M Laanaiya

A Zaoui
email: azaoui@polytech-lille.fr

Piezoelectric response and failure behavior of cement paste under external loading

Keywords: Cement, C-S-H, Mechanical properties, piezoelectricity, Molecular dynamics

We study the elastic behavior and rupture mechanism of Calcium Silicate Hydrates (C-S-H) in response to tensile loading. For the three tensile axes, initial defects are spotted in the interlayer regions. However the crack propagation is rather different depending on the axis of tensile. The cup-and-cone failure surface shows the ductile feature of C-S-H in the x and y directions; while the devastating rupture mode confirms the brittle feature of C-S-H in the z direction. Piezoelectricity was investigated using the charge fluctuation method. The polarization variation in response to small strain was also investigated and piezoelectric coefficients were derived. Furthermore, dependence of elastic and piezoelectric properties over external pressure was analyzed. Results reveal an improvement of the mechanical properties and the ultimate strength especially in the z direction; whereas the nonpiezoelectricity remains unchanged despite the rearrangement of atoms induced by the external applied pressure.

I. Introduction

The Calcium-Silicate-Hydrates (C-S-H), considered as the major component of the cement hydrated products with 60-70% volume fraction [START_REF] Ji | Comparison of computational water models for simulation of calcium-silicate-hydrate[END_REF]. Experimental studies exhibit that C-S-H has a similar structure of tobermorite with different compositions [START_REF] Grangeon | Structure of nanocrystalline calcium silicate hydrates: insights from X-ray diffraction, synchrotron X-ray absorption and nuclear magnetic resonance[END_REF]. However, a great controversy over the structure nature of C-S-H whether it is an amorphous or a crystalline material. Taylor suggests that the structure of C-S-H at nanoscale is composed of imperfect layers of 14 Å tobermorite (Ca5Si6O16(OH)2.7H20) [START_REF] Bonaccorsi | The crystal structure of tobermorite 14 A (Plombierite), a C-S-H phase[END_REF] with a C/S ratio of 0.83 and density d=2.18 g/cm 3 and jennite (Ca9(Si6O18)(OH)6.8H2O [START_REF] Gard | A reexamination of jennite[END_REF]) with C/S=1.5 and g=2.27 g/cm 3 [START_REF] Taylor | Proposed structure for calcium silicate hydrate gel[END_REF].

Nevertheless, small-angle neutron scattering (SANS) has proven that C-S-H has a C/S ratio of 1.7 and density d=2.6 g/m 3 [START_REF] Allen | Composition and density of nanoscale calciumsilicate-hydrate in cement[END_REF]. Unfortunately, those values cannot be found either by tobermorite or jennite. Hence, using molecular simulations, many authors developed several models of C-S-H that agree the most with the experiment results and correctly predict the C-S-H properties. Pellenq et al. [START_REF] Pellenq | A realistic molecular model of cement hydrates[END_REF] constructed a C-S-H model ((CaO)1.65(SiO2)(H2O)1.75 ) with values of C/S ratio and density close to those provided by Neutron scattering measurements (C/S=1.7 and d=2.6 g/m 3 ). Initially starting from an 11Å Tobermorite structure and adopting a combinatorial method to produce defects in the silica chains to increase the C/S ratio from 1 to 1.65 and then using Monte Carlo simulations for water adsorption. Pellenq's model is considered as a turning point in the MD simulation of the C-S-H system as it has proven its great capabilities to predict structural and mechanical properties of C-S-H in consistency with the experiment. Many posterior works used the Pellenq model of C-S-H to describe the C-S-H structure at the nanoscale. Manzano et al. [START_REF] Manzano | Confined Water Dissociation in Microporous Defective Silicates: Mechanism, Dipole Distribution, and Impact on Substrate Properties[END_REF] used the C-S-H realistic model by Pellenq. et al. to study the mechanism of water dissociation to hydroxyl groups in the micropores of C-S-H using the REAXFF reactive force field [START_REF] Van Duin | ReaxFF: A reactive force field for hydrocarbons[END_REF] and the influence that it has on the structural and mechanical properties.

Manzano et al. have calculated the elastic tensor of the structure and compared the deduced mechanical properties of C-S-H before and after water dissociation. Unlike most silicates that manifest a "hydrolytic weakening" effect [10], the presence of water has a hardening effect since it reacts with the silicate chains transforming the layered two-dimensional like structure of C-S-H to a three dimensional like structure. Bauchy el al. [START_REF] Bauchy | Order and disorder in calciumsilicate-hydrate[END_REF] also developed the realistic model described by Pellenq el al. within the reactive forcefield REAXFF [10] parameterized by Manzano et al. that allows the water molecules to dissociate into hydroxyl to form Si-OH and Ca-OH groups to study the atomic order in C-S-H. According to this study, an investigation of the atomic order of the C-S-H structure was carried out and C-S-H was described as an intermediate structure between a crystalline and an amorphous material.

Recently, the elastic behavior of C-S-H was simulated using several realistic C-S-H models [START_REF] Pellenq | A realistic molecular model of cement hydrates[END_REF][START_REF] Manzano | Confined Water Dissociation in Microporous Defective Silicates: Mechanism, Dipole Distribution, and Impact on Substrate Properties[END_REF] using molecular dynamics approach. However, only elastic behavior was considered to study the mechanical behavior of C-S-H. Few MD studies have characterized the mechanical response of C-S-H beyond the elastic limit. The failure mechanism of C-S-H in response to uniaxial tensile along the weakest direction of the structure was studied under different hydration states [START_REF] Hou | Calcium silicate hydrate from dry to saturated state: structure, dynamics and mechanical properties[END_REF] and temperatures [START_REF] Xin | Temperature effects on tensile and compressive mechanical behaviors of CSH structure via atomic simulation[END_REF]. In addition, the fracture behavior of C-S-H globules and interfaces was simulated by Fan and Yang [START_REF] Fan | Mechanical properties of CSH globules and interfaces by molecular dynamics simulation[END_REF] using series of C-S-H models by Richardson [START_REF] Richardson | Model structures for C-(A)-SH (I)[END_REF] with Ca/Si lower than 1.4. In another study, Hou et al. have found that the mechanical strength along x and y directions is mainly due to the interaction between the silicate chain and calcium, while the weak resistance to tensile along z direction is rather due to the unstable hydrogen bonds and the shielding of the interlayer Ca 2+ ions [START_REF] Hou | Mechanical properties of calcium silicate (C-S-H) at nano-scale: a molecular dynamics study[END_REF]. On the other hand, the response of C-S-H to shear deformation was also simulated on the nanoscale using different C-S-H models in both the elastic and plastic phases [START_REF] Rivas Murillo | Computational modeling of shear deformation and failure of nanoscale hydrated calcium silicate hydrate in cement paste: Calcium silicate hydrate Jennite[END_REF][START_REF] Manzano | Shear deformations in calcium silicate hydrates[END_REF][START_REF] Wang | Molecular dynamics simulation study on interfacial shear strength between calcium-silicate-hydrate and polymer fibers[END_REF].

Piezoelectricity, defined as the electric polarization induced by mechanical strain, is one of the most important mechanisms in smart materials applications. Enhancing the piezoelectric properties provides the material smart properties as self-sensing. Experimental works have been conducted to enhance the piezoelectricity of cement. Dong and Li [START_REF] Dong | Cement-based piezoelectric ceramic smart composites[END_REF] experimentally fabricated specimens of cement based piezoelectric ceramic composites by incorporating piezoelectric ceramic powder into Portland cement and measured the mechanical-electrical properties of the modified cement. It was proven that adding piezoelectric ceramics greatly enhance the piezoelectric response of cement by measuring the piezoelectric strain factor d33. However, accounting for polarization and thus for piezoelectricity has always been a shortcoming of Molecular dynamics methods. Classical molecular dynamics approaches typically uses static bonds and considers atoms as fixed charge points. Such formalism does not allow an explicit description of the atoms polarization as a response to an external electric field or a charge perturbation of the system and thus cannot accurately describe the polarization effect. Several methods have been developed to account for polarization in order to remedy this shortcoming. The most common approaches are: Drude oscillators [START_REF] Lemkul | An Empirical Polarizable Force Field Based on the Classical Drude Oscillator Model: Development History and Recent Applications[END_REF],

induced-point polarizable model [START_REF] Ponder | Current Status of the AMOEBA Polarizable Force Field[END_REF] and charge fluctuation method (Qeq) [START_REF] Chen | Theory and Applications of Fluctuating-Charge Models[END_REF]. The first method consists on introducing "Drude" particles to the system connected to the original particles of the system "Cores" by a spring of a rigidity Kb that depends on the atom's type.

The "induced point" polarizable method introduces polarizable atomic multipoles. The "Qeq method" is a model of variable partial charges of atoms, which adapt based on the electronegativity equalization method developed by Mortier et al. [START_REF] Mortier | Electronegativity equalization method for the calculation of atomic charges in molecules[END_REF] under constraints of charge neutrality to the local environment of atoms [25]. This approach does not require adding new particles to the system and allows the charge transfer between atoms and molecules, reasons why we are adopting this method to investigate polarization. Therefore, it is necessary to use a force field that enables the charge variation and charge transfer, which is a key feature of REAXFF reactive force field developed by van Dui et al. [START_REF] Van Duin | ReaxFF: A reactive force field for hydrocarbons[END_REF] that explicitly model the response of charges toward the local environment by the Qeq method and accounts for polarization effects by using a geometry-dependent charge calculation scheme [START_REF] Chenoweth | ReaxFF reactive force field for molecular dynamics simulations of hydrocarbon oxidation[END_REF].

ReaxFF provides a dynamic description of charges of species, overcoming the inherent limitations of with traditional MD force fields that consider charges as fixed. Moreover, ReaxFF is based on the concept of bond-order that provides a dynamic description of bonds and smooth changes in the particles connectivity. Consequently, ReaxFF allows the bonds formation and dissociation that occur in chemical reactions or deformation processes.

In this study, we will investigate the structural, mechanical and piezoelectric properties of C-S-H using the recent realistic model by Bauchy el al. [START_REF] Bauchy | Order and disorder in calciumsilicate-hydrate[END_REF]. A particular attention is paid to the characterization of the mechanical response of C-S-H to loading by studying the elastic, plastic and failure behaviors. The ultimate strengths as well as breakdown points are determined along the three axes. The piezoelectric response of C-S-H will be also investigated by analyzing the system polarization variation under strain. Moreover, the pressure dependence of elastic and piezoelectric properties will be studied.

II. Computational details

We prepared a 3x3x3 supercell composed of 13527 atoms based on the C-S-H model of Bauchy et al. [START_REF] Bauchy | Order and disorder in calciumsilicate-hydrate[END_REF] with a C/S ratio of 1.7. The system was simulated using REAXFF forcefield implemented in the Large-Scale Atomic/Molecular Massively Parallel Simulator (LAMMPS) [27] package. Manzano et al. extended the REAXFF capacity to perform calculation on calcium silicate systems by the parameterization of the Ca-O/H interactions within the reactive force field [START_REF] Manzano | Hydration of calcium oxide surface predicted by reactive force field molecular dynamics[END_REF]. Timestep was set to 0.25 fs and the Verlet algorithm was used for time integration. The structure was relaxed in the NPT ensemble using the Nose-Hoover thermostat and barostat at T=300 K and zero external pressure for 2.5 ns until the convergence of energy and lattice parameters was achieved. The lattice parameters of the relaxed triclinic box are: a=39.00 Å, b=54.29 Å, c=71.91 Å. α=91.62°, β=91.68°, γ=88.35°and the relaxed box is presented in Fig. 1.

III. Results and discussion

Structural properties

We plot in Fig. 2.a the radial distribution function g(r). Five peaks of RDF are situated in the 0.99 Å, 1.51 Å, 1.62 Å, 2.23 Å and 2.65 Å regions were observed. The first and third peaks situated in the 0.99 Å and 1.62 Å regions respectively are quite high and sharp compared to the second and the two last peaks that are much lower. To investigate the origin of these peaks, we plot the contributions of the species of the system to RDF. Nine labels are used to distinguish between the local environments of the atoms. The Oxygen atoms are classified in four categories: Ow refer to oxygen of the water molecules, Oh are oxygen atoms of the hydroxyl groups, Ob are the bonding oxygen atoms in the Silica chains and O are the nonbridging oxygen atoms in the silica/calcium layers. We also make difference between two Calcium types: Ca is the intralayer calcium and Cw is the interlayer calcium. Finally the hydrogen atoms have two types: The Hw atoms in the water molecules and H atoms in the hydroxyl groups. We see from Fig. 2.b that the first sharp peak situated in the 0.99 Å region is mainly due to the water and hydroxyl groups atoms (Ow, Hw, O and H). The second peak situated in the 1.51 Å is much shorter and is fully due to Hw atoms contribution. The third peak at 1.62 Å is due to Si atoms as well as the oxygen atoms O, Ob and Oh. The Forth peak in the 2.23 Å region is dominated by both calcium types Ca and Cw contributions and the rest of the atoms with smaller contributions. The fifth peak at approximately 2.63 Å region is due mostly to Ob atoms and less significantly to Ca, O of the intralayer space and Cw, Ow and Oh atoms in the interlayer space.

Based on the information provided by the atoms contributions to RDF, we plot the partial radial distribution function (PRDF) of each pair of atoms spotted in each peak. Fig. 3.a shows that the first peak is mainly due to Oh-H and Ow-Hw interactions with a mean bond length of 1 Å for both and coordination numbers of hydrogen atoms around oxygen atoms of 0.97 and 1.81 respectively within a sphere of 1.3 Å. The position of this first peak was also found by Manzano et al. [START_REF] Manzano | Confined Water Dissociation in Microporous Defective Silicates: Mechanism, Dipole Distribution, and Impact on Substrate Properties[END_REF] by both DFT and MD simulations. The second peak is fully due to Hw-Hw correlation with a coordination number of 0.98 within a sphere of 1.6 Å as illustrated in Fig. 3.b while the third peak at 1.62Å is due to Si-O Si-Oh and Si-Ob interactions (see Fig. 3.c) With coordination numbers of oxygen atoms around Si atom of about 2.21, 1.08 and 0.7 respectively within a sphere of 2.5Å. Bauchy et al. [START_REF] Bauchy | Order and disorder in calciumsilicate-hydrate[END_REF] also found that the first peak in the 0.99 Å region is due H-O bonds. However, only a second peak in the 1.6 Å, associated with a superposition of both H-H and Si-O correlations, was spotted. The rest of peaks were not distinguishable. Here, we see that the Hw-Hw interactions result in an intermediate peak at 1.51 Å region while the peak in the 1.62 Å region is mainly due to correlations between Si and Oxygen atoms. Fig. 4 shows that the peak situated in the 2.23 Å region is mainly due to Ca-O interactions in the intralayer as well as the Cw-Oh interactions in the interlayer while the last peak in the 2.65 Å is mainly due to the Ob-O, Ob-Ob and Cw-Ow interactions with a smaller contribution of Cw-Oh interactions. Manzano et al. also found a peak at approximately 2.6Å by calculating partial RDF of Ca-O. However, no precisions were given about the oxygen types that contribute the most to this peak. Moreover, we can see from

Mechanical properties

After equilibrating the system, uniaxial strain (X, Y and Z) and shear strain (XZ, YZ and XZ) were applied with an engineering strain rate of 0.007ps -1 in the NVT ensemble and the corresponding stresses are calculated. The linear part of the stress-strain response enables to calculate the 21 elastic constants Cij that we compared to other Molecular Dynamics (MD) works in Table 1. However, we only retain the 9 most important values of the elastic tensor C11, C22, C33, C44, C55, C66, C12, C13 and C23 since the remaining elastic coefficients are very weak and can be neglected. The calculated values of Cij are close to those found by previous MD works with an average difference of 5.6% in comparison with the Cij values by Pellenq et al. [START_REF] Pellenq | A realistic molecular model of cement hydrates[END_REF]. Although different geometries and interatomic potentials were used in the mentioned MD works, values of the calculated elastic constants are quite comparable. We see that C11 and C22 values are higher than C33 value indicating that the system is more resistant in the XY plane corresponding to the silicate layers. From the elastic tensor, we calculated the bulk (K) and shear (G) moduli according to the Voight-Reuss-Hill (VRH) bounds [START_REF] Hill | The elastic behaviour of a crystalline aggregate[END_REF]:

= ( ) (1)
= ( ) (2)
= ( ) ( ) ( ) (3)
= ( ) ( ) (4)
The equivalent isotropic Young's modulus (E), Poisson ratio (ν) and indentation modulus (M)

were derived from K and G using the formulas:

= (5) ν = 1 -! " (6)
M = 4G & ' & ' (7)
The calculated elastic quantities are summarized in agreement with that by nanoindentation 65 GPa [30].

Crack propagation

Shrinkage crack in cement materials is greatly related to tensile strength. The crack potential gets more important as the tensile strength decreases In order to investigate the tension strength of the system in the x, y and z directions, the stress evolution with respect to tensile strain in the x, y and z directions is plotted in Fig. 5. The stress of the entire systems of atoms is given by the following formula:

( = - )! * + - ∑ -. . .1 . 2 .
3 .

(

) 8
Where N is number of atoms, K is Boltzmann constant, T is temperature, d is dimensionality of the system, and V is volume. ri and fi are respectively the position and force vector of atom i.

In x and y directions, Stress evolution is very similar. Stress rapidly increases with strain in the elastic phase that ends at 0.03 Å/Å strain approximately. The ultimate strength in the x direction (4.05 GPa) is slightly higher than the y direction (3.85 GPa) corresponding to 0.13 Å/Å and 0.11 Å/Å respectively. Then, the stress slowly decreases in the plastic phase. The slow decreasing of the stress in the plastic phase is an indicator of the ductile behavior in the x and y directions.

In the z direction, the response to tensile is quite different. Stress increases in the elastic phase as strain increases up to 0.02 Å/Å strain. Subsequently, the stress continues to increase up to an ultimate strength of 1.46 GPa at 0.06 A/A strain. Then, the stress sharply decreases to zero at 0.09 Å/Å strain indicating a brittle behavior of the system in the z direction.

Understanding the fracture mechanism generated by tensile is important to improve the durability of cement materials. Therefore, we investigated the C-S-H system response to tensile in x, y and z directions. The relaxed structure is slowly elongated in the desired direction up to 70%. The intermediate configurations are recorded all along the process in order to spot first defects and cracks in the structure and to follow up the crack propagation.

With a tensile loading along the x direction, Fig. 6.a shows initial small defects in the interlayer regions at 0.17 Å/Å strain soon after reaching the yield point. As long as strain increases, the interlayer defects grow and form visible cracks in the structure as shown in Fig. 6.b. Then, calcium atoms and silicate chains nearby the cracks dissociate leading to crack overlapping the structure as shown in Fig. 6.c. In Fig. 6.d corresponding to 0.63 Å/Å strain, cracks continue to grow and overlap in the +/-45° direction and tend to form one larger crack indicating the rupture of the structure.

These results are very similar to those found by Hou et al. who studied the fracture mechanism of C-S-H in presence of nano-voids. However, the crack propagation is significantly slower compared to D.Hou results [START_REF] Manzano | Hydration of calcium oxide surface predicted by reactive force field molecular dynamics[END_REF]. The crack propagation rate is highly affected by the present void in D.Hou [START_REF] Manzano | Hydration of calcium oxide surface predicted by reactive force field molecular dynamics[END_REF] simulation. The present void localized in the center of the box also influences the crack initiation that was located near the central void, while the crack was initiated in the interlayer regions in the case of our study. However, the present void in C-S-H didn't affect the direction of the crack propagation that was found to be the same (+/-45° from x axis). Moreover, the cup-and-cone failure surface at the end of the tension simulation is also observed in both studies confirming the ductile failure feature of C-S-H. Fig. 7 shows the crack propagation of the structure elongated in the y direction. Small defects are initialized in the interlayer regions right after the yield point as shown in Fig. 7.a corresponding to 0.14 Å/Å strain. Initial defects grow to bigger cracks as we can see at 0.19 Å/Å deformation stage (Fig. 7.b). This deformation stage corresponds to the rapid stress reducing after reaching the yield point in the stress-strain curve (Fig. 5). Then, the interlayer cracks propagate into the neighboring calcium silicate chains as shown in Fig. 7.c corresponding to 0.34 Å/Å strain. The interlayer calcium atoms Cw attempt to reconstruct the calcium silicate chains by bridging the fractured parts. This explains the slight stress increase at 0.2 Å/Å strain and the slow-down of the stress decreasing rate afterwards in the stressstrain evolution. The crack propagation mode is very similar to that of x tension. The crack grow along a direction of +/-45° from y axis and overlap to form a larger crack as strain increases from 0.34 Å/Å to 0.48 Å/Å as we can see in Fig. 7.d. As in the case of tension along

x axis, the rupture surface exhibits a cup-and-cone geometry indicating a ductile failure of C-S-H in the y direction.

The response of C-S-H to a tension along the z direction is illustrated in Fig. 8 The defects are visible in the interlayer regions as soon as the strain reaches a value of only 0.063 Å/Å as shown in Fig. 8.a. Many small defects can be seen in the same level of the interlayer region.

As strain increases from 0.063 Å/Å to 0.09 Å/Å, the initial cracks grow very fast in the interlayer region as can see from Fig.

Mechanical behavior under pressure

In order to understand the mechanical behavior of C-S-H under pressure, we applied a hydrostatic external pressure ranging from 0 to 1GPa with a step of 100 MPa. For each pressure, the structure was relaxed in the NPT ensemble during 1ns. The convergence of energy and volume was verified. Elastic constants Cij were then calculated using the stress-strain relationship. The variation of the difference ΔCij=Cij-C 0 ij (where C 0 ij =Cij(Press = 0) is the coefficient Cij of the initial structure at zero pressure) under the applied pressure was plotted in Fig. 9. We can see that the three first diagonal components of the elastic tensor: C11, C22 and C33 are the most sensitive coefficients by the applied pressure with a slightly higher slope obtained for ΔC33, whereas the non-diagonal elements C12 and C13 and C23 vary less with pressure with a slightly higher increasing rate for C13 and C23. On the other hand, the shear components C44, C55 and C66 remain almost unchanged with the pressure variation.

Thereafter, we have calculated the Young's modulus, bulk and shear moduli (K and G respectively) using equations ( 1) to ( 5) and plotted their variations with Pressure (see Fig. 10).

We see that the resistance of the structure to shear is almost unaffected by the applied pressure as the shear modulus remains almost constant (around 22 GPa), while the bulk modulus and Young's modulus increase up to 11% and 5% respectively when the external pressure reaches 1GPa. These results agree with those of Zaoui [START_REF] Zaoui | Insight into elastic behavior of calcium silicate hydrated oxide (C-S-H) under pressure and composition effect[END_REF] who found that for both values 1 and 0.83 of the C/S ratio, shear modulus has a stable value for all the pressure values while the bulk modulus increases by 178% for C/S=1 and 220% for C/S=0.83 when external pressure reaches 30GPa.

Furthermore, we have investigated the pressure effect on tensile strengths Δσ ultim (where Δσ ultim = σ ultimσ(ε=0)) in the three directions. We see from Fig. 11 that the ultimate strengths in all directions tend to increase as the applied external pressure rises. It is important to note that for z axis, we obtain the highest increasing rate with a 45% increase of Δσz ultim as applied pressure reaches 1GPa whereas Δσx ultim and Δσy ultim increase only by 19% and 21% respectively.

Piezoelectric properties

We fixed the bottom region of the structure and displaced the upper atoms with a small uniaxial tensile strain of about 0.01%. The resulting deformed structure is then relaxed in the NVT ensemble for 20ps. The loading cycle is repeated 10 times to reach a final deformation ɛ3 f of ~ 1.0% as illustrated in Fig. 12.

To calculate polarization vector along the x, y and z axes (Pr where r=x,y or z), we select only the middle atoms situated outside the boundary region, which corresponds to the upper and lower atoms (See Fig. 11). First, we define the polarization Pr as [START_REF] Dai | Piezoelectric constants for ZnO calculated using classical polarizable core-shell potentials[END_REF]:

Pr=Pr elec (u(ɛ),ɛ)+Pr dis (u(ɛ)) (9)
Where ɛ is the strain and u is the coordinates of the strained atoms. Pr elec stands for the electron polarization and Pr dis represents the polarization due to relative displacement between atoms. The piezoelectric constants are calculated from polarization as follows [30]:

e 56 =
Here, the rigid ion approximation is used and no shell particles are considered in our model.

Therefore, there is no polarization between the core and shell, which also corresponds to the polarization due to the electron delocalization in ab initio studies [START_REF] Dai | Piezoelectric constants for ZnO calculated using classical polarizable core-shell potentials[END_REF]34]. As a result, P elec is eliminated as well as F GH C . Only the displacement-based polarization Pr dis is considered.

Therefore we consider here that the piezoelectric constants only represent the contribution of atomic fractional coordinate's variation u to the piezoelectric properties. This corresponds to the internal strain term eij int in ab initio:

e 56 5DE = 785 7@ A ɛ ; B@ Bɛ ; (11)
Here, The Voigt's notation is used for the piezoelectric constants and the strain tensor. The improper piezoelectric constants eijk are calculated using the expression:

e 56I = e 56I 5DE = 785 7ɛ ;J (12)
Nevertheless, we have to make a distinction between proper and improper piezoelectric constants in the classical approach. Vanderbilt [START_REF] Vanderbilt | Berry-phase theory of proper piezoelectric response[END_REF] pointed out the issue of the «branchdependence» of polarization. He explained how polarization is a multivalued quantity that depends on the position in the crystal lattice. Consequently, it is important to define proper piezoelectric constants that are branch-independent. The improper piezoelectric constants eijk and proper piezoelectric F KLM N are related as follows:

F KLM N = e 56I + δ 6I P 5 -δ 56 P I (13)
The polarization along r-axis was calculated using the following formula:

P Q = P Q B5RS = ∑ T 9 Q 9 9 U (14)
Where qi and ri are the electric charge and the r th coordinate of atom i respectively and V is the total volume.

We plot the calculated polarization along the three axes as function of strain. The linear fit of the corresponding point enables to calculate the eij as the slope of each line. In Fig. 13, we can see the linear trend of the variation of polarization along the three axes as functions of strain ɛ3. The linear fit of the corresponding point enables to calculate the improper piezoelectric coefficients e3j as the slope of each line and then the improper piezoelectric coefficients using equation [START_REF] Hou | Calcium silicate hydrate from dry to saturated state: structure, dynamics and mechanical properties[END_REF]. The calculated piezoelectric coefficients values are rather small. The most important value is the induced polarization in the z direction per unit strain applied in the z direction with a proper piezoelectric coefficient F N = -0.12 C/m². Fig. 14 shows the variation of the three components of polarization as function of strain ɛ2. Here, we can see that Px the polarization along x axis tends to lose its linear trend when strain exceed 1%. We then apply the linear fit only for strains below 1% to calculate the piezoelectric coefficients e2j. The calculated values are quite small with a maximum value (in absolute value) of -0.02 C/m 2 obtained for F N . Similarly, when the strain ɛ1 is applied along the x axis, polarization starts to lose its linear trend when the strain exceeds 1% as we can see from Fig. 15 Therefore, we have only retained data for which strain is below 1% and apply a linear fit to calculate the piezoelectric coefficients e1j. The induced polarizations per unit strain in the three directions are found to have the same magnitude (in absolute value) of about ±0.1 C/m². The most important value is -0.15 C/m² obtained for the induced polarization per unit strain in the y direction.

Piezoelectricity under pressure

We have investigated the effect of external pressure in the Z direction on the piezoelectricity of C-S-H. We have used the same method as before to plot the polarization evolution as a function of the applied strain. The corresponding slopes are the piezoelectric coefficients we aim to calculate.

Table 3 summarizes the piezoelectric constants corresponding to the variation of polarization per unit stress for each value of pressure Pressz. We see that the values of the piezoelectric coefficients change with the application of pressure but remain small. The most important are e33=-0.16 C/m² and e32=0.16 C/m² achieved for Pressz=100 MPa and Pressz= 1GPa respectively against e33 0 =-0.12 C/m² and e32 0 =-0.02 C/m² for the uncompressed initial structure. In the other hand, the applied pressure Pressz reduces the most important piezoelectric constant e21 0 =-0.15 C/m² to about the tenth as Pressz reaches 900 MPa. Overall, applying an external pressure in the z direction of magnitude of hundreds of MPa slightly increases some values of piezoelectric coefficients and decreases others with a maximum absolute difference of 0.15 C/m² in comparison with the initial uncompressed structure. This result proves that the application of a uniaxial compression in the z direction doesn't stimulate the piezoelectricity of C-S-H. Recent works by Lushnikova and Zaoui [START_REF] Lushnikova | Improving mechanical properties of C-S-H from inserted carbon nanotubes[END_REF][START_REF] Lushnikova | Influence of single-walled carbon nantotubes structure and density on the ductility of cement paste[END_REF] have proven that the insertion of carbon nanotubes (CNT) in C-S-H enhances the piezoelectric properties of CSH in the z direction with a highest value of e33=20.5 C/m² by inserting the "(3, 0)

Zigzag" type of CNT.

IV. Conclusion

In this work, the structural, mechanical and piezoelectric properties of C-S-H have been studied using MD methods. REAXFF reactive force field was used together with the Qeq method to account for polarization effects in order to predict the piezoelectric response of C-S-H. The realistic model of C-S-H was used to describe the C-S-H system and the structure of C-S-H was investigated. The contributions of pair interactions to the main peaks of the RDF were determined and coordination between atoms was studied. Elastic properties were evaluated using Stress-Strain relationship. The crack propagation was observed and the fracture mechanism was investigated. According to the rupture modes, C-S-H exhibits a ductile behavior in the x and y directions, while the catastrophic rupture mode shows the brittle behavior of C-S-H in the z direction. The effect of external pressure up to1GPa on the elastic properties of C-S-H was also studied. Results show a remarkable improvement of the ultimate strength in the z direction up to 45% respectively as pressure reaches 1GPa compared to only 19% and 21% increase for the ultimate strengths in the x and y directions. However, the application of pressure along the z direction wasn't able to improve the piezoelectric coefficients of C-S-H that remain after all very small with a magnitude of ±0.1 C/m². The piezoelectric results were derived by observing the polarization variation in response to small strain values and prove the insensitivity of piezoelectricity of C-S-H to pressure application along the z axis.

Figures Caption

Fig. Tables

Fig. 4 .

 4 Fig.4.a that the highest coordination number of about 5.0 was calculated for O atoms around intralayer Calcium atoms Ca suggesting a dominant geometry of 5 O-type oxygen atoms around Ca within a sphere of 3 Å in the intralayer space. On the other hand, Fig.4.b shows that the oxygen atoms around the interlayer calcium atoms Cw oxygen within a 3.0Å sphere are mostly Oh oxygen-type with a coordination number Cw-Oh of 3.5. In addition, Oxygen atoms of Ow and O types are also found around Cw atoms within a 3.0Å sphere with a coordination number of about 1.33 for both Cw-Ow and Cw-O . Finally, The Ob atoms are mainly surrounded by O-type oxygen atoms and less significantly by Ob-type atoms with coordination numbers of 4.0 and 0.92 for Ob-O and Ob-Ob respectively as shown in Fig.4.c.

  8.b. At only 0.15 Å/Å tensile strain (Fig.8.c), the box is almost separated in two halves that continue to move away from each other as strain increases as shown in Fig.8.d. The rate of the crack propagation and the rupture surface geometry demonstrate the brittle behavior of the C-S-H system along the z direction. The "catastrophic" rupture mode along the z direction was also observed by Hou et al.[START_REF] Hou | Molecular dynamics study on the mode I fracture of calcium silicate hydrate under tensile loading[END_REF]

1 :

 1 Fig.1: Atomic structure of C-S-H.

Fig. 2 :

 2 Fig.2: (a) Radial pair distribution functions of C-S-H, (b) The contribution of pair interactions to RDF.

Fig. 3 :Fig. 4 :

 34 Fig.3: Radial distribution function and coordination number of (a) H-Oh and Hw-Oh interactions, (b) Hw-Hw interaction. (c) Si-O Si-Oh and Si-Ob interactions.

Fig. 5 :

 5 Fig.5: Stress-strain relationships for tension along x, y and z axes.

Fig. 6 :Fig. 7 :Fig. 9 :Fig. 10 :

 67910 Fig.6: C-S-H tensioned along x axis at (a) 0.17 Å/Å strain, (b) 0.30 Å/Å strain, (c) 0.50 Å/Å strain, (d) 0.6 Å/Å strain

Fig. 11 :

 11 Fig.11: Variation of ultimate strength (Δσ ultim ) in x, y and z directions with respect to applied pressure Press.

Fig. 12 :

 12 Fig.12: (a) Loading cycle along z axis, (b) Loading cycle along y axis, (c) Loading cycle along x axis.

Fig. 13 :

 13 Fig.13: Polarization along x, y and z axis against the deformation ɛ3.

Fig. 14 :

 14 Fig.14: Polarization along x,y and y axis against the deformation ɛ2.

Fig. 15 :

 15 Fig.15: Polarization along x,y and y axis against the deformation ɛ1.

Fig. 1

 1 Fig. 1

Fig. 2

 2 Fig.2

Fig. 3

 3 Fig.3

Fig. 4

 4 Fig.4

Fig. 6

 6 Fig.6

Fig. 7 Fig. 8

 78 Fig.7

Fig. 9

 9 Fig.9

Fig. 10

 10 Fig.10

Fig. 11

 11 Fig.11

Fig. 12

 12 Fig.12

Fig. 13 29Fig. 14

 1314 Fig. 13

Fig. 15

 15 Fig.15

Table 2

 2

against other MD works. Our results are very close to those found by Pellenq et al. and Manzano et al. Moreover, we can also compare with the experiment by calculating the indentations modulus (M) that can be determined by nanoindentation measurements. The found value 63.7 GPa is in great

Table 1 :

 1 Calculated elastic constants in comparison with preceding theoretical works.

			MD	MD
		This work	(Pellenq et al. [7])	(Manzano et al.
		(REAXFF)		[8])
	C11 (GPa)	85.74	93.5	90.9
	C22(GPa)	83.18	94.9	91.7
	C33(GPa)	67.80	68.5	72.6
	C44(GPa)	19.04	19.2	21.4
	C55(GPa)	18.72	16.1	21
	C66(GPa)	31.27	31.2	28.6
	C12(GPa)	45.31	45.4	33.1
	C13(GPa)	26.49	26.1	30
	C23(GPa)	27.01	30.01	29.6

Table 2 :

 2 Calculated Bulk modulus (K), shear modulus (G), Young's modulus (E), Poisson's ratio (ν) and indentation modulus (M).

		This work (REAXFF)	MD (Pellenq et al.) [7]	MD ( Manzano et al.) [8]
	K (GPa)	47.39	47 -51	48.6
	G (GPa)	22.45	22 -24	24.7
	E (GPa)	58,16	66 -55	74 -58.3
	ν	0.3	0.3	0.28
	M (GPa)	63.72	65	69

Table 3 :

 3 Calculated proper piezoelectric coefficients.

	Pressz	e11	e21	e31	e12	e22	e32	e13	e23	e33
	(MPa)	(C/m²)	(C/m²)	(C/m²)	(C/m²)	(C/m²)	(C/m²)	(C/m²)	(C/m²)	(C/m²)
	0	0.105 -0.150 -0.124 -0.015 -0.016 -0.024 0.053 -0.102 -0.117
	100	0.094 -0.056 -0.046 -0.009 -0.001 -0.004 0.063 -0.103 -0.157
	200	0.001 -0.095 0.014 -0.050 -0.005 -0.004 0.050 -0.088 -0.118
	300	0.069 -0.014 -0.049 -0.008 -0.017 0.030 0.041 -0.033 -0.098
	400	0.009 -0.077 -0.039 0.006 0.010 0.018 0.028 -0.059 -0.139
	500	0.066 0.002 -0.053 -0.024 -0.024 0.018 0.052 -0.069 -0.140
	600	0.002 0.012 -0.016 -0.015 -0.042 0.003 0.037 -0.063 -0.136
	700	0.030 -0.053 0.018 -0.024 -0.011 0.050 0.027 -0.064 -0.124
	800	-0.001 -0.041 -0.037 -0.079 -0.033 0.043 0.032 -0.059 -0.116
	900	0.030 -0.015 -0.047 -0.009 -0.017 0.013 0.032 -0.059 -0.121
	1000	0.009 -0.072 0.080 -0.019 -0.016 0.163 0.048 -0.059 -0.124

Fig. 5


Marie Dworczak
email: marie.dworczak@gmail.com

Marie-Cécile Le Deley

Antoine Adenis

Guillaume Piessen

Éric Lartigau

Xavier Mirabel

Thomas Lacornerie

David Pasquier

Marie Dworczak1

Marie-Cécile Le Deley2

Antoine Adenis3

Guillaume Piessen5

Éric Lartigau1

Xavier Mirabel1

Thomas Lacornerie7

David Pasquier1

Facteurs dosimétriques liés aux complications pulmonaires postopératoires dans les cancers de l'oesophage localement avancés traités par radiochimiothérapie préopératoire : revue de la littérature

Keywords: Esophageal cancer, Preoperative chemoradiotherapy, Dosimetric factors, Postoperative complication, Pulmonary complication

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

Facteurs dosimétriques liés aux complications pulmonaires post opératoires dans les cancers de l'oesophage localement avancés traités par radiochimiothérapie préopératoire : Revue de la littérature.

Résumé INTRODUCTION : Le cancer de l'oesophage localement avancé peut relever d'une radiochimiothérapie préopératoire. La radiothérapie est susceptible d'accroître les complications pulmonaires postopératoires. La plupart des contraintes de dose aux poumons utilisées en radiothérapie sont anciennes, et employées par extrapolation de la prise en charge des cancers pulmonaires. L'objectif de ce travail est de faire une revue critique des corrélations rapportées dans la littérature entre critères dosimétriques et complications pulmonaires postopératoires. MÉTHODE : Nous avons répertorié et sélectionné les études publiées entre 1987 et 2019 selon la méthode PRISMA. Les articles ont été identifiés sur la base d'une recherche PubMed et des connaissances des auteurs via les termes « cancer de l'oesophage », « radiochimiothérapie », « facteurs dosimétriques », « complications pulmonaires postopératoires ». RÉSULTATS : Quatorze articles ont été sélectionnés, et cinq n'ont pas mis en évidence de corrélation entre facteurs dosimétriques et taux de complications pulmonaires post-opératoires. Le V20 (volume pulmonaire recevant plus de 20 Gy) était identifié dans trois études comme facteur prédictif de complications pulmonaires, de même que le V10, le V15 et la dose moyenne pulmonaire (proche de 10 Gy) dans deux études. Le V30≥20% était identifié dans une étude. DISCUSSION : Les paramètres dosimétriques associés aux complications pulmonaires postopératoires les plus fréquemment identifiés sont le V20 et la dose pulmonaire moyenne. Seuls les résultats d'études prospectives pourront nous amener à préciser lequel de ces paramètres est le plus pertinent pour prédire le risque de complication pulmonaire postopératoire. La pathogénèse, l'anatomie et les modalités de traitement des cancers pulmonaires et des cancers de l'oesophage sont également différentes, ce qui suggère l'emploi de contraintes dosimétriques propres à chaque localisation. À ce jour, il n'y a à notre connaissance, pas de recommandations de contraintes pulmonaires spécifiques à la prise en charge préopératoire des cancers de l'oesophage.

Mots

Le travail du QUANTEC (Quantitative Analysis of Normal Tissue Effects in the Clinic) suggère de limiter le V20 (volume pulmonaire recevant ≥20 Gy) à 30-35 % et la dose moyenne pulmonaire ≤ 20-23 Gy pour un fractionnement classique, afin d'obtenir un risque de pneumopathie radique ≤20 % chez les patients traités par radiothérapie exclusive pour un cancer du poumon non à petites cellules (4).

Les contraintes dosimétriques pulmonaires du RECORAD concernant l'irradiation de cancers intra-thoraciques en fractionnement classique sont les suivantes : V20 ≤ 35-37 % ; dose moyenne pulmonaire ≤20Gy (5).

Le NCCN (National Comprehensive Cancer Network) guidelines for Esophageal and

Esophagogastric Junction Cancers version 4.2019 [START_REF] Mcmillian | Esophageal and Esophagogastric Junction Cancers NCCN Guidelines Version 4[END_REF] précise qu'un consensus sur les contraintes de doses optimales n'a pas encore émergé pour la prise en charge préopératoire. Les contraintes suivantes sont toutefois proposées : V40 (volume pulmonaire recevant ≥40 Gy) ≤10 %, V30≤15 %, V20≤20 %, V10≤40 %, V5≤50 %, dose moyenne <20Gy.

Dans ce contexte, notre objectif est de faire une revue des données publiées en matière de corrélations entre facteurs dosimétriques et complications pulmonaires postopératoires après radio chimiothérapie concomitante préopératoire dans les cancers de l'oesophage localement avancés.

MATÉRIELS ET MÉTHODES

Cette revue de la littérature a répertorié et sélectionné les études publiées entre 1987 et 2019. Les recherches ont été réalisées sur la base de données électroniques MEDLINE (Pubmed), et des connaissances des auteurs, selon la méthode PRISMA (Preferred Reporting Items for Systematic Reviews and Meta-Analyses) [START_REF] Moher | Preferred Reporting Items for Systematic reviews and Meta-Analyses: The PRISMA statement[END_REF].

Les termes « cancer de l'oesophage », « radiochimiothérapie », « facteurs dosimétriques », « complications pulmonaires postopératoires » ont permis de sélectionner les études.

Les études rétrospectives et prospectives ont été incluses. L'utilisation d'une chimiothérapie d'induction n'était pas un critère d'exclusion.

Les études traitant uniquement de radiochimiothérapie exclusive étaient exclues.

Il n'y avait pas de restriction de langage de publication.

Seuls les résultats significatifs en analyse multivariée ont été sélectionnés.

Les données ont été actualisées jusqu'au 6 décembre 2019.

RÉSULTATS

Au total, 14 articles publiés entre 2003 et 2019 ont été retenus pour l'analyse (Figure 1). Parmi les 14 études analysées (Tableau 1), les effectifs s'étendaient de 23 à 444 patients.

Deux études étaient prospectives [START_REF] Kumar | Analysis of dosevolume parameters predicting radiation pneumonitis in patients with esophageal cancer treated with 3D-conformal radiation therapy or IMRT[END_REF][START_REF] Borggreve | PV-0099: Neoadjuvant radiation dose to the lungs and the risk of postoperative pneumonia in esophageal cancer[END_REF]. Seule l'étude de Kup et al. était multicentrique [START_REF] Kup | The Prognostic Value of Irradiated Lung Volumes on the Prediction of Intra-/ Post-Operative Mortality in Patients after Neoadjuvant Radiochemotherapy for Esophageal Cancer. A Retrospective Multicenter Study[END_REF].

Les stades tumoraux allaient de I à IV.

La définition des volumes cibles était précisée dans 11 articles [START_REF] Kumar | Analysis of dosevolume parameters predicting radiation pneumonitis in patients with esophageal cancer treated with 3D-conformal radiation therapy or IMRT[END_REF][START_REF] Lee | Postoperative pulmonary complications after preoperative chemoradiation for esophageal carcinoma: Correlation with pulmonary dose-volume histogram parameters[END_REF][START_REF] Tonison | Radiation Pneumonitis after Intensity-Modulated Radiotherapy for Esophageal Cancer: Institutional Data and a Systematic Review[END_REF][START_REF] Wang | Investigation of clinical and dosimetric factors associated with postoperative pulmonary complications in esophageal cancer patients treated with concurrent chemoradiotherapy followed by surgery[END_REF][START_REF] Tucker | Dose-volume modeling of the risk of postoperative pulmonary complications among esophageal cancer patients treated with concurrent chemoradiotherapy followed by surgery[END_REF][START_REF] Hsu | Association of clinical and dosimetric factors with postoperative pulmonary complications in esophageal cancer patients receiving intensity-modulated radiation therapy and concurrent chemotherapy followed by thoracic esophagectomy[END_REF][START_REF] Dähn | Influence of Irradiated Lung Volumes on Perioperative Morbidity and Mortality in Patients After Neoadjuvant Radiochemotherapy for Esophageal Cancer[END_REF][START_REF] Hurmuzlu | Highdose preoperative chemoradiotherapy in esophageal cancer patients does not increase postoperative pulmonary complications: Correlation with dose-volume histogram parameters[END_REF][START_REF] Leibl | Adenocarcinoma of the esophagogastric junction: Neoadjuvant radiochemotherapy and radical surgery: Early results and toxicity[END_REF][START_REF] Shaikh | Risk of radiation pneumonitis in patients receiving taxane-based trimodality therapy for locally advanced esophageal cancer[END_REF][START_REF] Cho | Dosimetric predictors for postoperative pulmonary complications in esophageal cancer following neoadjuvant chemoradiotherapy and surgery[END_REF] et n'était pas homogène. Le CTV (Clinical Target Volume) correspondait au GTV (Gross Tumor Volume) avec une marge allant de deux à cinq centimètres en cranio-caudal et des marges latérales de 0,5 à 2 cm. Le référentiel de délinéation n'était précisé que dans une étude [START_REF] Tonison | Radiation Pneumonitis after Intensity-Modulated Radiotherapy for Esophageal Cancer: Institutional Data and a Systematic Review[END_REF]. L'information sur le volume moyen du Planning Target Volume (PTV) était disponible dans une seule étude [START_REF] Kup | The Prognostic Value of Irradiated Lung Volumes on the Prediction of Intra-/ Post-Operative Mortality in Patients after Neoadjuvant Radiochemotherapy for Esophageal Cancer. A Retrospective Multicenter Study[END_REF].

Concernant les organes à risque, la définition du volume pulmonaire n'était pas renseignée dans quatre études [START_REF] Kumar | Analysis of dosevolume parameters predicting radiation pneumonitis in patients with esophageal cancer treated with 3D-conformal radiation therapy or IMRT[END_REF][START_REF] Borggreve | PV-0099: Neoadjuvant radiation dose to the lungs and the risk of postoperative pneumonia in esophageal cancer[END_REF][START_REF] Shaikh | Risk of radiation pneumonitis in patients receiving taxane-based trimodality therapy for locally advanced esophageal cancer[END_REF][START_REF] Wang | Predictors of postoperative complications after trimodality therapy for esophageal cancer[END_REF]. Dans l'étude de Hsu et al. ( 15 Les doses de radiothérapie s'étendaient de 36 à 66Gy avec des schémas normo fractionnés uniquement. Les logiciels de planification de traitement n'étaient pas indiqués dans quatre études [START_REF] Borggreve | PV-0099: Neoadjuvant radiation dose to the lungs and the risk of postoperative pneumonia in esophageal cancer[END_REF][START_REF] Kup | The Prognostic Value of Irradiated Lung Volumes on the Prediction of Intra-/ Post-Operative Mortality in Patients after Neoadjuvant Radiochemotherapy for Esophageal Cancer. A Retrospective Multicenter Study[END_REF][START_REF] Shaikh | Risk of radiation pneumonitis in patients receiving taxane-based trimodality therapy for locally advanced esophageal cancer[END_REF][START_REF] Cho | Dosimetric predictors for postoperative pulmonary complications in esophageal cancer following neoadjuvant chemoradiotherapy and surgery[END_REF]. Les algorithmes de calcul pour la prise en compte de l'hétérogénéité pulmonaire n'étaient décrits que dans deux études [START_REF] Dähn | Influence of Irradiated Lung Volumes on Perioperative Morbidity and Mortality in Patients After Neoadjuvant Radiochemotherapy for Esophageal Cancer[END_REF][START_REF] Hurmuzlu | Highdose preoperative chemoradiotherapy in esophageal cancer patients does not increase postoperative pulmonary complications: Correlation with dose-volume histogram parameters[END_REF].

Les protocoles de chimiothérapie les plus utilisés étaient à base de 5FU, taxanes ou de sels de platine.

Les cinq études les plus anciennes proposaient un traitement d'induction [START_REF] Lee | Postoperative pulmonary complications after preoperative chemoradiation for esophageal carcinoma: Correlation with pulmonary dose-volume histogram parameters[END_REF][START_REF] Wang | Investigation of clinical and dosimetric factors associated with postoperative pulmonary complications in esophageal cancer patients treated with concurrent chemoradiotherapy followed by surgery[END_REF][START_REF] Tucker | Dose-volume modeling of the risk of postoperative pulmonary complications among esophageal cancer patients treated with concurrent chemoradiotherapy followed by surgery[END_REF][START_REF] Hsu | Association of clinical and dosimetric factors with postoperative pulmonary complications in esophageal cancer patients receiving intensity-modulated radiation therapy and concurrent chemotherapy followed by thoracic esophagectomy[END_REF][START_REF] Dähn | Influence of Irradiated Lung Volumes on Perioperative Morbidity and Mortality in Patients After Neoadjuvant Radiochemotherapy for Esophageal Cancer[END_REF].

DISCUSSION

Quatorze études ont pu être identifiées dans cette revue de la littérature évaluant les facteurs dosimétriques corrélés significativement aux complications pulmonaires postopératoires dans les cancers de l'oesophage localement avancés relevant d'une radiochimiothérapie pré-opératoire.

Ces études étaient hétérogènes en termes de populations, d'effectifs, de volumes traités, de doses et fractionnements de radiothérapie délivrés, de type de traitement systémique concomitant, de type de chirurgie réalisée.

Peu d'informations étaient disponibles quant aux méthodes de prise en compte de l'hétérogénéité pulmonaire. Bien que la dose pulmonaire moyenne et le V20 soient peu sensibles aux changements entre les algorithmes de calculs d'après l'étude de Nielsen et al. [START_REF] Nielsen | Influence of dose calculation algorithms on the predicted dose distributions and NTCP values for NSCLC patients[END_REF], il semble qu'aucune équipe parmi les quatorze n'ait employé un algorithme de type B prenant en compte les hétérogénéités pour le parcours des électrons secondaires, et considéré actuellement comme la norme [START_REF] Md Anderson | Heterogeneities:Approved Algorithms[END_REF].

Les définitions des complications pulmonaires étudiées étaient également hétérogènes.

Le SDRA par exemple est un syndrome pour lequel plusieurs définitions ont été proposées et dont aucune ne permet d'apprécier la complexité de sa physiopathologie [START_REF] Srlf | Syndrome de détresse respiratoire aiguë[END_REF]. De même, la définition de la pneumopathie tient compte de facteurs cliniques, fonctionnels et radiographiques, avec différentes cotations selon les échelles de toxicité utilisées [START_REF] Jain | Radiation pneumonitis: Old problem, new tricks[END_REF].

Six facteurs dosimétriques sont toutefois restés significatifs en analyse multivariée (Tableau 2).

Le V20 a été le facteur le plus souvent identifié [START_REF] Kumar | Analysis of dosevolume parameters predicting radiation pneumonitis in patients with esophageal cancer treated with 3D-conformal radiation therapy or IMRT[END_REF][START_REF] Leibl | Adenocarcinoma of the esophagogastric junction: Neoadjuvant radiochemotherapy and radical surgery: Early results and toxicity[END_REF][START_REF] Shaikh | Risk of radiation pneumonitis in patients receiving taxane-based trimodality therapy for locally advanced esophageal cancer[END_REF] avec des seuils de 10 % à 25 %.

Les recommandations du NCCN proposent de limiter le V20≤20 %, tandis que le RECORAD et le QUANTEC proposent des valeurs proches de 30 %.

La dose pulmonaire moyenne semble aussi être une piste intéressante, identifiée dans deux études de grand effectif avec des valeurs similaires, autour de 10Gy [START_REF] Cho | Dosimetric predictors for postoperative pulmonary complications in esophageal cancer following neoadjuvant chemoradiotherapy and surgery[END_REF][START_REF] Wang | Predictors of postoperative complications after trimodality therapy for esophageal cancer[END_REF] avec le V5 associé à la survenue de pneumopathies radiques symptomatiques [START_REF] Shaikh | Risk of radiation pneumonitis in patients receiving taxane-based trimodality therapy for locally advanced esophageal cancer[END_REF].

Enfin, il est important de prendre en compte le type de chimiothérapie administrée de manière concomitante, certains auteurs ayant suggéré une majoration des pneumopathies avec l'association taxanes-radiothérapie [START_REF] Mccurdy | Induction and Concurrent Taxanes Enhance Both the Pulmonary Metabolic Radiation Response and the Radiation Pneumonitis Response in Patients With Esophagus Cancer[END_REF][START_REF] Chen | Comparing paclitaxel plus fluorouracil versus cisplatin plus fluorouracil in chemoradiotherapy for locally advanced esophageal squamous cell cancer: A randomized, multicenter, phase III clinical trial[END_REF].

CONCLUSION

Des études prospectives multicentriques avec des schémas thérapeutiques homogènes selon les recommandations thérapeutiques actuelles sont nécessaires pour améliorer les connaissances et préciser les critères dosimétriques qui permettraient de minimiser les complications pulmonaires post-opératoires.

En ce sens, il sera intéressant d'analyser les résultats de l'étude PROTECT [START_REF] Messager | Preoperative chemoradiation with paclitaxel-carboplatin or with fluorouracil-oxaliplatinfolinic acid (FOLFOX) for resectable esophageal and junctional cancer: The PROTECT-1402, randomized phase 2 trial[END_REF] (comparaison d'un schéma FOLFOX à un schéma Carboplatine-Taxol, associés à la radiothérapie préopératoire des cancers de l'oesophage) dont le recrutement est en voie d'achèvement. Cette étude a pour objectif principal d'étudier le taux de résection complète et la fréquence des complications postopératoires sévères, et l'un de ses objectifs secondaires est l'étude des corrélations entre facteurs dosimétriques et toxicité pulmonaire.

Conflit d'intérêt : aucun.

LÉGENDE DE FIGURE

  -clés : Cancer de l'oesophage ; Radiochimiothérapie préopératoire ; Facteurs dosimétriques ; Complications postopératoires ; Complications pulmonaires INTRODUCTION Le cancer de l'oesophage localement avancé peut relever d'un traitement multimodal par radio chimiothérapie concomitante préopératoire (1). Malgré l'amélioration des techniques, la morbimortalité d'un tel traitement n'est pas négligeable. Les complications pulmonaires postopératoires (pneumopathie, pleurésie, syndrome de détresse respiratoire aiguë…) sont parmi les plus fréquentes (2). Dans une étude randomisée de radiochimiothérapie pré-opératoire versus chirurgie seule (essai CROSS), elles concernaient 46 % des patients ayant reçu le traitement multimodal préopératoire (3). Ces complications sont principalement liées au geste chirurgical. Elles peuvent être favorisées par l'association préopératoire de la chimiothérapie à l'irradiation médiastino pulmonaire. L'un des défis actuels est d'optimiser chacune des étapes de la prise en charge multimodale pour tenter de réduire ces complications pulmonaires. En ce qui concerne la radiothérapie, la plupart des contraintes de dose aux poumons actuellement employées sont anciennes et issues d'extrapolations de la prise en charge des cancers pulmonaires. Elles reposent principalement sur le risque de survenue de pneumopathie radique, et proviennent de séries utilisant des techniques d'irradiation exclusives et obsolètes, avec des calculs de dose basés sur des algorithmes eux aussi dépassés.

  ), le volume étudié correspondait au volume pulmonaire total avec soustraction du CTV. Dans les autres études, le volume étudié correspondait au poumon total. Cinq études ont utilisé la Radiothérapie Conformationnelle en 3 Dimensions (RC 3D) seule, trois études ont utilisé la Radiothérapie Conformationnelle avec Modulation d'Intensité (RCMI) seule, six études ont inclus des patients traités par différentes techniques de radiothérapie (RC 3D, RCMI, ou protonthérapie).

  La chirurgie était réalisée selon différentes techniques (Lewis Santy, oesophagectomie transhiatale…). Les études d'Hurmuzlu et al. (17) et de Cho et al. (20) n'incluaient que des patients ayant une oesophagectomie transthoracique. Le type de complication pulmonaire étudiée était variable (syndrome de détresse respiratoire aiguë, pneumonie, insuffisance respiratoire, pneumopathie radique, épanchement pleural), ainsi que le délai durant lequel elles étaient recueillies (jusqu'à deux mois post-opératoire). Les échelles de toxicité étaient la CDCPAECC (Center of Disease Control and Prevention and the American and European Consensus Conference) (22) dans six études, la classification CTCAE (Common Terminology Criteria for Adverse Events) dans cinq études. L'UPS (Uniform Pneumonia Score) a été employée dans une étude (9), la classification de Clavien-Dindo également (20), l'échelle de toxicité du RTOG (Radiation Therapy Oncology Group) a été utilisée en association à la CTCAE dans l'étude de Tonison et al. (12). Le taux de complications pulmonaires s'étendait de 5,5 % dans l'étude de Tonison et al. chez des patients traités en RCMI (12) jusqu'à 91 % dans l'étude de Kumar et al. qui évaluait les pneumopathies de grades 2 à 4 chez des patients traités en RC 3D (8). Cinq études, dont l'essai multicentrique de Kup et al., n'ont pas mis en évidence de facteur dosimétrique significativement corrélé aux complications pulmonaires post-opératoires en analyse multivariée. Le V20 était associé au risque de complications pneumologiques postopératoires dans trois études : V20 ≥10 % (p = 0,008) corrélé à la survenue de pneumonies dans l'étude de Leibl et al. (23 patients traités en RCMI), V20 ≥15 % (p = 0,03) corrélé à la survenue de pneumopathies radiques et pneumonies aiguës dans l'étude de Kumar et al. (45 patients traités en RC 3D ou RCMI), et V20 ≥25 % (p = 0,028) corrélé à la survenue de pneumopathies radiques dans l'étude de Shaikh et al. (139 patients traités en RC 3D ou RCMI avec une dose médiane de 50,4Gy en 1,8Gy par fraction) (8,18,19). Le V10 était associé au risque de complications pneumologiques postopératoires dans deux études (11,18). Dans l'étude de Lee et al. avec 61 patients traités en RC 3D, lorsque le V10 était au-delà de 40 % on constatait 35 % de complications pulmonaires post-opératoires versus 8 % (p=0,014). Dans l'étude de Leibl et al., le V10≥20% avait un impact sur la survenue de pneumonies (p = 0,023). Le V15 (volume pulmonaire recevant ≥15 Gy) était associé au risque de complications pneumologiques post-opératoires dans deux études. Dans l'étude de Lee et al., lorsque le V15 était au-delà de 30 %, le taux de complications pulmonaires post-opératoires était de 33 % versus 10 % (p=0,036). Dans l'étude de Leibl et al, le V15 ≥13 % était associé de façon significative aux complications pulmonaires postopératoires (p=0,008) (11,18). La dose moyenne pulmonaire était associée au risque de complications pulmonaires postopératoires dans l'étude de Cho et al. (308 patients traités en RC 3D, RCMI ou VMAT, dose moyenne prescrite de 44Gy) avec une médiane à 9,6Gy (1,23-30,5 ; p=0,012) et dans l'étude de Wang et al. (444 patients traités en RC 3D, RCMI ou protonthérapie, dose moyenne prescrite de 50,4Gy) une dose moyenne pulmonaire médiane en RC3D à 10,7Gy (2,8-19,7), et à 10Gy (3,4-16,5) en RCMI (p=0,044). Le VS5 (Volume pulmonaire épargné par les doses supérieures à 5Gy ou volume absolu de poumon recevant des doses inférieures à 5Gy) était retrouvé inversement corrélé aux complications pulmonaires dans deux études ayant le même effectif (110 patients traités en RC 3D) (13,14). Dans l'étude de Kumar et al., lorsque le V30 (volume pulmonaire recevant 30 Gy ou plus) dépassait les 20 % chez les patients traités en RC 3D, il y avait un impact significatif sur la survenue de pneumopathie aiguë (p=0,007). Dans l'étude de Shaikh et al., le V5 (volume pulmonaire recevant 5 Gy ou plus) était significativement associé à la survenue de pneumopathies radiques symptomatiques.

  , inférieures au seuil de 20Gy préconisé par le NCCN, le QUANTEC ou le RECORAD chez les patients traités pour un cancer bronchique. Les doses pulmonaires irradiées étant inférieures dans les cancers de l'oesophage par rapport aux cancers pulmonaires, une V20≤20 % et une dose pulmonaire moyenne limitée à 10Gy pourraient permettre de réduire les complications pulmonaires post-opératoires. Du fait de la multimodalité du traitement, on peut également supposer que les patients traités pour un cancer de l'oesophage localement avancé sont plus sensibles à des faibles doses d'irradiation pulmonaire. Dans une étude de Gergel et al., chez 20 patients traités par radiochimiothérapie exclusive, la diminution de la capacité de diffusion du monoxyde de carbone (DLCO) et de la capacité pulmonaire totale (CPT) étaient corrélées au volume pulmonaire recevant des faibles doses, de 7 à 10Gy (27). Dans notre analyse, les résultats des études de Wang et al., et Tucker et al.(13,14), réalisées sur la même population confirment cette hypothèse, avec des VS5 inversement corrélées aux complications pulmonaires. Il en va de même pour l'étude de Shaikh et al.

Figure 1 .Tableau 1 .

 11 Figure 1. Diagramme de flux selon PRISMA (Preferred Reporting Items for Systematic Reviews and Meta-Analyses) décrivant le processus de sélection des études traitant des corrélations entre facteurs dosimétriques et toxicité pulmonaire chez les patients traités par radio chimiothérapie pré opératoire pour un cancer de l'oesophage localement avancé.

  Centers for Disease Control and Prevention and the American and European Consensus Conference ; CTCAE : Common Terminology Criteria for Adverse Events ; UPS : Uniform Pneumonia Score ; RTOG : Radiation Therapy Oncology Group ; NR : non renseigné ; Vx Gy : volume recevant xGy ou plus ; VS5 : Volume pulmonaire épargné par des doses≥5Gy ; RC 3D : Radiothérapie Comparaison entre les recommandations du NCCN, du QUANTEC et du RECORAD (chez les patients traités pour un cancer bronchique) avec les facteurs dosimétriques significatifs identifiés dans notre revue de la littérature.

	Shaikh et al., 2016 (19) Borggreve et al., 2018 (9) Cho et al., 2019 (20) Tonison et al., 2019 (12) ABRÉVIATIONS : V40 ≤10 % 139 135 308 73 V30 ≤15 % V20 ≤20 % V10 ≤40 % V15 V5 VS5 ≤50 % Fr : fraction ; CDCPAECC : NCCN(6) DMP <20 Gy	1,8-2Gy/fr 45-60Gy 1,8Gy/fr 41,4Gy 1,8Gy/fr 43-45Gy 1,8-2,15Gy/fr 41,4-50Gy QUANTEC(4) RECORAD(5) Rétrospective mono centrique RC 3D RCMI pré-OP Prospective mono centrique RC 3D, RCMI, VMAT pré-OP Rétrospective mono centrique RC 3D RCMI VMAT pré-OP Rétrospective mono centrique RCMI def, pré-OP ≤30-35 % ≤35-37 % ≤10 % (18) ≤15 % (8) <25 % (19) 5FU + taxanes ou sels de platine ou monothérapie 24% Carboplatine paclitaxel ou Cisplatine 5FU 23% grade ≥2 Carboplatine paclitaxel 30,4% Cisplatine 5FU 22,1% 5FU + taxanes ou sels de platine 5,5% Dworczak et al. ≤20 % (8) ≤40 % (11) ≤20 % (18) ≤30 % (11) ≤13 % (18) <65 % (19) >2L (13) >2,3L (14) <20-23 Gy <20 Gy 10Gy (21) 9,6Gy (20)	0 V5>65% P=0,022 V20>25% p=0,028 NR DMP médiane 9,6Gy (1,23-30,5) p = 0,012 0	SDRA Pneumonie Pneumopathie radique Pneumonie post opératoire Pneumonie, SDRA, épanchement pleural, insuffisance respiratoire Pneumopathie radique	CTCAE CTCAE UPS Clavien-Dindo CTCAE RTOG

Conformationnelle 3D ; CPT : Capacité Pulmonaire Totale ; RCMI : Radiothérapie Conformationnelle avec Modulation d'Intensité ; VMAT : Volumetric Modulated Arc Therapy ; FEV1 : Forced Expiratory Volume 1 ; DMP : Dose Moyenne Pulmonaire ; SDRA : Syndrome de Détresse Respiratoire Aigu ; DLCO : Diffusion Libre du CO ; def : radio chimiothérapie exclusive ; pré-OP : radio chimiothérapie pré opératoire ; post-OP : radio chimiothérapie post opératoire ; 0 : aucun facteur significatif retrouvé ; 5FU : 5-fluorouracile ; VP16 : Étoposide.

Tableau 2. ABRÉVIATIONS : NCCN : National Comprehensive Cancer Network ; DMP : Dose Moyenne Pulmonaire ; QUANTEC : Quantitative Analysis of Normal Tissue Effects in the Clinic ; Vx Gy : volume recevant xGy ou plus ; VS5 : Volume pulmonaire épargné par des doses≥5Gy.

Remerciements

Joséphine Vogel, Ségolène Hautecloque, Côme De Metz.

RÉFÉRENCES BIBLIOGRAPHIQUES