Florine Berthy
email: f.berthy@eren.smbh.univ-paris13.fr

Joséphine Brunin

Benjamin Allès

Anouk Reuzé

Serge Hercberg

Denis Lairon

Philippe Pointereau

François Mariotti

Julia Baudry

Emmanuelle Kesse-Guyot

Mathilde Touvier

Higher adherence to the EAT-Lancet reference diet is associated with higher nutrient adequacy in the NutriNet-Santé cohort: a cross-sectional study

Keywords: sustainable diet, nutritional quality assessment, healthy eating, food system. Trial registration number: NCT03335644

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Introduction

Currently, the greatest challenge facing food systems is providing an affordable and nutritionally adequate diet for a growing population while preserving the integrity of the planet (1)(2)[START_REF] Hlpe | Nutrition and food systems[END_REF]. The current food production is one of the main factors of environmental degradation, whereas, in 2022, numerous planetary boundaries have already been transgressed, threatening humanity's viability on Earth [START_REF] Steffen | Planetary boundaries: Guiding human development on a changing planet[END_REF][START_REF] Campbell | Agriculture production as a major driver of the Earth system exceeding planetary boundaries[END_REF][START_REF] Kemp | Climate Endgame: Exploring catastrophic climate change scenarios[END_REF]. Several studies have shown that diets based on high intakes of plant-based products, and low intakes of meat and dairy products have lower environmental impacts [START_REF] Aleksandrowicz | The Impacts of Dietary Change on Greenhouse Gas Emissions, Land Use, Water Use, and Health: A Systematic Review[END_REF][START_REF] Perignon | Improving diet sustainability through evolution of food choices: review of epidemiological studies on the environmental impact of diets[END_REF][START_REF] Wilson | Achieving Healthy and Sustainable Diets: A Review of the Results of Recent Mathematical Optimization Studies[END_REF]. Moreover, it is now established that modern diets, low in fiber and based on unhealthy energy-dense foods, animal and processed foods, that is, rich in salt, sugars and saturated fats [START_REF] Popkin | Global nutrition dynamics: the world is shifting rapidly toward a diet linked with noncommunicable diseases[END_REF], have harmful effects on health (2). Suboptimal diets, including Western diets, are therefore the third leading risk factor for mortality among adults worldwide [START_REF] Murray | Global burden of 87 risk factors in 204 countries and territories, 1990-2019: a systematic analysis for the Global Burden of Disease Study 2019[END_REF] and contribute to the development of morbidity [START_REF] Hlpe | Food security and nutrition: building a global narrative towards[END_REF][START_REF] Gbd | Diet Collaborators. Health effects of dietary risks in 195 countries, 1990-2017: a systematic analysis for the Global Burden of Disease Study 2017[END_REF](14). In contrast, diets containing low to moderate amounts of animal products and rich in plant-based foods can help lower the prevalence of these chronic diseases (2,[START_REF] Lindgren | Sustainable food systems-a health perspective[END_REF][START_REF] Clark | Multiple health and environmental impacts of foods[END_REF][START_REF] Springmann | Analysis and valuation of the health and climate change cobenefits of dietary change[END_REF]. However, these diets cover various eating practices, both healthy and unhealthy [START_REF] Satija | Plant-Based Dietary Patterns and Incidence of Type 2 Diabetes in US Men and Women: Results from Three Prospective Cohort Studies[END_REF][START_REF] Satija | Healthful and Unhealthful Plant-Based Diets and the Risk of Coronary Heart Disease in U.S. Adults[END_REF][START_REF] Baden | Changes in Plant-Based Diet Quality and Total and Cause-Specific Mortality[END_REF][START_REF] Gehring | Consumption of Ultra-Processed Foods by Pesco-Vegetarians, Vegetarians, and Vegans: Associations with Duration and Age at Diet Initiation[END_REF]. Despite not being well planned, vegetarian diets may be associated with nutritional inadequacy and an increased risk of micronutrient deficiencies [START_REF] Neufingerl | Nutrient Intake and Status in Adults Consuming Plant-Based Diets Compared to Meat-Eaters: A Systematic Review[END_REF][START_REF] Agnoli | Position paper on vegetarian diets from the working group of the Italian Society of Human Nutrition[END_REF][START_REF] Tso | Unintended Consequences: Nutritional Impact and Potential Pitfalls of Switching from Animal-to Plant-Based Foods[END_REF][START_REF] Mariotti | Dietary Protein and Amino Acids in Vegetarian Diets-A Review[END_REF].

In 2019, the EAT-Lancet Commission developed a universal planetary healthy reference diet, which is an evidence-based diet considering the multiple links between nutrition, health and the environment (2). Overall, the EAT-Lancet reference diet is a 2,500 kcal per day-diet, mainly characterized by vegetables, fruits, whole grain products, legumes, oleaginous, dairy products, and unsaturated oils. It consists of very moderate amounts of seafood, eggs, and poultry and considerably low amounts of products rich in added fats and sugars as well as animal-based products, including beef, pork and lamb.

Whether the EAT-Lancet reference diet, which is developed for global targets and setting very low or no intake values for several nutrient-rich food groups, is adequate to satisfy the nutritional needs of different populations remains debated. The EAT-Lancet reference diet has been applied, compared with various dietary guidelines, and studied in different socioeconomic and nutritional contexts; the results are inconsistent [START_REF] Lassen | Development of a Danish Adapted Healthy Plant-Based Diet Based on the EAT-Lancet Reference Diet[END_REF][START_REF] Sharma | A comparison of the Indian diet with the EAT-Lancet reference diet[END_REF][START_REF] Blackstone | Comparing the Recommended Eating Patterns of the EAT-Lancet Commission and Dietary Guidelines for Americans: Implications for Sustainable Nutrition[END_REF][START_REF] Tucci | An Italian-Mediterranean Dietary Pattern Developed Based on the EAT-Lancet Reference Diet (EAT-IT): A Nutritional Evaluation[END_REF][START_REF] Hanley-Cook | EAT-Lancet diet score requires minimum intake values to predict higher micronutrient adequacy of diets in rural women of reproductive age from five low-and middle-income countries[END_REF][START_REF] Bäck | Sustainability analysis of Finnish pre-schoolers' diet based on targets of the EAT-Lancet reference diet[END_REF][START_REF] Vallejo | Associations Between Adherence to a Dietary Index Based on the EAT-Lancet Reference Diet with Nutritional, Anthropometric and Ecological Sustainability Parameters: Results From the German DONALD Cohort Study[END_REF][START_REF] Campirano | Adherence to the EAT-Lancet Recommendations in a Sample of Mexican Health Workers[END_REF]. For example, Blackstone and Conrad observed marked differences between the EAT-Lancet reference diet and the dietary guidelines for Americans for whole grains, fruits, starches, red meat, nuts, and discretionary foods, which are mostly key components of the EAT-Lancet reference diet [START_REF] Blackstone | Comparing the Recommended Eating Patterns of the EAT-Lancet Commission and Dietary Guidelines for Americans: Implications for Sustainable Nutrition[END_REF].

Overall, these studies documented that, depending on the country and culture, compliance with the EAT-Lancet reference diet may require strong changes in an individual's dietary habits and that the nutritional quality does not frequently seem to be guaranteed.

However, the nutritional adequacy of the EAT-Lancet reference diet, favoring plant-based products and greatly limiting the consumption of animal products, has not yet been studied in the French context.

Therefore, this study aimed to investigate the nutritional quality of the diets of participants of the NutriNet-Santé cohort according to the level of adherence to the EAT-Lancet reference diet. Across various levels of adherence to the EAT-Lancet reference diet, the following were the specific objectives: 1) describe the food and nutritional intakes of the French population, 2) evaluate the nutrient quality, and 3) study the consistency between the French national recommendations and the EAT-Lancet reference diet.

Methods

Data were collected from the NutriNet-Santé study, a French web-based prospective cohort launched in 2009. Adult volunteers aged 18 years old or older were recruited from the general population through a large multimedia campaign. Registration and follow-up are made online on a dedicated website (www.etude-nutrinet-sante.fr). The NutriNet-Santé study's design and methods are described elsewhere [START_REF] Hercberg | The Nutrinet-Santé Study: a web-based prospective study on the relationship between nutrition and health and determinants of dietary patterns and nutritional status[END_REF]. The NutriNet-Santé study is conducted in accordance with the Declaration of Helsinki and was approved by the Ethics Committee of the French Institute of Health and Medical Research (IRB Inserm Research n° 0000388FWA00005831) and by the National Commission on Informatics and Liberty (CNIL n° 908450 and n°909216). This cohort is registered in ClinicalTrials.gov (NCT03335644). At inclusion, all participants signed an electronic informed consent via the online platform. This procedure is appropriate for web-based cohorts and has been validated by the abovementioned ethical and regulatory authorities.

Data collection

Sociodemographic and lifestyle factors

Participants completed a set of validated self-administered questionnaires [START_REF] Hercberg | The Nutrinet-Santé Study: a web-based prospective study on the relationship between nutrition and health and determinants of dietary patterns and nutritional status[END_REF] at baseline, in the same period during which they completed the first 24-h dietary records, and their sociodemographic and lifestyle characteristics as well as health status information were collected. Data collected included sex, age, education level, monthly household income, occupation, and marital status. Monthly household income was calculated per consumption unit (c.u.) according to a weighting system, where 1, 0.5, and 0.3 are attributed to the first adult in the household, each person aged 14 years or older, and all children under 14 years old, respectively (35). Lifestyle and anthropometric characteristics were self-reported using validated questionnaires [START_REF] Touvier | Comparison between web-based and paper versions of a self-administered anthropometric questionnaire[END_REF][START_REF] Lassale | Validity of webbased self-reported weight and height: results of the Nutrinet-Santé study[END_REF] and body mass index (BMI) was calculated from the formula weight (kg)/height in meter squared (m 2 ). Three levels of physical activity were defined based on the metabolic equivalent of task (MET) minutes per week (MET-min/week): low (<600 MET-min/week), moderate (600-1500 MET-min/week), and high (>1,500 MET-min/week).

For females, menopausal status was also collected.

Dietary data

Dietary intakes were assessed at enrollment and twice a year thereafter using a series of three non-consecutive 24-h dietary records, randomized over a 2-week period (two weekdays and one weekend day). Participants reported all food and beverages (type and quantity) consumed during a 24-h period: three main meals (breakfast, lunch, and dinner) and all other eating occasions. Supplements were not considered in nutrition intakes. Portion sizes were estimated according to standard measurements or using photographs from a previously validated photo booklet [START_REF] Moullec | Validation du manuel-photos utilisé pour l'enquête alimentaire de l'étude SU.VI.MAX. Valid Man-Photos Util[END_REF]. Collection methods were validated against biomarkers of nutritional status and conventional data collection methods [START_REF] Lassale | Correlations between Fruit, Vegetables, Fish, Vitamins, and Fatty Acids Estimated by Web-Based Nonconsecutive Dietary Records and Respective Biomarkers of Nutritional Status[END_REF][START_REF] Lassale | Validation of a Web-based, self-administered, non-consecutive-day dietary record tool against urinary biomarkers[END_REF][START_REF] Lassale | Validity of webbased self-reported weight and height: results of the Nutrinet-Santé study[END_REF]. Daily energy, macronutrient and micronutrient intakes were calculated using a published food composition table [START_REF] Arnault | Table de composition des aliments, étude NutriNet-Santé[END_REF]. Intake from composite dishes was calculated using reference recipes validated by nutrition professionals. Energy under-reporters were identified following Black's method (43) using Goldberg's cut-offs (44), and the basal metabolic rate was determined based on Schofield's equations [START_REF] Schofield | Predicting basal metabolic rate, new standards and review of previous work[END_REF] according to sex, weight, and height collected upon study enrollment.

Computation of nutritional scores

EAT-Lancet Diet Index (ELD-I)

Adherence to the EAT-Lancet reference diet was estimated using the ELD-I. This dietary score has been described elsewhere [START_REF] Kesse-Guyot | Environmental and nutritional analysis of the EAT-Lancet diet at the individual level: insights from the NutriNet-Santé study[END_REF].

The ELD-I for an individual j can be written as follows, equation ( 1):

(1) ELD-I j = where i refers to the 14 EAT-Lancet food groups and j is the individual. a i = 1 for component to limit and a i = -1 for component to promote.

Computing of the ELD-I leads to a continuous variable (positive or negative). The higher the score, the higher the adherence to the EAT-Lancet reference diet. In the present study, the ELD-I was estimated for each participant using the average of all 24-h dietary records during the first 2 years following inclusion in the NutriNet-Santé cohort. All mixed dishes have been decomposed into ingredients, which were subsequently allocated to the ELD-I food groups.

Cut-offs values are presented in Supplementary Table 1.

French nutritional recommendation scores

As complementary approaches in the study of the quality of the EAT-Lancet scheme in the French context, we calculated the following two scores: the Programme National Nutrition Santé -Guidelines Score 2 (PNNS-GS2) and the PANDiet score.

The PNNS-GS2, which reflects adherence to current French food-based dietary guidelines [START_REF] Chaltiel | Programme National Nutrition Santéguidelines score 2 (PNNS-GS2): development and validation of a diet quality score reflecting the 2017 French dietary guidelines[END_REF], includes 13 dietary components, which are divided into six adequacy components and seven moderation components.

The PANDiet is a diet quality whose objective is to estimate the probability of adequacy of nutrient intakes [START_REF] Verger | Evaluation of a Diet Quality Index Based on the Probability of Adequate Nutrient Intake (PANDiet) Using National French and US Dietary Surveys[END_REF]. This score is decomposed into the following two sub-scores: an adequacy score based on the probabilities of the adequacy of 27 nutrients and a sub-score including 6 nutrients and 12 penalty values referring to the probabilities of exceeding the upper limits of intakes. We presented the complement to 100 of the PANDiet score (100 -[PANDiet × 100]) to be consistent with estimates of the prevalence of nutritional inadequacy.

Statistical analyses

This study included participants registered in the NutriNet-Santé cohort between 2009 and 2015, and who validated at least three 24-h dietary records during the first 2 years following enrollment into the cohort. Owing to dietary intakes potentially not representative of the usual diet, female participants who were pregnant during the dietary data collection period were excluded as well as those who had missing sociodemographic or socioeconomic data and resided in overseas territories (Supplementary Figure 1).

Our sample was weighted to improve its representativeness in relation to the French population. Individual weights were calculated, by sex, according to the 2009 national census on age, presence of children aged <18 years in the household, education level, occupation status, marital status, and area of residence using the iterative proportional fitting procedure, to adjust the percentage of individuals in each stratum to the actual percentage in the French population [START_REF] Sautory | La macro Calmar. Redressement d'un échantillon par calage sur marges[END_REF]. In case of rare presence of certain socio-demographic profiles, this method can lead to very high weights. Participants with extreme weights were excluded from the analyses.

Baseline characteristics were described across weighted sex-specific quintiles (Q) of the ELD-I using mean and standard deviation or percentage. Food intakes were adjusted for total energy intake (EI) and usual nutrient intakes for usual EI without alcohol (EIWA) using the residual method [START_REF] Willett | Nutritional Epidemiology[END_REF]. Food and nutrients data were presented as means with their standard errors (SEM). P-values were estimated using the Mantel-Haenszel χ² test for dichotomized or ordinal variables, χ² for other categorical variables, and generalized linear models with linear contrast for continuous variables.

To estimate the proportion of participants meeting each specific item of the EAT-Lancet reference diet in our sample, we estimated the mean intakes for each food group considered in the EAT-Lancet reference diet for the total sample and by ELD-I quintiles and subsequently calculated the proportion of participants reaching these recommendations. For this, we used the reference values proposed by Willett et al (2).

Nutrient inadequacy was defined as the prevalence of individuals whose usual intakes were below their individual nutrient requirements. For the estimation of inadequacy prevalence, the effects of day-to-day intake variability were removed to estimate a long-term mean nutrients intake, that is, the usual nutrient intake. We performed variance reduction using the National Cancer Institute method [START_REF] Tooze | A new statistical method for estimating the usual intake of episodically consumed foods with application to their distribution[END_REF][START_REF] Tooze | A mixed-effects model approach for estimating the distribution of usual intake of nutrients: The NCI method[END_REF][START_REF] Kipnis | Modeling data with excess zeros and measurement error: application to evaluating relationships between episodically consumed foods and health outcomes[END_REF]. The usual intake modeling was performed from MIXTRAN macro followed by INDIVINT macro, using a one-part model, with age at inclusion and sex as variable parameters. Nutrient inadequacy was assessed using the estimated average requirement (EAR) cut-point method [START_REF] Carriquiry | Assessing the prevalence of nutrient inadequacy[END_REF]; for each nutrient, the threshold value considered was the estimated average requirement declined according to age and sex. The proportion of participants whose usual intake was below the EAR was estimated for each nutrient across sex and ELD-I quintiles. At the population level, this proportion represents an unbiased estimate of the proportion of participants with inadequate intakes relative to their individual requirements [START_REF] Carriquiry | Assessing the prevalence of nutrient inadequacy[END_REF]. When the EAR was not available for a nutrient, we considered the proportion of participants with a low intake, using the adequate intake (AI). For zinc and iron, the threshold values considered were those of the estimated average physiological requirements. Therefore for each participant the bioavailable zinc and iron were computed using the published formula [START_REF] Miller | Mathematical model of zinc absorption: effects of dietary calcium, protein and iron on zinc absorption[END_REF][START_REF] Armah | A complete diet-based algorithm for predicting nonheme iron absorption in adults[END_REF]. Of note, because the nutritional requirement for iron in menstruating females is not symmetrical around the population mean [START_REF]Nutrient Adequacy:: Assessment Using Food Consumption Surveys[END_REF][START_REF]Requirements of vitamin A, iron, folate and vitamin B12. Report of a Joint FAO/WHO Expert Consultation[END_REF], the EAR-cut point method could not be used for this subgroup [START_REF] Carriquiry | Assessing the prevalence of nutrient inadequacy[END_REF]. Therefore, for menstruating females we performed out the probabilistic approach based on the distribution of the physiological requirement for iron, as modelled for females of reproductive age [START_REF] De Gavelle | Patterns of Protein Food Intake Are Associated with Nutrient Adequacy in the General French Adult Population[END_REF] . The EAR and AI used were those proposed by the French Agency for Food, Environmental and Occupational Health Safety (ANSES) (60) (Supplementary Table 2). Furthermore, we calculated the PANDiet complementary across the ELD-I quintiles.

Finally, sensitivity analyses were performed. First analyses were performed after removing prevalent cancer, cardiovascular diseases, and types 1 and 2 diabetes. Subsequently, we estimated the proportion of participants meeting the recommendation for each component of the PNNS-GS2, by the adherence level to the ELD-I to investigate the coherence between the EAT-Lancet reference diet and the official French dietary guidelines.

All tests were two-sided, and P < 0.05 was considered statistically significant. Statistical analyses were performed using SAS ® version 8.3 (SAS Institute) and R ® version 4.0.4 (R Foundation).

Results

Sociodemographic and lifestyle characteristics

The final study sample included 98,465 participants followed between 2009 and 2015.

(Flowchart in Supplementary Figure 1). Participant characteristics in the overall sample and across quintiles of the ELD-I are presented in Table 1. The sample was 78% female, and the average ELD-I score was 41.2 (range, -161.5 to 428.6) points (Supplementary Table 3).

Better adherence to the EAT-Lancet reference diet was more frequently associated with older age and lower physical activity.

Food consumption and usual nutrient intakes according to the ELD-I

By construction, higher consumption of fruits, vegetables, legumes, nuts, and seafood was associated with higher ELD-I scores. Conversely, a higher score was associated with lower consumption of meat, eggs, tubers, fat, fatty and/or sweetened products, and sweetened soft drinks (Table 2).

Participants with high adherence to the EAT-Lancet reference diet had, on average, lower EI than those with low adherence (Table 3). We observed a minimal decrease in the overall protein intake as the ELD-I increases; however, across ELD-I sex-specific quintiles, the percentage of animal protein decreased in favor of plant proteins. Compared with the participants with the lowest ELD-I, those with the highest had slightly increased carbohydrate consumption, whereas fat intake decreased. Moreover, as the score increased, so did the fiber intake. Across ELD-I quintiles, an increase in the intake of beta-carotene, calcium, copper, total iron, iodine, potassium, magnesium, manganese, phosphorus, vitamin A and vitamin B9 and vitamin C was observed while intake of cholesterol, vitamin B12 and heme-iron intake decreased. The polyunsaturated fatty-acid, zinc, retinol, sodium, selenium, vitamins B1, B2, B3, B5, B6 and vitamin E intake was similar across quintiles.

The proportion of individuals meeting the different EAT-Lancet reference diet components widely varied across food groups (Figure 1 and Supplementary Table 4). The components for which the proportions of participants meeting the recommendations varied the most across quintiles were fruits, vegetables, and red meat. However, it was observed that for legumes, nuts, and whole grains as well as unsaturated oils, the recommendations were overall very poorly met regardless of the ELD-I.

Nutrient quality

The complement to 100 of the PANDiet score and mean values of prevalence inadequacy for main macronutrients and micronutrients are shown in Table 4.

PANDiet complement gradually decreased across the ELD-I. Inadequacy prevalence for vitamins B9 and C gradually decreased across the ELD-I quintiles. This was also the case for vitamin A and calcium; however, this decrease stagnates between the fourth and fifth quintiles. Conversely, zinc was the only nutrient for which the inadequacy prevalence was the highest in quintile 5 (42.9 %) and the lowest in quintile 1 (38.6 %). In our sample, inadequacy intakes for protein (1.8 %), copper (1.9 %), vitamin B3 (3.6 %) and iron in males and menopausal females (1.4 %) were small. In non-menopausal females, the prevalence of bioavailable iron inadequacy of approximately 35% equal in all quintiles. Regarding fiber intake, although the inadequacy prevalence decreased with increasing ELD-I, the intake was by far insufficient whatever the quintile. The results of the sensitivity analysis after removing participants with prevalent chronic diseases were unchanged (Supplementary Table 5).

Sex differences in the prevalence of nutrient inadequacy are presented in Supplementary Table 6

As shown in supplementary table 7, the average proportion of participants with an intake is considered low (i.g. below the AI for the French population); however, in some cases, these intakes may potentially meet their individual micronutrient requirements. For vitamins B1, B6, E, magnesium, and manganese, this proportion gradually decreased across the ELD-I quintiles. Moreover, for selenium, vitamin B1 and magnesium a high prevalence of participants had intakes that were considered low. Regarding phosphorus, < 1% of our sample had intakes that were considered low.

Consistency between the EAT-Lancet reference diet and the French dietary recommendations

The PNNS-GS diet quality score gradually increased across ELD-I quintiles (Table 5).

Regarding adherence to individual components of the PNNS-GS2 across ELD-I quintiles (Supplementary Figure 2 andTable 5), we observed similar trends for the components common to the EAT-Lancet reference diet. That is, across ELD-I quintiles, we observed a marked increase in the proportion of participants following the recommendations for fruits, vegetables and red meat as well as moderate-to-low proportions in whatever quintiles for nuts, legumes, fish, and dairy products. Regarding the groups of foods specific to the PNNS, including processed meats, alcohol, and salt, the proportion of participants respecting the recommendations decreased in the first quintile and subsequently increased in the other quintiles. The proportion of participants following the recommendations for salt was equal in quintiles 1 and 5 and lower in the fifth quintile for alcohol consumption.

Discussion

In the present study, we investigated the dietary and usual nutrient quality of French adults across adherence levels to the EAT-Lancet reference diet. Attention is needed regarding fiber, calcium, vitamin C, bioavailable zinc, and bioavailable iron (in non-menopausal females) intakes. Nutrient inadequacy regarding macronutrient as protein and fiber decreased across ELD-I. For micronutrients, the lowest prevalence of inadequacy was observed for the participants with the highest adherence to the EAT-Lancet reference diet. Differences in food consumption according to ELD-I levels were substantial for only a few foods, with plantbased consumption being too low for any adherence level to the EAT-Lancet reference diet. Therefore, participants in the highest ELD-I score quintile remain far from meeting the recommendations of the EAT-Lancet reference diet. Additionally, the specific components of the French PNNS recommendations (salt, alcohol, and processed meat) were not better followed for higher adherence to the EAT-Lancet reference diet.

First, as noted in other studies [START_REF] Tucci | An Italian-Mediterranean Dietary Pattern Developed Based on the EAT-Lancet Reference Diet (EAT-IT): A Nutritional Evaluation[END_REF][START_REF] Vallejo | Associations Between Adherence to a Dietary Index Based on the EAT-Lancet Reference Diet with Nutritional, Anthropometric and Ecological Sustainability Parameters: Results From the German DONALD Cohort Study[END_REF], animal protein intake decreased across ELD-I quintiles. Although this decrease was largely offset by an increase in plant protein intake, as Hanley-Cook and Vallejo [START_REF] Hanley-Cook | EAT-Lancet diet score requires minimum intake values to predict higher micronutrient adequacy of diets in rural women of reproductive age from five low-and middle-income countries[END_REF][START_REF] Vallejo | Associations Between Adherence to a Dietary Index Based on the EAT-Lancet Reference Diet with Nutritional, Anthropometric and Ecological Sustainability Parameters: Results From the German DONALD Cohort Study[END_REF], we observed, a decrease in the proportion of energy provided by protein with increasing adherence to the EAT-Lancet reference diet.

Nevertheless, current evidence shows that, in high-income countries, plant-based diets can provide sufficient protein and essential amino acid intakes [START_REF] Mariotti | Dietary Protein and Amino Acids in Vegetarian Diets-A Review[END_REF][START_REF] Gardner | Maximizing the intersection of human health and the health of the environment with regard to the amount and type of protein produced and consumed in the United States[END_REF]; therefore, more attention should be focused on fiber-related issues. The increase in plant-based foods promoted by the EAT-Lancet reference diet unequivocally allowed for an increase in fiber intake whatever the context [START_REF] Lassen | Development of a Danish Adapted Healthy Plant-Based Diet Based on the EAT-Lancet Reference Diet[END_REF][START_REF] Tucci | An Italian-Mediterranean Dietary Pattern Developed Based on the EAT-Lancet Reference Diet (EAT-IT): A Nutritional Evaluation[END_REF][START_REF] Vallejo | Associations Between Adherence to a Dietary Index Based on the EAT-Lancet Reference Diet with Nutritional, Anthropometric and Ecological Sustainability Parameters: Results From the German DONALD Cohort Study[END_REF]. In our sample, the participants, whatever their ELD-I quintile, were very far from the cut-off point provided by the PNNS. Higher adherence to plant-based components, including fruits, vegetables, legumes, and whole grains, would also lead to better adherence to the French reference values (30 g/day). Contrary to other studies [START_REF] Lassen | Development of a Danish Adapted Healthy Plant-Based Diet Based on the EAT-Lancet Reference Diet[END_REF][START_REF] Tucci | An Italian-Mediterranean Dietary Pattern Developed Based on the EAT-Lancet Reference Diet (EAT-IT): A Nutritional Evaluation[END_REF][START_REF] Vallejo | Associations Between Adherence to a Dietary Index Based on the EAT-Lancet Reference Diet with Nutritional, Anthropometric and Ecological Sustainability Parameters: Results From the German DONALD Cohort Study[END_REF], in the French context, we noted a decrease in the total fat intake across ELD-I quintiles. This should be ascribed to the fact that higher scores are mainly related to higher fruit and vegetable consumption and the decrease in meat, with lower increases in other products, such as nuts, which therefore cannot contribute to limiting the decrease in fat intake.

In our study, except for bioavailable zinc, the prevalence of nutrient inadequacy decreased with increasing adherence to the EAT-Lancet reference diet, particularly for vitamins C and B9, wherein the inadequacy prevalence was greatly reduced between the least and most adherent to the reference diet. In the study by Tucci et al. [START_REF] Tucci | An Italian-Mediterranean Dietary Pattern Developed Based on the EAT-Lancet Reference Diet (EAT-IT): A Nutritional Evaluation[END_REF], zinc and vitamin B12 intakes were lower in participants who followed the EAT-Lancet reference diet; however, in these participants, intakes of these nutrients both met the national reference values, whereas calcium intakes were inadequate. A study conducted in the Danish population reported similar results for vitamin B12 and calcium [START_REF] Lassen | Development of a Danish Adapted Healthy Plant-Based Diet Based on the EAT-Lancet Reference Diet[END_REF]. In these two populations, the insufficient intakes among participants who followed better the EAT-Lancet reference diet were explained by the low consumption of animal-based foods and more particularly of dairy products for calcium; however, dairy products are encouraged in the EAT-Lancet reference diet. However, in our study, the participants with higher adherence to the EAT-Lancet reference diet showed some intakes of these products, and in particular a higher consumption of dairy products than those in the first quintiles, which may explain that a high prevalence of inadequate intakes of calcium, zinc and vitamin B12 was not observed. Our results were consistent with the results of an observational study conducted on a sample of French adults, simulating a total or partial replacement of meat by plant-based substitutes, resulting in a decrease in the adequacy of vitamin B12 and bioavailable zinc and iron [START_REF] Salomé | Substituting Meat or Dairy Products with Plant-Based Substitutes Has Small and Heterogeneous Effects on Diet Quality and Nutrient Security: A Simulation Study in French Adults (INCA3)[END_REF]. Nutritional references for bioavailable iron and zinc often appear to be the primary limiting factors in a transition to a plant-based diet; however, official thresholds lower than current values, not jeopardizing overall health, would allow for the identification of healthier diets [START_REF] Dussiot | Modeled healthy eating patterns are largely constrained by currently estimated requirements for bioavailable iron and zinc-a diet optimization study in French adults[END_REF]64). Furthermore, among non-menopausal females, although the prevalence of inadequacy was high, they were not reduced in the quintiles where meat consumption was the highest.

Overall, nutritional quality was better in the highest ELD-I quintiles. However, a study by Hanley-Cook [START_REF] Hanley-Cook | EAT-Lancet diet score requires minimum intake values to predict higher micronutrient adequacy of diets in rural women of reproductive age from five low-and middle-income countries[END_REF] showed that in some populations, it is essential that the diet still include some nutrient-dense foods for nutritional adequacy to be improved by the EAT-Lancet reference diet. In our study the participants with the highest adherence to the EAT-Lancet reference diet did not attain the consumption target for all 14 components. In our study, participants with high adherence to the EAT-Lancet reference diet had a suboptimal and improvable diet. For example, on average they had a very high tuber and starchy vegetable consumption and a very low legume, whole grain, and nut consumption. However, dietary intakes remained sufficiently varied to cover most nutritional needs. However, other studies that have developed a plant-based diet that meets the EAT-Lancet targets adapted to Italian [START_REF] Tucci | An Italian-Mediterranean Dietary Pattern Developed Based on the EAT-Lancet Reference Diet (EAT-IT): A Nutritional Evaluation[END_REF] and Danish [START_REF] Lassen | Development of a Danish Adapted Healthy Plant-Based Diet Based on the EAT-Lancet Reference Diet[END_REF] intakes showed that these highly strict targets can be challenging in achieving certain national references values.

Dietary recommendations varied from country to country and were nearly consistent with the EAT-Lancet reference diet. The PNNS-GS2 was consistent with the EAT-Lancet reference diet for fruits and vegetables, dairy products, and unsaturated fats (65); components for which (except for fruits) the Dietary Guidelines for Americans recommendations were also consistent with those of the EAT-Lancet Commission [START_REF] Blackstone | Comparing the Recommended Eating Patterns of the EAT-Lancet Commission and Dietary Guidelines for Americans: Implications for Sustainable Nutrition[END_REF]. However, the two national recommendations differed from the EAT-Lancet reference diet in several aspects, including the recommended serving sizes of whole grains, red meat and poultry, nuts, and legumes, which were essential components of this reference diet. These facts show the significance of adapting dietary recommendations to the habits and cultures of each country, to account for the variability in the food offered and cultural specificities [START_REF] Alexandropoulou | Basics of Sustainable Diets and Tools for Assessing Dietary Sustainability: A Primer for Researchers and Policy Actors[END_REF]. Processed meat, alcohol, or salt, which are typical components of the French diet and therefore are to be limited according to the PNNS (65), are not specifically considered in the EAT-Lancet reference diet and that higher adherence to this reference diet tended to result in lower compliance with recommendations related to these components. These disparities in components between the EAT-Lancet reference diet and the French PNNS recommendations partly explain the lower associations previously observed between the ELD-I score and the occurrence of cancers and the nonsignificant associations with cardiovascular diseases (67) compared with those with the PNNS-GS2 score [START_REF] Chaltiel | Prospective association between adherence to the 2017 French dietary guidelines and risk of death, CVD and cancer in the NutriNet-Santé cohort[END_REF], wherein the inverse associations were highly significant. These two studies focused on existing dietary recommendations, defined differently (EAT-Lancet and Official French dietary guidelines), and the risk of chronic diseases. Additionally, it is observed that intakes were similar between quintiles, for some food groups and nutrients, suggesting that the differences observed in terms of health impact were more related to those components for which large differences were observed such as fruits, vegetables, red meat, sweet products, and whole grains for foods, and vitamins C, B9, and magnesium for nutrients.

Moreover, adherence to the EAT-Lancet reference diet has been studied in other settings, particularly in Gambia [START_REF] Ali | Adherence to EAT-Lancet dietary recommendations for health and sustainability in The Gambia[END_REF]. In this population, as in our study, the intake of unhealthy plantbased foods, including sugars and refined cereals, was excessively high and that of healthy plant-based foods was excessively low. However, in the Gambian context, the consumption of red and white meat and dairy products was below the EAT-Lancet reference diet range in most households. In this country, beyond the financial barrier, the production and supply of these food groups are challenging. Furthermore, consistent with our study, Bäck et al [START_REF] Bäck | Sustainability analysis of Finnish pre-schoolers' diet based on targets of the EAT-Lancet reference diet[END_REF] estimated the proportion of participants meeting each of the EAT-Lancet reference diet target in Finnish children. In both populations, very low proportions (<10%) of participants met the EAT-Lancet reference diet target for whole grains, legumes, nuts, saturated oils, and sugars, which are key components of the reference diet. These different comparisons confirm the need for not only adapting dietary recommendations to cultural habits [START_REF] Drewnowski | Analysing the affordability of the EAT-Lancet diet[END_REF][START_REF] Hirvonen | Affordability of the EAT-Lancet reference diet: a global analysis[END_REF] and the capacities of each country in terms of production and provisioning but also for specifically adapting them to individual preferences since a remarkable change from their usual food consumption could make several individuals reluctant to adhere to these new reference diet [START_REF] Collins | Sustainable Food Consumption at a Sub-national Level: An Ecological Footprint, Nutritional and Economic Analysis[END_REF]. In our study, we observe that the recommendations were followed differently according to participants profiles and that the EAT-Lancet reference diet was more followed by older and higher income participants. Therefore, it is also significant to adapt the messages related to the dietary recommendations to less-adherent individuals.

This study had some limitations. First, there is a lack of official values for the EAR of certain nutrients. When these values were unavailable although the AI was, we used the AI, which provides an indication of the proportion of participants with low intakes compared with an arbitrary threshold; however, for some participants, this intake may be sufficient as regards their individual physiology. Furthermore, some limitations inherent to the NutriNet-Santé cohort should be acknowledged. Indeed, owing to the voluntary-basis recruitment, the participants of the NutriNet-Santé cohort may be more health conscious and therefore exhibit healthier dietary habits [START_REF] Andreeva | Comparison of the sociodemographic characteristics of the large NutriNet-Santé e-cohort with French Census data: the issue of volunteer bias revisited[END_REF][START_REF] Andreeva | Comparison of Dietary Intakes Between a Large Online Cohort Study (Etude NutriNet-Santé) and a Nationally Representative Cross-Sectional Study (Etude Nationale Nutrition Santé) in France: Addressing the Issue of Generalizability in E-Epidemiology[END_REF] that may differ from those of the general population in particular regarding health and risk factors including diet. However, the large sample includes usually inaccessible individuals, including young adults, older or jobless population [START_REF] Andreeva | Comparison of the sociodemographic characteristics of the large NutriNet-Santé e-cohort with French Census data: the issue of volunteer bias revisited[END_REF].

However, this limited representativeness is minimized herein by weighting on a number of socioeconomic characteristics to best mimic the national population. Moreover, the small number of studies on the topic and the disparities in dietary habits between countries make comparisons challenging.

However, our study also exhibited significant strengths. First, we have used very detailed and high-quality nutritional data, with an average number of 5.9 24-h dietary records per participant. Additionally, the dietary assessment method used in the NutriNet-Santé cohort was validated by comparing with urinary and blood biomarkers [START_REF] Lassale | Correlations between Fruit, Vegetables, Fish, Vitamins, and Fatty Acids Estimated by Web-Based Nonconsecutive Dietary Records and Respective Biomarkers of Nutritional Status[END_REF][START_REF] Lassale | Validation of a Web-based, self-administered, non-consecutive-day dietary record tool against urinary biomarkers[END_REF] as well as supervised assessment performed by dieticians [START_REF] Lassale | Validity of webbased self-reported weight and height: results of the Nutrinet-Santé study[END_REF].Furthermore, the nutritional adequacy study was performed on usual consumption data, which allows limiting the intra-individual variation.

Additionally, to better consider the ingredients of different foods, complex recipes were disaggregated into individual ingredients. Lastly, the very large sample of participants allows assessing a wide range of dietary profiles.

Conclusion

In French context, overall, although some key nutrient intakes remain challenging, including fibers, calcium, bioavailable zinc and vitamin C, a higher adherence to the global EAT-Lancet reference diet is associated with higher nutritional adequacy. In the context of environmental emergency, the inadequacy prevalence in certain nutrients should not be a barrier to a transition to a higher proportion of plant-based foods in the diet, especially since, overall, these diets present better nutritional profiles. However, the acceptability of this type of recommendation is a major issue of this diet as well as accessibility and cost, which must be studied to determine if they are fully compatible with a sustainable diet. Abbreviations: Q: Quintile; ELD-I: EAT-Lancet Diet Index; EIWA: Energy intake without alcohol; PUFA: Poly unsaturated fatty acids; MUFA: mono unsaturated fatty acids; SFS: saturated fatty acids. 1 P-value for comparison between quintiles of ELD-I estimated by linear contrast models. All p-values were significant, except added carbohydrates (p=0.1087). 2 Sex-specific cut-offs for quintiles of EAT-Lancet Diet Index (ELD-I) were -161.5/22.2/36.5/48.1/62.4/428.6 for females and -148.7/18.2/31.8/42.5/55.7/332.2 for males. 3 Values are means (SD). 4 Means (standard errors) adjusted for energy intake without alcohol using the residual method, except for alcohol.

Weighted sex-specific quintiles of ELD-I

2 Q1 Q2 Q3 Q4 Q5
Energy intake (kcal) 3 1,829.2 (424.9) 1,897.9 (385.1) 1,888.7 (366.5) 1,865.5 (357.2) 1,791.7 (357.1) Energy intake without alcohol (kcal) 2 <.0001 Mean (standard deviation) for quantitative variables and percentages for qualitative variables. 1 The probability of nutrient intakes below the estimated average requirements for the French population, %. Probability estimated only for nutrients for which ANSES has proposed an EAR. 2 Sex-specific cut-offs for quintiles of EAT-Lancet Diet Index (ELD-I) were -161.5/22.2/36.5/48.1/62.4/428.6 for females and -148.7/18.2/31.8/42.5/55.7/332.2 for males. 3 P-value for comparison across weighted quintiles of ELD-I estimated by test from generalized linear models with linear contrast for numeric variables and Mantel-Haenszel χ² for binary variables. 4 Complementary to 100 of the diet quality index based on probability of adequate nutrient intake (100 -[PANDiet × 100]) (n=98,120). 5 Due to the non-symmetry distribution around the iron requirements average in non-menopausal females, the EAR-cut method is not applicable in this sub-population. Bioavailable iron was obtained using complementary to 100 of the probability of adequate nutrient intake as calculated in the PANDiet.

Table 5 .

 5 Proportion (%) of participants meeting each PNNS recommendation 1 according to weighted sex-specific quintiles of the EAT-Lancet Diet Index. NutriNet-Santé study, 2009 -

Table 2 . Daily food consumption 1 according to weighted sex-specific quintiles of the EAT-Lancet Diet Index. NutriNet-Santé study, 2009 -2015, France (n=98,465)

 2

		Target 1			Weighted sex-specific quintiles 3
		(g/day)	All	Q1	Q2	Q3	Q4	Q5	P-trend 4
	Whole grains	≥ 232	45.4 (60.1)	26.2 (47.7)	35.2 (50.7)	42.8 (54.3)	52.3 (59.2)	70.3 (73.2)	<.0001
	Tubers and starchy vegetables ≤ 50	65.0 (60.4)	82.0 (80.4)	68.5 (58.9)	63.7 (54.7)	59.8 (51.5)	51.2 (51.8)	<.0001
	Vegetables	≥ 300 309.6 (185.3) 212.1 (152.0) 249.7 (142.9) 291.2 (140.8)	342.9 (148.5)	452.0 (224.4) <.0001
	Fruits	≥ 200 263.8 (211.5) 107.6 (116.1) 160.4 (112.7) 221.0 (121.9)	308.4 (132.7)	521.3 (240.0) <.0001
	Dairy foods	≤ 250 225.9 (210.3) 238.0 (219.4) 229.1 (205.7) 227.4 (196.0)	239.1 (201.5)	258.0 (232.2) <.0001
	Protein sources								<.0001
	Beef and lamb	≤ 7	30.6 (46.7)	70.3 (78.2)	32.0 (36.6)	22.0 (29.5)	16.9 (25.5)	11.9 (23.5)	<.0001
	Pork	≤ 7	17.5 (30.0)	32.6 (50.7)	19.1 (26.9)	15.4 (22.9)	12.4 (19.7)	8.1 (16.4)	<.0001
	Poultry	≤ 29	37.8 (45.3)	48.6 (64.8)	40.8 (43.1)	35.4 (38.4)	33.9 (38.5)	30.3 (38.2)	<.0001
	Eggs	≤ 13	20.5 (27.9)	31.4 (44.4)	21.3 (25.6)	18.3 (22.6)	16.7 (19.9)	14.8 (20.2)	<.0001
	Fish	≥ 28	43.8 (49.9)	37.9 (59.0)	40.7 (48.3)	42.4 (44.8)	45.8 (44.2)	51.9 (52.6)	<.0001
	Legumes	≥ 75	15.8 (32.1)	12.8 (30.4)	14.2 (29.2)	15.9 (31.9)	16.3 (29.2)	19.7 (38.3)	<.0001
	Dry beans, lentils and peas	≥ 50	14.3 (32.3)	12.6 (30.5)	13.7 (29.4)	15.0 (31.3)	14.6 (29.9)	15.5 (39.1)	<.0001
	Soy foods	≥ 25	1.5 (13.8)	0.2 (5.2)	0.5 (7.2)	0.9 (8.9)	1.7 (13.7)	4.2 (23.8)	<.0001
	All nuts	≥ 50	5.7 (17.7)	1.4 (7.0)	2.6 (9.5)	4.2 (11.4)	6.9 (16.1)	13.4 (29.9)	<.0001
	Peanuts	≥ 25	1.8 (7.4)	0.3 (2.7)	0.7 (3.8)	1.2 (4.4)	2.2 (6.7)	4.6 (13.0)	<.0001
	Tree nuts	≥ 25	3.9 (11.3)	1.1 (5.1)	1.9 (6.6)	3.0 (8.2)	4.7 (10.5)	8.8 (18.4)	<.0001
	Added fats								<.0001
	Unsaturated oils	≤ 40	7.0 (9.4)	5.3 (9.1)	6.1 (8.4)	6.9 (8.7)	7.9 (9.5)	9.0 (10.5)	<.0001
	Saturated oils	≤ 11.8	0.0 (0.1)	0.0 (0.0)	0.0 (0.0)	0.0 (0.2)	0.0 (0.0)	0.0 (0.1)	0.13
	Added sugars	≤ 31	44.5 (25.8)	54.7 (35.7)	50.5 (25.8)	45.1 (21.7)	39.9 (19.4)	32.1 (18.7)	<.0001
	1 Food consumption (g/d) standardized about 2,500 kcal/day.
	2 Dietary targets of the EAT-Lancet reference diet.
	3 Sex-specific cut-offs for quintiles of EAT-Lancet Diet Index (ELD-I) were -161.5/22.2/36.5/48.1/62.4/428.6 for females and -
	148.7/18.2/31.8/42.5/55.7/332.2 for males.
	4 P-value for comparison across quintiles of ELD-I estimated by linear contrast models.

Table 3 . Daily usual nutrient intakes according to weighted sex-specific quintiles of the EAT-Lancet Diet Index 1 . NutriNet-Santé study, 2009 -2015, France (n=98,465)

 3

Table 4 . Prevalence of nutrient inadequacy 1 , full sample, and by weighted sex-specific quintiles of the EAT-Lancet Diet Index. NutriNet-Santé study, France, 2009 -2015 (n=98,465)

 4

		All	Q1	Weighted sex-specific quintiles of ELD-I Q2 Q3 Q4	Q5	P-value 3
	PANDiet complement to 100 4	36.6 (8.7)	41.3 (8.2) 39.3 (7.5) 37.4 (7.5) 34.5 (7.5) 30.2 (8.1)	<.0001
	Proteins	1.8	3.1	1.5	1.5	1.1	2.0	<.0001
	Fibers	95.9	99.5	98.9	98.3	95.9	86.7	<.0001
	Vitamin A	6.4	11.9	6.5	5.2	3.9	4.7	<.0001
	Vitamin B3	3.6	4.0	3.4	3.4	3.5	3.5	0.01
	Vitamin B9	18.4	37.8	23.7	15.7	9.6	5.5	<.0001
	Vitamin C	34.6	59.0	45.7	34.7	22.8	10.8	<.0001
	Calcium	27.9	39.0	29.4	24.6	23.2	23.3	<.0001
	Copper	1.9	4.7	2.1	1.4	0.9	0.6	<.0001
	Bioavailable iron
	Males and menopausal females	1.4	2.9	1.2	0.7	0.9	1.6	<.0001
	Non-menopausal females 5	35.0 (23.7) 33.7 (26.2) 35.9 (23.6) 35.7 22.7) 34.7 (22.5) 35.4 (23.6)	0.0026
	Bioavailable zinc	40.8	38.6	40.3	40.8	41.2	42.9

Proportion of participants meeting each EAT-Lancet reference diet item according to weighted sex-specific quintiles of the EAT-Lancet Diet Index. NutriNet-Santé study, 2009 -2015, France (n=98,465)

	Figure 1.
			.4	11.9	27.7	47.2	73.3	93.4	<0.0001
	Organic fruits and vegetables 4 Nuts	Most of the time ≥ 1 serving/ d	11.1 5.1	5.5 1.0	8.0 2.1	10.2 4.0	12.8 6.9	17.9 10.9	<0.0001 <0.0001
	Legumes	≥ 1 servings / week	4.7	3.8	4.9	4.7	4.3	6.0	<0.0001
	Organic legumes 4	Most of the time	10.1	3.6	6.2	9.0	12.4	18.0	<0.0001
	Whole grain food	1-2 servings/ d	22.3	11.4	16.5	20.4	27.3	34.8	<0.0001

The following are considered: prevalent cases of type 1 and type 2 diabetes, cancers excluding basal cell cancer and cardiovascular diseases.

Among

75,890 participants.

Acknowledgements

We thank Thi Hong Van Duong, Régis Gatibelza, Jagatjit Mohinder and Aladi Timera (computer scientists); Fabien Szabo de Edelenyi, Ph.D. (data management supervisor); Julien Allegre, Nathalie Arnault, Laurent Bourhis, Nicolas Dechamp (data-manager/statisticians); Paola Ivroud (health event validator); Maria Gomes, Mirette Foham (Nutrinautes support), Cédric Agaesse, Rébecca Lutchia, Alexandre De Sa (dietitians); Younes Esseddik (IT supervisor); and Nathalie Druesne-Pecollo, Ph.D. (operational coordinator) for their technical contribution to the NutriNet-Santé study.

We thank all the volunteers of the NutriNet-Santé cohort.

Funding

Funding statement and statement of the independence of researchers from funders. The NutriNet-Santé study was supported by the following public institutions: Ministère de la Santé, Santé Publique France, Institut National de la Santé et de la Recherche Médicale (Inserm), Institut national de recherche pour l'agriculture, l'alimentation et l'environnement (INRAE), Conservatoire National des Arts et Métiers (CNAM) and Université Sorbonne Paris Nord. FB was supported by a Doctoral Fellowship from Université Sorbonne Paris Nord -Galilée Doctoral School.

Data sharing statement

Analytic code will be made available upon request pending. Researchers from public institutions can submit a collaboration request including information on the institution and a brief description of the project to collaboration@etude-nutrinet-sante.fr. All requests will be reviewed by the steering committee of the NutriNet-Santé study. If the collaboration is accepted, a data access agreement will be necessary and appropriate authorizations from the competent administrative authorities may be needed. In accordance with existing regulations, no personal data will be accessible.

Authors' contributions:

The authors' contributions were as follows: EKG and FB designed the study. FB performed statistical analyses and wrote the manuscript; EKG supervised statistical analysis and paper writing. All authors: contributed to the data interpretation and revised each draft for important intellectual content. All authors read and approved the final manuscript. FB and EKG had full access to all the data in the study, EKG takes responsibility for the integrity of the data and the accuracy of the data analysis, she is the guarantor. The corresponding author (FB) attests that all listed authors meet authorship criteria and that no others meeting the criteria have been omitted.

Transparency statement

Dr Emmanuelle Kesse-Guyot (the guarantor) affirms that the manuscript is an honest, accurate, and transparent account of the study being reported; that no important aspects of the study have been omitted; and that any discrepancies from the study as planned have been explained.

Conflict of Interest

The authors declare no conflict of interest.

Organic legumes 4 Most of the time 4 Dietary index reflecting the adherence to the 2017 French food-based dietary guidelines, penalized on energy intake (n=76,252). 5 Dietary index reflecting the adherence to the 2017 French food-based dietary guidelines, penalized on energy intake and simplified (n=92,770). 6 Among 76,252 participants.


Yoan Boussès
email: yoan.bousses@mines-paristech.fr

Nathalie Brulat-Bouchard

Pierre-Olivier Bouchard

Yannick Tillier

A numerical, theoretical and experimental study of the effect of thermocycling on the matrix-filler interface of dental restorative materials

1

1) Introduction

Polymer resin composites are widely used in the restoration of dental decays. In an oral environment, they are facing an aggressive environment. Mechanically, mastication produces complex loads on restorations. Other phenomena such as bruxism cause significant wear to the composites. Chemically, saliva creates an aqueous medium capable of damaging composites. As polar molecules, dental polymers are likely to absorb water. Moreover, the presence of ions can accelerate the hydrolysis of polymer molecules. Food residues also contribute to the degradation of restorations. Last but not least, teeth can face sudden temperature variations because of hot and cold food for example. Due to different thermal expansion coefficients between the tooth, the resin and fillers, thermal variations cause stress in a restoration. It is noteworthy not only at the interface between the tooth and the composite, but also at the interface between the matrix and the fillers.

For these reasons, it is important to study the stability of resin composites over time. In particular, a restoration must keep its mechanical properties unchanged. Several strategies exist to simulate the influence of an oral environment. One of them is to focus on thermal variations in an aqueous environment in vitro. The samples are alternatively plunged into "hot" and "cold" liquids. This process is called thermocycling; it does not take into consideration mechanical fatigue or wear phenomena.

Water is frequently used, but some experiments are done with alcohol or artificial saliva, that is water to which specific ions were added [START_REF] Brendeke | Effect of physicochemical aging conditions on the composite-composite repair bond strength[END_REF]. Moreover, a high diversity of experimental conditions are used because ISO 4049 for polymer-based restorative materials does not impose any standard protocol [START_REF] Iso | Dentistry -Polymer-based restorative materials[END_REF]. From 1970 to 1998, Gale did a review of thermal cycling procedures for laboratory testing of dental restorations [START_REF] Gale | Thermal cycling procedures for laboratory testing of dental restorations[END_REF]. This work was continued by Morresi from 1999 to 2014 [START_REF] Morresi | Thermal cycling for restorative materials: Does a standardized protocol exist in laboratory testing? A literature review[END_REF]. Systematically, low and high temperatures were recorded, as well as dwell times, transfer times and numbers of cycles. There seems to be a consensus for bath temperatures of 5°C and 55°C, especially in recent studies. Indeed, these two extreme temperature values correspond to the pain thresholds of the human body [START_REF] Palmer | Temperature extremes produced orally by hot and cold liquids[END_REF]. Such an extreme variation can correspond to the alternating consumption of coffee and ice cream for example. Therefore it is assumed that food with temperatures above or below these threshold values will not be kept in mouth.

The other parameters are more subjected to variations. Number of cycles varied from 100 to 100 000 cycles. However a median value of 500 cycles was found by Gale. The author also suggested that 10 000 cycles correspond to one year of clinical function. This hypothesis assumes that 20 to 50 thermal cycles occur in one day. This equivalence seems to be shared by many authors, but is also disputed. Dwell times are very different too. Some authors considered that such temperatures could not be tolerated for more than a few seconds [START_REF] Plant | The heat evolved and temperatures attained during setting of restorative materials[END_REF] whereas some numerical simulations suggested that close to one minute of immersion is necessary to homogenize the temperature at the centre of the samples. Dale reported a range from 4 s to 20 min, with a median value of 30 s for dwell time.

Regarding the transfer time, ISO 11405 for testing of adhesion to tooth structure [START_REF] Iso | Dentistry -Polymer-based restorative materials[END_REF] recommends between 5 and 10 s. However, the information was not systematically mentioned by the authors. In fact, most parameters seem to be chosen on the basis of convenience without any real justification for the choices made.

With such varied protocols and composites tested, results are very scattered. Some authors found a drastic drop in properties for short artificial aging periods [START_REF] Ilie | Macro-, micro-and nano-mechanical investigations on silorane and methacrylatebased composites[END_REF][START_REF] Egilmez | Does artificial aging affect mechanical properties of CAD/CAM composite materials[END_REF], whereas others observed a plateau before a more or less progressive decrease of properties [START_REF] Ilie | Macro-, micro-and nano-mechanical investigations on silorane and methacrylatebased composites[END_REF][START_REF] Brendeke | Effect of physicochemical aging conditions on the composite-composite repair bond strength[END_REF][START_REF] Egilmez | Does artificial aging affect mechanical properties of CAD/CAM composite materials[END_REF][START_REF] Ayatollahi | Effects of temperature change and beverage on mechanical and tribological properties of dental restorative composites[END_REF]. Some authors never found any decrease [START_REF] Ilie | Macro-, micro-and nano-mechanical investigations on silorane and methacrylatebased composites[END_REF], or their studies even show an improvement of some properties for a short number of cycles, before a degradation of mechanical properties [START_REF] Carreira | Thermocycling effect on mechanical and tribological characterization of two indirect dental restorative materials[END_REF]. This wide range of results may be a consequence of many phenomena that can occur, not all of which are well known. For example, Carreira [START_REF] Carreira | Thermocycling effect on mechanical and tribological characterization of two indirect dental restorative materials[END_REF] mentioned that his results were contrary to other studies on the same material with similar ageing conditions. Degradation mechanisms are complex and affect differently the matrix, the fillers and the interface between them [START_REF] Ilie | Macro-, micro-and nano-mechanical investigations on silorane and methacrylatebased composites[END_REF][START_REF] Ilie | Spatial and cure-time distribution of dynamic-mechanical properties of a dimethacrylate nano-composite[END_REF][START_REF] Morresi | Thermal cycling for restorative materials: Does a standardized protocol exist in laboratory testing? A literature review[END_REF][START_REF] Carreira | Thermocycling effect on mechanical and tribological characterization of two indirect dental restorative materials[END_REF][START_REF] Brendeke | Effect of physicochemical aging conditions on the composite-composite repair bond strength[END_REF]. Inorganic fillers are little affected, if ever [START_REF] Ilie | Spatial and cure-time distribution of dynamic-mechanical properties of a dimethacrylate nano-composite[END_REF][START_REF] Morresi | Thermal cycling for restorative materials: Does a standardized protocol exist in laboratory testing? A literature review[END_REF].

Otherwise, the Turcsányi model [START_REF] Turcsányi | Composition dependence of tensile yield stress in filled polymers[END_REF] can help to compare the matrix degradation to that of the interface. Indeed, this model links the yield stress of the composite to that of its matrix, to the filler ratio and to a numerical parameter which is directly correlated to the quality of the interface. This model was initially developed for non-dental materials using tensile test, but was found to be applicable to the 3-point bending test applied to dental materials [START_REF] Boussès | Theoretical prediction of dental composites yield stress and flexural modulus based on filler volume ratio[END_REF]. This paper aims at showing how the use of the Turcsányi model enables to compare the evolution of matrix ageing on the one hand, and the interface ageing on the other hand.

For this purpose, yield stress measurements were performed on different composite batches. Each sample is composed of the same matrix and fillers, and was cured with an identical protocol. Each batch includes eight different filler ratios in order to estimate the parameter of Turcsányi's model.

Then four batches with different thermocycling protocols were compared. Samples were observed using SEM and a profilometer was used to complete the analysis.

2) Materials and Methods

2.1) Materials

The composite resin, unfilled resin and fillers were supplied by DMG Chemisch-PharmazeutischeFabrik (Hamburg, Germany). Bis-GMA is the main component of the matrix (40.3% of the total weight). Eight materials were prepared by DMG© from the matrix and fillers described above, with different filler weight fractions: 0 wt% (no filler), 20 wt%, 30 wt%, 40 wt%, 50 wt%, 60 wt%, 70 wt% and 80 wt%. Thereafter, they will be named DMG0, DMG20, DMG30, DMG40, DMG50, DMG60, DMG70 and DMG80, respectively. They correspond to 0 vol%, 9 vol%, 14 vol%, 21 vol%, 28 vol%, 37 vol%, 48 vol% and 61 vol% filler volume fractions, respectively. The uncured resins were stored between 4 °C and 6 °C without exposure to light.

2.2) Sample preparation

The samples were prepared according to the same protocol that was detailed in a previous study [START_REF] Boussès | Theoretical prediction of dental composites yield stress and flexural modulus based on filler volume ratio[END_REF].

Bars of 25x2x2 mm 3 were manufactured in a Teflon mould. The light-curing was performed with a curing lamp (DeepCureParadigm MC , 3M ESPE, Saint-Paul, USA) whose wavelength was between 430 and 480 nm and whose intensity was 1 470 mW/cm². The resin was separated from the lamp by a mylar sheet and a glass slide. The samples were exposed to the light through five 1cm-diameter holes that overlap by 5 mm. The resin was exposed for 20 s through each hole, starting with the centre of the sample. Then the same sequence was used to expose the samples from the bottom too. Finally, the samples were stored for 24 h in distilled water at 37 °C to complete polymerization. The water was then cooled down to a controlled room temperature for approximately 20 minutes before performing bending tests or thermocycling. Five samples were taken for each thermocycling duration and each filler ratio, for a total of 160 samples.

2.3) Thermocycling

Since there is no standard protocol for thermocycling, our conditions were chosen based on those most commonly used in other studies. Samples were alternatively immersed in water at 5°C and 55°C. They were trapped in a metallic grid to keep them under the water surface. The dwell time was 21 s and the transfer time was 9 s. However, some water still surrounded the samples during the transfer. Therefore this whole process may be equivalent to a 30 seconds immersion in one bath immediately followed by another 30 seconds immersion in the other bath. Motors ensured the continuous movement of water in the tanks (Figure 1). The temperature was controlled with an accuracy of 0.1°C. Four series of samples with different thermocycling durations were tested. The numbers of cycles were 0 (no thermocycling), 1 000, 5 000 and 10 000 cycles. Thereafter, these durations are referred as T0, T1, T5 and T10, respectively. At the end of the thermocycling process, samples were stored for 40 minutes at room temperature before the bending test.

It is noteworthy that the campaign lasted for several months. In order to limit the variations that could occur in material properties or experimental conditions during such a long period of time [START_REF] Boussès | Theoretical prediction of dental composites yield stress and flexural modulus based on filler volume ratio[END_REF],

additional reference samples were produced for T5 and T10 batches for each filler ratio. These samples were tested without any previous thermocycling, and the properties were compared to the ones of thermocycled samples. The relative variation directly induced by thermocycling was calculated. Where appropriate, it was used to adjust T5-and T10-properties with respect to batch T0, so as not to bias the analysis by potential phenomena other than thermocycling, such as an ageing of the uncured resin for example.

2.4) Bending test

A ZwickRoellProLinestatic machine (BZ 2,5/TH1S, Ulm, Germany) was used to perform the 3-point bending tests according to the recommendations of ISO 4049 [START_REF] Iso | Dentistry -Polymer-based restorative materials[END_REF] (Figure 2). The flexural load was imposed by a cylindrical rod with a cross-head speed of 0.75 mm/min. The sample was supported by two other cylindrical rods, which were 20 mm apart. The room temperature was 23.5±0.5 °C.

Force and displacement were measured during the test. The maximal stress and deformation at the centre of the sample, on the surface subjected to tensile stress, were calculated as follows, using the beam theory:

= 3 2 ℎ² (1) = 6 ℎ ² (2)
where is the applied load, the distance between the two supporting rods, the width of the sample and ℎ its thickness. is the maximum deflection of the centre of the beam. From the stressstrain curve, the yield stress of the composite ( ) was calculated using the classic 0.2 %-strain criterion. The stress-strain curves presented a linear variation below 30 MPa. This slope corresponds to the elastic behaviour of the material and leads to the calculation of the flexural modulus with the following formula:

= 4 ℎ ( ) ( ) (3)

2.5) The Turcsányi and Pukánszky theories

The Turcsányi model [START_REF] Turcsányi | Composition dependence of tensile yield stress in filled polymers[END_REF] enables to predict the yield stress of a composite , knowing the yield stress of its matrix , its filler ratio , and a numerical parameter related to the quality of the interface between the matrix and the fillers, . The relation is the following:

= 1 - 1 + 2.5 exp ( ) (4)
This relation was proven to be suitable for dental materials associated to the 3-point bending test [START_REF] Boussès | Theoretical prediction of dental composites yield stress and flexural modulus based on filler volume ratio[END_REF]. Moreover, Pukánszky [START_REF] Pukánszky | Influence of interface interaction on the ultimate tensile properties of polymer composites[END_REF] managed to express the numerical parameter with respect to some properties of the filler and to the yield stresses of the interface and of the matrix:

= #1 + $ * & ' * ' ( * ln ( + ) ( 5
)
where $ is the interface thickness, & ' is the fillers specific surface area (m².kg -1 ), ' is the filler density (kg.m -3 ) and + is the interface yield stress. In order to calculate + , it was assumed that all the fillers are spherical particles of the same diameter, equal to the average size of the barium glass fillers. Under these conditions, one can write + as:

+ = * ,-. / 1 + 3 * $ 0 1 ( 6
)
where 0 is the mean radius of the particles. This approach underestimates the specific surface area as the particles are not perfectly spherical and because the distribution of particle sizes is not known.

The interface thickness could not be measured accurately either. A thickness of 500 nm was estimated from AFM pictures from Ilies's work. With this methodology, the exact value of + is not targeted and is not worth of interest. Nevertheless, a relative comparison is still valid. Therefore getting numerical values for + enables us to understand how the interface and the matrix relatively evolved with different thermocycling durations.

2.6) Surface observations

After the bending tests, the roughness of the fractured surface areas was measured with an optical confocal profilometer STIL CCS Prima, (Chromatic Confocal Sensor, Aix-en-Provence, France) with the MG140 optical detector. Samples were beforehand metallised. Then a few micrometres spot of white light sweeps across the surface and the intensity of the reflected light is analysed. As each wavelength has a different focal length, the most intense reflected wavelength gives information on the distance between the spot and the surface. The coupling with the global reflected intensity enables to draw the profile of the surface. The lateral resolution is 1 µm and the vertical resolution is 30 nm.

The roughness analysis was made with the Gwyddion software [START_REF] Nečas | Gwyddion: an open-source software for SPM data analysis[END_REF].

Samples were also observed with a Philips XL30 (Semtech Solutions, Billerica, Massachusets, USA) environmental Scanning Electron Microscope (SEM). There was no need to metallize the samples metallized prior to observations.

2.7) FEM simulations

Some simulations were made on Abaqus CAE (Dassault Systèmes, Abaqus 6.14, Providence, RI, USA)

in order to help in the understanding of thermocycling. We were particularly interested in the heat transfer within the sample and its mechanical effects during a thermal cycle. This Finite Element Method (FEM) was used to simulate 25x2x2 mm 3 samples in a water environment. The temperature varied instantaneously from room temperature (23 °C) to 5 °C for one minute, and then to 55 °C for another one minute. A convective heat transfer was used to simulate the interaction between the lateral faces of the sample and its environment, characterized by the heat transfer coefficient ℎ = 100 3/5² [START_REF] Carreira | Thermocycling effect on mechanical and tribological characterization of two indirect dental restorative materials[END_REF].

A coupled temperature/displacement analysis was performed. A sensitivity study was made to adjust time step and mesh size prior to the complete simulations. The mesh was based on isotropic hexaedral elements, fully integrated and linear (C3D8T element type). The non-linear geometrics option was activated. Three symmetry planes were used to avoid any rigid body motion. Different simulations were carried out with different materials and boundary conditions. They will be detailed further. The parameters used to describe the matrix and the fillers were found in the literature [START_REF] Carreira | Thermocycling effect on mechanical and tribological characterization of two indirect dental restorative materials[END_REF] or measured directly on our composite materials. They are presented in Table 1. Fillers were considered as purely elastic whereas the matrix behaviour was visco-elastic with two Prony branches.

Parameter

Matrix Fillers Thermal expansion coefficient (K -1 ) 80x 10 -6 5x 10 -6 Heat capacity at constant pressure (J.kg -1 .K -1 ) 1 000 720

Heat transfer coefficient with water (W.m -2 ) 100 100 Thermal conductivity (W•m - 3) Results

3.1)

Temperature evolution in a sample during thermocycling (FEM analysis)

A first preliminary numerical study was carried out to validate the minimal duration of the thermal cycle. A simplified composite (Figure 3) was used to record the evolution of temperature and stresses at the centres of the matrix and filler phases. Except the three symmetry planes that prevent any rigid body motion, no mechanical boundary condition was applied. The results are plotted in Figure 4. As expected, the bulk temperature of the material does not vary as instantaneously as the environment. Nevertheless, the temperature still evolves rapidly and similarly in both phases.

Moreover, the internal stress appears to be highly correlated with the temperature as it follows the same trend. Most of the variation occurs within the first 20 seconds of a bath. 30 seconds after a temperature jump of 50 °C, the remaining variations can be considered negligible. During the last 30 seconds of the calculation, the minor temperature changes (and thus the strain and stress) in the sample seem to indicate that it is not relevant to extend the bath beyond half a minute. Moreover, the temperature distribution in the sample (Figure 5) shows that the temperature at the centre of the sample, which is plotted on Figure 4, evolves less rapidly than the average temperature of the whole sample. Thus the average temperature after a 30 s immersion is even closer to the target-temperature than the curves of Figure 4. These results confirm that the 30"/30"-hot/cold thermocycling conditions

3.2) Effect of thermocycling on mechanical properties

The measurements of the composite yield stress from the bending tests are summarized in the Table 2. For a given thermocycling duration, the yield stress increases with the filler ratio. For a given filler ratio, increasing thermal cycles leads to yield stress decrease. Some points can be noticed for filler ratios from 40 vol% to 70 vol%, which do not follow the decreasing trend. However, they are marginal and are often combined with a higher standard deviation. The parameters of the Turcsányi model were also estimated for each thermocycling duration. The four experimental results batches do follow well the model (Figure 6), with determination coefficient (R²) greater than 0.99 for T0, T1 and T5, and equal to 0.98 for T10. Moreover, even though the yield stress decreased with thermocycling duration, remains stable at about 4.45 up to 5 000 cycles. It characterizes the ratio between the composite yield stress and the matrix yield stress. This ratio became less important for 10 000 cycles but remains close to 4.45. The interface yield stress was also calculated for each batch. It slightly decreases in the first 5 000 cycles from 1 072 MPa to 1 028 MPa. Then the drop between 5 000 cycles and 10 000 cycles is more important as it falls down to 879 MPa. The scales of matrix and interface degradation are compared in Table 3. The relative variation of and + show that the speeds are different. After 1 000 cycles, the yield stress matrix loses 2.8% of its unaged property, whereas the loss is half as great as for the interface. After 5 000 cycles, the yield stress matrix decreased for 6.3% whereas it was only 4.1% for the interface. After 10 000 cycles, the matrix loss continued to follow a linear trend to reach 12.6%. On the contrary, the interface yield stress suffered a sudden loss, dropping from -4.1% to -18.0%. Therefore, for the longest thermocycling process, the interface appeared to be more damaged than the matrix. The flexural modulus results followed a similar trend. The effect of thermocycling is visible too on the (absolute) properties of Table 4; they decrease as the number of thermal cycles increase. The flexural modulus ratios are also compared. Figure 7 presents the evolution of the composite modulus relatively to the matrix modulus with respect to the filler ratio. The curves for T0, T1 and T5 are very similar, whereas the T10-curve stands out with a slower increase. This evolution is similar to the yield stress plots. Nevertheless, no accurate theoretical model linking flexural modulus and interface quality was found for high filler ratio, such as the Turcsányi model for the yield stress [START_REF] Boussès | Theoretical prediction of dental composites yield stress and flexural modulus based on filler volume ratio[END_REF]. Thus it is not possible to correlate these curves to an evolution of the interface quality. Graphically, the same observation as for the yield stress is made: the curves for T0, T1 and T5 are very similar, whereas the T10-curve stands out with a slower increase.

3.3) Profilometry measurements

The fracture surface roughness of several samples from different filler ratios and thermocycling durations was measured. The results are reported in Table 5. The roughness was between 4 and 10 µm but no evolution could be measured with respect to the number of thermal cycles or the filler ratio.

However, these results were obtained after removing the points with no signal. These amounts of removed points were not quantifiable but the difference between unaged and thermocycled samples was qualitatively obvious. Figure 8 shows the example of three pictures (with same scale) of DMG70samples that were exposed to 0, 5 000 and 10 000 thermal cycles, respectively. The unaged sample showed few disconnected points whereas they were very numerous for the T10 sample. The T5 sample had slightly more disconnected points than the T0 sample but was far from the T10 state. The same comparison was made for every filler ratio, except for the unfilled sample, whose surfaces were smooth.

Roughness (Ra

3.4) Samples failure and SEM observations

SEM observations of the fracture areas were made to get a better understanding of composite ageing.

Figure 9 compares the fracture area of two DMG40 composites, respectively unaged and thermocycled for 10 000 cycles. Both pictures show a rough surface with some apparent fillers and matrix deformation. One can estimate that the T10 sample is rougher with more apparent particles. However, contrary to the profilometer images, it is difficult to quantify a real difference between the two failure surfaces with the SEM.

For different ageing conditions and filler ratios, the two fracture surfaces from the same broken sample were also observed in a mirror layout. Zooms on the pictures shown on Figure 7 and on their opposite faces are presented on Figure 10 and Figure 11. Several phenomena are highlighted. In the red circle, a filler is neatly broken into two parts. There is no relief around it and the fracture surface is planar; the crack propagated in a straight line. This configuration is frequent and can be observed on other spots of the picture. In the blue circle, it looks like the result of a debonding. The "hole" on the one side matches well with the pulled off particle on the opposite side. However, it is only partially uncovered, the matrix remaining partly stuck to at least half of the particle surface. A more extreme case is highlighted by the green circle. There, the shape of a particle is visible but it is completely covered by matrix. The complementary ridges on each side, which cannot appear on glass, are proof of this. Finally, on the purple circle, a broken particle is highlighted.

3.5) Stress and strain distribution along the sample (FEM analysis)

Temperature changes induce volume variations of a free material. However, in a tooth, a composite has to adapt to adapt to boundary conditions that limit its movements. It leads to internal thermal stress. FE simulations can help to understand how this stress is distributed in the composite.

For this purpose, further FE simulations were performed on two samples. One is a full-matrix sample and the other is the composite sample presented in Figure 3. The same thermal cycle was applied but, this time, the sample was fixed at its extremities to represent the boundary conditions of a restoration. After a thermal cycle of 120s, stress and mechanical strain were plotted along the sample.

The values for the matrix areas in both samples were compared. This comparison is thus only valid in the ranges [0;5mm], [10;15mm] and [20;25mm] on Figure 12, where there is matrix in both configuration. In the ranges [5;10mm] and [15;20mm], the material can be matrix or filler, depending on the simulation. Therefore the comparison makes no sense in these two ranges, and there are logically great differences in stress and strain.

For a full-matrix sample, strain and stress become constant 3 mm beyond its extremities. For a composite configuration, the evolution is more complex. The matrix length between the fillers (5 mm) is therefore not long enough to reach a plateau. This explains that the stress is not constant along the matrix areas. In both configurations, there are peaks of stress and strain less than 1 mm to the interface. They are higher for the composite sample than for the sample fully made of matrix. The mean stress and strain values are also higher in the matrix area of the composite than in the full-matrix sample.

4) Discussion

The preliminary numerical study (Figure 4) showed that a 30 s-immersion of a 25x2x2 mm 3 -sample in water is enough to homogenise the temperature within a sample. In particular, the temperature at the centre of the sample is nearly equal to the one at the surface. Temperature variations in the immersion times were a point raised by Gale and Morresi reviews [START_REF] Gale | Thermal cycling procedures for laboratory testing of dental restorations[END_REF][START_REF] Morresi | Thermal cycling for restorative materials: Does a standardized protocol exist in laboratory testing? A literature review[END_REF]. Here, it seems that (30"/30")-cycles are sufficient to reach the extreme temperatures of 5°C and 55°C. These temperatures are directly correlated to the stress in the composite. Such a short cycle duration time could eventually underestimate some viscous effects in the medium term, but this phenomenon is not likely to occur in the mouth a priori. The positive effect is to reduce efficiently the time of experimental campaigns.

The experimental study showed that thermocycling does have an impact on the composite properties. On a macroscopic scale, the good preservation of the properties observed for the first 1 000 cycles is comparable to the evolution of Carreira's results [START_REF] Carreira | Thermocycling effect on mechanical and tribological characterization of two indirect dental restorative materials[END_REF], who also found that the main properties (flexural strength, Work Of Fracture, micro-hardness) remain stable after 1 500 cycles between 5°C and 55°C. Considering the equivalence between 10 000 cycles and one year in-vivo of the restoration, 1 000 cycles correspond to less than two months; it seems rather reassuring that resin composites do not lose their properties after such a short time. Nevertheless, it is quite difficult to compare our results to those of other studies because, as reported in Gale and Morresi reviews [START_REF] Gale | Thermal cycling procedures for laboratory testing of dental restorations[END_REF][START_REF] Morresi | Thermal cycling for restorative materials: Does a standardized protocol exist in laboratory testing? A literature review[END_REF],

distinct laboratories can obtain very different results despite using apparent same protocols.

Regarding our study, yield stress and flexural modulus underwent a similar decrease of their properties. After 1 000 cycles, the loss is between 0% and 4%. Some batches even show a slight increase of their values, for example DMG50, but it does not seem significant since the variation is always in the range of the standard deviations. Composites with the lowest filler ratios had a relative variation closer to 4% whereas the more filled composites had more stable properties between 0 and 1 000 cycles. After 5 000 cycles, the relative variations are between -1% and -8%. The trends are more scattered after thermocycling but, once again, the less filled composites experienced a greater relative loss than more filled composites. After 10 000 cycles, the relative variations are between -9% and -15%, except for the 80 wt% filled composite whose loss is about -20%. This time, the most filled composites experienced a greater relative loss than the less filled composites. This observation seems to be consistent with the fact that composites age differently depending on their filler ratios.

The Turcsányi (4) and Pukánszky [START_REF] Palmer | Temperature extremes produced orally by hot and cold liquids[END_REF] equations that led to the results shown in Table 3 help to understand the origin of this phenomenon. Indeed, the decrease of matrix yield stress is nearly linear over time. On the other hand, the interface yield stress undergoes a sharp drop between 5 000 and 10 000 thermal cycles whereas its decrease was slow before. This means that the interface aged more slowly than the matrix at the beginning of thermocycling, and then more rapidly after 5 000 thermal cycles. As there is less matrix and more interface when the filler ratio increases, this explains why the composite macroscopic relative losses are different for the same thermocycling duration but different filler ratios.

The profilometry measurements illustrate this phenomenon too. It was noticed that disconnected points were much more present after 10 000 cycles than for shorter durations. These black dots in Figure 8 correspond to areas where no reflected signal was received by the sensor of the profilometer.

This can occur when no metallisation could be done on this area, when the slope of the surface is too steep, or when multiple reflections against multiple walls cause too massive signal reduction. These three cases correspond to a "hole" at the surface. In our case, these holes are caused by debonded particles which are missing on one surface of the fracture area, as can be seen in Figure 10. It means that the number of debonded particles is much more important after 10 000 cycles. Moreover, a debonding is the consequence of a weakness at or around the interface between the matrix and the particle, as it becomes easier to bypass the particles rather than to crack them. This confirms that the filler-matrix interfaces were relatively spared during the first 5 000 cycles, and that the damage begins afterwards.

From a chemical point of view, composite samples still uptake water during thermocycling.

Moreover, the successive contractions and expansions of the material due to temperature variations create fatigue micro-cracks that help water to penetrate into the matrix. These micro-cracks can appear a small amount of matrix also remains around them. It seems to confirm that the cracks propagated close to the interface but not directly within it.

In addition, SEM pictures confirmed the conclusions given by the Turcsányi's theory. Indeed, it predicted that the interface quality remained good even after 10 000 cycles (B value higher than 4). In Figure 11, some particles were broken (red and purple circles) after that the crack split them instead of bypassing them. This phenomenon can be observed multiple times on every sample. Moreover, even for debonded particles, matrix often remains stuck to them (blue and green circles). It corresponds to a cohesive failure (in opposition to an adhesive failure where the crack propagates directly at the interface). Bascom [START_REF] Bascom | Apparent interfacial failure in mixed-mode adhesive fracture[END_REF] confirmed years ago that a failure is adhesive if only the interface is not well prepared. Therefore, this is not the case for the composites of this study. Cohesive failures are even more visible for unaged composites, confirming the good quality of the interface treatment shown in a previous study [START_REF] Boussès | Theoretical prediction of dental composites yield stress and flexural modulus based on filler volume ratio[END_REF].

5) Conclusion

In the present study, the influence of thermocycling on dental composites was evaluated in different ways. FEM simulations showed that immersions of 30 s are sufficient to reach 5°C and 55°C at the centre of the samples. These conditions were used to age composites during 1 000, 5 000 and 10 000 cycles. Yield stress measurements, on which the Turcsányi and Pukánszky theories were applied, showed that the matrix and the interface do not age at the same rate. In the first 5 000 cycles, the matrix acts as a shield which protects the interfaces from fast damage. Between 5 000 and 10 000 cycles, water reaches the interface. This area is very sensitive to water and is quickly damaged, leading to more important debonded particles and macroscopic loss for yield stress and flexural modulus measured from the three-point bending test. However, SEM and profilometer pictures showed that the cracks propagated in the interphase around the fillers and not directly at the interface between the matrix and the fillers.

Figure 1 :

 1 Figure 1: Picture of the thermocycling machine

Figure 2 :

 2 Figure 2 : Drawing of the configuration of the 3-pt bending test

Figure 3 :

 3 Figure 3: 2D representation of the simplified composite and its symmetry planes, used to record temperature and stress evolutions on the two red spots with Abaqus

Figure 6 :

 6 Figure 6: Evolution of composite yield stress with respect to volume filler ratio for each thermocycling duration

Figure 7 :

 7 Figure 7: Evolution of the flexural modulus ratio with respect to the filler volume ratio for different thermocycling durations

Figure 8 :

 8 Figure 8 : « Altitude » signal given by Gwyddion software from profilometer data for three DMG70 samples thermocycled during 0 (a), 5 000 (b) and 10 000 cycles (c). Black points correspond to a signal loss. The square on picture c shows the area where the roughness were calculated to avoid any bias from the edges of the samples.

Figure 9 :Figure 11 :

 911 Figure 9: SEM pictures of the fracture area of a DMG40 composite after 0 (T0, left) and 10 000 (T10, right) thermal cycles

Figure 12 :

 12 Figure 12: FEM evolution of stress and mechanical strain along the sample for a composite sample and a full-matrix sample immediately after a full thermal cycle of 120 s. The composite configuration of the first simulation is reminded below the graph

Table 1 :

 1 Numerical parameters used to simulate thermal cycles in Abaqus for both components of the composite

	•K -1 )	0.2	2
	Density (kg/dm 3 )	1.15	2.5
	Elastic modulus (long-term) (GPa)	0.882	70
	Poisson's ratio	0.33	0.33

Table 2 :

 2 Yield stress of resin composites measured by 3-point bending test with respect to thermocycling duration

	Yield stress (MPa)

Table 3 :

 3 Comparison of the evolution of and + with respect to the number of thermal cycles

		T0	T1	T5	T10
	Relative variation 6 79 Relative variation 6 78	--	-2.8% -1.4%	-6.3% -4.1%	-12.6% -18.0%

Table 4 :

 4

	Flexural modulus (GPa)

Flexural modulus of resin composites measured by 3-point bending test with respect to thermocycling duration

Table 5 :

 5 Fracture surface Ra roughness of samples from different protocol conditions.

	) (µm)	T0	T5	T10
	DMG 0		*
	DMG 30	4.946	4.254	7.761
	DMG 50	10.369	6.394	8.003
	DMG 70	8.055	7.05	6.947
	DMG 80	6.905	9.058	*

* means that the roughness was not measurable on these samples.

Acknowledgements

This work was supported by the project TOOTHBOX ANR 16-CE08-0024 of the French National Research Agency (ANR). The LMI laboratory is also acknowledged for the exchanges we had. Finally, DMG© is acknowledged for the preparation of the composites and their availability.

Acknowledgements 22

This work was supported by the project TOOTHBOX ANR 16-CE08-0024 of the French National Research Agency (ANR). The LMI laboratory is also acknowledged for the exchanges we had. Finally, DMG© is acknowledged for the preparation of the composites and their availability.

we have imposed (section 2.3) are realistic and allow the target temperature values to be reached. This has the advantage of reducing the time of experimental trials without missing important phenomena. in the matrix, and especially at the interfaces between the matrix and the fillers because of different thermal expansion coefficients, which generate local overstress close to the interface. This interphase area frequently undergoes local plasticizing or micro-cracks to drastically reduce its energy. It is also well known that siloxane bonds, resulting from the silanization surface treatment of the fillers, offer a very weak resistance to hydrolysis [START_REF] Ilie | Macro-, micro-and nano-mechanical investigations on silorane and methacrylatebased composites[END_REF][START_REF] Morresi | Thermal cycling for restorative materials: Does a standardized protocol exist in laboratory testing? A literature review[END_REF]. But at the beginning of thermocycling, the interphases are protected by the matrix and are therefore barely affected. Once water has propagated through the matrix and reaches the interphase, its siloxane bonds and its micro-cracks, the interphase is severely damaged, leading to an accelerated decrease of the interface yield stress. Moreover, Ghavami measured that the Degree of Conversion (DC) of a commercial composite was still increasing in the first 4 000 thermal cycles of his study [START_REF] Ghavami-Lahiji | The effect of thermocycling on the degree of conversion and mechanical properties of a microhybrid dental resin composite[END_REF]. As a result, the water firstly absorbed by the composite could be trapped in the matrix to increase its DC, instead of damaging the interface. Thus the decrease of interface properties would be all the more delayed. As the mechanical properties of the matrix are strongly correlated to the DC too, the first thousands of cycles see two competitive phenomena facing up. Between the micro-cracking of the matrix and the increase of its DC, the macroscopic losses of properties are initially slow.

Numerical simulations, though based on simplified composite geometry, help to understand where cracks are likely to initiate. It is noteworthy that our model does not take into account plasticity or damage and fracture phenomena. The matrix behaviour is considered as visco-elastic and the interface as perfect and infinitely thin. Figure 12 represents a full-length sample with unrealistic enormous fillers, but a scaling gives an idea of what could happen at the microscopic level, to the matrix between particles. Indeed, in response to temperature changes, the matrix cannot expand or retract as freely as it would without fillers. Their high elastic modulus and low expansion coefficient make fillers act as immobile anchor points for the matrix, in a similar way to how the boundary conditions have an impact on numerical simulations. Overstrains and overstress occur at distance but still close to the interface. This area is the most likely to undergo micro-cracks after several thermal cycles. Then, water can later rush into these small gaps to enlarge them and enhance the hydrolysis of the interphase near the interface. Moreover, SEM pictures showed that debonded particles are easily spotted but that