Julien Moriceau

Patrick Houizot

Theany To

Abdessamad Mougari

Hervé Orain

Fabrice Célarié

Tanguy Rouxel
email: tanguy.rouxel@univ-rennes1.fr

Fabrice Celarié

Nucleation and crystallization of Ba 2 Si 3 O 8 spherulites in a barium aluminum silicate glass, and mechanical properties of the obtained glassceramics

Keywords: Glass-ceramic, nucleation, brium silicate, fracture toughness, SEPB

come

Nucleation and crystallization of Ba2Si3O8 spherulites in a barium aluminum silicate glass, and mechanical properties of the obtained glass-ceramics

Introduction

Glass-ceramics (GC)s mostly exhibit better stiffness, strength and hardness than their parent glasses [START_REF] Shinozaki | Elastic properties and Vickers hardness of optically transparent glassceramics with fresnoite Ba2TiSi2O8 nanocrystals[END_REF][START_REF] Sangleboeuf | Chapter 8 -Glass and crystallisation: mechanical properties[END_REF]. GCs are obtained by partial or full crystallization of a glass [START_REF] Deubener | Updated definition of glass-ceramics[END_REF], and the composition of this "parent" glass has a strong incidence on the one of the crystallizing phases, and thus on the final properties. Glasses from the SiO2-BaO and SiO2-BaO-Al2O3 chemical systems are nowadays considered as potential materials for application J o u r n a l P r e -p r o o f n° 1. A second batch was obtained from the residual glass stacked on the Pt-Rh crucible after pouring of the melt. This residual glass was crushed and re-heated at 1500 °C for 5 min in a 25 cm 3 Platinum-Gold (Pt-Au) flat crucible.

The liquid was then quenched directly in the crucible by projecting water on the side of the crucible and further annealed at 650 °C for 3 h. This resulted to batch n° 2. In order to determine the temperature of the main thermal changes (Tg, Tx), a small piece of the batch 1 glass was crushed to produce ≈ 50 mg of glass grains (granulometry between 100 and 200 µm) which was further studied by means of Differential Scanning Calorimetry (DSC) with a 404 F3 Pegasus DSC (Netzsch, Germany) at a ramp of 10 °C.min -1 . Then parallelepiped samples were cut with a diamond disk, carefully avoiding cracking upon cutting.

Nucleation and crystallization

The GC samples were obtained by submitting the glass to series of "nucleation" and "crystallization" heat treatments using 5x5x3 mm 3 specimens polished down to 3 µm (diamond paste). The nucleation process was investigated on the basis of the Tammann's method [29], involving a two stages heat treatment, namely i) the nucleation plateau, where both temperature and the duration were varied in a series of experiments, and ii) a crystallization plateau (30 min at 825 °C) favoring the growth of spherulites. For each treatment, the samples were placed in already preheated furnaces at the desired temperature. After temperature homogenization (≈ 5 min which corresponds to a heating rate of ≈ 140 °C/min), the samples were left in the furnace for the desired duration and were quenched in air (cooling rate is approximately 100 °C/min). After a brief polishing step with 3 µm diamond paste, the number of spherulites was counted in the volume of the samples by means of an optical microscope (Keyence VHX-5000, Japan) focused at different depth. The structure and the composition of the nuclei were observed with a JEOL 2100 TEM (JEOL, Japan) on a crushed glass sample submitted to a nucleation of 3 weeks at 700 °C. Crystallization was investigated by introducing the as-quenched glass in a preheated furnace at temperatures between 820 and 900 °C (crystallization temperature as determined by DSC: Tx≈876 °C). After completion of the plateau, the samples were quenched in air. The surface crystallization was removed by means of polishing suing diamond suspensions down to 3 µm. The state of progress of crystallization was further assessed by measuring the mean radius of the spherulites using an optical microscope (Keyence VHX-5000, J o u r n a l P r e -p r o o f 4 Japan) for each of the time/temperature couple. In addition, the microstructure of the spherulites was observed with a JSM7100F SEM (JEOL, Japan) on fractured surfaces and a X'Pert Pro Cu cathode diffractometer (Malvern PANalytical, UK) was used to characterize the crystallizing phase by means of X-Ray Diffraction (XRD). The 2θ diffraction signal was recorded between 5 and 90° with a 0.026° step. The HighScore Plus software (Malvern PANalytical, UK) was used for the data treatment. Samples that went through a nucleation stage are labelled B2S3_N and those being further submitted to crystallization are labelled B2S3_N_CX, where X is the duration of the crystallization treatment (with no nucleation treatment the label is shorten to B2S3_CX).

Mechanical and physical properties

The density (ρ) was obtained from an average of 5 measurements by means of the Archimedes method in distilled water. These values were used to calculate the elastic moduli from the sound wave velocities by means of ultrasonic echography measurements performed with 10 MHz piezoelectric transducers. Young's modulus, 𝐸, and the shear modulus, 𝐺, are given by Eqs. ( 1) and ( 2). Poisson's ratio (𝜈) is deduced from 𝐸 and 𝐺 with Eq. ( 3).

𝐸 = ρ 3𝑉 𝑙 2 -4𝑉 𝑡 2 𝑉 𝑙 2 𝑉 𝑡 2 -1 (1)
𝐺 = ρ𝑉 𝑡 2 (2) 𝜈 = 𝐸 2𝐺 -1 (3)
Where 𝑉 𝑙 and 𝑉 𝑡 are the longitudinal and transversal wave velocities, respectively.

The shear viscosity coefficient (η) was estimated from the creep rate during the nucleation stage using a vertical dilatometer L75 PT (Linseis, Germany) with a specimen with a 1.7x1.7 mm² section area and a 9.3 mm height (L0), and a compressive (uniaxial) stress (𝜎) of 50 kPa at a temperature of 700 °C for a duration of one month. The displacement (𝛿𝐿) was recorded and, for convenience, was fitted in function of time with a 3 rd degree polynomial function (R²=0.999). The derivative of this function was then used to estimate η, as a function of time according to Trouton's law (Eq. ( 4)).

η = 𝜎 3𝜀̇

J o u r n a l P r e -p r o o f

where 𝜎 is the applied stress and 𝜀̇=

1 𝐿 0 * 𝑑(𝛿𝐿) 𝑑𝑡
is the strain rate.

Let us note that at 700 °C,  is less than 2.10 12 Pa.s, and G is about 0.92xG(20 °C) and is thus about 25 GPa [START_REF] Gueguen | Structure and viscosity of phase-separated BaO-SiO2 glasses[END_REF], so that the Maxwell relaxation time (𝜏 = 𝜂 𝐺 ) is about 1.3 min. This rough estimation supports the fact that creep adopts a pure viscous regime at times larger than several hours, which validates the use of Eq. ( 4).

The thermal expansion coefficient of the glass was measured with the same dilatometer at a rate of 10 °C.min -1 on a 2x2x9.5(height) mm 3 sample.

The fracture toughness (𝐾 𝐼𝑐 ) of the glass and of the GCs was measured by means of the SEPB method.

This self-consistent technique is among the few suitable ones in the case of brittle materials as it involves an "ideally" sharp pre-crack [START_REF] Rouxel | The fracture toughness of inorganic glasses[END_REF][START_REF] To | Fracture toughness, fracture energy and slow crack growth of glass as investigated by the Single-Edge Precracked Beam (SEPB) and Chevron-Notched Beam (CNB) methods[END_REF]. 3x4x25 mm 3 parallelepiped bars were cut and polished (down to 3 µm diamond paste) from samples having experienced different heat-treatments. Each experiment involves three steps: i) introduction of an indentation line, ii) pre-cracking, and iii) fracture in three-point bending (Fig. 1). The line of indents (Vickers in the present case) is generated in the middle of the specimen bottom surface (surface in tension during the pre-cracking stage) using a 5 N load for 15 sec; each imprint was separated from the next one by a distance of 150 µm. The pre-crack was obtained using a bridge compression set-up loaded with a cross-head speed of 0.05 mm.min -1 . The compression was stopped manually when the pre-crack had propagated to around 50 % of the specimen height (Fig. 1). The pre-cracked beam was further fractured in three-point bending at a rate of 10 µm.sec -1 . The displacement was recorded by means of a piezoelectric displacement actuator (N-216 NEXLINE ® Linear Actuator from Physik Instrumente, Germany). The load was measured by a 1 kN capacity load cell, MS02 type from Scaime company, France, exhibiting of 6.7 MNm -1 stiffness. 𝐾 𝐼𝑐 is determined from the maximum load during the final fracture step using Eq. ( 5) [START_REF] Astm | Standard test methods for determination of fracture toughness of advanced ceramics at ambient temperature, Mechanical Properties and Performance[END_REF].

Where a is the length of the pre-crack, and B and W are the broadness and the width of the specimen respectively. In order to correlate 𝐾 𝐼𝑐 to the microstructure, the crystallized fraction (Cf) was determined on the fractured surface by measuring the surface ratio occupied by the spherulites. This was done by observing a zone of 1500x300 µm in the vicinity of the pre-crack with a JSM7100F SEM (JEOL, Japan) or by optical microscopy (Keyence VHX-5000 microscope, Japan).

mm

Cracks from indentation Precrack arrest line.

J o u r n a l P r e -p r o o f 3 Results

Nucleation and crystallization

The glass transition temperature (Tg=728 °C), was determined by DSC as the crossing point of asymptotes on the foot of the endothermal peak (Fig. 2) and is in agreement with previously reported values for glasses with close compositions [START_REF] Hasegawa | Effect of replacing SiO2 by ZnO on the physical properties of aluminosilicate glasses[END_REF][START_REF] Lara | Sintering of glasses in the system RO-Al2O3-BaO-SiO2 (R=Ca, Mg, Zn) studied by hot-stage microscopy[END_REF]. The onset for the 1 st crystallization (Tx=876 °C) was taken as the foot of the exothermal peak. In order to study the nucleation process, glass samples were heated at different temperatures between 680 and 740 °C for 8 hours and the resulting nuclei density was measured (Fig. 3a). The nucleation rate was found to be optimum in the 690-720 °C interval. It is noteworthy that the samples that were treated in this temperature range exhibit the same microstructure after complete crystallization. Although this range is below Tg (728 °C) it is in agreement with previously published data on similar glasses [START_REF] Freiman | Controlled spherulitic crystallization in 3BaO-5SiO2 Glass[END_REF][START_REF] Ramsden | The effects of amorphous phase separation on crystal nucleation kinetics in BaO-SiO2 glasses. Part 1[END_REF]. However, the maximum nuclei density (≈2.10 12 m -3 ) is several orders of magnitude smaller than the ones that were reported earlier. This is likely due to the presence of alumina (3 mol. %) in the present case, as alumina is known to stabilize the glass [START_REF] Warren | Atomic consideration of immiscibility in glass systems[END_REF][START_REF] Martel | Controlling the size of nanodomains in calcium aluminosilicate glasses[END_REF] and thus to decrease the nucleation rate [START_REF] Ramsden | The effects of amorphous phase separation on crystal nucleation kinetics in BaO-SiO2 glasses. Part 1[END_REF]. The nucleation kinetics was studied at 720 °C by performing heattreatments of different durations up to 220 hours at this temperature (Fig. 3b). A linear evolution of the nuclei density with time was previously reported for glasses in the BaO-SiO2 system for nucleation durations smaller than 60 hours [START_REF] Martel | Controlling the size of nanodomains in calcium aluminosilicate glasses[END_REF]. In the present work, the evolution would fit a linear dependence on time but for the largest duration (>200 hours) where some saturation seems to show up. This behavior will be further discussed in § 4. The compositions in the different areas were determined by EDS during the TEM observation (Table 1).

Oxygen was detected but its quantification relative to other elements is poor due to the low energy of emitted X rays which generates a lack of accuracy in the quantification of this element. The key result is that barium is by J o u r n a l P r e -p r o o f far the predominant cation in the crystallized areas (Zone 1, Fig. 4a). Indeed, the Si/Ba ratio is around 0.1 whereas it is 1.5 in the nominal glass composition. In addition, no aluminum was found in the crystals. Conversely, the surroundings of the nuclei are nearly entirely depleted in barium (Zone 2, Si/Ba ratio around 32, Fig. 4a), whereas the Ba content faraway of the nuclei is a bit smaller than the nominal content in the parent glass (Si/Ba around 2.1), likely because of the high concentration of Ba in the nuclei (Zone 3, Fig. 4a). Ba coalescence was previously reported as the origin of nucleation in the BaO-SiO2 system [START_REF] Zanotto | The effects of amorphous phase separation on crystal nucleation kinetics in BaO-SiO2 glasses. Part 3[END_REF], but nuclei were mostly not observed [START_REF] Takahashi | Structural heterogeneity and homogeneous nucleation of 1BaO-2SiO2 glass[END_REF][START_REF] Takahashi | Formation of spherulite and metastable phase in stoichiometric Ba2Si3O8 glass[END_REF][START_REF] Ramsden | The effects of amorphous phase separation on crystal nucleation kinetics in BaO-SiO2 glasses. Part 1[END_REF].

The enrichment of barium in the nuclei induces the formation of a silica rich layer in the surrounding shell. The calcium found in the nuclei probably originates from the CaO impurities contained in the precursor powders. The sub micrometer-scale crystal observed in Fig. 4a differs much from the crystallized phase that shows up after a nearly complete glass to ceramic conversion. The diffraction pattern in Fig. 4a inset was taken from 3 slightly disoriented crystals (see red circle in Fig. 4a) which explains why each diffraction spot is tripled. Fig. 4d is typical of a monocrystal and gave some information on the nature of those early crystals. Indeed, the interplanar distance of the main diffraction spots (measured between 3.76 and 3.83 Å) is very similar to the lattice parameter (𝒂 length ≈ 3.80 Å) in tetragonal barium peroxides BaOx (with 1.5<x<2) [START_REF] Vernooy | Redetermination of the structure of barium peroxide by single-crystal X-ray diffraction[END_REF][START_REF] Königstein | Structural properties of nonstoichiometric barium and strontium peroxides: BaO2-x(1.97≥2-x≥1.72) and SrO2-x(1.98≥2-x≥1.90)[END_REF]. These observations corroborate previous ones suggesting that the composition and structure of the nuclei could be different from the ones of the main resulting crystallized phase obtained after a crystallization treatment at higher temperature, especially in the SiO2-BaO system [START_REF] Takahashi | Formation of spherulite and metastable phase in stoichiometric Ba2Si3O8 glass[END_REF].

In addition to homogeneous nucleation, observations performed on glass samples from areas close to the walls of the platinum-based crucible reveal some heterogeneous nucleation sites, where nucleation originated from platinum (Fig. 5). This effect is more pronounced when the Pt-Au crucibles are used instead of the Pt-Rh ones, regardless of the fact that the same melting temperature is used, because Pt-Rh is more refractory and more durable so that it is less chemically etched at 1500°C. The dissolution of platinum as a source for a heterogeneous nucleation was already reported [START_REF] Lewis | Crystallization mechanisms in glass-ceramics[END_REF][START_REF] Mishima | Effect of the thermal history of glass melts on crystallization in lithium and sodium disilicate glasses doped with platinum as a nucleating agent[END_REF].

J o u r n a l P r e -p r o o f The crystallization process was first studied by means of one-hour long heat-treatments at different temperatures in the 820-900 °C interval. The average radius of the spherulites that grew in the glass after these treatments was measured, and an exponential dependence of the mean radius with the temperature was found (Fig. 6a). The apparent activation energy associated with this growth rate is about 174 ± 24 kJ.mol -1 . This energy is slightly lower than those previously reported (200-230 kJ.mol -1 ) for a barium disilicate glass (molar composition of 33 BaO -67 SiO2) [START_REF] Ramsden | The effects of amorphous phase separation on crystal nucleation kinetics in BaO-SiO2 glasses. Part 1[END_REF][START_REF] Rodrigues | Crystal growth and viscous flow in barium disilicate glass[END_REF]. The kinetics of the spherulitic growth, as studied at 825 °C for heat-treatment durations up to 15 hours (Fig. 6b), corresponds to a linear dependence with time, which is in agreement with the literature [START_REF] Keith | A phenomenological theory of spherulitic crystallization[END_REF]. J o u r n a l P r e -p r o o f 14

The diffraction pattern obtained from a sample heat-treated for 72 h at 825 °C, and thus after nearly complete crystallization, displayed several mains peaks (Fig. 7). It was compared to 5 crystal phases of the BaO-SiO2 system (for clarity they are not all shown in the figure: BaSiO3, Ba2Si3O8, Ba5Si8O21, Ba3Si5O13 and BaSi2O5).

The best match was obtained with the Ba2Si3O8 crystalline phase which indicates a strong predominance of this crystal. Some preferential crystal orientations at the surface could explain the light discrepancies with the reference pattern regarding the relative intensity of the main peaks [START_REF] Ding | Preparation of polar oriented Sr2TiSi2O8 films by surface crystallization of glass and second harmonic generation[END_REF]. A series of relatively large samples allowing further for mechanical testing were prepared combining both nucleation and crystallization treatments. This series aimed at understanding the incidence of such thermal cycles on the microstructure and thus on the mechanical performance. The thermal cycles are summarized in Table 2, and some examples of 3 mm thick heat-treated samples are shown in Fig. 8.

As crystallization proceeds, the samples become less transparent. They are still translucent after 72 hours heat-treatment though. The observation of mirror polished -and post-mortem fracture (SEPB specimens)surfaces (Fig. 9 and Fig. 10) allowed for the measurement of the spherulite fraction (Cf, Table 2). B2S3 and B2S3_N exhibit no crystallization (Cf ≈ 0). In the B2S3_N_C30m samples, spherulites, 10 µm in diameter in average, are homogeneously dispersed and represent 5 ± 2 %S of the sample surface (Fig. 10a,b). The size of the spherulites reaches about 30 microns after 2 hours at 825 °C (Fig. 9a,b) and 40 microns after 4 hours (Fig. 9c). The sample crystallized at 825 °C for 1 week (B2S3_C1w) exhibits a nearly fully crystallized microstructure with impinged spherulites (Fig. 9d). In this latter case, as well as when Cf is larger than 50 %, some microcracks were observed after cooling, preventing from any further mechanical evaluation. In the case of B2S3_N_C2h samples, cut from batch 2, the crystallization is not homogenous and depends on the distance to the crucible walls due to the platinum diffusion in the glass. The surface in contact with the platinum is where the density of the spherulites is the largest, as a result of heterogeneous nucleation from platinum nuclei in this region (as discussed above).

For B2S3_N_C2h-1 and 2 the density of the spherulites could be estimated directly on fractured surfaces from SEPB experiments, and values of 22 % and 49 % (Fig. 10c) were found respectively for Cf on B2S3_N_C2h-1 and 2 respectively.

J o u r n a l P r e -p r o o f

Mechanical characterization

The specific mass and the elastic properties are given for different states of progress of the glass to ceramic conversion in Table 3. It is noteworthy that ρ is found to decrease as the volume content in crystallized phase is increased. This effect is due to the lower density of Ba2Si3O8 crystal (3.93 g.cm -3 , [START_REF] Goodier | Dictionary of Ceramic Science and Engineering[END_REF]) as compared to the parent glass (3.99 g.cm -3 ). The Young's and shear moduli of the glass B2S3 are 68 and 27 GPa, respectively, which results in a Poisson's ratio of 0.28. When the material is fully crystallized 𝐸 and 𝐺 are increased by 12.5 and 10.5 %, respectively. The elastic moduli can be seen as reflecting the mean volume density of interatomic bonding energy. Therefore, the increase of the elastic moduli in spite of a decrease of the density suggests that the increase of the mean cohesive energy stemming from the GC conversion compensates for the decrease of the atomic packing density. At crystal content smaller than ≈5 % the increase of the moduli due to crystallization The fracture toughness (𝐾 𝐼𝑐 ) of the glass, as measured by the SEPB method on three specimens, is 0.57 ± 0.2 MPa.√m, that is lower than that of a window glass (0.72 MPa.√m, [START_REF] To | Fracture toughness, fracture energy and slow crack growth of glass as investigated by the Single-Edge Precracked Beam (SEPB) and Chevron-Notched Beam (CNB) methods[END_REF]). The nucleation does not improve significantly this value (+0.01 MPa.√m, i.e. within the experimental error of the method). In contrast, 𝐾 𝐼𝑐 is significantly enhanced by the crystallization stage (Fig. 11), and reaches values 14, 18 and 27 % larger than the one of the parent glass at crystallized phase content of 5, 22 and 49 % respectively (B2S3_N_C30m, B2S3_N_C2h-1 and B2S3_N_C2h-2). The bowing of the crack front observed at the vicinity of the spherulites (Fig. 10b,c), and the tortuous fracture surface due to the crack bypassing the second phase particles suggests that the crystallized inclusions resists crack extension and are thus a likely source for toughening, as will be discussed in §4.2.

J o u r n a l P r e -p r o o f

Discussion

Nucleation kinetics

In the framework of the CNT theory, the nucleation rate is correlated to the diffusion one. Diffusion kinetics in liquids is, in average, proportional to temperature and inversely proportional to the viscosity coefficient (Einstein's law). However, in the case of a multicomponent liquid, where each species would tend to diffuse at a different rate, and when the chemistry of the nuclei differs from the one of the parent liquid, there is no straightforward relationship between the nucleation rate and the liquid viscosity. An in-depth study of the diffusion process in the complex chemical system of concern is far beyond the scope of the present work.

Nevertheless, the influence of time on the viscosity during the course of nucleation was investigated (Fig. 12). A creep experiment was conducted at 700 °C, i.e. within the optimum temperature range for the nucleation J o u r n a l P r e -p r o o f process. The surrounding of the nuclei was found to be dramatically enriched in Ba (ratio Si/Ba ≈ 0.1) leaving a bit further (within 100 nm distance) a shell of glass nearly completely depleted in Ba (ratio Si/Ba ≈ 32), extending to a few hundreds nanometers (the composition at about 0.5 m is close to the nominal composition of the parent glass). Therefore, the silica-rich shell may act as a diffusion barrier that slows down the diffusion of Ba toward the growing crystal, especially at large time. Gueguen at al. [START_REF] Gueguen | Structure and viscosity of phase-separated BaO-SiO2 glasses[END_REF] studied the composition dependence of the viscosity in the SiO2-BaO system and came to the conclusion that at 700 °C, 𝜂 is increased by about one order of magnitude as the Ba/Si ratio is decreased from above 0.5 to 0.25. It is thus concluded that the lowering of the nucleation rate at large duration (>100 hours) is due to the slowdown of the diffusion of Ba resulting from the formation of silica-rich shell around the growing nuclei. This type of mechanism has been already observed in other glass systems [START_REF] Liu | Crystallization of a highly viscous multicomponent silicate glass: Rigidity percolation and evidence of structural heterogeneity[END_REF][START_REF] Bhattacharyya | Experimental evidence of selflimited growth of nanocrystals in glass[END_REF]. A significant increase of 𝐾 𝐼𝑐 with the crystal content was found. The observation of the fractured surface of the B2S3_N_C30m and B2S3_N_C2h samples (Fig. 10) reveals that the crack propagation is hampered by the presence of the crystallized spherulites (particles). The phenomenon of crack front bowing indicates that the particles are obstacles opposing crack passing through and thus leading to a tortuous crack path. There are two straightforward consequences: i) the fracture surface is increased, in comparison to a straight through crack path, and ii) the crack experiences shearing and tearing modes II and III as a result of twisting and tilting on approaching the particles. Nevertheless, in order to reach a quantitative analysis of the observed reinforcement, one must identify both the second order stress field at particle site and the crack path. Toughening may arise from the increase of the fracture surface area due to any deviation for the natural and shortest path, assumed normal to the load axis (opening mode), as well as from the contribution of the toughness of the particles to the overall toughness, provided the particles are cleaved by the propagating crack. What actually prevails in a particular case depends on the strength of the particle/matrix interface, on the secondary stress field centered on the particles, and on the volume fraction of particles. There are two contributions to the secondary stress field at particle site, namely: i) thermally induced residual stresses that arose upon cooling from the annealing temperature due to thermal expansion coefficient mismatch between the particles and the matrix, and ii) second order perturbations induced by the far field loading due to a mismatch of the elastic properties between the particles and the matrix. The intensity of the residual stress field as well as the critical radius of the particles that might lead to micro-cracking (𝑅 𝑐 ) can be calculated with the Eq. ( 6) [START_REF] Selsing | Internal stresses in ceramics[END_REF] and Eq. ( 7) [START_REF] Davidge | The strength of two-phase ceramic/glass materials[END_REF], respectively:

𝜎 𝑇 = (α 𝑝 -α 𝑚 ) Δ𝑇 𝐾 𝑒 (6)
𝑅 𝑐 = 2𝛾 𝑚 𝜎 𝑇 2 𝐾 𝑒 = 2𝛾 𝑚 𝐾 𝑒 ((α 𝑝 -α 𝑚 ) Δ𝑇) 2 (7)
Where subscripts "m" and "p" stand for the glass matrix and the crystallized particles respectively, α p and α m are the thermal expansion coefficients (13.2 x 10 -6 °C-1 for the Ba2Si3O8 crystal [START_REF] Kerstan | Barium silicates as high thermal expansion seals for solid oxide fuel cells studied by high-temperature X-ray diffraction (HT-XRD)[END_REF] and 10.8 x 10 -6 °C-1 for the glass, as measured by dilatometry at 10 °C.min -1 ), Δ𝑇 is the temperature difference between the annealing Equation ( 6) results in a residual stress at the spherulite/glass interface of about 100 MPa, which means that the radial nominal stress component, 𝜎 𝑟𝑟 , is in tension. Therefore, the fact that the spherulites shrink more than the matrix on cooling and that a tensile radial normal stress follows is in favor of the crack bypassing the particles. Besides, the second order perturbations induced by the far field loading due to a mismatch of the elastic properties between elastic particles and matrix was recently studied [START_REF] Lacondemine | Role of Poisson's ratio mismatch on the crack path in glass matrix particulate composites[END_REF] and it was found that, when 𝜈 𝑝 >𝜈 𝑚 and 𝐸 𝑝 >𝐸 𝑚 , the crack is deflected by the second phase particles and a moderate toughening follows. Thus, a crack propagating in the x direction in the xy plane, normal to the loading axis (z), is expected to experience some tilt around the y axis (toward the z axis) and some twist of the fracture plane around the x axis. The stress intensity on the tilted crack has opening (mode I) and sliding (mode II) contributions, whereas opening and tearing (mode III) contributions shows up on the twisted crack front. This is why the fracture surface energy sounds more appropriate that the stress intensity factor to discuss the reinforcement. Actually, in the case of crack bypassing the particles (deflection), the sign and magnitude of the residual stress do not have a direct incidence on the magnitude of the reinforcement [START_REF] Faber | Crack deflection processes -I. Theory[END_REF]. This is because i) most of the stored residual elastic energy (local scale) is relieved on the propagating crack arriving at the vicinity of a particle, and this ease the crack growth, and ii) the influence of the residual stress field is very short range as its intensity follows a 1/r 3 dependence on the distance to the center of the particle [START_REF] Keith | A phenomenological theory of spherulitic crystallization[END_REF]. But in the present case where 𝛼 𝑝 >𝛼 𝑚 the crack is deflected, and this geometrical effect provides a strong toughening. A theoretical analysis of the crack deflection process in the case of dispersed elastic particles was proposed by Faber et al. [START_REF] Faber | Crack deflection processes -I. Theory[END_REF], accounting for the increase of the driving force for crack extension due to the tilting and twisting of the crack on approaching the second phase particles. The fracture surface energy of the composite (𝛾 reinforced by spherical particles inducing both tilt and twist of the crack was given as a function of the volume fraction of the second phase (Cf) in Fig. 6 in ref.

[52] and was extracted to calculate the gain on the apparent "macroscopic" (equivalent homogeneous medium) fracture toughness (Eq. ( 8)).

J o u r n a l P r e -p r o o f

K I C = √ (1 -𝜈 𝑚 2 )𝐸 (1 -𝜈 2 )𝐸 𝑚 * γ γ 𝑚 K I C m (8)
When the second phase content becomes large, crack deflection may not be favorable anymore as it would involve unsustainable tilt and twist angles, and some particles may be cleaved, inasmuch as the spherulite/glass interface is very cohesive. In such a situation toughening may solely derived from the contribution of the intrinsic fracture toughness of the second phase, provided it is larger than the one of the glass matrix, and a simple rule of mixture writes:

𝛾 = 𝛾 𝑝 𝐶 𝑓 + 𝛾 𝑚 (1 -𝐶 𝑓 ) (9)
So that:

𝐾 𝐼𝑐 2 (1 -𝜈 2 ) 𝐸 = (1 -𝐶 𝑓 ) * 𝐾 𝐼𝐶 𝑚 2 (1 -𝜈 𝑚 2 ) 𝐸 𝑚 + 𝐶 𝑓 * 𝐾 𝐼𝐶 𝑝 2 (1 -𝜈 𝑝 2 ) 𝐸 𝑝 (10)
It was recently shown that in a first approximation the fracture surface energy of a glass and crystallized phases having the same stoichiometry scale with their relative density (Eq. ( 11), [START_REF] Rouxel | The fracture toughness of inorganic glasses[END_REF]):

𝛾 𝑔𝑙𝑎𝑠𝑠 𝛾 𝑐𝑟𝑦𝑠𝑡 ≈ ( ρ 𝑔𝑙𝑎𝑠𝑠 ρ 𝑐𝑟𝑦𝑠𝑡 ) 2 3 (11)
For example, in the case of SiO2, 𝛾 𝑣𝑖𝑡𝑟𝑒𝑜𝑢𝑠 𝑠𝑖𝑙𝑖𝑐𝑎 =4.36 J.m -2 , ρ 𝑔𝑙𝑎𝑠𝑠 =2.2 g.cm -3 , and ρ 𝑞𝑢𝑎𝑟𝑡𝑧 =2.65 g.cm - suggesting that, at least for Cf below 50%, the crack front tilt and twist induced by the presence of the crystallized spherulite, is the major source for the observed toughening.

J o u r n a l P r e -p r o o f

In addition, it is noteworthy that in regard of the mean radius of the spherulites in the B2S3_C1W sample, which is larger 40-50 µm, and thus larger than 𝑅 𝑐 in Eq. ( 7), the thermally induced residual stress field is large enough to cause fracture in this grade. This provides an explanation for the extensive microcracking experienced by this material on cooling.

Conclusion

The nucleation and crystallization of spherulites composed of Ba2Si3O8 crystals and the incidence on the mechanical properties (elastic moduli and toughness) was studied. The nucleation stage involves the formation of Ba rich crystals having a crystal structure similar to those of barium peroxides. The optimum temperature range for nucleation is from 690 to 720 °C. Some nuclei were found to initiate at platinum impurities due to crucible contamination. The crystallization of spherulites, 10 to 100 microns in diameter, occurs at temperature above 815 °C and evolves exponentially with the temperature up to at least 900 °C. The spherulite growth is linear with time. A diffraction pattern obtained by XRD revealed those spherulites are most probably composed of Ba2Si3O8. After crystallization, the elastic moduli are increased by over 10 % despite a decrease of the density.

The fracture toughness is significantly increased, by about 26 % for the glass-ceramic containing 49 vol. % of crystallized phase (20 to 30 microns spherulites) and is due to a crack deflection process involving tilting and twisting of the crack on approaching the spherulites. However, the thermally induced residual stress field leads to micro-cracking after cooling from the annealing temperature when the spherulites radius is over 30 µm (typically for volume fraction larger than 50 %). and F. Gouttefangeas and L. Joanny (CMEBA platform, Université de Rennes 1), for TEM and SEM observations respectively.

J o u r n a l P r e -p r o o f

J o u r n a l P r e -p r o o f 6 TheFig. 1 :

 61 Fig. 1: Pictures of a SEPB testing specimens. a) B2S3 during the precracking step, b) B2S3 after the three-point bending fracture and c) fractured surface of the B2S3_N_C2h_1 after the SEPB procedure.

Fig. 2 :

 2 Fig. 2: DSC signal at 10 °C/min for glass grains (50 mg with a granulometry comprised between 100 and 200 µm). The black lines represent asymptotes of the different foot peaks. The black dotted lines are place at the intersections of the asymptotes; they represent Tg and Tx.

15 J

 15 o u r n a l P r e -p r o o f

Fig. 3 :Fig. 4 :

 34 Fig. 3: a) Nuclei density as a function of the heat-treatment temperature; b) Nuclei density as a function of the nucleation treatment duration at 720 °C. The red plain and dotted lines represent the linear evolution and the hypothesized saturation plateau of the nuclei density respectively. The structure of the nuclei was observed by means of TEM, after a 3 weeks (504 hours) nucleation

Fig. 5 :

 5 Fig. 5: Spherulites crystallized from platinum nuclei.

Fig. 6 :

 6 Fig. 6: a) Temperature dependence of the mean radius of the spherulite crystals for a thermal treatment of 1 h between 820 and 900 °C; b) Evolution of the mean spherulite radius with time at 825 °C.

Fig. 7 :

 7 Fig. 7: Diffraction pattern of the GC after a heat treatment of 72 h at 825 °C (blue curve). For comparison, the diffract pattern of Ba2Si3O8 (00-027-1035) is also reported in black.

Fig. 8 :

 8 Fig. 8: Optical microscope observations of 3 mm thick samples after heat-treatment at 825 °C for 2, 4, 8, and 72 hours (left to right) (bar = 1 mm).

Fig. 9 :Fig. 10 :

 910 Fig. 9: Microstructures of the glass ceramics: SEM observations of a) the B2S3_N_C2h-1 grade (Cf=22 %) and b) the B2S3_N_C2h-2 grade (Cf=49 %); c) High magnification SEM images of a spherulite in the B2S3_C4h grade, and d) the almost fully crystallized B2S3_C1w grade.

  r n a l P r e -p r o o f 18 is counterbalanced by the decrease of the density, so that the moduli of B2S3_N_C30m are not different from the ones of the parent glass. A sole nucleation treatment has no detectable incidence on the elastic properties. As was discussed in the former paragraph, the crystal content in the B2S3_N_C2h grade is very heterogeneous, which prevents from sensible elasticity measurements.

Fig. 11 :

 11 Fig. 11: Toughness of the sample determined by SEPB. The dotted line represents a guide for the eyes.

Fig. 12 :

 12 Fig. 12: Evolution of glass viscosity in function of creep duration at 700 °C.

J o u r

  n a l P r e -p r o o f and room temperatures, 𝐾 𝑒 = 𝐸 from Table3), and 𝛾 𝑚 is the fracture surface energy of the glass (𝛾 𝑚 is deduced from the Irwin-Griffith similarity principle: 2 in plane strain).

  3 , which results in 𝛾 𝑐𝑟𝑦𝑠𝑡 =4.94 J.m -2 , further corresponding in 𝐾 𝐼𝑐 𝑐𝑟𝑦𝑠𝑡 =0.87 MPa.√m considering the Young's modulus (E=76 GPa) normal to the easy cleavage plane[START_REF] Zanotto | Experimental tests of the classical nucleation theory for glasses[END_REF][START_REF] Zanotto | The effects of amorphous phase separation on crystal nucleation kinetics in BaO-SiO2 glasses. Part 3[END_REF][START_REF] Cormier | Nucleation in glasses -New experimental findings and recent theories[END_REF][START_REF] Takahashi | Nucleation tendency and crystallizing phase in silicate glasses: A structural aspect[END_REF][START_REF] Takahashi | Structural heterogeneity and homogeneous nucleation of 1BaO-2SiO2 glass[END_REF][START_REF] Takahashi | Formation of spherulite and metastable phase in stoichiometric Ba2Si3O8 glass[END_REF][START_REF] Takahashi | Crystallization and morphology of glassy sanbornite[END_REF][START_REF] Araujo | Residual glass and crystalline phases in a barium disilicate glass-ceramic[END_REF][START_REF] Rodrigues | Structural and dynamic properties of vitreous and crystalline barium disilicate: molecular dynamics simulation and Raman scattering experiments[END_REF][START_REF] Zhang | Experimental investigation of liquidus and phase stability in the BaO-SiO2 binary system[END_REF] [START_REF] Selsing | Internal stresses in ceramics[END_REF]. This value is in agreement with the experimental one of 0.86 MPa.√m obtained by Iwasa et al.[START_REF] Iwasa | Cleavage of natural and synthetic single crystal quartz[END_REF]. Thus, in the absence of experimental data for the fracture toughness of the Ba2Si3O8, we follow the same reasoning and reach a value of 𝛾 Ba 2 Si 3 O 8 =2.18 J.m -2 (lightly smaller than the one of the glass), and further a fracture toughness 𝐾 𝐼𝑐 𝑐𝑟𝑦𝑠𝑡 =0.59 MPa.√m. The predictions from Eqs. (8) and[START_REF] James | Kinetics of crystal nucleation in silicate glasses[END_REF] are shown together with the experimental results in Fig.10. The implementation of Eq. (8) was done using a simple rule of mixture for 𝐸 𝑝 and 𝜈 𝑝 (𝐸 𝑝 = (1 + 0.13 * 𝐶 𝑓 )𝐸 𝑚 and 𝜈

𝑝 = (1 + 0.107 * 𝐶 𝑓 )𝜈 𝑚 ). The prediction based on crack deflection is in agreement with our experimental data,

Table 1 :

 1 Average compositions (atomic percent) by EDX determined over 3 measurements. Zone 1: acicular nucleus. Zone 2: Glass surrounding the nuclei. Zone 3: Glass far away from the nuclei. Zones 1 to 3 are pointed out in Fig.4a. nd = not detected. nq = detected but not quantified. na = not applicable.

	Element	Nominal composition (%)	Zone 1 (%)	Zone 2 (%)	Zone 3 (%)
	O	na	nq	nq	nq
	Si	56.5	8.6 ± 3.3	94.0 ± 5.6	60.9 ± 11.8
	Ba	37.7	85.4 ± 3.5	4.3 ± 3.3	33.9 ± 10.0
	Al	5.8	nd	2.9 ± 2.5	5.1 ± 2.1
	Ca	na	6.0 ± 0.5	nd	nd
	Si/Ba	1.5	0.1 ± 0.1	32.0 ± 18.7	2.1 ± 1.3

Table 2 :

 2 Thermal treatments, corresponding sample names, and resulting volume fractions of spherulite (Cf). "N" refers to a nucleation step of 64 h at 700 °C and "CX" to a crystallization treatment at 825 °C (X: duration of the treatment in minutes (m), hours (h) or weeks (w)). nt: not treated.

	Sample name Batch n° Nucleation treatment Crystallization treatment Cf (%)
	B2S3	1	nt	nt	0 %
	B2S3_N	1	700 °C -64 h	nt	≈0 %
	B2S3_N_C30m	1	700 °C -64 h	825 °C -30 minutes	5 %
	B2S3_N_C2h-1	2	700 °C -64 h	825 °C -2 hours	22 %
	B2S3_N_C2h-2	2	700 °C -64 h	825 °C -2 hours	49 %
	B2S3_C1w	1	nt	825 °C -1 week	100%

Table 3 :

 3 Density and elastic moduli as measured by the Archimedes and the ultrasonic echography methods respectively. nm: not measured.

	Sample	Cf (%)	𝛒 (g

.cm -3 ) 𝑬 (GPa) 𝑮 (GPa)

					𝝊
	B2S3	0	3.99 ± 0.01 68 ± 3	27 ± 3	0.28 ± 0.01
	B2S3_N	≈ 0	3.98 ± 0.01 67 ± 3	26 ± 3	0.29 ± 0.01
	B2S3_N_C30m	5 ± 2	3.97 ± 0.01 68 ± 3	26 ± 3	0.30 ± 0.01
	B2S3_N_C2h Heterogeneous	nm
	B2S3_C1w	≈ 100	3.95 ± 0.01 77 ± 3	29 ± 3	0.31 ± 0.01

Acknowledgments

The European Research Council is greatly acknowledged for the Advanced Grant 320506 (DAMREG) of the 7 th framework program "Ideas". We are also very grateful to V. Dorcet (THEMIS platform, Université de Rennes 1), J o u r n a l P r e -p r o o f

Declaration of interests

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.


Marta Nuñez-Garcia

Nicolas Cedilnik

Shuman Jia

Maxime Sermesant

Hubert Cochet

Automatic multiplanar CT reformatting from trans-axial into left ventricle short-axis view

Keywords: Automatic image reformatting, Short-axis view, Deep learning segmentation, Cardiac imaging

The short-axis view defined such that a series of slices are perpendicular to the long-axis of the left ventricle (LV) is one of the most important views in cardiovascular imaging. Raw trans-axial Computed Tomography (CT) images must be often reformatted prior to diagnostic interpretation in short-axis view. The clinical importance of this reformatting requires the process to be accurate and reproducible. It is often performed after manual localization of landmarks on the image (e.g. LV apex, centre of the mitral valve, etc.) being slower and not fully reproducible as compared to automatic approaches. We propose a fast, automatic and reproducible method to reformat CT images from original trans-axial orientation to short-axis view. A deep learning based segmentation method is used to automatically segment the LV endocardium and wall, and the right ventricle epicardium. Surface meshes are then obtained from the corresponding masks and used to automatically detect the shape features needed to find the transformation that locates the cardiac chambers on their standard, mathematically defined, short-axis position. 25 datasets with available manual reformatting performed by experienced cardiac radiologists are used to show that our reformatted images are of equivalent quality.

Introduction

Multiplanar reformatting refers to the process of converting imaging data acquired in a certain plane into another plane. Standard imaging planes are useful to determine normal anatomy and function and to investigate anatomic variants or pathologies. The basic cardiac imaging planes include planes oriented with respect to the heart (e.g. horizontal and vertical long-axis and short-axis (SAX)), and planes oriented with respect to the major axes of the body (e.g trans-axial (TA), sagittal, and coronal). Cardiac pathologies are commonly evaluated using cardiac-oriented planes and therefore the position of these planes should be prescribed very accurately. In Computational Tomography (CT) imaging, raw TA images are typically reformatted into SAX view (often the interpretation plane) after manual landmark placement [START_REF] Lu | Reformatted four-chamber and short-axis views of the heart using thin section (≤ 2 mm) MDCT images[END_REF]. This manual interaction is operator-dependent and time-consuming as compared to automatic methods. Moreover, the definition of LV SAX plane as going from LV base to apex may differ between observers providing different reformatted images and associated metrics. Marchesseau et al. [START_REF] Marchesseau | Influence of the short-axis cine acquisition protocol on the cardiac function evaluation: a reproducibility study[END_REF] showed the influence on the evaluation of cardiac function of 4 different SAX acquisition protocols (considering the 2 atrioventricular junctions, considering only the left atrioventricular junction, considering the septum, and considering the LV long-axis).

To the best of our knowledge, no method has been proposed for fully automatic CT image reformatting. However, several methods can be found in the literature for automatic landmark detection and subsequent image reformatting in cardiac MRI. For example, Lu et al. [START_REF] Lu | Automatic view planning for cardiac MRI acquisition[END_REF] proposed landmark detection using LV segmentations; Le et al. [START_REF] Le | Computationally efficient cardiac views projection using 3D Convolutional Neural Networks[END_REF] used 3D Convolutional Neural Networks to reformat 4D Flow MR images; and Blansit et al. [START_REF] Blansit | Deep Learning-based Prescription of Cardiac MRI Planes[END_REF] proposed to use U-Net-based heatmap regression to reformat cine steady-state free precession series. While these methods require manual annotation of anatomical landmarks (tedious and time-consuming) Alansary et al. [START_REF] Alansary | Automatic view planning with multi-scale deep reinforcement learning agents[END_REF] used acquired standard views for training avoiding the need for any manual labeling. The authors employed a multi-scale reinforcement learning agent framework that enables a natural learning paradigm mimicking operators' navigation steps.

Reformatting to SAX view can be done by resampling the raw TA image along its subject-specific LV SAX plane. In this paper, we propose to first segment the left and right ventricles and use the masks to automatically locate a few anatomical features needed to accurately compute the LV SAX plane. As compared to Deep Learning (DL) methods, our approach does not require annotated data or training a model, usually expensive and time-consuming.

Methods

Let m = {XYZ} be the coordinate system in original TA view and let m = {X'Y'Z'} be the coordinate system in standard SAX view (see Figure 1). The standard SAX view can be defined as follows: the LV long-axis is aligned according to the Z'-axis; and the right ventricle (RV) is positioned on the left side of the LV as seen in the X'Y'-plane. The reformatting to SAX view is computed by resampling the input TA view along its subject-specific LV SAX plane. Image resampling involves 4 components [START_REF]SPIE2019 COURSE, 02 Images and resampling[END_REF]:

1. The image that is sampled, given in coordinate system m (i.e. the input image in TA view). 2. A resampling grid, regular grid of points given in coordinate system m . 3. The transformation T m m that maps points from coordinate system m to coordinate system m. 4. An interpolator method for obtaining the intensity values at arbitrary points in coordinate system m from the values of the points defined by the sampled image.

Z' Y' X' Z' X Y Z Z' LV RV LV RV X' Y' Z' LV RV X' Z' Y' LV RV LV X'Y' plane clipping X Y Z X' Y' Z' X'Y' plane XY plane LV SAX plane T m' m LV SAX plane
In our approach, cardiac ventricles are first segmented from the original CT image and surface meshes are computed from the corresponding masks (Section 2.1). Mesh coordinates are used to calculate the subject-specific transformation T m m (Section 2.2) that is finally used to resample the input TA image generating its corresponding SAX view (Section 2.3).

Image segmentation

Automatic segmentation of the cardiac ventricles is performed using a DL-based framework. The method, previously described in [START_REF] Jia | Automatically segmenting the left atrium from cardiac images using successive 3D U-nets and a contour loss[END_REF][START_REF] Cedilnik | Fully Automated Electrophysiological Model Personalisation Framework from CT Imaging[END_REF] relies on the use of two successive 3D U-nets [START_REF] Ronneberger | U-net: Convolutional networks for biomedical image segmentation[END_REF]. The high spatial resolution of CT images requires high memory resource while at the same time the ventricles take only a fraction of the entire CT volume. In our approach, we input to the first network a low-resolution version of the input data. The output (coarse segmentation) is used to locate the ventricles and keep only the region around them. A high-resolution cropped subvolume is input to the second 3D U-net. The resulting segmentations are post-processed to obtain clean and non-overlapping masks including up-sampling to the original CT image resolution. The model was trained using 450 CT scans with corresponding expert segmentations of the LV endocardium and epicardium, and the right ventricular epicardium. 50 CT scans were used for validation with a loss function defined as the opposite of the Dice score. Importantly, the trained model was already available to us and we only use it for inference (i.e. prediction or testing) in this work. Therefore, any labeled data or training phase is required for the work presented in this paper.

After image segmentation, triangular surface meshes are computed from the masks using the marching cubes algorithm [START_REF] Lorensen | Marching cubes: A high resolution 3D surface construction algorithm[END_REF] and they are next uniformly remeshed to improve their quality [14] 5 .

Transformation computation

The transformation T m m that maps points from coordinate system m to coordinate system m can be computed as the inverse of the rotation matrix that rotates points from TA orientation to SAX orientation. Let this rotation matrix be R SAX R 3×3 . It takes into account 3 different rotations that locate 3 different LV features on their target position in SAX view:

1. R M V R 3×3 aligns the mitral valve (MV) plane. 2. R S R 3×3 aligns the LV septum (location of the RV with regard to the LV). 3. R LAX R 3×3 aligns the LV long-axis. R SAX is computed as the result of the matrix multiplication:

R SAX = R LAX R S R M V (1)
Figure 2 depicts two examples where the alignments are shown consecutively for illustrative purposes only.

All rotation matrices in our approach are computed using the following processing. Given two unit vectors, u 1 and u 2 , a rotation matrix R that aligns u 1 to u 2 can be computed as follows:

R = I 3 + V × + V × V × 1 -c s 2 (2)
where,

I 3 = 3×3 Identity matrix v = u 1 × u 2 , s = v , c = u 1 • u 2 , and
V × def =   0 -v 3 v 2 v 3 0 -v 1 -v 2 v 1 0   is the skew-symmetric cross-product matrix of v = (v 1 , v 2 , v 3 )
5 https://github.com/valette/ACVD MV plane alignment The rotation matrix R M V is computed using equation 2 where the unit vectors to be aligned are: u 1 = subject-specific MV normal in TA view; and u 2 = MV normal in standard SAX view, i.e. opposite of the X'Y'-plane normal ( u 2 = (0, 0, -1)). To compute u 1 , the region corresponding to the MV orifice is first automatically detected. Distances are computed from each point in the LV endocardial mesh to the LV wall mesh. Similarly, distances are computed from each point in the LV endocardial mesh to the RV epicardial mesh. The MV orifice area is detected as the points in the LV endocardial surface that are far from the LV wall (more than 5 mm), and far from the RV epicardial surface. The latter ensures that the MV orifice is not confused with the aortic orifice and it avoids getting orientations corresponding to this artery. The threshold distance was defined to take into account the LV size and was empirically set to more than half the maximum distance between LV endocardium and RV epicardium. All distances are computed using the distance transform [START_REF] Danielsson | Euclidean distance mapping[END_REF][START_REF] Fabbri | 2D Euclidean distance transform algorithms: A comparative survey[END_REF], that assigns to every point in the mesh a value indicating its distance to the nearest point in the other surface. The MV normal ( n M V ) is computed averaging the normals of all points belonging to the MV orificie area, and u 1 is defined as the corresponding unitary vector:

n M V n M V .
LV septum alignment The rotation matrix R S is computed using equation 2 where now the unit vectors to be aligned are: u 1 = unit vector within the MV plane pointing from the RV to the LV; and u 2 = unit vector within the X'Y'-plane pointing horizontally from RV position to LV position in standard SAX view ( u 2 = (1, 0, 0)). White arrows in Figure 2 depict these orientations.

To compute u 1 , the surface corresponding to the MV orifice is first extracted using the same procedure explained above. This surface is uniformly remeshed to increase its spatial resolution and distances to the RV are re-computed. Let p 0 be the point with minimum distance value and let p 1 be the point with maximum distance value. The unitary vector u 1 is computed as p1-p0 p1-p0 .

LV long-axis alignment The rotation matrix R LAX is computed using equation 2 where now the unit vectors to be aligned are: u 1 = subject-specific LV long-axis unit vector; and u 2 = standard LV long-axis unit vector in SAX view ( u 2 = (0, 0, 1)). The LV long-axis is defined as the line connecting the centre of the MV orifice and the LV apex. Yellow arrows in Figure 2 show schematically these orientations. To compute u 1 , the centre of the MV is detected as the centre of mass of the MV orifice surface previously extracted. Let p M V be that point. Distances are computed from p M V to all points in the LV endocardial surface (see Figure 2, 2nd and 4th rows). The LV apex is detected as the point (p A ) that is farthest from p M V . Then, u 1 is computed as p A -p M V p A -p M V .

Image reformatting

Prior to image resampling, a reference image is created with desired origin, size, and resolution. The voxels in this reference image determine the resampling grid that is used to sample the input TA image after mapping the voxel's position from m to m using T m m . The final transformation also includes a translation to the area where the image to be sampled is located. In our method we propose to use reference origin = (0,0,0); reference image size = 512 × 512 × 512; and reference image resolution = input image physical size / reference image size.

Results

The method was applied to 25 images with available reformatting to SAX view performed by expert radiologists. Original CT image dimensions were 512 × 512 voxels in the X and Y axes and 402 ± 103 voxels in the Z-axis. The average original voxel size was 0.40 ± 0.05 mm × 0.40 ± 0.05 mm × 0.45 ± 0.15 mm.

The average time to complete the full image reformatting was 28.38 ± 7.73 s (Intel i7 2.60GHz × 12 CPU and 32 GB RAM). Several examples of results are shown in Figure 3. It can be seen how our method replicates the manual reformatting and it even outperforms it for some cases. For example in (b), (c), and (d) the LV long-axis is more accurately aligned along the Z-axis using our approach than using manual reformatting.

Conclusions

Cardiovascular image interpretation often relies on multiplanar reformatted images typically computed manually being time-consuming and lacking reproducibility. Automatic methods such as DL-based techniques often require lots of annotated data and computationally expensive resources. We have presented a method to reformat raw trans-axial CT images to standard SAX view that it is automatic, fast, accurate, reproducible and it does not require labeled data. The main drawback is however the dependency of the method on the quality of the segmentation masks. Previous studies have shown highly precise segmentation results using our proposed method (median Dice score of 0.9 [START_REF] Cedilnik | Fully Automated Electrophysiological Model Personalisation Framework from CT Imaging[END_REF]) but the image segmentation step (Section 2.1) could be easily replaced by any desired segmentation method (including manual segmentation performed by a radiologist which is yet considered the gold standard). Computing accurate standard SAX images may be useful to compare different image modalities such as CT and MRI since SAX cardiac MRI is currently one of the most common acquisition views in clinical practice. The origin, size, and resolution, of the reformatted SAX image can be specified by the user which is useful in many applications where a standard representation of the data is required (e.g. to use a pre-trained network).

  Image in original TA view 2 view orientations in m = XYZ coordinate system Image in standard SAX view 3 view orientations in m' = X'Y'Z' coordinate system

Fig. 1 :

 1 Fig. 1: Schematic representation of multiplanar reformatting to SAX view. On the left, original TA view in m coordinate system. On the right, corresponding SAX view in m coordinate system. For simplicity, only surface models of the LV and RV are shown. LV = Left Ventricle; RV = Right Ventricle; TA = Trans-axial; SAX = Short-axis.

Fig. 2 :

 2 Fig. 2: Two examples of rotation to SAX view using surface meshes. The LV endocardial surface is colored according to its distance to the RV (1st and 3rd row) and according to its distance to the centre of the MV (2nd and 4th row). LV wall and RV epicardial surfaces are shown semitransparent. LV = Left Ventricle; RV = Right Ventricle; MV = Mitral Valve.

Fig. 3 :

 3 Fig. 3: Example results. On the left, 3 views of original trans-axial images; on the right, 3 views of corresponding short-axis images reformatted with our method (top), and the provided manual reformatting (gold standard) (bottom).

Acknowledgements. Part of this work was funded by the ERC starting grant EC-STATIC (715093), the IHU LIRYC (ANR-10-IAHU-04), the Equipex MUSIC (ANR-11-EQPX-0030) and the ANR ERACoSysMed SysAFib projects. This work was also supported by the French government, through the 3IA Côte d'Azur Investments in the Future project managed by the National Research Agency (ANR) with the reference number ANR-19-P3IA-0002. We would like to thank all patients who agreed to make available their clinical data for research.


Pierre Benoit

Jean Pierre Cravedi

Jean-Claude Desenclos

Christophe Mouvet

Guido Rychen

Michel Samson

Environmental and human health issues related to long term contamination by chlordecone in the French Caribbeans

Chlordecone is an organochlorine insecticide extensively used in the French Caribbeans (FC), Guadeloupe andMartinique, from 1972 to 1993. This pesticide, which was applied on banana plantations to control banana weevil, undergoes an extremely slow degradation in the environment and is still present in soils where it was applied. It was only in 1999 that French health and environmental authorities became aware of the extent of the pollution due to chlordecone. In addition to soils, it was detected in rivers and groundwaters as well as in coastal ecosystems, and was found to contaminate the terrestrial and aquatic food chains. From that date, the consequences of long-term environmental contamination by chlordecone on human and ecosystem health were considered of major concern. Chlordecone toxicological studies performed in rodents demonstrated evidence of kidney lesions, hepatotoxicity, neurotoxicity, reprotoxicity, developmental toxicity, and carcinogenicity. Chlordecone is also an endocrine-disrupting chemical due to its estrogenic properties both in vitro and in vivo. Epidemiological studies have recently shown that the exposure to chlordecone is associated with the occurrence of adverse health events including prostate cancer.

Since early 2000's, surveys conducted in French Caribbeans have confirmed that in contaminated areas soils, rivers, spring and ground waters, aquatic biota, crops were polluted by chlordecone. This situation became a major concern for FC citizens and for French health authorities, giving rise, among other initiatives, to several research programs encouraged and founded in the frame of the PNAC (national action plan chlordecone) supported by the French Government which started in 2008 through 3 successive plans (PNAC 1 2008-2010, PNAC 2 2011-2013and PNAC 3 2014-2020). These programs aimed at filling gaps and providing data on the occurrence of chlordecone in environmental matrices, on its carry over and transfer in the food chain, on human exposure as well as its social factors and on the (eco-)toxicological and health effects of chlordecone.

A scientific conference on chlordecone followed by public restitution days were held in Martinique and in Guadeloupe from October 16 th to 19 th 2018. During the conference, which gathered more than 200 scientists and experts, recent advances in different scientific fields of research dealing with environmental issues, plant and animal production sectors, human health concerns , humanities and social sciences, were presented. The conference aimed at fostering interactions and synergies between scientific disciplines around the « one Health » concept which promotes integrated and systemic approaches of human and ecosystem health. The goal was to present and discuss possible solutions to reduce the contamination of ecosystems and human populations' exposure.

Improving the knowledge of chlordecone contamination in soils and its migration to waterbodies remains necessary before promoting measures to reduce its dispersion at the catchment scale. Field observations, experimental studies and modelling approaches addressing the dispersion of chlordecone have been conducted in instrumented sites dedicated to pesticides in both Guadeloupe and Martinique (OPALE observatory). These catchments are representative of contaminated areas with a significant proportion of land occupied by formerly treated banana crops. Processes regulating the interactions between the soil and water fluxes have to be thoroughly understood at the plot and catchment scale in order to precise the seasonal dynamics of chlordecone emissions to river and ground waters, the predominance of soluble versus suspended particles in these fluxes in relation to rainfall intensity, soil types, landscape position, land-use and cropping practices.

Ecotoxicological impacts of chlordecone concern terrestrial, river, coastal and marine ecosystems. Bioaccumulation of chlordecone in the food chain, via biomagnification processes is evidenced for most aquatic organisms. Improving the aquatic ecosystem exposure measurements remains a challenge and standardized and integrated protocols are needed for in situ monitoring of chlordecone and other pesticides in these ecosystems. Integrating new results at different levels of organisation of the food web is critical to address the difficult question of long-term effects of chlordecone even at low concentrations A c c e p t e d m a n u s c r i p t in waterbodies. It is therefore necessary to rely on new tools and methods, e.g. sensors, biomarkers,omics, analytical platforms, dedicated to ecotoxicological approaches, predictive toxicology and epidemiological studies.

Decontaminating soils remains a real challenge knowing the very low degradability of chlordecone and the large areas impacted. Different remediation strategies have been developed at different scales. The process based on strongly reducing conditions achieved through addition of zero valent iron has proven its effectiveness for a nitisol in the field conditions of an actual banana plantation. Enhanced microbial biodegradation remains presently limited to anaerobic laboratory conditions. Other strategies may rely on the use of plant and phytoextraction processes. Once tested in laboratory conditions, the different strategies have to be tested in situ with the different soil types present in the French Caribbeans since various processes, g. different diffusion and ageing of chlordecone in the soil matrix according to the soil type, influence the effectiveness of remediation. Conversely, the enhancement of sequestration processes by addition of exogeneous organic matter in soils represents a way to reduce the transfer from soil to water and crops.

It is well recognized that the contamination process of agricultural products by chlordecone is related to the transfer to the plant of the contaminant present in soil, to the bioaccumulation in animal tissues of chlordecone present in surrounding environment (e.g. bioconcentration in aquatic species) or by the intake of contaminated soil or feed by farm animals. Indeed, for some species, involuntary ingestion of contaminated soil is a very significant route of contamination. The sources of contamination and the toxicokinetic properties of chlordecone in the main target species should therefore be determined in order to recommend breeding practices that can limit the contamination of tissues intended for human consumption. A reduction of chlordecone uptake can be achieved through the use of sequestering agents added to the soil or incorporated into feedstuffs (activated carbons, biochars). If toxicokinetic studies are useful to better understand the contamination process, they may also help to define adequate decontamination strategies, i.e. periods of decontamination of animals compatible with breeding practices.

In humans, exposure via food may vary considerably, depending on the origin of the food. It is therefore essential to have through appropriate and repeated population survey accurate data on the levels of contamination of different commodities, but also to identify the foods and supply chains that contribute the most to exposure. The biomonitoring of the population is another way of assessing the exposure. It allows not only to know the range and median levels of chlordecone in blood in the West Indian population, but also to assess the decline of its concentration in blood over time and therefore the effectiveness of the public policies and interventions implemented in French Caribbeans.

Hazard identification and human health effects resulting from the exposure to chlordecone are a subject of important research efforts. Not all of the toxicological effects of chlordecone are known yet, and this may warrant further investigations on the mechanisms of action of this pollutant. Thus, experiments of cell biology or on animal models can be helpful. Further epidemiolo gical investigation, based on large cohorts studies are also required to find out more on the links between exposure to chlordecone and health outcomes. This include follow-up from conception until death, including pregnancy and child development outcomes, the assessment of the impact on risk of chronic diseases, and cancer, the contribution of occupational exposure… This special issue on chlordecone will provide state-of-the art information on occurrence, fate and toxicity of this bioaccumulative and persistent organochlorine insecticide in the Caribbean environment, as well as on human exposure and health effects associated with its presence in the food chain. Studies providing

  s c r i p t specific solutions in the field of remediation and decontamination strategies are also included in this volume.A c c e p t e d m a n u s c r i p t

Scientific Council of Inserm (2017-2021), member of Administrative Council of EHESP (National school of Public health) (2018-present), member of Administrative Council of AFEF (French society of Hepatology) (2018-2021), member of SAB of RISUQ (Réseau Intersectoriel de recherche en Santé de l'Université du Québec, Canada) (2019-present). He studies the inflammation, cell death and the impact of environmental factors in liver pathologies. He has published more than 100 papers in reputed journals (Nature, Cell, J Exp Med, Hepatology, J Hepatol., etc...), with already more than 9400 citations and H-index 40.

Pierre Benoit, PhD, is a soil scientist and director of research at the French National Research Institute for Agriculture, Food and Environment (INRAE) working at Joint Research Unit INRAE/AgroParisTech ECOSYS in Thiverval-Grignon. His research interests concern soil science and the coupling of biological and physico-chemical processes involved in the fate and transport of pesticides and other organic contaminants in soil and water. Applications concern the assessment of several management and cropping practices such as organic waste recycling in agricultural soils, soil tillage practices, cover crop introduction, ecological infrastructures such as grassed buffer strips and wetlands and their impacts on the fate and transport of pesticides and other organic contaminants.

Jean-Pierre Cravedi, PhD, is a toxicologist and is director of research at the French National Research Institute for Agriculture, Food and Environment (INRAE) at Toulouse. He was until 2019 deputy head of the human nutrition and consumer behaviour division, in which he was in charge food safety scientific programmes. He published more than 350 articles and reports in scientific journals, most of them being in the field of food safety, environment and health. In the last 10 years he coordinated 3 national or international projects and contributed to 11 research programmes. He is currently member of several working groups at the European Food Safety Authority (EFSA), and the French Agency for Food, Environmental and Occupational Health and Safety (ANSES).