Yohann Corvis

Nicolas Guiblin

Philippe Négrier

Ivan Marenco

Oumar Dembele

Philippe Espeau

Scalemic Mixtures Preparation for Optimized Composition of Ibuprofen Solid Dosage Forms

Keywords: Drug-drug interaction, Enantiomeric mixtures, Thermal behavior, X-ray pattern, Phase diagram, Solid solution, Racemate

The stable and metastable phase diagrams between the sinister and the rectus ibuprofen enantiomers were established by means of thermal analysis and X-ray powder diffraction experiments as a function of temperature. The results obtained allow proving for the first time the existence, for the stable system, of a solid solution by mixing the ibuprofen racemate with one of its enantiomers for low concentration of the enantiomer. Since the rectus ibuprofen is a non-active pharmaceutical agent which can be partially bio-converted into the sinister enantiomer, the present work offers a new approach for scalemic mixtures preparation in order to improve the benefit/risk ratio related to ibuprofen administration.

INTRODUCTION

Racemate ibuprofen is one of the most non-steroidal anti-inflammatory drugs used in the pharmaceutical field [START_REF] Srisanga | Racemic compound, conglomerate, or solid solution: Phase diagram screening of chiral compounds[END_REF][START_REF] Lee | Effects of homochiral molecules of (s)-(+)-ibuprofen and (s)-(-)-sodium ibuprofen dihydrate on the crystallization kinetics of racemic (r,s)-(±)-sodium ibuprofen dihydrate[END_REF]. RS-ibuprofen crystallizes in the monoclinic P21/c lattice [START_REF] Mcconnell | The 2-(4-isobutylphenyl) propionic acid. Ibuprofen or prufen[END_REF][START_REF] Romero | Stereochemical aspects of the molecular pharmaceutics of ibuprofen[END_REF][START_REF] Shankland | Refinement of ibuprofen at 100 k by single-crystal pulsed neutron diffraction[END_REF][START_REF] Derollez | Ab initio structure determination of phase ii of racemic ibuprofen by x-ray powder diffraction[END_REF] while the chiral counterpart, or enantiomer, crystallizes in the monoclinic P21 [START_REF] Romero | Stereochemical aspects of the molecular pharmaceutics of ibuprofen[END_REF][START_REF] Freer | Structure of (s)-(+)-ibuprofen[END_REF][START_REF] Hansen | Redetermination and h-atom refinement of (s)-(+)-ibuprofen[END_REF][START_REF] King | Understanding the terahertz spectra of crystalline pharmaceuticals: Terahertz spectroscopy and solid-state density functional theory study of (s)-(+)-ibuprofen and (rs)-ibuprofen[END_REF]. The ibuprofen rectus enantiomer has no therapeutic activity and is partially stocked in the adipose tissues (~ 30% of the total ibuprofen dose) -the other part being bio-converted in the sinister enantiomer which is the pharmaceutical active form [START_REF] Lee | Effects of homochiral molecules of (s)-(+)-ibuprofen and (s)-(-)-sodium ibuprofen dihydrate on the crystallization kinetics of racemic (r,s)-(±)-sodium ibuprofen dihydrate[END_REF][START_REF] Lee | Stereoselective disposition of ibuprofen enantiomers in man[END_REF][START_REF] Mills | Metabolism of ibuprofen[END_REF][START_REF] Wechter | Enzymic inversion at saturated carbon. Nature and mechanism of the inversion of r(-) p-isobutyl hydratropic acid[END_REF][START_REF] Kirkiacharian | Guide de chimie médicinale et médicaments[END_REF][START_REF] Adams | Pharmacological differences between the optical isomers of ibuprofen: Evidence for metabolic inversion of the (-)-isomer[END_REF][START_REF] Geisslinger | Pharmacokinetics of s(+)-and r(-)-ibuprofen in volunteers and first clinical experience of s(+)-ibuprofen in rheumatoid arthritis[END_REF][START_REF] Evans | Comparative pharmacology of s(+)-ibuprofen and (rs)-ibuprofen[END_REF]. Such bio-conversion pathway may contribute to the in vivo sustained ibuprofen action. In a physicochemical point of view, previous phase diagrams between ibuprofen enantiomers were reported in the literature [START_REF] Romero | Stereochemical aspects of the molecular pharmaceutics of ibuprofen[END_REF][START_REF] Burger | Rs-ibuprofen and s-ibuprofen (dexibuprofen). Binary system and unusual solubility behavior[END_REF][START_REF] Dwivedi | Ibuprofen racemate and enantiomers: Phase diagram, solubility and thermodynamic studies[END_REF]. All the results agree to state that a eutectic system is formed between one enantiomer and the racemate. But contradictory results are reported especially for the location of the eutectic point and the eutectic melting point. Indications are given about an unstable phase encountered near the eutectic point but the results were unexploited [START_REF] Burger | Rs-ibuprofen and s-ibuprofen (dexibuprofen). Binary system and unusual solubility behavior[END_REF]. Moreover, on each of the three phase diagrams [START_REF] Romero | Stereochemical aspects of the molecular pharmaceutics of ibuprofen[END_REF][START_REF] Burger | Rs-ibuprofen and s-ibuprofen (dexibuprofen). Binary system and unusual solubility behavior[END_REF][START_REF] Dwivedi | Ibuprofen racemate and enantiomers: Phase diagram, solubility and thermodynamic studies[END_REF], the eutectic invariant near the pure components has never been observed and no clear explanations have been given. However, a complete immiscibility domain in the solid state is proposed from x = 0 to 0.5 and from x = 0.5 to 1. On this statement, we decided to examine carefully the thermal behavior of the stable and metastable phases from samples prepared from pure enantiomers and from mixtures between one enantiomer and the racemate. On the basis of these experiments, a new stable phase diagram is thus proposed, and the contribution of a metastable system is discussed.

MATERIALS AND METHOD

Chemicals. S-and RS-ibuprofen were purchased from Acros Organics (99% purity). Ribuprofen was purchased from Santa Cruz Technology (purity higher than 98%). The components were used as received.

Binary mixture preparations. The compounds were separately weighted, then gently mixed by grinding in a mortar during 5 minutes at room temperature.

Thermal experiments. The DSC runs were performed at 2 K.min -1 under atmosphere of dry nitrogen gas, using a differential scanning calorimeter 822e (Mettler-Toledo, Switzerland), calibrated beforehand using high purity indium (99.9 % provided by Mettler-Toledo. Tfus = 156.6 °C; ∆fusH = 28.45 J.g -1 ) and zinc (99.9 % provided by Mettler-Toledo. Tfus = 409.6 °C; ∆fusH = 107.50 J.g -1 ). The samples were introduced in DSC aluminum pans at room temperature, and then hermetically sealed.

X-ray powder diffraction experiments. X-ray data collection was performed on a homemade diffractometer with a Rigaku RA-HF18 rotating anode generator (50 kV, 300mA).

Monochromatic Cu Kα1 (λ = 1.5406 Å) radiation was selected by means of a nickel filter. The sample was placed inside a cryofurnace (TBT -Air Liquide) with a temperature range between -190 and 210 °C, using liquid nitrogen. Each data scan was recorded between 4 and 30 deg. in 2θ, with a step size of 0.02 deg. and a counting time of 1 second per step.

RESULTS AND DISCUSSION

To apprehend the stable phase diagram, thermal analyses were carried out on scalemic mixtures prepared from R-or S-and RS-ibuprofen. The sinister and racemate compounds have previously been characterized thermodynamically in our group by using calorimetry experiments [START_REF] Corvis | Physicochemical stability of solid dispersions of enantiomeric or racemic ibuprofen in stearic acid[END_REF]. With regard to the R-ibuprofen enantiomer, the results are clearly comparable to those of the S-enantiomer.

As far as the establishment of the phase diagram is concerned, selected DSC curves are presented in Figure 1. For mixtures containing less than 85% of enantiomer (R-or S-), two endothermic signals were observed. The first one takes place at constant temperature and corresponds, undoubtedly, to the crossing of a eutectic invariant, as previously reported in the literature [START_REF] Romero | Stereochemical aspects of the molecular pharmaceutics of ibuprofen[END_REF][START_REF] Burger | Rs-ibuprofen and s-ibuprofen (dexibuprofen). Binary system and unusual solubility behavior[END_REF][START_REF] Dwivedi | Ibuprofen racemate and enantiomers: Phase diagram, solubility and thermodynamic studies[END_REF]. The second endothermic signal necessarily refers to the crossing of the (liquid + RS-ibuprofen) biphased region ending by the crossing of the liquidus curve.

The mean eutectic temperature value, obtained from the DSC experiments, is equal to 48.8 ± 0.7 °C and is in close agreement with the previous reported values of 48 °C for Romero and Rhodes [START_REF] Romero | Stereochemical aspects of the molecular pharmaceutics of ibuprofen[END_REF] as well as Burger et. al [START_REF] Burger | Rs-ibuprofen and s-ibuprofen (dexibuprofen). Binary system and unusual solubility behavior[END_REF], but disagrees with the value found by Dwivedi et al.

(i.e. 37 °C) [START_REF] Dwivedi | Ibuprofen racemate and enantiomers: Phase diagram, solubility and thermodynamic studies[END_REF]. For mixtures containing more than 85% of enantiomer (R-or S-), only 1 endothermic peak is observed (cf. the two upper curves in Figure 1). The same statement is made when the mixtures are freshly prepared from R and S enantiomers. Even after 56 days of annealing at room temperature, no change is observed on the shape of the DSC signals. This suggests that the so-obtained samples are stable over the time. Furthermore, the related onset temperatures are slightly higher than those of the stable eutectic invariant for mixtures enriched in one enantiomer. This could indicate, the presence of a partial solid solution [START_REF] Mbodji | Evidence of conglomerate with partial solid solutions in ethylammonium chlocyphos[END_REF] between R-and Sibupofen near the pure enantiomer fractions.

Unfortunately, the region of demixing could not have been detected by DSC due, certainly, to endothermic effects too small. Consequently, the solubility curve of RS-ibuprofen, between the two eutectic points, was examined using the Prigogine-Defay equation [START_REF] Prigogine | Thermodynamique chimique[END_REF]:

1 1 ln(4 .(1 )) fus fus x H x x R T T   ∆ - = ⋅ -     
 where x stands for the mol fraction in enantiomer; Tx, the liquidus temperature of the corresponding mixture. ∆fusH and Tfus are respectively the enthalpy and the temperature of fusion of the racemate. R is the gas constant. The temperatures are in Kelvin.

The plot of ln[4x.(1-x)] vs. (1/Tfus-1/TX) is linear (Figure 3). The melting enthalpy of the racemic compound is deduced from the slope of the straight line: ∆fusH = 53.6 ± 2.7 kJ per mol of RS-ibuprofen, i.e. 26.8 ± 1.4 kJ.mol -1 on the basis of ½ mole of each enantiomer. This value is in agreement with the one found from DSC experiments (25.5 ± 0.3 kJ.mol -1 ). in the liquid state of addition compounds [START_REF] Rastogi | Thermodynamic properties of associated mixtures[END_REF]. This complete dissociation involves, as well, an ideal state for the liquid state (i.e. no excess quantities in the liquid). This is the reason why the solubility curve of RS-ibuprofen follows an ideal behavior, as it will be confirmed further below.

The two extreme data points in Figure 2 correspond to the racemate melting point (x = 0.5) and the eutectic point. Since the eutectic temperature was determined to be comprised between 48.1 and 49.5 °C, it comes that, from that graph, the eutectic composition can be extrapolated for both limits (dotted lines) and the mean value is equal to xe = 0.056 ± 0.003 mol fraction in enantiomer.

To highlight the solid solution obtention for mixtures enriched in one enantiomer, scalemic mixtures of R-and S-ibuprofen were freshly prepared in the solid state before thermal analysis investigations, since ibuprofen does not spontaneously recrystallize from its molten state. The corresponding DSC thermograms are presented in Figure 3. For composition comprised between the 2 eutectic points (i.e. for mol fractions comprised between 0.06 and 0.94 in R-ibuprofen), one can observe an exothermic signal appearing just after the first endothermic signal. The first signal can be attributed to the melting of the metastable solid solution -due to partial miscibility in the solid state [START_REF] Mbodji | Evidence of conglomerate with partial solid solutions in ethylammonium chlocyphos[END_REF] -formed between both enantiomers. The formation of such a solid phase has been also confirmed by X-ray experiments performed with S-and R-ibuprofen mixture samples (xR-ibuprofen = 0.01 and 0.37) annealed at temperature higher than room temperature (Figure 4). Interestingly, when the scalemic mixture is composed of an enriched fraction of one of the enantiomers (e.g. xRibuprofen = 0.01), the annealing protocol at 47 °C does not change the phase contrary to xRibuprofen = 0. The two different thermal behaviors confirm that the metastable domain is formed by a solid solution with lower melting temperatures than that of the stable eutectic invariant between 0.06 and 0.94 in the chiral counterpart. As far as the second endothermic signal from the DSC results is concerned, it corresponds to the recrystallization in the stable state of the liquid obtained after the melting process of the solid solution (Figure 3). Upon heating, after the recrystallization, another endothermic signal takes place. This signal is identical to the one obtained, at the same mol fraction, from mixtures prepared from one enantiomer and the racemate. As a result, this signal corresponds to the crossing of the liquidus curve.

Interestingly, the recrystallization phenomenon highlighted upon heating is followed by a liquidus event (Figure 3) at the same temperature as that of the liquidus event of the stable system (Figure 1), while no recrystallization and no second endothermic signals were noticed for the mixtures enriched in one enantiomer.

When the samples are annealed, at room temperature, for 56 days (Figure 5), the first endotherm is shifted to higher temperature corresponding to the eutectic one, and the exothermic event disappear. Concerning the liquidus point, it remains unchanged. This clearly indicates that the solid solution melts at lower temperature than the (S+RS) or (R+RS) mixtures.

This entails that the solid solution is a metastable phase compared to the mixtures between one enantiomer and the racemate in the mol fraction range 0.06 -0.94 in R-enantiomer. The stable phase diagram has the same shape as the menthol dextrorotatory/levorotatory stable diagram established by our group in 2012 [START_REF] Corvis | Insights into the crystal structure, polymorphism and thermal behavior of menthol optical isomers and racemates[END_REF]. However, in the case of the ibuprofen study, the solution solid melting points (metastable phase) and the invariant points (stable phase) are close from one to another, regardless of the mixture composition. This can be explained by the fact that both racemate and enantiomer crystallize in the monoclinic P21 lattice, the former being centrosymmetric. Furthermore, variation of the molecular volume between S-and RS-ibuprofen, ∆(%), has been determined from crystal structure of the related racemate [START_REF] Mcconnell | The 2-(4-isobutylphenyl) propionic acid. Ibuprofen or prufen[END_REF][START_REF] Shankland | Refinement of ibuprofen at 100 k by single-crystal pulsed neutron diffraction[END_REF] and chiral counterpart [START_REF] Hansen | Redetermination and h-atom refinement of (s)-(+)-ibuprofen[END_REF][START_REF] King | Understanding the terahertz spectra of crystalline pharmaceuticals: Terahertz spectroscopy and solid-state density functional theory study of (s)-(+)-ibuprofen and (rs)-ibuprofen[END_REF] in order to check if the Wallach's rule [START_REF] Brock | On the validity of wallach's rule: On the density and stability of racemic crystals compared with their chiral counterparts[END_REF][START_REF] Wallach | Terpenes and ethereal oils[END_REF] can be applied in the case of ibuprofen. Interestingly, ibuprofen verify the Wallach's rule between room and cold temperatures since ∆(%) is 1.9%, and 2.4% at 25 and -173 °C, respectively. For that range of temperature, one can confirm that racemic crystal of ibuprofen is denser than its chiral counterparts. Noteworthily, according to Wallach or Brock, RSibuprofen belongs to group II, i.e. the group of chemical compounds presenting enantiomers that can be resolved. The relative stability of the racemic ibuprofen over its enantiomers can be also confirmed by determining the Pettersson value i [START_REF] Pettersson | Stereochemical studies in the α-aryl carboxylic acid series[END_REF][START_REF] Bredikhin | Spontaneous resolution among chiral glycerol derivatives: Crystallization features of orthoalkoxysubstituted phenyl glycerol ethers[END_REF], or the Gibbs free energy of the R + S = RS transformation at the melting temperature of the chiral counterpart since Tfus, S- or R-ibuprofène < Tfus, RS-ibuprofen [START_REF] Bredikhin | Spontaneous resolution among chiral glycerol derivatives: Crystallization features of orthoalkoxysubstituted phenyl glycerol ethers[END_REF][START_REF] Li | Characterization of racemic species of chiral drugs using thermal analysis, thermodynamic calculation, and structural studies[END_REF]. Indeed, stable racemic compounds should present i > 1.5 and ∆G° << 0. From the data of the present study, the i and ∆G°(Tfus, S-or R-ibuprofen) values have been calculated as follows: 9.6 (non-dimensional data) and -3.6 kJ.mol -1 respectively.

A B Notably, Li et al. have obtained the same ∆G°(Tfus, S-or R-ibuprofen) value for racemic ibuprofen [START_REF] Li | Characterization of racemic species of chiral drugs using thermal analysis, thermodynamic calculation, and structural studies[END_REF]. Finally, to complete the stable phase diagram survey, a 48.8 °C temperature invariant is also proposed via data analysis (Figure 6). The composition range of this invariant is comprised between 0.03 and 0.97.

Simulation of the metastable phase diagram was performed using the LIQFIT thermodynamic method [START_REF] Bouwstra | A thermodynamic method for the derivation of the solidus and liquidus curves from a set of experimental liquidus points[END_REF], taking into consideration the thermal properties of the enantiomers. Thus, a

Roozeboom's type III diagram has been obtained [START_REF] Prigogine | Thermodynamique chimique[END_REF][START_REF] Bouwstra | A thermodynamic method for the derivation of the solidus and liquidus curves from a set of experimental liquidus points[END_REF][START_REF] Roozeboom | Solubility and melting point as criteria for racemic compounds, pseudoracemic mixed crystals and inactive conglomerates[END_REF][START_REF] Chen | Chiral co-crystal solid solution: Structures, melting point phase diagram, and chiral enrichment of (ibuprofen)2(4,4-dipyridyl)[END_REF], confirming the existence of a solid solution between the two ibuprofen enantiomers. The related solidus and liquidus temperatures decrease when approaching the equimolar composition from the pure chiral counterpart composition (Figure 6, red curves). At a given composition on the richenantiomer part of the diagram, the small difference of temperature between the solidus and the liquidus justifies that the two beginnings of melting loops are merged when the composition approaches the center of the diagram. This results in the existence of a continuous solid solution that is metastable between the two eutectic points, i.e. in the 0.06 -0.94 composition range. Over this range, the solid solution is the stable phase of the scalemic namely RS-ibuprofen phase II [START_REF] Dudognon | Evidence for a new crystalline phase of racemic ibuprofen[END_REF]. Also, the modelling gives rise to two minima (x = 0.20 and 0.80) for the metastable phase diagram. These points do not necessarily have a physical meaning but were the only solution of the modelling from the experimental points. The xR-ibuprofen = 1% sample formulated between S-and RS-ibuprofen is a physical mixture at room temperature since one can observe on the corresponding XPRD pattern a superposition of racemate and enantiomer signal (Figure 7A) [START_REF] Corvis | Physicochemical stability of solid dispersions of enantiomeric or racemic ibuprofen in stearic acid[END_REF]. However, before melting, the physical mixture transits to a solid solution as expected from the thermal analysis experiments (Figures 1, 3 and6). The latter transition takes place between 37 and 42 °C. Indeed, the peak at 6.1 deg. which belongs to the racemate ibuprofen XPRD pattern disappears in the patterns recorded from 42 °C, presenting the solid solution XPRD signals (Figure 7B). The X-ray diffraction experiments hence confirm the assumption if the solid solution between xR-ibuprofen = 0 and 0.06, as well as for the symmetric composition. Consequently, the pseudo-racemate that has been highlighted in the present work (Tfus = 47 °C) is a solid solution formed from the stable chiral counterparts in equimolar proportions. This solid solution may correspond to the "unstable phase near the eutectic point" proposed by Burger and co-workers [START_REF] Burger | Rs-ibuprofen and s-ibuprofen (dexibuprofen). Binary system and unusual solubility behavior[END_REF] although it is stable for mol fraction of enantiomer comprise between 0 to 0.06, but metastable for mol fraction of enantiomer higher than 0.06 since the stable state is, in such a case, the physical mixture between the racemate and one of the enantiomer.

CONCLUSIONS

The rectus/sinister ibuprofen stable phase diagram proposed here is an overlapping of a Roozeboom's type III solid solution curve with the racemate solubility curve, crossing at low concentration of one of the enantiomers. The existence of the solid solution has been demonstrated in this work for the first time and corresponds to the scalemic S+R-ibuprofen mixtures that are stable for mol fractions in enantiomer lower than 6% and metastable for higher values until 94%. As far as the latter range of concentrations is concerned, the stable state is the S+RS-ibuprofène or R+ RS-ibuprofen eutectic mixtures. The kinetics of metastability vs stability conversion has also been apprehended by annealing of the materials at room temperature. Such data can be of interest for preparation of non-steroidal antiinflammatory drugs with new ratio of ibuprofen chiral counterparts with optimized bioavailability, pharmacokinetics, metabolism, and toxicity parameters. As an example, amphetamine can be marketed either in its racemic form (Eveko ® , approved by the FDA in 2012) or as a 75:25 S:R scalemic mixture (Adderall ® , approved by the FDA in 1996).

Therefore, Adderall ® can be considered as a formulation with improved therapeutic effect since differences in onset and duration of action between the S-and R-amphetamine have been described in rats [START_REF] Segal | Behavioral characterization of d-and l-amphetamine. Neurochemical implications[END_REF][START_REF] Taylor | Differential effects of d-and l-amphetamine on behavior and on catecholamine disposition in dopamine and norepinephrine containing neurons of rat brain[END_REF] and a stereospecific metabolism of amphetamine has been evidenced in human [START_REF] Gunne | The urinary output of d-and l-amphetamine in man[END_REF][START_REF] Cody | Amphetamine excretion profile following multidose administration of mixed salt amphetamine preparation[END_REF] and rat [START_REF]Mass spectra of n-[(s)-α±-methoxy-α±-(trifluoromethyl)phenylacetyl] derivatives of chiral amines. Stereochemistry of amphetamine metabolism in the rat[END_REF][START_REF] Gunne | Stereoselective metabolism of amphetamine[END_REF][START_REF] Gunaratna | Investigation of stereoselective metabolism of amphetamine in rat liver microsomes by microdialysis and liquid chromatography with precolumn chiral derivatization[END_REF] in vivo studies.

Figure 1 .

 1 Figure 1. Selected DSC curves of mixtures containing RS-and S-ibuprofen as a function of the mol fraction in R-ibuprofen (from top to bottom): 0.02, 0.09, 0.25, 0.30, 0.42 and 0.46.

Figure 2 .

 2 Figure 2. Dependence of mole fraction with the liquidus temperature using the Prigogine-Defay model.

Figure 3 .

 3 Figure 3. (A) Selected DSC curves of mixtures containing R-and S-ibuprofen as a function of the mol fraction in R-ibuprofen (from top to bottom): 0.05, 0.10, 0.15, 0.28, 0.38 and 0.50. (B) The DSC curve obtained for 0.15 mol fraction in R-ibuprofen sample after integration by using the STARe software (version 15.00) from Mettler-Toledo. The recrystallization events are marked with an asterisk (*).

Figure 4 .

 4 Figure 4. X-ray powder diffraction patterns obtained at room temperature for S-ibuprofen (─), and R-and S-ibuprofen mixtures after 6 days annealing (─). (A) xR-ibuprofen = 0.01 and Tannealing = 47 °C, (B) xR-ibuprofen = 0.37 and Tannealing = 40 °C.

Figure 5 .

 5 Figure 5. Effect of the time on the stability of the R-/S-ibuprofen mixtures. DSC curves obtained for the freshly prepared samples (dotted line), and for the same composition sample after 56 days annealing at room temperature (solid line). Mol fraction in R-ibuprofen: (A): 0.42; (B): 0.50.

  mixtures. Interestingly, by comparing this range to the 0.03 -0.97 range of the eutectic invariant, one can deduce a symmetrical ∆x = 0.03 for the crossing regions between the stable enantiomer/racemic physical mixture and the stable scalemic solid solution. In addition, the Roozeboom's type III diagram presents a single point at x = 0.5, suggesting the existence of a pseudo-racemate which melts at 47.2 °C. This racemic solid solution might correspond to a new polymorph different from the one discovered by Dudognon et al. which melts at 17 °C,

Figure 6 .

 6 Figure 6. Stable and metastable T-x phase diagrams established between the chiral counterparts of ibuprofen. The experimental data obtained from the DSC results interpretations (full circles and squares) were modeled for the eutaxia (horizontal ─), the liquidus (─), and the solid solution (─).

Figure 7 .

 7 Figure 7. X-ray powder diffraction patterns obtained for a given RS-and S-ibuprofen mixture, xR-ibuprofen = 1%, as a function of temperature. (A) Temperature: 22, 42, 47, and 52 °C, from the top curve to the bottom curve, respectively. (B) Patterns for 2θ scale comprises between 6 and 8 deg. Temperature: (─) 22, (••••) 27, (─) 32, (••••) 37, (─) 42, (─) 47, and (─) 52 °C.

  [START_REF]Mass spectra of n-[(s)-α±-methoxy-α±-(trifluoromethyl)phenylacetyl] derivatives of chiral amines. Stereochemistry of amphetamine metabolism in the rat[END_REF] samples which transform into RS/S physical mixtures.

					A
											*
											*
											*
											*
	4	6	8	10	12	14	16	18	20	22	24	4	6	8	10	12	14	16	18	20	22	24
					2θ (deg.)											2θ (deg.)
					B
											*


Corentin Jouault
email: jouaultc0@gmail.com

Michael S Engel
email: msengel@ku.edu

Andre Nel

A new baissopterid snakefly (Raphidioptera: Baissopteridae) from mid-Cretaceous amber of northern Myanmar

Keywords: Cenomanian, New species, Paleodiversity, Systematic

Electrobaissoptera liui sp. nov., a new species of the snakefly family Bassopteridae, is described and figured from an individual preserved in mid-Cretaceous amber from Tanai, northern Myanmar.

Electrobaissoptera liui sp. nov. preserves nearly all of the known characters used to circumscribe the family and genus, and is unique among bassopterids for possessing a complete ma-mp crossvein in the hind wing, thereby dividing cell m1.

Introduction

Species of the order Raphidioptera, most frequently known as snakeflies, are easily distinguished from other holometabolous insects owing to the combination of a prognathous head, a slender and elongate prothorax, the presence of a pigmented pterostigma, and a long ovipositor. As larvae, with a terrestrial life-style, they may be recognized by their elongate flattened body, a prognathous head with chewingmandibulate mouthparts, and a soft 10-segmented abdomen. Adults and larvae are known to be entomophagous and/or necrophagous, with larvae living under tree bark, and amid detritus around the roots of shrubs [START_REF] Kovarik | Development and behavior of a snakefly, Raphidia bicolor Albarda (Neuroptera: Raphidiidae)[END_REF][START_REF] Aspöck | The biology of Raphidioptera: a review of present knowledge[END_REF]. Some adults have been observed feeding on pollen [START_REF] Aspöck | Raphidioptera (snakeflies)[END_REF]. Most remarkably and unique among homometabolan insects, snakeflies have active pupae, with dectitious mouthparts, and are predators of small arthropods [START_REF] Engel | Phylogeny and evolution of Neuropterida: Where have wings of lace taken us?[END_REF].

The Raphidioptera, together with Megaloptera and Neuroptera, comprise the superorder Neuropterida, which has been presumed to have first diverged from other early Holometabola during the Late Carboniferous [START_REF] Vasilikopoulos | An integrative phylogenomic approach to elucidate the evolutionary history and divergence times of Neuropterida (Insecta: Holometabola)[END_REF]. This estimate seems to agree with the age of the oldest putative stem-representatives of the superorder dated to the Permian (e.g., [START_REF] Shcherbakov | Permian ancestors of Hymenoptera and Raphidioptera[END_REF].

The oldest definitive Raphidiidae and Inocelliidae (the two extant families) are from Eocene, even if an enigmatic taxon, Sinoinocellia liaoxiensis, was described as an inocelliid from the Callovian of China [START_REF] Wang | Early Mesozoic insects (sic) fossils from western Liaoning[END_REF]. Sinoinocellia was poorly documented and needs to be critically reevaluated. However, the Early Cretaceous age proposed by [START_REF] Vasilikopoulos | An integrative phylogenomic approach to elucidate the evolutionary history and divergence times of Neuropterida (Insecta: Holometabola)[END_REF] for crown-Raphidioptera is an illustration of the discrepancies between node-dating estimates and stratigraphic/fossil evidence. The 'time divergence estimate using node-dating' method that [START_REF] Vasilikopoulos | An integrative phylogenomic approach to elucidate the evolutionary history and divergence times of Neuropterida (Insecta: Holometabola)[END_REF] employed, only allows for the integration of families with extant representatives, which is a minor part of snakefly diversity (25% of familial diversity, or even less if Mesoraphidiidae are paraphyletic, and definitively much less at the specific level). Therefore, [START_REF] Vasilikopoulos | An integrative phylogenomic approach to elucidate the evolutionary history and divergence times of Neuropterida (Insecta: Holometabola)[END_REF] dated a potential divergence time for the families Inocelliidae and Raphidiidae (i.e., Neoraphidioptera), rather than Raphidioptera. This is further complicated if Neoraphidioptera are polyphyetic, as one hypothesis considers Inocelliidae and Raphidiidae to have originated separately from among clades of Mesoraphidiidae or other Cretaceous snakeflies (e.g., [START_REF] Lu | A new and diverse paleofauna of the extinct snakefly family Baissopteridae from the mid-Cretaceous of Myanmar (Raphidioptera)[END_REF]. To offer consistent dating, only a tip-dating or totalevidence dating approach would make it possible to properly consider the entire fossil record of the order, and to propose ages that are more reflective of the true paleontological diversity of the lineage (Jouault et al., 2021a,b). Nevertheless, putative representatives of stem-group Raphidioptera have been recorded from deposits as early as the Permian [START_REF] Shcherbakov | Permian ancestors of Hymenoptera and Raphidioptera[END_REF][START_REF] Engel | Phylogeny and evolution of Neuropterida: Where have wings of lace taken us?[END_REF] suggesting that the order is at least of Permian age. During the Mesozoic, the order was speciose (e.g. [START_REF] Lu | A new and diverse paleofauna of the extinct snakefly family Baissopteridae from the mid-Cretaceous of Myanmar (Raphidioptera)[END_REF] and widely distributed (http://fossilworks.org/), but it declined rapidly prior to and after the Cretaceous/Cenozoic (K/T) event. The mid-Cretaceous amber from Myanmar provides important insight into their diversity and morphology prior to this decline. Herein, we describe and figure a new species of snakefly from this rich deposit.

Material and methods

The amber piece containing the specimen comes from the deposits of Noije Bum in the Hukawng Valley (26° 29′ N, 96° 35′ E), Kachin State, northern Myanmar (see detailed map in Grimaldi and Ross, 2017: fig. 2). Radiometric data established an early Cenomanian age (98.79 ± 0.62 Ma) for Kachin amber, based on zircons from volcanic clastes found within the amber-bearing sediments [START_REF] Shi | Age constraint on Burmese amber based on U-Pb dating of zircons[END_REF]. Some ammonites found in the amber-bearing bed and within the amber itself corroborate a latest Albian-earliest Cenomanian age [START_REF] Cruickshank | Geology of an amber locality in the Hukawng Valley, northern Myanmar[END_REF][START_REF] Yu | An ammonite trapped in Burmese amber[END_REF].

The holotype of Electrobaissoptera liui sp. nov. is nearly complete, only damaged at the apices of the left wings and abdomen. The amber piece was polished using a polisher (Buehler EcoMet 30) and a thin silicon carbide sanding paper (grit size = 7000), and the specimen was examined and photographed with a Leica MZ APO with an attached Canon EOS 5D Mark II camera. All images were digi-tally stacked photomicrographic composites of several individual focal planes, which were obtained using Helicon Focus 6.7. The figures were composed with Adobe Illustrator CC2019 and Photoshop CC2019. The wing venation and cell nomenclature follows [START_REF] Lu | A new and diverse paleofauna of the extinct snakefly family Baissopteridae from the mid-Cretaceous of Myanmar (Raphidioptera)[END_REF]. The amber piece is housed in the amber collection of the Geological Department and Museum of the University of Rennes, France Diagnosis. Tarsomere III symmetrically bilobed, with a pair of wide lobes; forewing long elliptical, ca. 3.25× as long as wide; pterostigma ca. 6.0× as long as wide; RA simple distad pterostigma; hind wing with cell m1 divided into two parts by a complete ma-mp crossvein.

Description. Body length ca. 6.39 mm (as preserved); antenna length ca. 3.24 mm; forewing length ca. 6.69 mm and width ca. 1.99 mm; hind wing partially preserved.

Body dark brown without distinctive color pattern (Fig. 1); head narrowly rectangular, with vertex slightly longer than compound eye; occiput short; compound eyes ovoid, exophthalmic; ocelli present (Figs. 1; 2A). Prothorax slender, elongate, slightly longer than head; meso-plus metathorax as long as prothorax. Legs slender, densely covered with microtrichia; tarsomere III symmetrically bilobed, with a pair of slender lobes (Fig. 2B); pretarsal claws forked at distal third, with an acutely tapering inner ramus (Fig. 2B). Forewing long elliptical, ca. 3.25× as long as wide (Figs. 1A,C; 3A); costal space broadened at proximal third, with five simple crossveins; ScP terminating into costal margin slightly distad wing midpoint; four simple RA veinlets present; pterostigma ~6.0× as long as wide, uniformly colored, closed by a crossvein proximally, distally ending at second veinlet of RA, with a straight but distinctly inclined incorporated veinlet of RA; three radial crossveins present, three radial cells gradually shortened, r1 longest, r2 broadest; RP forked proximad its midpoint, with two simple branches; two rp-ma crossveins, forming two discal cells; MA with stem originating at MP1, distinctly distad initial branching point of MP; MA deeply forked proximad its midpoint, with two simple branches, length of branching of MA as long as branching of RP; three ma-mp crossveins, forming three medial cells; MP deeply forked, with three terminal branches and a series of three discoidal cells; CuA marginally forked;

CuP simple; two cua-cup crossveins present; A1 and A2 simple. Hind wing slightly shorter and narrower than forewing (Figs. 1A; 3B); costal space narrow, with five crossveins; ScP terminating into costal margin slightly proximad wing midpoint; four simple RA veinlets present; pterostigma similar to that of forewing; five radial crossveins present, r3 longest and broadest, remaining radial cells almost of equal lengths; RP forked proximad its midpoint, with two simple branches; two rp-ma crossveins, forming two discal cells; MA with stem originating from base of MP stem, long and sinuate; MA forked at its midpoint, with two simple branches, branching of MA as long as branching of RP; four ma-mp crossveins, forming three medial cells; MP deeply forked, with four terminal branches and a series of three discoidal cells; cell m1 divided into two parts (m1a and m1b on the drawing) by a mamp crossvein, directed toward stem of MA; three mp-cua crossveins, with 1mp-cua almost vertical to stem of MP; CuA distally forked; CuP simple; two cua-cup crossveins present; A1 and A2 simple.

Terminalia not preserved.

Discussion

The order Raphidioptera was quite diverse during the Mesozoic, with numerous genera and species described from amber inclusions and compression fossils (e.g., Lyu et al., 2017a,b;[START_REF] Lu | A new and diverse paleofauna of the extinct snakefly family Baissopteridae from the mid-Cretaceous of Myanmar (Raphidioptera)[END_REF]. This diversity has been organized into six extinct families Priscaenigmatidae, Chrysoraphidiidae (perhaps best considered a subfamily of the former family), Juroraphidiidae, Baissopteridae, Mesoraphidiidae, and Metaraphidiidae (also perhaps best classified as a subfamily of the preceding family) [START_REF] Liu | New transitional fossil snakeflies from China illuminate the early evolution of Raphidioptera[END_REF]. The present fossil cannot be placed among the Priscaenigmatidae (sensu [START_REF] Engel | The smallest snakefly (Raphidioptera: Mesoraphidiidae): a new species in Cretaceous amber from Myanmar, with a catalog of fossil snakeflies[END_REF] owing to the presence of a broad costal area (vs. narrow); a short Sc that does not extend to the wing apex, and fuses into C near the wing midpoint (vs. extending nearly to the wing apex before fusing with R); a different configuration of CuP; and a distinct 'ovoid', basal cell between A1 and A2 (vs. absent) (Whalley, 1985: figs. 45-46). Similarly, the present specimen cannot be placed in Chrysoraphidiidae as diagnosed by [START_REF] Liu | A remarkable new genus of basal snakeflies (Insecta: Raphidioptera: Priscaenigmatomorpha) from the Early Cretaceous of China[END_REF] owing to the possession of a simpler wing venation (i.e., fewer radial cells and ScA not present); a short closed pterostigma (vs. elongate, open proximally, closed distally by veinlet of R); Sc meeting C before the pterostigma (vs. running within the pterostigma to its distal end, connecting to R by a distal oblique crossvein); MA branching (vs. simple); crossveins not arranged in two series of gradate crossveins in the radial and mediocubital fields (vs. arranged as stated); A1 short and simple (vs. long, pectinately branched, with two branches). The current fossil cannot be placed in Juroraphidiidae (as defined by [START_REF] Liu | New transitional fossil snakeflies from China illuminate the early evolution of Raphidioptera[END_REF] due to the more complex wing venation (i.e., with numerous cells and three discoidal cells); a relatively wide costal region (vs. narrow); the tarsi tetramerous, with tarsomere III bilobed (vs. pentamerous and tarsomere III simple); a short closed pterostigma (vs. elongate, open proximally); a short Sc, terminating before the pterostigma (vs. long, running within the pterostigma); and forewing MA forked (vs. simple). The fossil does not fall within Mesoraphidiidae as circumscribed owing to the presence of ocelli (vs. absent or rarely present) (Liu et al., 2016: figs 2, 5, 7); a more developed wing venation (i.e., with three cells doi, two cells dc; a pterostigmal RA veinlet, vs. absent); pretarsal claws with a pre-apical ramus (vs. simple). The family Metaraphidiidae was proposed by [START_REF] Bechly | A new fossil genus and species of snakefly (Raphidioptera: Mesoraphidiidae) from Lower Cretaceous Lebanese amber, with a discussion of snakefly phylogeny and fossil history[END_REF] to accommodate the peculiar genus Metaraphidia [START_REF] Whalley | The systematics and palaeogeography of the Lower Jurassic insects of Dorset, England[END_REF]. They used the following forewing venation characters in the diagnosis of the family: pterostigma divided by two crossveins; A2 and A3 not fused; no crossvein between CuA and CuP. Our specimen does not possess such wing venation since only one RA veinlet is present in the pterostigma, and more importantly CuA and CuP are connected by a crossvein, while their absence in Metaraphidia is considered to be an apomorphic character of the family. In actuality, Metaraphidiidae is likely merely an autapomorphic member of the Mesoraphidiidae as there are no convincing synapomorphies for mesoraphidiids excluding Metaraphidia. Metaraphidiidae should be seriously reevaluated as either considered a subfamily of Mesoraphidiidae or synonymized outright.

Recently, [START_REF] Lu | A new and diverse paleofauna of the extinct snakefly family Baissopteridae from the mid-Cretaceous of Myanmar (Raphidioptera)[END_REF] revised the diagnosis of the family Baissopteridae and proposed the following characters to differentiate the family: ocelli present; RA veinlet within pterostigma usually present; forewing M with stem usually shorter than doi1; forewing M and CuA diverging at an angle of more than 40°; venation enriched, especially crossvenation, forming at least three radial cells in the forewing and four radial cells in the hind wing, at least two discal cells in both fore-and hind wings, usually four or more discoidal cells in both fore-and hind wings; male gonocoxites IX paired and shelllike; male gonapophyses IX reduced. All of these wing venational and body characters are present in the present fossil, with the exception of those genital characters as these cannot be observed owing to the incomplete preservation of the specimen. Therefore, it is clear that the current fossil belongs to the family Baissopteridae.

Following the key to genera of Baissopteridae of [START_REF] Lu | A new and diverse paleofauna of the extinct snakefly family Baissopteridae from the mid-Cretaceous of Myanmar (Raphidioptera)[END_REF], the present fossil keys out to the genus Electrobaissoptera [START_REF] Lu | A new and diverse paleofauna of the extinct snakefly family Baissopteridae from the mid-Cretaceous of Myanmar (Raphidioptera)[END_REF] owing to the hind wing with the stem of MA long, slightly sinuate; the head with normal-sized compound eyes and a well-developed vertex; the hind wing cell doi1 with a crossvein directed toward or connecting to the stem of MA; the generally small body size, with forewing 5.5-7.0 mm long; the forewing RP with only two branches; the forewing MA separating from MP obviously distad the initial branching point of MP; and with RP branches almost as long as MA branches in the forewings.

The new specimen is relatively small with a forewing about 6.70 mm (compared to most other Baissopteridae with wings longer than 15 mm), thereby excluding affinities with other Burmese amber genera (e.g., Allobaissoptera [START_REF] Lu | A new and diverse paleofauna of the extinct snakefly family Baissopteridae from the mid-Cretaceous of Myanmar (Raphidioptera)[END_REF]; the head is narrowly rectangular, but its exact width is unknown (the amber piece cannot be prepared for a direct dorsal view due to the position of syninclusions); and the vertex is nearly as long as the compound eye (diameter of compound eye about onethird head length). All of these characters fit well with those of Electrobaissoptera burmanica [START_REF] Lu | A new and diverse paleofauna of the extinct snakefly family Baissopteridae from the mid-Cretaceous of Myanmar (Raphidioptera)[END_REF], even if the place occupied by the compound eyes and their lengths differ. However, the present fossil differs from E. burmanica in tarsomere III symmetrically bilobed, with a pair of wide lobes, rather than slender in E. burmanica (Lu et al., 2020: fig. 11e); forewing long elliptical, ca. 3.25× as long as wide, vs. 3.5× as long as wide; pterostigma ca. 6.0× as long as wide, vs. 5.0× as long as wide; RA simple distad pterostigma vs. forked in E. burmanica; hind wing with cell m1 divided into two parts by a complete ma-mp crossvein, vs. incomplete in E. burmanica (Lu et al., 2020: fig. 12d-e). Notice that the two veins are less pigmented than the surrounding veins but clearly present. Although several dif-ferences are recorded between E. burmanica and the current fossil, these are more trivial features and not suggestive of distinct genera but instead closely related species. The venation of Electrobaissoptera liui sp. nov. is not aberrant (and certainly not teratological), and demonstrates that Baissopteridae may display several intermediates in wing venation with species lacking or possessing a rudimentary or complete ma-mp crossvein. Nonetheless, given the general rarity of these fossils it is not possible to critically evaluate potential ranges of morphological variation within any given fossil species. Based on observed variations in modern snakeflies, albeit of different families from those in the Mesozoic, the observed differences in wing venation between the current fossil and other baissopterids certainly suggests separate species rather than extremes of a range of population variation.

Conclusion

Amber from northern Myanmar provides once again novel insights into the paleodiversity of the West Burma Block (WWB) during its break-up and migration from South Gondwana to Asia during the Cretaceous. The description of Electrobaissoptera liui sp. nov. serves to increase the diversity of baissopterid documented from the WWB during the mid-Cretaceous and helps to clarify some wing venation characters originally presumed to be potential aberrations in E. burmanica. If the fossil record of the order continues to grow, it seems obvious that a phylogeny integrating the whole of the fossil diversity of Raphidioptera will be needed to clarify the classification and estimate times of divergence among the various clades, and ultimately to propose clear hypotheses concerning snakefly diversification and eventual and decline.

(Figs

  Figs. 1-3 Lsid: XXXX Type material. Holotype: IGR.BU-028 deposited in the Geological Department and Museum of the University of Rennes, France (IGR) (in an amber piece measuring 20 × 16 × 5 mm, with several minute syninclusions and an orthopteran nymph plus a platypodid beetle). Locality and horizon. Noije Bum Hill, Hukawng Valley, Kachin State, Myanmar; upper Albian to lower Cenomanian, mid-Cretaceous.

Figure 1 .

 1 Figure 1. Electrobaissoptera liui sp. nov., holotype IGR.BU-028. A: Habitus in left lateral view; B: Detailed view of head; C: Detailed view of forewing. Scale bars equal 0.5 mm.

Figure 2 .

 2 Figure 2. Detailed view of Electrobaissoptera liui sp. nov., holotype IGR.BU-028. A: Head with black arrows pointing ocelli; B: Mid-legs with black arrow pointing the pre-apical ramus. Scale bars equal 0.25 mm Figure 3. Line drawing of wing venation with cell and vein names labelled. A: Forewing; B: Hind wing. Scale bars equal 0.5 mm.

Acknowledgments

The authors thanks the two anonymous reviewers for their valuable comments and precisions provided in early draft and review of the paper. We also thank Dr. Eduardo Koutsoukos for managing the article during the editing process. This work is part of the Ph.D. project of Corentin Jouault on the « Impact des interactions biotiques et paléo-évènements sur la diversification des insectes Neuropterida ».


Gauthier Dot

Raphael Licha

Florent Goussard

Vittorio Sansalone
email: vittorio.sansalone@u-pec.fr

A new protocol to accurately track long-term orthodontic tooth movement and support patient-specific numerical modeling

Keywords: Tooth Movement, Dental Models, Cone-Beam Computed Tomography, Finite Element Analyses

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

INTRODUCTION

Orthodontic treatments usually rely on an orthodontic archwire passing through braces bonded on the teeth, which can be associated to accessory elements like elastic chains or springs. Orthodontic forces transmitted to the teeth are related to the elastic deformation of these materials and to the friction and sliding of the archwire in the braces. These forces trigger alveolar bone remodeling and lead to orthodontic tooth movement (OTM) [START_REF] Henneman | Mechanobiology of tooth movement[END_REF][START_REF] Krishnan | On a path to unfolding the biological mechanisms of orthodontic tooth movement[END_REF][START_REF] Wise | Mechanisms of tooth eruption and orthodontic tooth movement[END_REF]. Nowadays, orthodontic treatment strategies are primarily based on orthodontists' clinical experience. In some cases, unwanted effects may appear like orthodontic external root resorption (OERR) [START_REF] Viecilli | Effects of initial stresses and time on orthodontic external root resorption[END_REF][START_REF] Zhong | In vivo effects of different orthodontic loading on root resorption and correlation with mechanobiological stimulus in periodontal ligament[END_REF] or difficulties in planning and predicting tooth movement might arise [START_REF] Burstone | Physics and clinical orthodontics : 100 years ago and today[END_REF].

Modeling and simulation have a great potential to support clinical activity [START_REF] Likitmongkolsakul | Development and Validation of 3D Finite Element Models for Prediction of Orthodontic Tooth Movement[END_REF]. In solid mechanics, Finite Element Analysis (FEA) is one of the most attractive numerical approaches. Recent advances in imaging techniques allow the set-up of imagebased, patient-specific FEA whose relevance is largely acknowledged in several clinical domains. However, numerical simulation of long-term (several weeks or months) OTM remains a challenge despite the wealth of works existing on this subject (Table 1) [START_REF] Bourauel | Application of bone remodeling theories in the simulation of orthodontic tooth movements[END_REF][START_REF] Chen | A periodontal ligament driven remodeling algorithm for orthodontic tooth movement[END_REF][START_REF] Hamanaka | Numeric simulation model for long-term orthodontic tooth movement with contact boundary conditions using the finite element method[END_REF][START_REF] Hasegawa | Computer simulation of orthodontic tooth movement using CT image-based voxel finite element models with the level set method[END_REF][START_REF] Likitmongkolsakul | Development and Validation of 3D Finite Element Models for Prediction of Orthodontic Tooth Movement[END_REF][START_REF] Marangalou | Numerical simulation of orthodontic bone remodeling[END_REF][START_REF] Schneider | Numerical experiments on long-time orthodontic tooth movement[END_REF][START_REF] Wang | Simulation of bone remodelling in orthodontic treatment[END_REF].

A critical issue in the development of FEA of long-term OTM concerns the availability of suitable clinical data. Most of the existing works based on FEA showed no experimental calibration or validation. To the best of our knowledge, only two studies compared their numerical results with clinical data of one and two patients, respectively (Table 1) [START_REF] Chen | A periodontal ligament driven remodeling algorithm for orthodontic tooth movement[END_REF][START_REF] Likitmongkolsakul | Development and Validation of 3D Finite Element Models for Prediction of Orthodontic Tooth Movement[END_REF]. Numerical models cannot trustfully support clinical practice as long as they are not properly validated against experimental data [START_REF] Albogha | Generic finite element models of orthodontic miniimplants : are they reliable[END_REF][START_REF] Hannam | Current computational modelling trends in craniomandibular biomechanics and their clinical implications[END_REF]. In order to generate accurate three-dimensional (3D) patient-specific models of craniofacial structures, the main imaging techniques that may be used are Computed-Tomography (CT) and Cone Beam CT (CBCT) (Table 1). Due to its broad accessibility and low-dosimetry protocols, CBCT is more commonly used in orthodontics procedures [START_REF] Kapila | CBCT in orthodontics: assessment of treatment outcomes and indications for its use[END_REF]. Although CBCT cannot be regarded as a standard method of diagnosis, its use can be justified for carefully designed research purposes [START_REF] Kapila | CBCT in orthodontics: assessment of treatment outcomes and indications for its use[END_REF]. As with any radiographic examination, the three basic principles of radiation protection (justification, optimization and limitation) must be strictly observed, and CBCT scans cannot be repetitiously used to track OTM all along an orthodontic treatment. As shown in Table 1, only one published study tracked clinical OTM in order to update its model geometry, using scanned dental models [START_REF] Likitmongkolsakul | Development and Validation of 3D Finite Element Models for Prediction of Orthodontic Tooth Movement[END_REF]. Furthermore, modeling assumptions, including loading conditions and material behavior, are key in order to set up reliable FEA. Accurate modeling of clinically realistic force systems is a major challenge of orthodontic simulations [START_REF] George | A preliminary approach in the prediction of orthodontic bone remodeling by coupling experiments, theory and numerical models[END_REF][START_REF] Roberts | Biology of biomechanics : finite element analysis of a statically determinate system to rotate the occlusal plane for correction of a skeletal class III open-bite malocclusion[END_REF]. For example, friction and sliding of the archwire is very rarely considered, even in situations where it can have a major clinical impact (Table 1) [START_REF] Hamanaka | Numeric simulation model for long-term orthodontic tooth movement with contact boundary conditions using the finite element method[END_REF]. The friction between the archwire and the braces can be hardly measured in vivo and therefore prevents an accurate calibration of patient-specific biomechanical models [START_REF] George | A preliminary approach in the prediction of orthodontic bone remodeling by coupling experiments, theory and numerical models[END_REF]. More generally, a proper definition of the boundary conditions is a critical issue as long as the orthodontic forces are statically indeterminate as it is usually the case with traditional orthodontic treatments. Additionally, an inaccurate description of the orthodontic forces entails issues in the calibration of the constitutive models of the materials making up the maxillary structures. Indeed, an accurate knowledge of the prevailing mechanical forces and of the stress-strain distribution in the maxillary structures is required to understand the mechanical response and to calibrate suitable constitutive models for these materials. Thus, coarse approximations on the description of the orthodontic forces can seriously threaten the reliability of the numerical simulations.

The main goal of this paper is to propose a new tracking protocol to generate 3D models of the maxillary system (bone and teeth) that can be used to set up and validate numerical models. It relies on one initial CBCT scan and monthly intra-oral scans (IOS). The frequency of IOS corresponds to the typical frequency of appointments in orthodontic practice. We tested the relevance of our proposal in a clinical situation, and used the 3D models to develop preliminary FE models (FEM) of the relevant maxillary structures. In order to reduce the bias in modeling the orthodontic forces, a frictionless and statically determinate lingual device for maxillary canine retraction was designed. Material parameters of the FEM were matched against clinical data.

MATERIALS AND METHODS

Clinical procedure

After verbal and written information about the research, one patient accepted to be included in the study. This 28-year-old patient showed a class I malocclusion, with significant anterior crowding and protrusion of incisors. The orthodontic treatment plan aimed at correcting the malocclusion with avulsion of upper and lower first premolars, recoil of the canines and repositioning of the incisors with controlled posterior anchorage loss. In the maxilla, after the avulsion of the upper first premolars, three Temporary Anchorage Devices (TADs) and a personalized lingual device were placed (Figure 1). This device was designed so as to apply a statically determinate system of orthodontic forces at the theoretical initial center of resistance of the canines-the point that a force should pass through in order to obtain a pure translation of the tooth. Details about the clinical procedure are given in the Supplementary Materials, Section A. This study was approved by the ethical committee of protection of persons (CPP Paris Ile-de-France 1, reference 2016-dec.14420 ND).

Data acquisition

A CBCT scan of the maxilla was acquired before the placement of the TADs using NewTom

VGi EVO (NewTom, Verona, Italy) set at 110 kV, 6.9 mA, exposure time of 4.3 seconds, 12 x 8 cm field of view and 0.150 mm voxel size. The DICOM (digital imaging and communications in medicine) files were exported. On the same day (T*), an IOS of the maxilla arch was performed with TRIOS scanner (3SHAPE, Copenhagen, Denmark) and the Standard Tessellation Language (STL) file was exported. These two acquisitions were used to digitally design and manufacture the personalized lingual device.

The orthodontic treatment started 14 days later (T0). A new IOS of the maxilla arch was done on this day and at every appointment of the patient (every four to five weeks). This resulted in the export of n STL files of the maxillary teeth crowns in high resolution, which were used to create the initial and intermediate models.

Once the retraction of the canines was clinically acceptable, the lingual mechanism was removed. A CBCT scan of the maxilla was acquired using the same unit and the same settings as the first one. The study then stopped, and the orthodontic treatment of the patient was carried on with vestibular braces.

3D reconstruction of initial (T0) model

The segmentation of the initial CBCT scan was performed by a trained operator using Mimics Innovation Suite software (version 17 Research edition, Materialise, Leuven, Belgium). A semi-automated process was followed in accordance with best practice usage, by thresholding the main elements (maxilla and teeth) and manually refining the missing parts and artifacts. The maxillary bone and the teeth were individually isolated into different elements (see Figure 2, top-left panel) and, for each of them, 3D surface parts were exported in STL files. At this step, the periodontal ligament was not modeled.

For the following steps of the study, detailed anatomy of the posterior teeth crowns (premolars and molars) was needed. This anatomy could not be retrieved from the CBCT scan, due to the resolution of the acquisition and to artifacts caused by metallic restorations [START_REF] Baan | Fusion of intra-oral scans in cone-beam computed tomography scans[END_REF][START_REF] De Waard | A novel method for fusion of intra-oral scans and cone-beam computed tomography scans for orthognathic surgery planning[END_REF]. To get a surface model with precise anatomy of posterior teeth crowns, Geomagic Studio software (version 2012, Geomagic, Rock Hill, USA)

was used to fuse the result of the segmentation of the initial CBCT and T0 IOS (no clinical changes were found between superimposed T* and T0 IOS which were taken 14 days apart, see Figure S1). In order to align the IOS with the segmentation, we used an Iterative Closest

Point algorithm (ICP) [START_REF] Besl | A method for registration of 3-D shapes[END_REF] localized on the posterior teeth crowns ("Best Fit Alignment" in Geomagic software). ICP registration is a reliable and frequently used method for alignment of similar surfaces [START_REF] Baan | Fusion of intra-oral scans in cone-beam computed tomography scans[END_REF][START_REF] De Waard | A novel method for fusion of intra-oral scans and cone-beam computed tomography scans for orthognathic surgery planning[END_REF][START_REF] O'toole | Investigation into the accuracy and measurement methods of sequential 3D dental scan alignment[END_REF]. This process is illustrated in Figure 2 and detailed in the Supplementary Materials, Section B.

3D reconstruction of intermediate (T1 to Tn) models

To reconstruct the intermediate 3D models (named T1 to Tn), Geomagic Studio software was used to reposition the segmented canines of the T0 model on the canines' crowns of the intermediate IOS.

To align the IOS on the model, we used the same process of ICP alignment ("Best Fit

Alignment" in Geomagic software) localized on the crowns of the premolars and molars, considered as stable references. These "Best Fit Alignments" of several IOS using a reference structure have been shown to be highly reliable [START_REF] O'toole | Investigation into the accuracy and measurement methods of sequential 3D dental scan alignment[END_REF]. Then, we used a second ICP alignment localized on the canine crowns to align the segmented canines (T0 model) with the intermediate position of the canines. Since the segmented teeth contained their roots, we were able to precisely track the position of the canines in the maxilla at any time of the study. This process is illustrated in Figure 3 and detailed in the Supplementary Materials, Section B.

Validation of the tracking protocol

To validate our intermediate model reconstruction, a CBCT was used to retrieve the final position of the canines. This final position was compared to the position of canines from the last intermediate model (Tn).

First, the final CBCT was aligned with the initial CBCT using a local 3D voxel-based superimposition taking the maxillary bones as stable structures [START_REF] Dot | Voxel-based superimposition of Cone Beam CT scans for orthodontic and craniofacial follow-up: Overview and clinical implementation[END_REF]. To this aim, we used the open-source software ITK-SNAP (version 3.6.0; www.itksnap.org) [START_REF] Yushkevich | User-guided 3D active contour segmentation of anatomical structures : significantly improved efficiency and reliability[END_REF] and 3D Slicer (version 4.7.0; www.slicer.org) [START_REF] Fedorov | 3D Slicer as an image computing platform for the quantitative imaging network[END_REF], following Dental and Craniofacial Bionetwork for Image Analysis (DCBIA) method [START_REF] Ruellas | Comparison and reproducibility of 2 regions of reference for maxillary regional registration with conebeam computed tomography[END_REF].

Once the final CBCT was aligned with the initial one, it was imported in Mimics software to retrieve the segmented models of the canines at the end of the study. Rigid body displacements between the position of canines in the Tn model with these latter segmented canines were calculated.

Evaluation of clinical results

The displacement of the canines was evaluated both qualitatively and quantitatively using 3D Slicer software. We performed visualization via the "Model To Model Distance" and "Shape Population Viewer" modules of the SlicerSALT project (salt.slicer.org) [START_REF] Vicory | SlicerSALT: Shape AnaLysis Toolbox[END_REF].

The global rigid body displacements of the canines' centroids were calculated. Rigid body translation components were calculated along the x, y and z axis. Euler extrinsic angles were calculated based on a right-handed orthogonal basis centered on the centroid of the canines, with the z axis pointing towards the apex of the teeth, the y axis towards their distal side and the x axis orthogonal to the yz plane. The order of the rotations was x, y', z''.

Finite element analysis

A preliminary FEM was developed to underpin the relevance of our tracking protocol in supporting FEA. Only the key points of the FEM are outlined here. More details are given in the Supplementary Materials, Section C.

In order to reduce the computational time, part of the T0 model was used to set up the geometry of the FEM which included the trans-canine arch, the two canines, their periodontal ligament (PDL) and part of the maxillary bone (Figure 4). The two bone parts were extracted from the whole maxilla by making virtual cuts far enough from the studied teeth, and their displacement was restricted (Figure S4). The personalized orthodontic device designed for this study allowed an accurate description of the point of application and orientation of the orthodontic forces in the FEM (Figure S4). Their magnitude was set to 100 cN according to clinical data.

Maxillary structures are heterogeneous and exhibit an anisotropic, nonlinear behavior. As our goal was to show the relevance of our 3D tracking protocol to support FEA, we were not concerned with detailed constitutive modeling. Thus, as a first step and for illustration purposes, we used simplified constitutive models for all the structures of the FEM. Teeth were considered as rigid bodies. The lingual device and the PDL were modeled as linearly elastic materials. In order to allow for irreversible OTM, bone was modeled through a Zener model (Figure S5), whose constitutive law reads:

= + , = ℂ , = 2 ,
where is the stress tensor, additively split into an elastic stress -related to the elastic strain through the elastic tensor ℂ-and a (deviatoric) viscous stress -related to the (deviatoric) viscous strain rate through the viscosity coefficient , the latter being related to the characteristic time of the OTM. This parameter is strongly patient-specific: patient's age and health state, biological activity, bone microstructure-just to mention a few-may affect the value of . Moreover, as the mechanobiological response of bone is likely nonlinear, it should not be expected to be a constant.

All the elastic coefficients were fixed according to relevant literature. Thus, overall, only one free material parameter was left, i.e. the characteristic time τ, that was calibrated against clinical data (models T0 to Tn). Comparison between clinical and numerical results was performed with respect to the rigid body translations and Euler extrinsic angles of the canines.

RESULTS

Clinical results and surface models

The retraction treatment lasted 7 months. Figure 5 shows the clinical calendar and the associate data acquisition. Starting from T0, a total of 8 IOS were acquired, leading to models T0 (initial model) to T7 (final model).

Validation of the tracking protocol

A qualitative evaluation of the 3D voxel-based superimposition of initial and final CBCT visually showed no displacement of maxillary premolars and molars (Figure 6 and Supplementary movie SM1). This confirmed the possibility of using these teeth as stable structures for the construction of the intermediate models. Incisors teeth and especially left lateral incisor showed a small displacement with a spontaneous resolution of a few millimeters of their crowding, probably due to the space created by the recoil of the canines.

These observations justified the assumption to have considered only the maxillary bone around the canines in this study.

The differences in positions of the canines in the T7 model and in the final CBCT were quantified by the rigid body displacements between the two models, computed through Geomagic Studio software (Table ST1 of Supplementary Materials). These displacements were less than 0.2 mm in translation and less than 1° in rotation. They were clinically acceptable and within the actual spatial resolution of CBCT. These results validated the proposed tracking protocol and our process of reconstruction of intermediate models.

Evaluation of clinical results

Figure 7 shows the displacement fields of the right and left canines in models T3, T5, and T7, taking T0 as reference. Colors refer to the magnitude of the displacement. At T7, the range of values [minimal -maximal] taken by the magnitude of the displacement field was [2.4 -5.6 mm] for the right canine, and [2.2 -6.2 mm] for the left one. The higher displacement was found at the tip of the cusps, and a slight intrusion (around 2 mm) was observed at the apex.

The measured rigid body displacements of the canines (translations and Euler angles in the x, y', z'' order, referred to the canine centroids) from step T0 to T1 through T7 are reported in Figure 8 and in Table ST2 of Supplementary Materials.

Finite Elements Analysis

Clinical data obtained from models T0 to T7 were used to calibrate the free parameter of our FEM, i.e. the OTM characteristic time τ. To this aim, we performed a parametric analysis searching for the values of τ best matching the clinical data. A preliminary observation of clinical data revealed two main features. First, the OTM in the direction of the applied loads is much larger than in the other directions. Secondly, OTM is characterized by two time scales, being slower during the first half of the treatment. Therefore, for the sake of simplicity, the identification of the characteristic time τ was performed only with respect to the translation of the canines in the y direction and separately in the two phases of the treatment. A good match was found by taking τ = 0.12 hours between T0 and T4, then τ = 0.06 hours between T4 and T7. Simulated displacements (translations and rotations) of both right and left canines showed a good agreement with the corresponding clinical data, with exception of the translations along z axis. Rotations around the x axis were also slightly overestimated by the numerical model. The simulated rigid body displacements of the canines (referred to the canine centroids) from step T0 to T1 through T7 are reported in Figure 8 and in Table ST2 of Supplementary Materials.

A qualitative assessment of the simulation results can be made using transparent overlays of the clinical canine models over the simulation models. As showed in Figure 9, the simulated teeth showed a movement of rotation around their apex, in accordance to the clinical data.

The clinical displacement that was not simulated correctly was the intrusion of the teeth.

DISCUSSION

Tracking 3D orthodontic tooth movement

The main goal of this paper was to propose a protocol to effectively track the 3D orthodontic movement of the canines. Our method of tooth movement tracking, using only one acquisition with ionizing radiation, proved to be effective and showed a clinically acceptable error. The ability to track teeth and roots displacements is clinically appealing, and the possibility to do so with a low ionizing radiation dose is a main asset [START_REF] Lee | Three-dimensional monitoring of root movement during orthodontic treatment[END_REF][START_REF] Lee | Monitoring of typodont root movement via crown superimposition of single cone-beam computed tomography and consecutive intraoral scans[END_REF].

We tested our protocol by tracking the 3D OTM of a patient undergoing canine retraction over a seven-month period. Intermediate models of the canines were generated monthly at each clinical appointment. The efficiency of our process of reconstruction of intermediate models was checked by a second CBCT scan at the end of the study. Being used only for validation purposes, the second CBCT scan shall not be included in the clinical protocol. This final validation shows the clinical transfer potential of this technique, and had not been performed previously [START_REF] Likitmongkolsakul | Development and Validation of 3D Finite Element Models for Prediction of Orthodontic Tooth Movement[END_REF]. Our new protocol represents an improvement of a technique previously described by our team [START_REF] Bouton | New finite element study protocol : clinical simulation of orthodontic tooth movement[END_REF]. Our new technique is more accurate and automatized as it uses an ICP algorithm and can be applied to a much longer treatment.

Supporting FEA

FEA has a great potential to improve quality and efficiency of orthodontic treatments, but for now there is no prospective model of human OTM. The main issue is the availability of reliable clinical data to calibrate and validate the models. Our new protocol can usefully support FEA of OTM. We illustrated this point by developing a preliminary, patient-specific FEM to simulate the seven-month canine retraction of a patient. Clinical data were used to calibrate the OTM characteristic time τ in the FEA. Calibration was eased by the personalized orthodontic device designed for this study, delivering a statically determinate system of forces. Other orthodontic devices could be used but this may introduce uncertainty in the calibration process. Calibration was performed with respect to the main orthodontic displacement, i.e. the canine retraction in the occlusal plane (y direction). The numerical model was able to reproduce the latter with excellent accuracy. However, translation along z axis did not match the clinical intrusion movement, which suggests that this movement might be due to functional forces (i.e. occlusal or muscular forces) not simulated in our study.

Moreover, the value of τ was observed to change somewhere between T4 and T5. This might be due to a change of the occlusal forces or of the biological activity but the source of this effect remains unclear (de Gouyon Matignon de [START_REF] De Gouyon Matignon De Pontouraude | Highly variable rate of orthodontic tooth movement measured by a novel 3D method correlates with gingival inflammation[END_REF]. These difficulties underline the relevance of clinical data to support the development of reliable FEM.

Perspectives and limitations

Our preliminary model could be used to explore the consequences of variations of the force system and therefore provide clinical cues. For example, it is possible to assess the position of the 3D center of resistance of the canines or to identify the line of action of the forces producing a target OTM.

This study has some limitations that may impact our goals and conclusions. These issues are briefly discussed below and will be addressed in future investigations.

1. The proposed 3D tracking procedure can be used for research purposes but a higher degree of automation shall be attained before it to be transferred to clinical practice.

Indeed, our protocol requires operators trained in computer modelling and remains tedious because of the need of thorough segmentation of the CBCT image and manipulation of the 3D models to fuse the crowns of the IOS with the tooth models obtained from the segmentation. It would also be useful to test this procedure using CBCT images acquired using low dose protocols, which might hinder the segmentation process.

2. Our procedure needs stable landmarks to align the intermediate IOS on the initial model.

In our study, we were able to use the posterior crowns as stable structures, as they were not included in the force system. To apply this method with more traditional orthodontic appliances, TADs or palatal rugae could be used as stable structures [START_REF] Chen | Stable region for maxillary dental cast superimposition in adults, studied with the aid of stable miniscrews[END_REF][START_REF] De Gouyon Matignon De Pontouraude | Highly variable rate of orthodontic tooth movement measured by a novel 3D method correlates with gingival inflammation[END_REF][START_REF] Likitmongkolsakul | Development and Validation of 3D Finite Element Models for Prediction of Orthodontic Tooth Movement[END_REF]. We could not use them in our study because these structures were not properly recorded in our IOS.

3. Canine root morphology was clear at the time the device was made and the initial center of resistance was estimated as per Fig. 1-C. However, the position of the center of resistance depends on the type of OTM [START_REF] Meyer | Does the center of resistance depend on the direction of tooth movement ?[END_REF] and mechanical considerations should be made for each case [START_REF] Kum | Moment to force ratio characteristics of three Japanese NiTi and TMA dosing loops[END_REF]. Therefore, our estimate of the center of resistance might not be accurate. This could have a relation with the tipping of the canines clinically observed, as the real position of the center of resistance of the canines was probably apical to the line of action of our forces.

4. Boundary conditions of the FEM may not be accurate. In particular, we did not include functional forces in our model. This could have a relation with the difference between clinical and numerical results in terms of intrusion/extrusion. This shows the major difficulty to obtain the full force system experienced by the teeth, undesired functional forces being sometimes non-negligible. The use of light-cured cement placed on top of molars to create a gap between upper and lower teeth might have helped to reduce undesired occlusal loading of the moving canines due to contacts with the lower teeth [START_REF] Zhong | In vivo effects of different orthodontic loading on root resorption and correlation with mechanobiological stimulus in periodontal ligament[END_REF].

5. The constitutive models of our FEM shall be improved, namely to account for the anisotropic, nonlinear response of the PDL and for the alveolar bone remodeling, as well as for the heterogeneity of maxillary structures. This question is out of the scope of this paper and will be addressed in future work. It should be mentioned that several models of bone remodeling have been proposed [START_REF] Chen | A periodontal ligament driven remodeling algorithm for orthodontic tooth movement[END_REF][START_REF] George | A preliminary approach in the prediction of orthodontic bone remodeling by coupling experiments, theory and numerical models[END_REF][START_REF] Hamanaka | Numeric simulation model for long-term orthodontic tooth movement with contact boundary conditions using the finite element method[END_REF]. However, clinical data to support these models are hardly accessible and it is still challenging to obtain reliable information about mechanobiologically relevant parameters [START_REF] Van Schepdael | Mechanobiological modeling can explain orthodontic tooth movement : three case studies[END_REF], bone density and micro-anatomy [START_REF] Cattaneo | The finite element method : a tool to study orthodontic tooth movement[END_REF], and precise periodontal ligament comportment [START_REF] Uhlir | Biomechanical characterization of the periodontal ligament : orthodontic tooth movement[END_REF].

Figure 1 :

 1 Figure 1: Individualized lingual mechanism used in this study. A: intra-oral occlusal view (see

Figure 2 :

 2 Figure 2: 3D reconstruction of initial (T0) Model. Red/blue colors: selected/unselected parts for

Figure 3 :

 3 Figure 3: 3D reconstruction of the intermediate model Ti (i=1..n). Only the teeth of T0 model are

Figure 4 :

 4 Figure 4: T0 surface model after preparation for FEA with coordinate system. A. Front view with

Figure 5 :

 5 Figure 5: Clinical calendar and data acquisition.

Figure 6 :

 6 Figure 6: Cross-section in the axial plane of initial (greylevel) and final (red) superimposed CBCT

Figure 7 :Figure 8 :

 78 Figure 7: Vector fields of right (upper panel) and left (lower panel) canine displacement from

Figure 9 :

 9 Figure 9: Qualitative evaluation of canine displacement from situation T0 (plain white) to T7 clinical

Table 1 .

 1 OTM: Orthodontic Tooth Movement; CAD : Computer-aided design; CT : computed tomography; CBCT : cone beam computed tomography; n/a : not applicable. Published numerical models for long-term orthodontic tooth movement (OTM)

	1

Acknowledgements

The authors would like to thank Dr Jean-Paul Forestier (AP-HP) for his clinical and biomechanical advice which greatly assisted this study.

Funding

This research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors.

Conflict of interest statement

None to declare.

Research Data

3D surface model files of IOS, T0 model used for the simulation and canines models (T0 to T7) are available from the authors upon request.