, and especially in the case of magic blue, a benzotriazole derivative was isolated as the major product (see BT in Scheme S2 and SI). Several comparable synthesis of benzobistriazole derivatives were previously achieved via the diazotation of tetraaminobenzene derivatives in presence of sodium nitrite, [START_REF] Tomé | Product Class 13: 1,2,3-Triazoles[END_REF] suggesting that, in our case, the formation of this unexpected compound is presumably due to the decomposition of a portion of 4b, acting as a source of nitrogen atoms.

Removal of the tert-butyl groups in P1 was achieved by heating the compound to 110 °C in acidic medium, affording the unsubstituted phenazine P5 with 90% yield. Unlike compounds P1-P4, which were purified by flash column chromatography, the low solubility of P5 allowed the removal of the impurities by simply washing the precipitate with water and DCM. Attempts to reduce the nitro functions of the phenazines P1-P4 were carried out using Pd/C with H2 or N2H4, SnCl2, Fe or Zn in acidic medium. These conditions led to either the recovery of starting material or inextricable mixtures containing unidentified species. However, reduction of P5 using Pd/C and H2 followed by an aerobic workup gave P6 in 77% yield (Scheme 2). The compound was characterized by HRMS, showing a molecular peak at m/z = 269.1256 (m/ztheo = 269.1258) corresponding to [P6+H + ]. The 1 H NMR of P6 revealed an unsymmetrical structure with two singlets corresponding to the two CH protons at 6.52 and 6.26 ppm, two singlets imine protons at 12.05 and 6.37 ppm, and four broad singlets corresponding to the amine functions (Figure S31). The structure depicted in Scheme 2 is also the most stable tautomer obtained by DFT calculations (vide infra). In acidic medium, the 1 H NMR of P6 shows two equivalent CH protons at 6.33 ppm (Figure S34), suggesting a symmetrical structure corresponding to the dicationic species P6•2H 2+ , which could be isolated with 83% yield. Scheme 2. Formation and protonation states of P6.

The slow evaporation of a P4 solution in DCM afforded single crystals (Figure 1). The bond length analysis confirms a centrosymmetric structure with aromatic rings, and shows an intramolecular hydrogen bond between one H atom of the amine substituent in position 3 and one O atom of the nitro function in position 4. The electrochemical properties of P1-P4 were investigated by cyclic voltammetry in DCM and revealed irreversible redox processes (Table S6 and Figure S74). Both phenazines P1 and P2 exhibit similar electrochemical signatures with first reduction and oxidation waves at ca. -0.88 and 0.56 V vs. Fc/Fc + , respectively. Replacing alkyl N-substituents with electron-donating p-methoxyphenyl groups in P3 mainly impacts the reduction process that is shifted to -1.19 V. In contrast, the triisopropylsilylacetylenes on positions 2,7 of P4 facilitate the reduction, with a wave at -0.62 V and shifts the oxidation to a more anodic potential at 1.02 V.

The phenazines P1-P5 display significantly redshifted absorptions compared to the triamine precursors 4a-d due to their π-extended tricyclic structure (Figure 2 and Figure S75). Their lowest energy absorption bands are found in the green region, peaking at ~510 nm with an extinction coefficient of ca. 10,000 M -1 cm -1 , except for N-aryl substituted P3, for which the absorption maximum is slightly redshifted to 533 nm (Table S6). Interestingly, the four phenazines exhibit emission in the orange-red with maxima at ca. 580-600 nm for P1, P2 and P4, and 650 nm for P3. The fluorescence quantum yields (Φ) are estimated <0.1%, except for P4 (Φ=0.45%). The weak fluorescence is typical of nitro-substituted dyes, which generally promote deexcitation via various non-radiative pathways including intersystem crossing, [START_REF] Poronik | Revisiting the Non-Fluo-rescence of Nitroaromatics: Presumption versus Reality[END_REF] and calculations indeed predict small S-T gaps in P1-P4, though with relatively small SOC couplings (see the SI). However, the latter was ruled out through measurements in degassed 2-methyltetrahydrofuran at 77 K, which did not reveal the presence of triplet state emission in the spectral window studied (Figure S77). Interestingly, solid-state fluorescence was detected from the powders of phenazines P1, P2, and P4. Thin films of these compounds were thus prepared by dropcasting on glass substrates and revealed emissions with comparable maxima but higher intensity compared to solution (Figure S78). This emission enhancement was studied in THF/H2O mixtures allowing for the progressive precipitation of P1. From THF to a 4:3 THF/H2O mixture, the absorption features remain unchanged and the weak emission is maintained, with Φ≤0.2% (Figure S79 and Table S7). For higher water content, the absorption is markedly broadened and lowered due to the precipitation of the dye. However, the Φ value is increased to 10.4% in a 2:8 THF/H2O mixture, as a result of the aggregated state of P1 decreasing nonradiative deactivation. The absorption spectrum of P6 in methanol solution displayed in Figure 2 shows a broad band centered at 642 nm, which is blueshifted to ca. 600 nm in DMSO (Figure S76). On the one hand, in the presence of DBU, the band is blueshifted to the UV region, hinting at deprotonation of the solvated species, whereas, on the other hand, in the presence of TFA, an intense band appears in the NIR at ca. 830 nm. Such large redshift can be attributed to the formation of coupled cationic trimethine cyanines (Scheme 2). To determine the protonation states of P6 and fully understand its acid-base properties, the pH-dependent absorption was investigated and compared to theoretical calculations.

The absorption spectra of fresh P6 solutions recorded at different pH values in a CH3OH/H2O mixture (8:2 w/w) were first found to agree with those measured in pure CH3OH (Figure S80). While these solvent conditions ensured a good solubility of P6, a slow kinetics most likely related to hydrolysis of the iminium functions was found with fading of the visible-NIR absorptions of P6 over time (Figures S75-76). This is consistent with p-benzoquinone mono-and diimine related compounds described to undergo rapid hydrolysis in water. [START_REF] Corbett | II. Hydrolysis of p-Benzoquinone Monoimine and p-Benzoquinone Di-Imine[END_REF] Based on these observations, absorption spectrophotometric titrations vs. pH were performed to cover a wide pH range and prevent as much as possible hydrolysis reactions (Figures S77-79). Two protonation values attributed to the imine functions (pKa1= 2.5±0.7 and pKa2= 10.1±0.1) were determined and are characterized by absorption in the visible-NIR region. The difference in the pKa values can be explained by the strong electrostatic repulsion within the dicationic species. These data are consistent with phenylene blue (indamine), [START_REF] Corbett | Part XI. Mechanism and Kinetics of the Reaction of p-Benzoquinone Di-Imines with Aniline and Its Derivatives[END_REF] which has a pKa of 7.55 and whose protonation induces the formation of a cationic species with an absorption maximum shifting from 484 to 672 nm. Finally, under very acidic conditions, the P6•2H 2+ species was shown to undergo further protonations, characterized by the loss of the NIR absorptions (Figure S86).

We have then used TD-DFT to model P1-P4 and P6 (see SI for details). The electron density difference (EDD) plots for the lowest transition of P1 in Figure 3 indicates a clear π-π* character. Interestingly, the lateral amino and nitro groups have a rather small role in the transition that is centered on the phenazine core, its central pyrazine moiety acting as a strong accepting unit (mostly in red). The topology of the transitions remains similar in both P3 and P4, i.e., the side groups attached at positions 2 and 7 have trifling influence on the lowest transition, consistent with the very similar λmax measured. For P6, we have performed a thorough tautomer search for the neutral, mono-and diprotonated species, and in all three forms, one tautomeric form clearly emerged as most stable (Scheme 2), the other tautomers being less stabilized by at least 5 kcal.mol -1 . Protonation of the central pyrazine rather than side amines clearly leads to less stable species (see SI). For the stable forms of neutral and protonated P6, we modelled the excited states using calculations including CC2 corrections [START_REF] Christiansen | The Second-Order Approximate Coupled Cluster Singles and Doubles Model CC2[END_REF] as well as cLR 2 solvation corrections. [START_REF] Guido | Simple Protocol for Capturing Both Linear-Response and State-Specific Effects in Excited-State Calculations with Continuum Solvation Models[END_REF] For the lowest transition, this yields 566 nm (f=0.070) for non-protonated P6, the transition inducing an obviously strong chargetransfer (CT) from the diamino-phenyl towards the pyrazine moiety (Figure 3), corresponding to the very broad weak band at 642 nm experimentally (Figure 2). After a single protonation, theory foresees transitions at 703 nm (f=0.019) and 622 nm (f=0.146), both involving CT (see Figure 3 for the former), which does not fit well the experimental observation of a band redshifted by 186 nm and much more intense upon TFA addition. In contrast, the diprotonated P6•2H 2+ presents a calculated vertical transition that is both strongly redshifted (+166 nm) and much more intense: 732 nm (f=0.363), clearly fitting the experimental observations. Strikingly, this low-lying excited state presents a totally different topology. An analysis of the DFT bond lengths in P6•2H 2+ indicates that the structure presents two trimethine units with negligible bond length alternation, as represented in Scheme 2.

In conclusion, a new synthetic approach allowed the preparation of functionalized tetraamino-phenazines in at least three steps. These dyes present photophysical properties in the visible region and hold potential for future applications in material sciences or as platforms to reach π-extended fused chromophores. Finally, the characterization of an intriguing fused benzoquinonedimine-quinoxaline and its protonated forms showing NIR absorption further stimulates the research on overlooked coupled polymethine dyes.

Supporting Information

Experimental protocols, single-crystal X-ray, NMR spectra, computational, and spectroscopic characterization data (PDF).

Single-crystal X-ray CCDC 2256019 (compound 3b), 2256023 (compound P1) and 2256032 (compound P4), contain the supplementary crystallographic data for this paper. These data can be obtained free of charge via www.ccdc.cam.ac.uk/data_request/cif, or by emailing data_request@ccdc.cam.ac.uk, or by contacting The Cambridge Crystallographic Data Centre,

Figure 1 .

 1 Figure 1. Single crystal structure of P4: side and top views with distances indicated in Å. Anisotropic displacement ellipsoids plot at the 50% probability level.

Figure 2 .

 2 Figure 2. Top: electronic absorption (plain lines) and emission (dashed lines) spectra of P1-P4 in DCM and absorption of P5 in DMSO. Bottom: Electronic absorption spectra of P6 in MeOH without or with the presence of 0.1 M 1,8-diazabicyclo[5.4.0]undec-7-ene (DBU) or 0.1 M trifluoroacetic acid (TFA).

Figure 3 .

 3 Figure 3. EDD plots of the lowest singlet transition of selected dyes. The blue and red lobes represent decrease and increase of density upon absorption, respectively.

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ACKNOWLEDGMENT

We thank the Région SUD and the Agence Nationale de la Recherche for the attribution of grants in the frame of the MALDI project and the SOCOOL project (ANR-20-CE07-0024), respectively. We acknowledge Michel Giorgi and Valérie Monnier (Spectropole, Aix-Marseille Univ) for the X-ray and HRMS analyses, respectively. D.J. is indebted to the CCIPL/GliciD center for computational time.