Chinh Duc
email: duc.chinh.chu@imt-lille-douai.fr

Joelle Chu

Mouhamadou Kleib

Mahfoud Amar

Edine Benzerzour

Nor-Edine Abriak

Duc Chinh

Joelle Kleib

Mouhamadou Amar

Chu

Determination of the degree of hydration of Portland cement using three different approaches: Scanning electron microscopy (SEM-BSE) and Thermogravimetric analysis (TGA)

Keywords: Cement, Hydration, Portlandite, Bound water, SEM-BSE, Compressive strength

I. Introduction

Portland cement is a mixture of clinker and calcium sulfate in a ratio of approximately 95:5% [1]. Cement is one of the essential constituents in the manufacture of concrete; the most widely used building material in the world. The mineralogical composition of clinker consists of alite (C3S: Ca3SiO5), belite (C2S: Ca2SiO4), tricalcium aluminate (C3A: Ca3Al2O6) and tetra-calcium aluminoferrite (C4AF: Ca4Al2O10Fe2). During hydration, the cement reacts with water resulting in the formation of different hydrates. Ettringite is formed from the reaction of calcium sulfate, tricalcium aluminate and water. The reaction of the silicates leads to the formation of portlandite (CH) and a Calcium Silicate Hydrate (C-S-H).

Previous studies [2, 3] have shown that C-S-H is the main hydrate of hydrated cement paste and contributes significantly to macro-properties of concrete such as strength and durability.

The composition of the C-S-H, depends on the water to cement ratio (w/c ratio), the temperature as well as the composition of the cement [4][5][6]. Indeed, in the literature, there are three distinct phases C-S-H depending on the C/S (CaO/SiO2) ratio:

• C-S-H (α): 0.66 < C/S < 1 formed when the [Ca 2+ ] concentration is less than 2 mmol/l.

• C-S-H (β): 1 < C/S < 1.5 formed when the [Ca 2+ ] concentration is between 2 and 22 mmol/l.

• C-S-H (ϒ): C/S = 1.7 formed when the [Ca 2+ ] concentration is greater than 22 mmol/l. In addition, Phung et al [7] have shown that the C/S molar ratio of the cement paste was critical in determining the microstructure of C-S-H and the decrease in the C/S ratio can alter the microstructure of C-S-H.

The amount of hydrates formed during hydration depends on the degree of hydration which is defined as a ratio of the amount of hydrated cement to that of the initial anhydrous cement. There are several experimental approaches to determine the degree of hydration of cement such as:

• Scanning electron microscopy (SEM-BSE) [8, 9].

• X-ray diffraction (XRD) [10].

• Thermogravimetric analysis (TGA) [11].

• Measurement of the heat of hydration by isothermal calorimetry [9,12].

• Nuclear magnetic resonance (NMR) [3,[START_REF]mécanisme de rétention des alcalins -Thèse doctorante[END_REF].

• Compressive strength [14]. Several studies have employed the thermal analysis method (TGA) to determine the degree of hydration of cement. The basic idea is to use the following simplified equations ((Eq1) -> (Eq8)) to measure the portlandite amount (CH) [10,11] and chemically bound water [12] generated during hydration [START_REF] Bordy | Influence des conditions thermo-hydriques de conservation sur l ' hydratation de matériaux cimentaires à base d ' une fine recyclée[END_REF][START_REF] Elkarim | Use of grinded hardened cement pastes as mineral addition for mortars[END_REF][START_REF] Bresciani | Simulation numérique de l ' hydratation et du développement des propriétés physiques et mécaniques d ' une pâte de ciment afin de sélectionner de nouveaux ajouts minéraux[END_REF]

2 C3A + C6AS̅ 3H32 + 4H -> 3 C4AS̅ H12 (7) 2 C4AF + C6AS̅ 3H32 + 12 H -> 3 C4AS̅ H12 + 2 CH + 2 FH3 (8)
In a recent study, Lei et al [3] used the Ca(OH)2 quantification method measured by TGA analysis and the NMR method for the determination of the degree of hydration of cement paste (W/C = 0.3). The 29 Si NMR and 27 Al NMR is used to quantify the phases containing these element in a cementitious material. Good consistency between the two methods was observed (74.0% for the Ca(OH)2 quantification method at 28 days and 78.4% for the NMR method at 28 days). However, in his study, the degree of hydration was calculated according to the equation (Eq9):

α(t) = .% * 100 (9)
Knowing that the 25% value is not always constant because the mineral composition of cement is always variable. In addition, the NMR method is a complicated method (long analysis time, 1 day for 29 Si NMR analysis), therefore, in this study, three methods used are: Method 1: Portlandite quantification method, Method 2: Bound water of quantification method, Method 3: SEM-BSE image analysis method.

The first approach for evaluating the degree of hydration is to use the following equations to calculate the Ca(OH)2 amount estimated from the TGA analysis according to (Eq10):

m Ca(OH)2 = ∆ ° ° . (10)
with: m Ca(OH)2 : Amount of Ca(OH)2. ∆ 450° -550° : The mass loss of the samples between 450 °C and 550 °C from the TGA analysis. M Ca(OH)2 : Molar mass of Ca(OH)2 equal to 74.09 g/mol. MH2O: Molar mass of water equal to 18 g/mol. Then the degree of hydration of the cement can be calculated using the equation below (Eq11):

α(t) = .
The mass of the sample can be calculated using the equation (Eq12):

(11) mc = !" #$% & ' (. $%) * (12)
with: α(t): Degree of hydration of the cement at time t. m sample: Mass of the samples. mc: Mass of the initial cement. ϒ0: Amount of Ca(OH)2 produced upon complete hydration of the cement. This value depends on the composition of the cement as well as the stoichiometry of the C-S-H gel of the cement hydration reactions (Eq(1) -> Eq(8)). w/c: the water to cement ratio of the paste. LOI: loss of cement on ignition.

The second experimental approach for determining the degree of hydration of cement recommended by the National Institute of Standards and Technology (NIST) consists in determining the amount of water chemically bound according to the following equation (Eq13):

α(t) = +, +, - * 100 (13)
with: α(t): degree of hydration of the sample at time t. Wn(t): amount of bound water for a sample at time (in gram of water per 100 g of anhydrous cement). Wn(∞ : amount of water bound for a completely hydrated sample (in gram of water per 100 g of anhydrous cement). The Wn(t) value can be determined experimentally by (Eq14) if the two following conditions are met:

• No carbonation in the cement paste.

• Low weight loss of anhydrous cement before 1000° C

Wn(t) = ∆ !" $ ° $ ° !" $ ° * 100 (14)
In order to determine the Wn(∞) value, NIST provides an approximate theoretical estimation of the amount of bound water produced for the five main mineral phases of cement after hydration is complete [18].

The third method consists of the SEM-BSE image analysis technique to study the distribution of phases in the observation area. Indeed, this technique has been frequently applied to examine the cementitious material's microstructure [START_REF] Wong | Pore segmentation of cement-based materials from backscattered electron images[END_REF]. In an SEM-BSE image, the backscatter coefficient increases monotonically with the average atomic number of each phase [START_REF] Goodhew | Electron Microscopy and Analysis[END_REF]. This allows differentiating and quantifying of each crystalline phases in the analysis area. However, in cement-based materials, the backscattering coefficients of numerous hydration products (C-S-H, Ettringite, etc.) are too similar to be separated individually on the histogram [START_REF] Wong | Pore segmentation of cement-based materials from backscattered electron images[END_REF]. Because the epoxy backscatter coefficient is substantially lower than the other phases, the pores may be easier to segment [START_REF] Wong | Pore segmentation of cement-based materials from backscattered electron images[END_REF].

The SEM-BSE image analysis has been used to quantify phases of hydrated cement paste [START_REF] Scrivener | Analysis of Phases in Cement Paste using Backscattered Electron Images[END_REF], to study the phase distribution in the mortar interphase zone [22], and to estimate the reaction fraction of mineral additions in the cement matrix [9]. The three steps in this approach are as follows:

• Choice of magnification and resolution of the image.

• Phase segmentation by gray level thresholds.

• Quantification of phases in the analysis area. Table 1 summarizes the advantages and disadvantages of the three methods of determining the degree of hydration used in this study.

Table 1

Advantages and disadvantages of the three methods (Method 1: Ca(OH)2 quantification method, Method 2: Bound water of quantification method, Method 3: SEM-BSE image analysis method).

Method

Method 1 Method 2 Method 3

Advantages

• Ease of sample preparation.

• Ease of processing the result.

• Ease of sample preparation.

• Ease of processing the result.

• Apply cement containing a pozzolanic mineral addition, a slag.

Disadvantages

• Do not apply cement containing a pozzolanic mineral addition.

• An adequate analysis program to avoid the loss of bound water.

• Difficulty of sample preparation • Difficulty of processing the result.

There have been no researches published to far that compare the various methods for determining the degree of hydration of CEM I cement. Therefore, the purpose of this study is to compare the feasibility and reliability of the SEM -BSE image analysis approach for estimating the degree of hydration of cement with two other methods using the thermogravimetric analysis (TGA).

II.

Material and method II.1.

Method of characterization of the synthesized clinker and cement

The clinker cement (OPC 97TM) used in this study was synthesized in the laboratory by burning a mixture of limestone (CaCO3), silica oxide (SiO2), aluminum oxide (Al2O3) and iron oxide (Fe2O3). The proportion of components was calculated using the modulus usually used in the cement industry: the Lime Saturation Factor (LSF), the Silica Ratio (SR) and the Alumina Ratio (AR). The calculations of modulus (LSF, SR and AR) are presented by the equations below ((Eq15) -> (Eq17)):

LSF = $ * %/01 .2 * %341 %$.$2 * %56 17% 8 * %9: 17 (15) SR = %SiO2 %Al2O3+%Fe2O3 (16) AR = %Al2O3 %Fe2O3 (17)
In this study, the values LSF = 97, SR = 2.6 and AR = 1.45 were used for the formulation of mixture. Table 2 shows the composition of the components of the formulation. The raw materials were first mixed by adding water with a water/material ratio = 0.6 in order to have good homogeneity. After drying at 105°C, pellets (with a diameter of 40 mm and a height of 15 mm) are formed using a press and a force of 5 KN. The pellets were burned in a furnace at 200°C for 20 minutes, then the temperature increases to 1450°C with a heating rate of 7°C/minute, and kept at this temperature for 15 minutes. After clinkerization, the obtained clinkers were cooled in the furnace to reach the room temperature. Portland cement was produced by adding gypsum (CaSO4.2H2O) to ground clinker in order to have an SO3/Al2O3 molar ratio of 0.6.

The content of free lime in the clinker was determined by the Schlafer-Bukokowski method. Indeed, cement manufacturers consider that a clinker, whose composition is perfectly dosed, has a CaOfree content of less than 2% wt. [START_REF] Gineys | Influence de la teneur en éléments métalliques sur les propriétés techniques et environnementales du ciment Portland[END_REF]. Therefore, in this study, the maximum acceptable CaO free content is set at 2%.

The mineralogical composition of the clinker was identified by X-ray diffraction (XRD) and quantified according to the Bogue modified formula, which takes into account the presence of CaO free [START_REF] Bogue | Hydration of Portland Cement Compounds[END_REF].

The chemical composition of the clinker and hydrated cement paste phases was analyzed on the polished sections using a Hitachi S-4300 SE/N scanning electron microscope operating in backscattered electron mode (20 keV) and equipped with an energy dispersive X-ray spectrometer (EDS). For the measurement, the points were carried out on several zones.

The particle size distribution of the OPC 97TM cement was measured using the Beckman Coulter -LS13 320 type device after dispersing in an ethanol solution. The absolute density of the OPC 97TM cement was carried out using an Accupyc 1330 helium pycnometer. The Blaine specific surface of the cement was measured according to standard NF EN 196-6 [START_REF]NF EN 196-6 : Méthodes d'essai des ciments -Détermination de la finesse[END_REF]. In this study, the Blaine surface of the cement is between 3500 and 4000 cm 2 /g. The chemical composition of the synthetized cement was verified by X-Ray fluorescence (XRF). The mineralogy of cement and hydrated cement paste was analyzed by X-ray diffraction (XRD) using a BRUKER D2 Advance device equipped with a Cu anticathode, λ = 1.5406 Å with the angle 2θ from 5° to 80° and a step of 0.02.

II.2. Method for determining the degree of hydration

In this study a cement pastes with a w/c ratio of 0.5 was used to determine the degree of hydration. After three minutes of mixing, the paste was introduced into the polytetrafluotethylene molds for measuring the degree of hydration, and into the 1x1x1 cm 3 size molds for the measurement of compressive strength. The cement pastes were demolded after 24 hours and stored in the saturated lime solution.

Based on previous studies [START_REF] Gineys | Influence de la teneur en éléments métalliques sur les propriétés techniques et environnementales du ciment Portland[END_REF][START_REF] Aouad | Dredged sediments used as novel supply of raw material to produce Portland cement clinker[END_REF][START_REF] Kleib | Ecoconception des ciments : synthèse , hydratation et durabilité-Thèse doctorant IMT Lille Douai et L'Université Libanaise[END_REF][START_REF] Kleib | Production of Portland cement clinker from French Municipal Solid Waste Incineration Bottom Ash[END_REF][START_REF] Kleib | Incorporation of zinc in calcium sulfoaluminate cement clinker[END_REF], the compressive strength of the cement paste was measured on the cube of dimension 1x1x1 cm 3 under a constant stress of 0.3 MPa/s using a uniaxial press at 2, 15 and 28 days of hydration. For each measurement, 6 samples were tested.

II.2.1. Determination of the degree of hydration by thermogravimetric analysis (TGA)

To prevent carbonation of the cement paste, in this study, no method of stopping hydration was used. The cement paste for the TGA analysis was analyzed immediately upon reaching the desired hydration time. The device used is the NETZSCH STA 409 type with the following experimental conditions:

• During the analysis the sample is kept under a flow of Argon at a flow rate of 75 ml/min.

• The temperature increases from 30 °C to 105 °Cat a rate of 2 °C/min, then maintained at 105 °C for 1 hour before increasing to 1100 °C at a rate of 3 °C/min.

II.2.2. Determination of the degree of hydration by the SEM-BSE image analysis method

To stop the hydration, the samples for image analysis were submerged in an acetone solvent solution. Indeed, drying samples at 105 °C has the potential to alter the microstructure of the cement paste [START_REF] Zhang | Comparison of methods for arresting hydration of cement[END_REF] and so impair image analysis results. A JEOL scanning electron microscope operating in backscattered electron mode (15 keV) with a magnification of 500 and a resolution of 1280 x 960 pixels was used to capture images of the sample. For the measurement, around 20 pictures were taken at various positions throughout the sample.

III. Results

This part presents, on the one hand, the result of characterization of the cement (OPC 97TM) and the cement paste in order to assess the quality of the cement synthesized in the laboratory, and on the other hand, the results of the degree of hydration of the paste determined by three different methods.

III.1. Characterization of clinker and synthesized cement

The CaOfree content of the clinker measured according to the Schlafer-Bukokowski method is 1.287%, which is less than the limit value (2%). This indicates that the clinker's composition is well dosed.

Table 3 and Table 4 show the chemical composition of the mineral phases of the clinker identified by SEM-EDS analysis. Approximately 30 points were measured for each phase in different areas. The results of SEM-EDS analysis showed that the ratio of the main oxides in the four phases was higher than the theoretical value. A similar result was found in Gineys's et al. research on clinker synthesized in the laboratory [START_REF] Gineys | Influence de la teneur en éléments métalliques sur les propriétés techniques et environnementales du ciment Portland[END_REF]. The difference between the theoretical and experimental values could be due to the presence of minor elements in the mineral phases, for example, Al and Fe in the C3S and C2S phases. This could influence the ratio of major elements in these phases. Table 5 show the physical characteristics of OPC 97TM cement. The Blaine surface of the cement reaches 3800 cm 2 /g, which respects the values of the Blaine surface targeted between 3500 and 4500 cm 2 /g. The chemical composition of OPC 97TM cement is also presented in Table 6. The chemical composition of the main elements of the hydrated calcium silicate by the SEM-EDS analysis measured on the sample of the hydrated cement paste at 2 days is presented in the Fig. 1. Around 100 points were measured in four different areas. The CaO-SiO2-Al2O3 ternary diagram is superimposed on the ternary diagram produced by Lothenbach [START_REF] Lothenbach | Supplementary cementitious materials[END_REF]. This diagram shows the positions of the main cement hydrates: Ca(OH)2, C-S-H (with two C/S ratios) or even C-A-S-H. The diagrams show that the hydrated calcium silicates are mainly concentrated in areas where the C/S ratio is greater than 1.7. A similar results have been found in previous studies on CEM I [11, 32]. Fig. 2 illustrates the C/S and Al2O3/SiO2 ratios of the different measured points.

The result show that:

• The C/S ratio (CaO/SiO2) obtained in the C-S-H phase varies from 2.5 to 3.5 but is always higher than the value of 1.7 used in the equations for the description of cement hydration (Eq1), (Eq2). This difference can be due to the EDS points made and to the size of the diffusion bulb which analyzes an area and not a point. Typically, the diffusion bulb's size is 1 µm 3 and the resolution of a SEM 20 kV tungsten filament is 3 nm. Thus, other hydrates are analyzed and will have an influence on the C/S and Al2O3/SiO2 ratios, in particular, the C/S ratio [START_REF] Berthomier | Etude de la lixiviation de l'aluminium de matériaux cimentaires à base de CEM III utilisés dans les canalisations d'eau potable : approche expérimentale et numérique[END_REF]. • The average value of the Al2O3/SiO2 ratio of hydrates measured is equal to 0.14 and this value is very consistent with the initial value of the Al2O3/SiO2 ratio in the anhydrous OPC 97TM cement (the Al2O3/SiO2 ratio in the cement is equal to 0.137). This result means that all of the aluminum in the cement is found in the C-A-S-H and C-S-H phases. The incorporation of aluminum into the C-S-H phase has been demonstrated in research by Richardson et al [START_REF] Richardson | Location of Aluminum in substituted calcium silicate hydrate, C-S-H, gels as determined by 29Si and 27Al NMR and EELS[END_REF]. This study showed an Al/Si ratio equal to 0.25, corresponding to the maximum aluminum that can be incorporated into C-S-H. The formation of additional phases such as ettringite and portlandite in the hydrated cement paste has been observed. These hydrates formed correspond to the products described in equations (Eq 1) -> (Eq 8). However, the presence of hydrated calcium silicate (C-S-H) is difficult to detect due to its amorphous nature.

The compressive strength of the cement paste is presented in the Table 7. This result is consistent with the previous XRD result showing the transformation of anhydrous phases to hydrates in hydrated cement paste, which is the origin of resistance development.

III.2. Degree of hydration of cement by portlandite quantification analysis by TGA analysis

The amount of portlandite produced during cement hydration was estimated by TGA analysis on cement pastes at 2 and 28 days of hydration. Table 8 shows the mineral composition of the cement and the Ca(OH)2 amount produced during complete hydration, according to the calculation from the simplified equations (Eq1) -> (Eq8). Indeed, the results of the SEM-EDS analysis on the clinker and the cement paste showed a different element ratio than the theoretical ratios used in these equations. Fig. 4 shows the TGA analysis curve of the cement paste after 2 days of hydration.

• Zone (I): the temperature increases from 30 °C to 105 °C to remove evaporable water.

• Zone (II): the temperature is maintained at 105 °C for 1 hour to remove the rest of evaporable water.

• Zone (III): the temperature between 650 °C and 800 °C corresponds to the decomposition of calcite temperature. In this case, the loss of weight of the sample is very low, this means that the protocol allows avoiding the phenomenon of carbonation and the quantity of Ca(OH)2 determined between 450 °C and 560 °C is the totality of the Ca(OH)2 produced during the hydration of the cement.

Fig. 4 TGA analysis of the cement paste (w/c = 0.5) after 2 days of hydration.

Table 9 shows the amount of portlandite as well as the degree of hydration calculated according to (Eq10), (Eq11) and (Eq12) taking the value ϒ0 (total amount of Portlandite produced when the hydration is completed) equal to 0.3329 (Table 8).

Table 9

Quantity of Ca(OH)2 and the degree of hydration of the cement paste over the time of hydration.

Time (days)

Portlandite mass (g/100 g of pastes) Degree of hydration (%) 2 days 13.24 60.09 28 days 20.44 92.16

III.3. Degree of hydration of cement by quantification of chemically bound water by TGA analysis

This approach determines the degree of hydration of the cement according to (Eq13) and (Eq14) using TGA analysis. The Wn(∞) value is calculated based on a theoretical approximation of the amount of chemically bound water for the five main phases of cement upon complete hydration. Table 10 shows the theoretical amount of water in the cement for complete hydration. From Table 10, we conclude that the Wn(∞) = 25.145 (g).

From the result of the TGA analysis (Fig. 4), we then obtain: ∆ EF GHI 105 ° -1000 ° 2 JFKE = 9.37 (g). EF GHI 1000° 2 JFKE = 66.21 (g).

wn

(2 days) = = ∆ !" $ ° $ ° !" $ ° * 100 = L.7M
88. $ * 100 = 14.152 (g).

The degree of hydration of the cement within 2 days of hydration was calculated using (

* 100 = 56.28 (%).

Table 11 shows the degree of hydration of the cement paste calculated according to the method of quantification of water bound over time of hydration.

Table 11

Degree of hydration of OPC 97TM cement estimated by the bound water quantification method.

Time (days)

Degree of hydration (%) 2 days 56. [START_REF] Kleib | Production of Portland cement clinker from French Municipal Solid Waste Incineration Bottom Ash[END_REF] 28 days 80.85

III.4. Degree of hydration of cement by SEM-BSE image analysis method

Fig. 5 shows the essential steps applied in this study to quantify the cement phases over time of hydration.

• Step 1: Acquisition of SEM-BSE images of the sample.

• Step 2: Acquisition of histogram of SEM-BSE images of the sample using Matlab software.

• Step 3: Quantification of phases on the diagram of histogram using Origin pro software. The segmentation of the pores from an image with gray levels (0-255), first requires the setting of a threshold value [START_REF] Zined | Influence de la microstructure sur le transport diffusif des pâtes, mortiers et bétons à base de CEM I avec ajout de fumée de silice[END_REF]. In the literature, many methods exist for determining this threshold value, which is very important for quantification with better precision, for example it corresponds to the point of intersection of the tangents to the peak curves of the pores and of the peaks of the hydrated phases (HP) (Fig. 5). This threshold level of pore segmentation is around 50 for the cement paste in this study. After setting the threshold level, the deconvolution method was applied using the Origin Pro 8.5 software for phase quantification. The quantity of phases from the analysis of the images corresponds to the volume fraction of these phases in the cement paste and the degree of hydration of the cement is estimated according to the following equation (Eq18):

α(t) = O ,PQRSTU V" ", O ,PQRSTU V" ", W * 100 (18)
The cement paste made with a W/C ratio equal to 0.5 corresponds to an initial volume fraction of the cement equal to 38.83%. 12 shows the result of the degree of hydration of the cement over time of hydration by the method of SEM -BSE image analysis.

III.5. Assessment of the relevance of method for determining the degree of hydration

Table 13 shows the degree of the OPC 97TM cement paste determined by three different methods. The deviation of the degree of hydration estimated by different methods was observed. In order to assess the relevance of these methods, the Power's approach (Eq19) was used [START_REF] Bentz | Guide to Using CEMHYD3D: A Three-Dimensional Cement Hydration and Microstructure Development Modelling Package[END_REF] which presents a model for estimating compressive strength as a function of the degree of hydration.

σc(t)= σ0(X(t)) n (19)
with: σc(t): Compressive strength at time t. σ0: Compressive strength when capillary porosity is zero. It is calibrated on the basis of determination of resistance at 2 days. n: Value taken between 2.6 and 3.0. In general, a value equal to 2.6 is applied for CEM I. X(t): Ratio of hydrate gel-space, is determined as following equation (Eq20):

X(t) = .82 X .7 X % Y Z (20)
with: α(t): Degree of hydration of sample at time t. W/C: water/cement ratio.

From the relationship between the compressive strength and the degree of hydration (Eq19) and (Eq20), the experimental value of the compressive strength was used to assess the suitability of the three methods. The principle is to determine the degree of hydration at 28 days from the hydration at 2 days in order to achieve desired compressive strength. The degree of hydration at 28 days is calculated using the following equation (Eq21):

α(28 days) = . [.\]^ ]_`ab /d[[e[.f ^ ] _`ab /d[[ * g hi ] _`ab hi ]j _`ab ].k .7 (21)
with: σc (2 days): Compressive strength at 2 days (Mpa). σc (28 days): Compressive strength at 28 days (Mpa). α (2 days): Degree of hydration at 2 days (%). α (28 days): Degree of hydration at 28 days calculated from the degree of hydration at 2 days to reach the desired resistance value at 28 days (%). Table 14 shows the value of the degree of hydration calculated according to (Eq21) from the degree of hydration at 2 days determined according to the three methods.

Table 14

Degree of hydration at 28 days calculated from (Eq21) according to three methods, Method 1: Portlandite quantification method, Method 2: Bound water of quantification method, Method 3: SEM-BSE image analysis method. The result shows that:

Degree of hydration

• Ca(OH)2 quantification method seems to give a better result compared to two other methods with the smallest deviation. However, the degree of hydration at 28 days calculated from method 1 and method 3 exceeds 100%. In addition, Zhang et al [START_REF] Zhang | Hydration of cement and pore structure of concrete cured in tropical environment[END_REF] found that the degree of hydration of CEM I cement paste varies between 55 and 80 % at 28 days depending on the W/C ration (W/C ration between 0.3 and 0.7). • Comparing with Zhang's result, method 2 seems to present a reasonable result. However, it should be noted that some phases (Ettringite, C-S-H) start dehydroxylation at a lower temperature than 105 °C [11]. In addition, we chose to compare the experimental quantities of Ca(OH)2 to evaluate the methods' relevance in our study because Ca(OH)2 is a relatively easy data set to determine thanks to TGA analysis. The SEM-BSE image analysis presents the volume of Ca(OH)2 over time of hydration. We convert from volume fraction to mass fraction using a CaOH)2 density of 2.24 (g/cm 3 ). The Ca(OH)2/initial cement mass ratio measured by the SEM-BSE images analysis method is calculated according to the following equation (Eq22): The result shows that:

l,l l ! V" ", = O O ,PQRSTU V" "
• Method 1 and method 3 seem to present the result consistent with method 2 by presenting a higher ration. But the deviation is small.

IV. Conclusion

The objective of this study is to estimate the degree of hydration of cement synthesized in the laboratory by three different approaches: method of quantification of portlandite, method of quantification of chemically bound water and method of image analysis. The results showed that:

• The C/S ratio in the alite and the belite in the clinker measured by the SEM-EDS analysis are higher than the theoretical ratio equal to 3 and 2 respectively. The CaO/Al2O3 and CaO/Fe2O3 ratios in C3A and C4AF are also higher than the theoretical value of 1.5 and 2 respectively. The difference between the theoretical and experimental values could be due to the presence of minor elements in the mineral phases, for example, Al and Fe in the C3S and C2S phases. This could influence the ratio of major elements in these phases. • The C/S ratio in the hydrated calcium silicate (C-S-H) phase measured by the SEM-EDS analysis on the hydrated cement paste at 2 days is also higher than the theoretical value of 1.7 used in the equations of cement hydration. This difference can be due to the EDS points made and to the size of the diffusion bulb which analyzes an area and not a point. In addition, the incorporation of aluminum in this phase has been detected. This could have an influence on the C/S ratio. • The bound water quantification method seems to present a reasonable result using the Power's approach and using the result in the literature. • The Ca(OH)2 quantification method seems to overestimate the degree of hydration. The result also depends on the temperature range of Ca(OH)2 quantification on the TGA curve. • The SEM -BSE image analysis method presents relatively similar results with the results by the Ca(OH)2 quantification method. This method demonstrates the feasibility used as a reliable method to determine the degree of hydration, the amount of hydrates in a cementitious material. However, it is necessary to improve the number of images and the resolution to increase the precision.

Declaration of competing interest:

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

Fig. 1

 1 Fig. 1 CaO-SiO2-Al2O3 ternary diagram obtained for the cement paste after 2 days of hydration.

Fig. 2

 2 Fig. 2 Ratio of the principal elements of hydrated calcium silicate measured by SEM-EDS analysis on the sample of the cement paste after 2 days of hydration.The evolution of the mineral phases over time of hydration identified by the XRD analysis is presented in Fig.3.

Fig. 3

 3 Fig. 3 X-Ray diffraction of OPC 97TM over time of hydration (1: C3S, 2: C2S, 3: C3A, 4: C4AF, 5: Gypsum, 6: Afm, 7: Ca(OH)2), 8: Ettringite (Aft).

Fig. 5

 5 Fig. 5 Methodology of phase quantification using image analysis technique (cement paste after 2 days of hydration) Several images were analyzed and the Table12shows the result of the degree of hydration of the cement over time of hydration by the method of SEM -BSE image analysis.

Table 2

 2 Mix design for the production of the clinker cement OPC 97TM.

	Formula	Limestone (wt. %)	Alumina oxide (wt. %)	Iron oxide (wt. %)	Silica oxide (wt. %)
	OPC 97TM	79.99	3.17	2.32	14.52

Table 3

 3 Results of the SEM-EDS analysis on the silicate phases of the synthesized clinker.

	Mineral phase	Formula	CaO/SiO2 (Theoretical	CaO/SiO2 (SEM-EDS
			ratio )	results)
	Alite	Ca3SiO5	3	3.42
	Belite	Ca2SiO4	2	2.44

Table 4

 4 Results of the SEM-EDS analysis on the interstitial phases of the synthesized clinker.

	Mineral phase	Formula	CaO/Al2O3 (Theoretical ratio)	CaO/Al2O3 (SEM-EDS results)
	Tricalcium aluminate	Ca3Al2O6	1.5	2.44
	Calcium aluminoferrite	Ca4Al2O10Fe2	2	2.575

Table 5

 5 Physical characteristics of OPC 97TM cement synthesized in the laboratory.

	Cement	Density (g/cm 3 )	Blaine surface (cm 2 /g)	BET surface (m 2 /g)	d10 (µm)	d90 (µm)
	OPC 97TM	3.15	3800	1.224	0.72	43.31

Table 6

 6 Chemical composition of OPC 97TM cement.

	Element	SiO2	Al2O3	Fe2O3	CaO	SO3	LOI at	Total
							950 °C
	(wt.%)	20.5	4.7	3.1	65.5	1.90	3.6	99.2

Table 7

 7 Compressive strength of the cement paste over the time of hydration.

	Time (days)	Compressive strength (Mpa)	Deviation (%)
	2 days	25.26	6.5
	15 days	57.98	9.5
	28 days	66.61	8.5

Table 8

 8 Ca(OH)2 production for a complete hydration of cement of OPC 97TM cement.

	Anhydrous phases	Mass content in cement (%)	CH mass for 1 g of anhydrous cement (g/g of cement)
	C3S	73.96	0.312
	C2S	4.77	0.0062
	C3A	5.93	0
	C4AF	9.77	0.0147
	CaO free	1.24	0
	Gypsum	4.33	0
	Total	100	0.3329

Table 10

 10 Theoretical amount of water bound for complete hydration of OPC 97TM cement.

	Anhydrous phases	Masse content in cement	Quantity of bound water	Mass of water related to
		(wt.%)	produced in g of water/g	complete hydration (g)
			of phase in the cement
	C3S	73.96	0.24	17.75
	C2S	4.77	0.21	1.00
	C3A	5.93	0.40	2.372
	C4AF	9.77	0.37	3.614
	CaO free	1.24	0.33	0.409
	Gypsum	4.33	0	0
	Total	100		25.145

Table 12

 12 Degree of hydration of cement estimated by the SEM -BSE image analysis method.

	Time (days)	Amount of anhydrous	Degree of hydration (%)	Deviation (%)
		cement (%)
	2 days	14.35	63.04	7.80
	28 days	2.46	93.66	8.40

Table 13

 13 Degree of hydration of the OPC 97TM cement paste determined by three different methods.

	Method

Table 15

 15 Cement density: 3.15 g/cm 3 (Table5). The result of three methods is presented in the Table15. Ca(OH)2/initial cement mass ratio measured by three methods.

	,	W	*	. 7.$	* 100	(22)

Acknowledgments:

The authors wish to acknowledge the SEDICIM project and the FEDER funds.


Tristan De Leissegues

MD Stanislas Gunst
email: stanislas.gunst@chu-lyon.fr

Cécile Batailler

Gunjan Kolhe

Sébastien Lustig

Elvire Servien

Prevalence of trochlear dysplasia in symptomatic isolated lateral patellofemoral osteoarthritis: transverse study of 101 cases

Keywords: IV; transverse study Patellofemoral osteoarthritis, Risk factor, Trochlear dysplasia, Valgus, BMI Abbreviations PFOA: Patellofemoral osteoarthritis ILPFOA: Isolated lateral patellofemoral osteoarthritis TD: Trochlear dysplasia CI: Confidence interval CDI: Caton-Deschamps index BMI: Body-mass index LVP: Lateral vertical patellectomy

2

TD prevalence was 88.1%. TD was significantly more advanced in patients under 45 years of age at surgery (64.5% stage 2 or 3; p=0.019). Non-TD cases showed significantly more frequent valgus deformity (83.3%; p=0.042) and overweight (BMI, 32±4.1; p<0.001).

Conclusion

TD is a known risk factor for PFOA, present in almost 9 in 10 cases in the present series of ILPFOA. These findings reinforce the hypothesis that it plays a role in onset of ILPFOA. TD also induces early pain, leading to surgery. Overweight and valgus deformity are contributing factors for ILPFOA.

Introduction

Patellofemoral osteoarthritis (PFOA) is usually associated with femorotibial osteoarthritis; isolated forms involve several specific risk factors. Trochlear dysplasia (TD) alters stress patterns in the patellofemoral joint, inducing PFOA. The association of TD and isolated PFOA was analyzed without distinguishing medial facet, global and lateral facet involvement.

The study hypothesis was that TD prevalence is high in isolated lateral PFOA (ILPFOA). The aim of the study was to assess TD prevalence in a symptomatic ILPFOA population and identify risk factors.

Patients and methods

Eighty-four patients (101 knees) underwent lateral vertical patellectomy (LVP) for symptomatic ILPFOA between November 1998 and September 2019. Demographic, clinical and radiographic data were collected retrospectively from preoperative records. TD was analyzed by 2 blinded surgeons on lateral radiographs.

Results

Introduction

Patellofemoral osteoarthritis (PFOA) is usually associated with global or bicompartmental osteoarthritis of the knee, but may also be isolated, sometimes bilateral, with typical symptomatology, often emerging in young patients [START_REF] Dejour | Histoire naturelle de l'arthrose fémoro-patellaire isolée[END_REF].

Epidemiological studies from the 1990s, notably by McAlindon et al. [START_REF] Mcalindon | Radiographic patterns of osteoarthritis of the knee joint in the community: the importance of the patellofemoral joint[END_REF], reported high prevalence of PFOA in of knee pain, with a correlation between radiographic PFOA and severity of disability [START_REF] Mcalindon | Radiographic patterns of osteoarthritis of the knee joint in the community: the importance of the patellofemoral joint[END_REF][START_REF] Cicuttini | Association of pain with radiological changes in different compartments and views of the knee joint[END_REF][START_REF] Bourlez | Are modern knee outcomes scores appropriate for evaluating patellofemoral degeneration in osteoarthritis? Evaluation of the ceiling and floor effects in knee outcomes scores[END_REF], and PFOA commonly involved the lateral facet [START_REF] Iwano | Roentgenographic and clinical findings of patellofemoral osteoarthrosis. With special reference to its relationship to femorotibial osteoarthrosis and etiologic factors[END_REF]. These findings stimulated the search for risk factors other than classical chondrocalcinosis and patellar fracture [START_REF] Hansen | Radiological aspects of chondrocalcinosis[END_REF][START_REF] Carpenter | Fractures of the Patella[END_REF]. Dejour and Allain focused on a history of patellar dislocation, analyzing TD in PFOA and found 78% prevalence of TD, indicating a major role in onset of PFOA.

Trochlear morphology acts as a passive structure affecting extensor system alignment in flexion-extension [START_REF] Hinman | Patellofemoral joint osteoarthritis: an important subgroup of knee osteoarthritis[END_REF][START_REF] Chassaing | How tibial tubercle torsion impacts patellar stability: A biomechanics study[END_REF]. The combination of compression, shear stress and lateral overload makes the patella the prime cartilage lesion site in the whole body [START_REF] Hungerford | Biomechanics of the patellofemoral joint[END_REF]. In pathological situations, there is translation of forces acting on the patellofemoral joint that can lead to lateral hyperpressure [START_REF] Huberti | Patellofemoral contact pressures. The influence of q-angle and tendofemoral contact[END_REF][START_REF] Duparc | biomécanique et physiopathologie : données récentes[END_REF]. The lateral facet is then subject to considerable stress, inducing isolated lateral PFOA (ILPFOA).

There have been no studies specifically on the association between TD and ILPFOA. This study hypothesized that TD prevalence is very high in ILPFOA.

The main aim of the study was to assess TD prevalence in patients undergoing lateral vertical patellectomy (LVP) for symptomatic ILPFOA. Secondary endpoints comprised the impact of TD on age at surgery and risk factors for ILPFOA.

Material and methods

Patients

This retrospective study included all patients undergoing LVP on native knee in our department between November 1998 and September 2019.

Exclusion criteria comprised: frontal lower-limb deformity requiring surgical correction, medial facet PFOA, history of patellar fracture, and postoperative pathologic diagnosis of any inflammatory pathology. All patients meeting the inclusion criteria were included. Cases of objective patellar instability or with history of instability were not excluded. Surgical indications were made by a senior surgeon. Surgery followed the procedure described by Neyret et al. [START_REF] Neyret | Données techniques du traitement chirurgical conservateur dans l'arthrose fémoro-patellaire[END_REF].

Clinical and radiographic analysis

Lower-limb axes were assessed by the surgeon in the preoperative consultation with the patient in bipedal weight-bearing. Demographic data were also collected then.

All radiographic measurements were made on the preoperative radiographs: AP knee view under standard weightbearing, lateral view under unipedal weight-bearing in 20° flexion as described by Dejour et al. [START_REF] Dejour | Dysplasia of the femoral trochlea[END_REF], schuss view in 30° flexion, and axial patella view following Merchant et al. [START_REF] Merchant | Roentgenographic analysis of patellofemoral congruence[END_REF]. TD grade was assessed on lateral view on the Dejour classification [START_REF] Dejour | Dysplasia of the femoral trochlea[END_REF][START_REF] Dejour | Factors of patellar instability: an anatomic radiographic study[END_REF]. Patellar height was measured on Caton-Deschamps index [START_REF] Caton | Patella infera. A propos of 128 cases[END_REF]. PFOA stage was assessed on axial patella view on the Iwano classification [START_REF] Iwano | Roentgenographic and clinical findings of patellofemoral osteoarthrosis. With special reference to its relationship to femorotibial osteoarthrosis and etiologic factors[END_REF]. All radiographs were analyzed by 2 blinded orthopedic surgeons, by consensus or with the opinion of a third surgeon.

Statistics

Demographic data were analyzed using descriptive statistics. Qualitative variables were reported as number and percentage, and quantitative variables as mean ± standard deviation.Chi-square and Fisher exact tests were used for comparison of qualitative variables.

Quantitative variable independence was assessed on Spearman correlation test. Mean values for non-matched groups were compared on Student t test. Interobserver concordance was assessed on weighted Kappa coefficient (linear system). The significance threshold was set at p <0.05. Analyses used R software version 3.6.1 (R Development Core Team, Vienna, Austria).

Results

Demographic data

Between November 1998 and September 2019, 127 patients (152 knees) underwent LVP on native knee. Sixteen knees undergoing concomitant osteotomy, 20 knees with history of patellar fracture, 9 diagnosed postoperatively with inflammatory arthropathy, and 6 with radiologic signs of medial facet PFOA were excluded (figure 1).

Eighty-four patients (101 knees) were analyzed: 46 women (55%) and 38 men (45%); mean age at surgery, 50±10 years (range, 28-71 years). TD prevalence was 88.1% (n=89 knees).

Twenty-six knees (25.7%) had history of objective patellar instability. Six knees (5.9%) had history of surgical patellar stabilization: anterior tibial tuberosity medialization [START_REF] Van Sambeeck | Complications of a self-centering sliding tibial tubercle osteotomy for patellofemoral complaints; low incidence of non-union and fracture[END_REF] or medial patellofemoral ligament reconstruction [START_REF] Servien | In vivo positioning analysis of medial patellofemoral ligament reconstruction[END_REF][START_REF] Roger | Axial patellar engagement index and patellar tilt after medial patello-femoral ligament reconstruction in children and adolescents[END_REF]. Table 1 shows demographic data. There was no significant correlation between PFOA stage and TD grade (p=0.863) (Table 2). There was a significant correlation between high TD grade and low age at surgery (p=0.009). Age at surgery also correlated with radiographic PFOA stage (p<0.001) (Table 3).

Comparison according to age at surgery

Patients aged ≤45 years showed a significantly higher rate of TD than older patients: 100% vs. 82.9% (p=0.016), and a higher proportion of TD grade 2 or 3 (p=0.019). Conversely, PFOA was less advanced in under-45 year-olds (p=0.021) (Table 4).

Comparison according to presence of TD

Patients free of TD had significantly higher BMI (32±4.1 vs. 26.4±5.2; p<0.001) and a greater proportion of valgus deformity (83.3% vs. 48.3%; p=0.042). The 2 groups were comparable for gender and patellar height (Table 5).

Interobserver concordance

Radiographic analysis of the 101 knees was performed by 2 independent assessors. Twentythree cases required a third opinion. The weighted Kappa coefficient was 0.78 (95% CI, 0.70 -0.86) (p<0.0001). Interobserver concordance was excellent [START_REF] Fleiss | Statistical Methods for Rates and Proportions[END_REF].

Discussion

The present state of knowledge ranks TD ahead of trauma and inflammation as a prime risk factor for isolated PFOA [START_REF] Dejour | Histoire naturelle de l'arthrose fémoro-patellaire isolée[END_REF]. TD prevalence data mainly concern mixed lateral and medial PFOA with or without knee pain. To our knowledge, no studies have specifically analyzed TD prevalence in symptomatic ILPFOA.

The present study confirmed the hypothesis of a major role of TD in symptomatic ILPFOA, with a TD rate of 88.1%. Literature prevalence estimates come from series combining lateral and medial facets. Dejour and Allain [START_REF] Dejour | Histoire naturelle de l'arthrose fémoro-patellaire isolée[END_REF] reported a rate of 78% on X-ray and CT analysis of 367 cases of PFOA. Montserrat et al. [START_REF] Montserrat | Partial lateral facetectomy plus Insall's procedure for the treatment of isolated patellofemoral osteoarthritis: survival analysis[END_REF] reported 71.3% in 87 knees undergoing LVP associated to Insall's procedure; history of patellar dislocation was an exclusion criterion, which may have reduced TD prevalence; only 80.5% of cases focused on ILPFOA, 11.5% had other PFOA locations and 8% lacked data. Mofidi et al. [START_REF] Mofidi | Association and impact of patellofemoral dysplasia on patellofemoral arthropathy and arthroplasty[END_REF] analyzed preoperative CT scans in 17 patients undergoing patellofemoral arthroplasty, and found a 100% rate of TD. Yercan et al. [START_REF] Yercan | The Treatment of Patellofemoral Osteoarthritis with Partial Lateral Facetectomy[END_REF] reported a 55% rate in 11 patients on X-ray and CT analysis. This diversity of findings is mainly due to differences in sample size: smaller series, with less statistical power; were more subject to chance effects and recruitment bias. Patient selection also needs to be considered. The present 88.1% TD prevalence was higher than in series larger than 50 cases, and notably those of Dejour and Allain [START_REF] Dejour | Histoire naturelle de l'arthrose fémoro-patellaire isolée[END_REF] and Montserrat et al. [START_REF] Montserrat | Partial lateral facetectomy plus Insall's procedure for the treatment of isolated patellofemoral osteoarthritis: survival analysis[END_REF].

Exclusion of global and medial PFOA, and inclusion of patients with history of patellar dislocation and experiencing pain may explain this higher prevalence. The results support the hypothesis of a close relation between TD and exclusively lateral PFOA.

The present demographics was comparable to that in other LVP series [START_REF] Montserrat | Partial lateral facetectomy plus Insall's procedure for the treatment of isolated patellofemoral osteoarthritis: survival analysis[END_REF][START_REF] Paulos | Partial lateral patellar facetectomy for treatment of arthritis due to lateral patellar compression syndrome[END_REF][START_REF] Wetzels | Patellofemoral osteoarthritis treated by partial lateral facetectomy: results at long-term follow up[END_REF][START_REF] López-Franco | Evaluation of a minimally aggressive method of patellofemoral osteoarthritis treatment at 10 years minimum follow-up[END_REF][START_REF] Becker | Surgical treatment of isolated patellofemoral osteoarthritis[END_REF], except for a lower age at surgery which corresponded to our strategy in ILPFOA, with first-line conservative management (LVP) in younger patients.

There were significant correlations between TD grade and age at surgery, and between PFOA stage and age at surgery: patients aged ≤45 years showed higher-grade TD and less advanced PFOA. Age at surgery was related to intensity and early onset of symptoms, and we believe there is a strong link between TD and the severity of clinical manifestations in ILPFOA.

Iwano 1 or 2 ILPFOA may be less well tolerated in case of high-grade TD.

The results reported by Dejour and Allain [START_REF] Dejour | Histoire naturelle de l'arthrose fémoro-patellaire isolée[END_REF], supported by the biomechanical study by Van Haver et al. [START_REF] Van Haver | The effect of trochlear dysplasia on patellofemoral biomechanics: a cadaveric study with simulated trochlear deformities[END_REF], showed an impact of TD grade on radiographic PFOA stage: using the classification of D. Dejour [START_REF] Dejour | Douleurs et instabilité rotulienne: essai de classification[END_REF], they showed that TD grades B, C and D correlated directly with PFOA stage. In the present study, there was no correlation between TD grade and radiographic ILPFOA stage at surgery. This difference may be due to our use of the older and strictly radiographic classification of H. Dejour [START_REF] Dejour | Dysplasia of the femoral trochlea[END_REF][START_REF] Dejour | Factors of patellar instability: an anatomic radiographic study[END_REF]. It seems more likely that the absence of correlation between TD grade and PFOA stage was due to age at surgery. Poorer clinical tolerance in case of severe TD casts doubt on the usefulness of analyzing the correlation between TD grade and PFOA stage in surgical series: the correlation would need to be studied in non-operated patients, taking age into account as a confounding factor.

Valgus morphotype and obesity are known risk factors for PFOA. McAlindon et al. reported a positive adjusted odds ratio for onset of PFOA in case of BMI in the top tercile [START_REF] Mcalindon | Are risk factors for patellofemoral and tibiofemoral knee osteoarthritis different?[END_REF]. In a transverse study, Elahi et al. [START_REF] Elahi | The association between varus-valgus alignment and patellofemoral osteoarthritis[END_REF] reported 63% valgus deformity in isolated PFOA, versus 26% in unicompartmental femorotibial osteoarthritis. Flury et al., using 3D models, found a linear relation between altered femoral axis and Q angle [START_REF] Flury | Linear influence of distal femur osteotomy on the Q-angle: one degree of varization alters the Q-angle by one degree[END_REF]; any variation in Q angle unbalances patellar pressure distribution, with increased maximum pressure [START_REF] Huberti | Patellofemoral contact pressures. The influence of q-angle and tendofemoral contact[END_REF]. Valgus deformity or altered Q angle may thus be risk factors for ILPFOA in the absence of TD, especially in cases of high BMI. This was analyzed in the present study in subgroups with and without TD; the TD groups showed significantly higher BMI (32±4.1) and a higher rate of valgus deformity (83.3%). These findings matched the literature, supporting the hypothesis that onset of ILPFOA is influenced by overweight and valgus deformity. Further analyses are required to demonstrate causality.

The present study had certain limitations due to its retrospective design without a control group. Secondly, exclusive recruitment of ILPFOA patients requiring surgery may have led to selection bias, not strictly reflecting the general ILPFOA population. Strict inclusion criteria were indispensable to avoid bias due to including global or medial PFOA. Thirdly, CT or MRI data, as recommended by Stäubli et al. [START_REF] Stäubli | Anatomy and surface geometry of the patellofemoral joint in the axial plane[END_REF], were not available in all cases, and X-ray does not allow fine analysis of TD, especially in case of deformities induced by severe PFOA; however, we used the classification of H. Dejour [START_REF] Dejour | Dysplasia of the femoral trochlea[END_REF][START_REF] Dejour | Factors of patellar instability: an anatomic radiographic study[END_REF], validated for radiographic use, with blinded double reading and excellent interobserver concordance. And lastly, the absence of multivariate analysis combined with the small size of the non-TD sample (n=12) prevented valgus deformity or BMI being demonstrated as risk factors for ILPFOA.

One strong point of the study was the number of patients: few previous series included so many cases of ILPFOA. The size of the sample was all the more remarkable as selection criteria were very restrictive. Postoperative recruitment enabled cases of ILPFOA associated with inflammatory arthropathy, which is diagnosed on pathologic examination, to be excluded. The study population, comprising patients suffering from ILPFOA, without excluding those with history of patellar dislocation, was typical of that seen in orthopedic surgery consultations. All in all, large sample size and very strict selection enabled ILPFOA to be analyzed more effectively than in any previous studies.

In our clinical practice, the present findings have focused the surgeon's attention on the cause of ILPFOA in preoperative consultation. Valgus deformity is rigorously analyzed on the appropriate radiographic views. If necessary, osteotomy is performed according to the site of the deformity. In all cases, it is essential to make the patient understand that weight plays an essential role in degenerative patellar pathology. Despite its recognized efficacy [START_REF] Montserrat | Partial lateral facetectomy plus Insall's procedure for the treatment of isolated patellofemoral osteoarthritis: survival analysis[END_REF][START_REF] Mofidi | Association and impact of patellofemoral dysplasia on patellofemoral arthropathy and arthroplasty[END_REF][START_REF] Yercan | The Treatment of Patellofemoral Osteoarthritis with Partial Lateral Facetectomy[END_REF][START_REF] Paulos | Partial lateral patellar facetectomy for treatment of arthritis due to lateral patellar compression syndrome[END_REF][START_REF] Wetzels | Patellofemoral osteoarthritis treated by partial lateral facetectomy: results at long-term follow up[END_REF][START_REF] López-Franco | Evaluation of a minimally aggressive method of patellofemoral osteoarthritis treatment at 10 years minimum follow-up[END_REF][START_REF] Becker | Surgical treatment of isolated patellofemoral osteoarthritis[END_REF],

LVP is a symptomatic treatment for ILPFOA and does not treat the underlying cause. It is indicated in isolation in ILPFOA associated with TD, for which patellar stabilization surgery is often no longer feasible.

Conclusion

FIGURE AND TABLE LEGENDS

  TD is found in almost 9 in 10 cases of ILPFOA. It alters the balance of stress within the patellofemoral joint, inducing osteoarthritis. Etiology should be carefully investigated in ILPFOA. Other contributing factors, and notably overweight and valgus deformity, are frequently found with no associated TD.Disclosure of interestTDL, SG, GK and CB have no conflicts of interest to disclose. SL: consultant for Smith and Nephew. ES: consultant for Corin. GK: data collection. SL: study design, correction. ES: study design, correction, supervision.

Figure 1

 1 Figure 1 Study flowchart

Table 1

 1 Demographic, clinical and radiographic data

Table 2

 2 Impact of TD on PFOA stage

Table 3

 3 PFOA stage and TD grade according to age at surgery

Table 4

 4 Comparison of the two groups according to age at surgery

Table 5

 5 Comparison of the two groups according to TD

	Figure 1
	152 native knees underwent partial lateral
	facetectomy between Nov 1998 and Sept 2019
		16 knees underwent
	20 knees had history of	concomitant osteotomy
	patellar fracture
		9 knees were diagnosed
	6 knees showed signs of medial patellofemoral	with inflammatory arthropathy
	osteoarthritis
	101 knees available for analysis

Table 3 Total

 3

		(n= 101)	p-value
		Mean age ±SD	Range
	PFOA stage			< 0.001*
	1	42.3 ± 6.8	(33.0 -62.0)
	2	46.9 ± 8.5	(30.0 -65.0)
	3	51.6 ± 10.9 (32.0 -71.0)
	4	53.9 ± 8.1	(28.0 -65.0)
	TD grade			0.009**
	None	52.7 ± 4.2	(47.0 -62.0)
	1	52.0 ± 10.6 (32.0 -71.0)
	2	49.8 ± 9.0	(32.0 -65.0)
	3	43.9 ± 9.9	(28.0 -61.0)
	PFOA=patellofemoral osteoarthritis, SD=standard deviation, TD=trochlear
	dysplasia, n=number
	*Spearman's correlation, rho=0.38 **Spearman's correlation, rho=-0.26

Funding

None.

Author contributions TL: study design, data collection, statistical analysis, article writing. SG: study design, data collection, article writing, correction. CB: study design, correction.