Juan Manuel

Ariza Chacon

Nathalie Bareille

Anne Lehebel

Kenny Oberle

Anne Relun

Raphaël Guatteo
email: raphael.guatteo@oniris-nantes.fr

J M Ariza

Evaluation of a biocide footbath solution in the occurrence and healing of digital dermatitis lesions in dairy cows: A clinical trial

Keywords: Bovine digital dermatitis, biocide, footbaths, clinical trial, risk factors

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

INTRODUCTION

Bovine digital dermatitis (bDD) is currently among the principal cause of infectious lameness in dairy cows [START_REF] Sogstad | Prevalence of claw lesions in Norwegian dairy cattle housed in tie stalls and free stalls[END_REF][START_REF] Cramer | Herd-and cow-level prevalence of foot lesions in Ontario dairy cattle[END_REF][START_REF] Refaai | Infectious diseases causing lameness in cattle with a main emphasis on digital dermatitis (Mortellaro disease)[END_REF][START_REF] Solano | Prevalence and distribution of foot lesions in dairy cattle in Alberta, Canada[END_REF]. bDD raises important economic, public-health and animal-welfare concerns. Indeed, bDD is associated with different challenges such as reduced farmers' incomes, increased use of antibiotics and, more importantly, lameness and thereby animal pain, impaired milk production and reproduction (Relun et al. 2013;[START_REF] Ettema | Modelling the economic impact of three lameness causing diseases using herd and cow level evidence[END_REF][START_REF] Bruijnis | Assessing economic consequences of foot disorders in dairy cattle using a dynamic stochastic simulation model[END_REF]. bDD can affect 96% of herds and between 7% to 30% of cows within a herd [START_REF] Solano | Prevalence and distribution of foot lesions in dairy cattle in Alberta, Canada[END_REF][START_REF] Cramer | Herd-and cow-level prevalence of foot lesions in Ontario dairy cattle[END_REF]. The disease is characterized by the occurrence of ulcerative lesions in the skin of the interdigital cleft which may persist or evolve to chronic forms [START_REF] Read | Papillomatous digital dermatitis (footwarts) in California dairy cattle: clinical and gross pathologic findings[END_REF]. Diseased cattle act as reservoirs and thereby as potential sources for outbreaks [START_REF] Döpfer | The dynamics of digital dermatitis in populations of dairy cattle: Model-based estimates of transition rates and implications for control[END_REF]. Although the precise cause of bDD has not been completely elucidated, it is known that certain farming practices have a notable impact on the environment in which the disease develops [START_REF] Somers | Risk factors for digital dermatitis in dairy cows kept in cubicle houses in The Netherlands[END_REF]. Therefore, bDD is considered to be a multifactorial disease consistently associated with unhygienic and wet conditions which mainly alter the integrity of feet skin. However, for clinical lesions to develop, the presence of specific Treponema species on feet suffering from cutaneous maceration is essential [START_REF] Gomez | An experimental infection model to induce digital dermatitis infection in cattle[END_REF]. Control strategies consequently aim to limit exposure to factors which might impact the spread of bDD. In practice, the control of bDD frequently relies on the individual treatment of active lesions and on the collective administration of disinfectant solutions through footbaths for prophylactic and healing purposes. However, evidence supporting the effectiveness of collective solutions remains scarce, mainly due to the limitations posed by small samples and design weaknesses [START_REF] Ariza | Effectiveness of collective treatments in the prevention and treatment of bovine digital dermatitis lesions: A systematic review[END_REF].

The banning of antimicrobial use in footbaths is a priority to respond to a growing antimicrobial resistance threat at human and animal levels [START_REF] Holzhauer | Comparing the curative efficacy of topical treatment with thiamphenicol and oxytetracycline on digital dermatitis lesions in dairy cattle[END_REF][START_REF] Hyde | Quantitative analysis of antimicrobial use on British dairy farms[END_REF]. Moreover, other common products used in footbaths, in some cases, represent an environmental risk, such as copper sulfate [START_REF] Ippolito | Copper impacts on corn, soil extractability, and the soil bacterial community[END_REF], or a harmful practice for farmers, such as formaldehyde, which has been recognized as carcinogenic [START_REF] Cogliano | Meeting report: Summary of IARC Monographs on formaldehyde, 2butoxyethanol, and 1-tert-butoxy-2-propanol[END_REF]. Several footbath solutions that claim to be effective and safe are currently available on the market without major scientific evidence supporting these claims [START_REF] Ariza | Effectiveness of collective treatments in the prevention and treatment of bovine digital dermatitis lesions: A systematic review[END_REF]. Furthermore, the currently available footbath solutions are not adapted to all farming conditions. Indeed, significant differences between farms, for example, in terms of hygiene, housing system, herd size or lameness prevalence, may have an important impact on the implementation and effectiveness of footbathing practices [START_REF] Relun | Effectiveness of different regimens of a collective topical treatment using a solution of copper and zinc chelates in the cure of digital dermatitis in dairy farms under field conditions[END_REF]Relun et al., 2013), and often this impact is ignored in controlled trials [START_REF] Ariza | Effectiveness of collective treatments in the prevention and treatment of bovine digital dermatitis lesions: A systematic review[END_REF]. Additionally, the increasing bDD prevalence and the development of non-healing lesions are raising concerns that highly pathogenic or resistant strains are emerging [START_REF] Evans | Association between bovine digital dermatitis treponemes and a range of 'non-healing' bovine hoof disorders[END_REF].

Therefore, new solutions for the collective disinfection of feet must consist of efficient and safe practices that can be easily adapted to the complex setting of each farm. Pink-step™ (Qalian, France) is a biocide that represents a potential alternative for bDD control. This is a safe and biodegradable disinfectant solution of confirmed bactericidal efficacy under soil conditions designed for the footbath administration (European Commission, 2016;European Chemicals Agency, 2017).

A clinical trial was developed to investigate the effectiveness of this new footbath biocide solution in delaying the occurrence of bDD lesions and in enhancing the healing of existent bDD lesions. In order to obtain reliable results, the main possible risk factors present at the cow and farm levels were concomitantly included in the trial analyses.

MATERIAL AND METHODS

This investigation is reported following the recommendations of the CONSORT statement, extension to within-person trials [START_REF] Pandis | CONSORT 2010 statement: extension checklist for reporting within person randomised trials[END_REF]. All procedures were carried out under the agreement of the Ethics Veterinary Committee in Clinical Research and Epidemiology from the Veterinary School of Nantes, France (CERVO, France) (registered number:

CERVO-2016-12-V.)

Trial design

The trial was designed to be a controlled within cow clinical trial in which the hind feet of cows from each farm were allocated either to the control group or to one of two footbath regimen groups using Pink-step™.

Study population

The trial was conducted on 10 dairy farms in western France from October 2016 to June 2017.

Farms were selected from a list provided by hoof-trimmers and veterinarians according to the trial protocol (Supplementary material S1). These farms were known to have experienced bDD during the preceding two-year period. However, none of the farms had administered footbaths during the two months preceding the trial. The herds were composed of Holstein cows to reduce the potential effects of breed on bDD. Cows were milked in a rotatory or conventional milking-parlor (location for bDD scoring). Additionally, to minimize possible imbalances between farms, after the pre-study visits, only farms with a herd prevalence ≥ 15% of active bDD lesions were included. Farmers milked on average 90 cows (range: 45-145) twice a day. Cows were mostly housed in cubicles (9 farms), and only one farm had no access to pasture during the spring and summer seasons.

Footbath regimen groups and concomitant treatments

The footbathing procedure consisted in placing a footbath at the milking parlor exit and administering a disinfectant solution over a complete 5-month period. A split walk-through footbath was used to administer the disinfectant solution. The footbath consisted of 2 baths separated by a grill which partially avoids contamination of the footbath by cow feces (Intra-Bath™, Intracare). Each bath measured 233 cm long × 32.5 cm wide × 19 cm high. The combined volume of the 2 sides of the footbath was 160 L. No pre-footbath foot wash was used in the study. The disinfectant solution administered, named Pink-step™, was a new biocide with recognized in-vitro efficacy (European Commission, 2016;European Chemicals Agency, 2017). Pink-step™ solution is composed of lactic acid (30%; w/w) and glycolic acid (10%; w/w) as active substances, anionic and non-ionic surfactants, and other excipients as a dye. The dose recommended by the manufacturer for footbathing was a 5% (v/v) solution in water. The split footbath made it possible to concurrently administer the Pink-step™ solution in one side of the footbath whilst the other side of the footbath remained empty and was used as a control. The feet of the lactating cows enrolled in the trial thus were allocated to three different groups, consisting of two different regimens of footbath administration frequencies and the empty bath (control group). According to the willingness of the farmers, farms were allocated to the moderate or intensive regimen. The Moderate Regimen (MR) was planned to resemble current field practices and consisted in footbath administration for 2 days (4 consecutive milkings) every week for the first month, then every two weeks for the second month, and then once a month until the end of the trial. The Intensive Regimen (IR) aimed to evaluate the possible advantages of increasing the frequency of footbathing over time, and consisted in footbath administration for 2 days every week for the first 2 months, and then every fortnight until the end of the trial. For both regimens studied, the biocide solution was expected to be renewed every 100 cow passages following the guidelines for the use of the solution.

Individual concomitant treatments were allowed during the trial for ethical and welfare reasons. Therefore, during the trial, farmers were expected to individually detect and treat all ulcerative-active bDD lesions using 2 applications of oxytetracycline (30 mg/ml) (Oxytetrin™, MSD) 2 days apart, regardless of whether the cow foot treated was allocated to the control or treatment groups.

Follow-up, data collection, and outcomes measures

Farms were visited by 3 investigators trained through practical lessons before the trial start to fill out the questionnaires and conduct the overall feet scoring. Each visit followed 3 steps: (1) scoring the hind feet of all lactating cows for bDD and feet hygiene during milking, (2) checking compliance with the protocol, and (3) checking any changes in herd management practices. The investigators filled out a questionnaire which included: i) the covariates presented in Table 1, ii) items related to the protocol compliance including assessments of the quantities of product used by month, and iii) items related to management practices such as the implementation of individual treatments or trimming according to two additional sheets prepared for these events. Baseline records on the prevalence and other covariates of the participant farms were recorded during pre-study visits which took place before the start of the trial.

Digital dermatitis status was assessed during milking using a swiveling mirror based on the methodology described by [START_REF] Relun | A simple method to score digital dermatitis in dairy cows in the milking parlor[END_REF]. The hind feet of all lactating cows were washed using tap water before the examination. The hind feet then were recorded using the M scoring system, modified from Döpfer et al. (1997) and Berry et al. (2012). In this system, the M0 stage corresponds to healthy feet without bDD lesions; M1 is considered as an early-stage ulcerative lesion (0-2 cm diameter); M2 represents painful ulcerative lesions with a diameter >2 cm; M3 is the healing stage with a lesion covered by a scab; M4 is the chronic stage characterized by dyskeratosis or surface proliferation; and M4.1 consists in a chronic lesion with a small area of ulceration. In addition, lesion scores were gathered into 2 different categories, inactive lesions (M3 -4) and active lesions (M1 -2 -4.1). Otherwise, feet dirtiness (tarsus (hock); metatarsus and digit (phalanges)) of the entire herd was assessed in the milking parlor prior to washing the feet for the bDD lesion diagnosis. The hind feet of each cow were scored using a 3-point nominal scale, varying from clean (score 1) to dirty (score 3), as described by [START_REF] Guatteo | Elaboration of a scoring grid to assess feet cleanliness in dairy cattle and identification of risk factors in the winter period[END_REF] (Figure 1). For each cow, the higher of the two foot scores (one for the left foot, the other for the right) was retained. The first scoring was performed immediately before the start of the administration of footbaths. Consecutive visits at intervals no longer than 30 days were made during the trial period. Additionally, for ethical and welfare concerns, farmers were informed about the overall prevalences of bDD lesions one week after the visit but without specifying which animals were affected. This was to avoid influencing the owners' perceptions of the study protocol and their decision-making process for individual treatment.

Two different outcome measures were recorded for each foot of the observed cows. A first outcome studied the healing effect and evaluated the healing of bDD lesions; the time in days to heal a bDD lesion was measured, counting from the first date of observation until the first date without any bDD lesion. The second outcome studied and evaluated the delay in the occurrence of bDD lesions, counting the time in days from the first observation of a foot without any bDD lesion until the first date of occurrence of a bDD lesion.

Sample size

Sample sizes were calculated for both outcomes studied using the formula for sample size estimation in clinical trials with clustered survival times as the primary outcome (Xie and Waksman, 2003). The sample size implemented in the trial was based on the second outcome because the detectable differences in the target effect between the treatment and control group were smaller (10%) compared with the healing outcome (20%). Therefore, a larger number of animals was needed to achieve statistical power for the occurrence outcome than the healing outcome. Due to the lack of previous data to account for the within cow correlation, a classical intra-cluster correlation coefficient (ICC) was set at 0.05 [START_REF] Adams | Patterns of intra-cluster correlation from primary care research to inform study design and analysis[END_REF]. The number of farms included was calculated based on the average French herd size of 60 lactating cows and on the occurrence rates (4 cases for 100 feet-months at risk) reported in a previous study following a similar approach (Relun et al., 2013). Therefore, with a type I error risk of 0.05 (α=0.1), at least 264 cows by each footbath regimen were necessary to guarantee 80% power (β=0.2) to detect the target difference between control feet and footbath feet (10%). These calculations led to the recruitment of 10 average French farms (n= 60 lactating cows) for the inclusion of at least 528 cows (2 footbath regimen) and accounting for 15% of cows lost during the follow up of the trial.

Treatment group allocation

The side allocation (left or right) of the control group was balanced between the farms.

Masked envelopes containing the side allocation were prepared and chosen randomly just before the first footbath administration. During the recruitment process and before any lesion scoring, half of the farms were allocated to the IR according to the farmers' willingness to spend more time administering the footbaths. The footbaths were administered by the farmers and therefore they were aware of the side containing the biocide product. Likewise, due to the pink color of the biocide substance, it might be possible that investigators were aware of the feet being treated during the trial.

Data analysis

WA). New covariates were built from the raw data using R (R Core Team, 2017). The effectiveness of both treatment regimens was evaluated on the clinical healing of bDD lesions and the reduced occurrence of bDD lesions through a survival analysis with a hind foot as the statistical unit. Survival analyses were carried out using the Frailtypack package in R [START_REF] Rondeau | R frailtypack: general frailty models: shared, joint and nested frailty models with prediction[END_REF]. Nested survival models [START_REF] Rondeau | frailtypack: An R Package for the Analysis of Correlated Survival Data with Frailty Models Using Penalized Likelihood Estimation or Parametrical Estimation[END_REF] were applied including a nested random effect for cows grouped in farms to adjust for clustering within observations, thereby feet in the models were considered as independent observations clustered at the farm level and subclustered at the cow level. Factors considered as potential effect modifiers of the healing and the occurrence of bDD lesions at the herd, cow and feet levels were included as covariates in the models (Table 1). The temporality between exposure and the outcomes studied was taken into account in the models, and when recurrent events were recorded timedependent covariates were constructed. The survival analysis was planned in 3 steps: (i) treatment regimens and all covariates were tested in univariate analyses. Those covariates which contributed to the model at a 20% significance level were selected for multivariable analysis including the 2 x 2 interactions between these covariates [START_REF] Dohoo | Veterinary Epidemiologic Research[END_REF]. (ii)

The proportional hazards assumption and the goodness-of-fit of the final model were checked by graphic procedures and the Schoenfeld residuals test [START_REF] Schoenfeld | Partial Residuals for The Proportionnal Hazards Regression Model[END_REF]. (iii) The multivariable models were checked for confounding for every covariate using backward stepwise selection with footbath regimen group forced into the model. Confounding was assumed to occur when the estimates changed by more than 20%.

For the purpose of analysis, when evaluating the healing outcome, and to ensure the true healed status of a lesion, only feet initially scored with an active or inactive lesion were considered to be healed in the models if in subsequent visits an M0 ("Healthy stage") score was noted on at least 2 consecutive visits. Likewise, for the outcome evaluating the occurrence of bDD lesions, only feet conserving the same M0 score during the 2 consecutive initial visits were included, ensuring the real absence of any lesion. The occurrence of a lesion was considered in the model if the included feet suffered any bDD lesion (active or inactive) during the trial period on 2 consecutive visits, to ensure the true lesion occurrence in the feet.

For both outcomes, feet with visits spaced more than 45 days apart were removed from the analysis, on the fact that bDD lesions may be completely healed within 1 month [START_REF] Holzhauer | Clinical course of digital dermatitis lesions in an endemically infected herd without preventive herd strategies[END_REF][START_REF] Nielsen | A study of the dynamics of digital dermatitis in 742 lactating dairy cows[END_REF]. Results of the models are presented as hazard ratios (HR) with their respective confidence intervals (CI), estimated for each covariate from the hazard function by taking the exponent of the estimates of effects. Therefore, the HR calculated for the occurrence outcome measures the instantaneous risk for a foot free of lesion to experience a bDD lesion being treated with one of the regimens versus being untreated. Meanwhile, the HR calculated for the healing outcome measures the instantaneous risk for a foot with a lesion to become healed being treated with one of the regimens versus being untreated. Finally, for the outcome evaluating the bDD occurrence, HR measures the instantaneous risk for the occurrence of a lesion in a foot being treated with one of the regimens versus being untreated.

RESULTS

Farms were recruited between October and December 2016. For each farm, hind feet were inspected between 1 and 6 times at a median frequency of 30 days from January to June.

Table 2 presents the main characteristics of the farms before the regimen side allocation. The baseline characteristics of the feet are summarized in Table 3. In total, 2,072 feet were allocated into one of the three groups, precisely, 394 in the MR group, 642 in the IR group, and 1,036 in the control group (Figure 2). During the follow-up period, there were no deviations from the trial protocol or adverse effects reported or observed.

Effect on Occurrence

At the start of the trial, 852 hind feet (41%) out of 2,072 hind feet (1,036 cows) were free of active bDD lesions during two consecutive visits. Then, 109 feet were excluded from the dataset because the interval between visits was longer than 45 days. Finally, 743 hind feet of 468 cows from 10 herds were included in the analysis (Figure 2, total initial feet without lesion). Only 275 cows shared the same bDD-free score in both hind feet at the start of the trial. Significant baseline differences were found between the feet allocation groups for cow feet hygiene, initial prevalence, proportion of heifers, herd size and farm feet hygiene covariates (Table 3). Among all of the feet included in the analyses, 161 (21%) experienced a bDD lesion during the trial period. Inactive lesions (142) were more prone to occur than active lesions (19). The median time before the occurrence of a bDD lesion was 80 days (37 to 142 days), and the mean incidence rate was 6 cases for 100 feet-months at risk. After the analyses, only the poor feet cleanliness at the cow level and the farm level were significantly associated with a high risk of bDD occurrence in the multivariable analysis (Figure 3). No effect of the Pink-Step™ solution was evidenced on the bDD occurrence during the trial. None of the other covariates included in the multivariable model or their interactions were statistically significant in the multivariable model. Finally, the estimated variance of the cluster effect at the farm level was 0.0073 (CI 0.0010 -0.0132, p value=0.0126), and at the cow level 3.65 (CI 2.29 -5.00, p value<0.001).

Effect on Healing

Initially, 1,107 hind feet (53%) out of 2,072 hind feet (1,036 cows) were affected with active or inactive bDD lesions. However, of these feet, 300 were excluded from the dataset because the interval between their visits was longer than 45 days. Therefore, 807 hind feet of 508 cows from 10 herds were included in the analysis (Figure 2, total initial feet with lesion). Among these cows, 299 had bDD lesions on both hind feet at the start of the trial. Significant baseline differences were found between the feet allocation groups for cow feet hygiene, preventive hoof-trimming, initial prevalence, proportion of heifers and herd size (Table 3). Among all of the feet included in the analyses, 186 (23%) achieved the healing either of an active lesion (74) or an inactive lesion (112). The median time before the healing of a bDD lesion was 46 days (30 to 140 days), and on average the healing rate was 5% between two visits. According to the group allocation, the mean healing rates by month were 4%, 8% and 5% in the control, MR, and IR, respectively. From the multivariable analyses, six covariates were significantly associated with the risk of bDD healing (Figure 4). Thus, the time to healing was improved in inactive lesions and by the use of Pink-Step™ footbaths in IR.

Otherwise, in feet trimmed during the trial period, the time to healing was reduced. Lesions in cows which either had a contralateral lesion or were at late lactation were identified to be at a higher risk of persisting. Moreover, in larger herds, the risk of lesion persistency was increased. A single interaction between the initial lesion aspect and the allocation footbath group was detected, indicating that feet with an active lesion in the IR group have a reduced time to healing compared to active lesions on feet allocated to the MR and control group.

None of the others covariates included in the multivariable model or their interactions were statistically significant in the multivariable model. Finally, the estimated variance of the cluster effect at the farm level was 0.0073 (CI 0.0010 -0.0132, p value=0.012), and at the cow level 1.52 (CI 0.97 -2.06, p value= 0.004).

DISCUSSION

The findings of this investigation indicate that the collective disinfection of herd feet using Pink-step™ footbaths significantly improved the healing of bDD lesions when administered at an intensive frequency. The time to healing of bDD lesions was increased importantly in feet with active lesions, in trimmed feet, in cows in late lactation, in cows with contralateral lesions, and especially in larger herds. Otherwise, the occurrence of bDD lesions was mainly affected by feet cleanliness at the cow and farm level, and no effect on delaying the occurrence of the footbath solution (Pink-step™) was evidenced.

The originality of our investigation was to conduct a controlled clinical trial allocating the feet of the same cow into the control and the intervention groups. This approach allowed a drastic reduction (over threefold) in the trial's sample size, which is important in veterinary studies [START_REF] Ariza | Effectiveness of collective treatments in the prevention and treatment of bovine digital dermatitis lesions: A systematic review[END_REF]. Furthermore, all of the feet shared the same risk whatever group they were allocated to (control or footbath), thereby reducing the farm effect. The findings of this investigation also enabled the estimation of the correlation between the feet of a same cow regarding bDD status, a parameter which has been largely suspected but not until now reported, to support the importance of developing and implementing prophylactic collective strategies. The trial was conducted on 10 farms in an effort to encompass the diversity of local herd management practices. Likewise, the multiple observations recorded over a long trial period were conceived to increase the precision of the measurements and to capture differences in the farming environment over time [START_REF] Ariza | Effectiveness of collective treatments in the prevention and treatment of bovine digital dermatitis lesions: A systematic review[END_REF]. Therefore, due to the major role of the farm factors and the dynamic nature of bDD, the trial was designed for a survival analysis, which enables one to adjust for covariates that change over time, such as feet cleanliness or lactation stage. Additionally, the nested survival model used for the analyses accounted for the heterogeneity caused by unmeasured covariates at the farm and cow level in the same model. In turn, due to the high prevalence of bDD lesions and the high frequency of observations planned, a scoring methodology which had no impact on daily farming practices had to be adopted even if it was less accurate than bDD scoring on restrained cows in a trimming chute (Se ≥0.90; Sp ≥ 0.80) [START_REF] Relun | A simple method to score digital dermatitis in dairy cows in the milking parlor[END_REF]. Nevertheless, the inter-digital space remains hard to approach using this methodology and therefore score misclassifications might lead to underestimating the hazards for all the covariates [START_REF] Dohoo | Veterinary Epidemiologic Research[END_REF]. Additionally, although the tree investigators received the same lesion scoring training, our trial protocol did not take into account the inter-observer agreement. However, as each farm was monitored entirely by a single investigator, the random farm effect might have reduced this bias effect. To reduce the risk of over or underestimation effects due to a misdiagnosis of "M1" or "M3" stages [START_REF] Cramer | Evaluation of agreement among digital dermatitis scoring methods in the milking parlor, pen, and hoof trimming chute[END_REF], for the data analyses the "M5" stages were gathered into active, inactive and healthy stages. Consequently, the healing or the occurrence of bDD lesions was mainly determined by the presence or the absence of a healthy stage. In contrast with prior studies, and to avoid a potential overestimation of the footbath effect, the "M3" and "M4" stages were considered in the models as a diseased status. This original approach is one of the important features of the present trial. Especially when taking into consideration that the M4 stage might represent the most infective stage in which diseased animals spend more time [START_REF] Biemans | Digital Dermatitis in dairy cattle: The contribution of different disease classes to transmission[END_REF]. Finally, the likelihood of obtaining beneficial effects by the implementation of a footbath might be enhanced by the usage of disinfectants tested in-vitro that mimic field soil conditions. Few high-quality trails have reported footbath solutions to be effective (Thomsen, 2015). To our knowledge, the only peer-reviewed controlled trial that found good results was that of [START_REF] Solano | Effectiveness of a standardized footbath protocol for prevention of digital dermatitis[END_REF], which used standardized footbaths of copper sulfate at 5% administered once a week. Another study also has reported successful results using copper sulfate at 5% for the healing of bDD lesions, however, the solution was administered by collective spraying [START_REF] Relun | Effectiveness of different regimens of a collective topical treatment using a solution of copper and zinc chelates in the cure of digital dermatitis in dairy farms under field conditions[END_REF]. The scarce evidence related to footbaths may indicate the difficulties entailed in the design and evaluation of such clinical trials, or the small effect of footbaths in practice when farm conditions are far from ideal for their implementation. The present trial also reports a beneficial effect of footbaths using a safe and a biodegradable solution.

Beneficial effects were only evidenced in the healing of bDD lesions. Beyond the bactericidal effect of footbaths on bDD lesions, a potential mechanism of Pink-step™ for improving skin healing may be the presumed dermal regenerative effects of the glycolic acids present in the biocide solution [START_REF] Green | Clinical and cosmeceutical uses of hydroxyacids[END_REF]. Otherwise, it is important to note that due to the design and duration of this trial, it was not possible to record lesion recurrence, a phenomenon already described in individual treatment trials which should be of interest when evaluating the long-term effectiveness of footbaths. Therefore, future studies must focus on the possible recurrence or recrudescence of bDD lesions and the effective healing of active lesions. The increased intensity in footbathing has previously been noted as beneficial by other studies [START_REF] Holzhauer | The effect of an acidified, ionized copper sulphate solution on digital dermatitis in dairy cows[END_REF][START_REF] Solano | Effectiveness of a standardized footbath protocol for prevention of digital dermatitis[END_REF]. These benefits were also evidenced in this study by the healing rates recorded during the first months and the healing efficacy evidenced by the IR group. To resemble field conditions, the administration frequencies implemented in the present trial changed over the time to mimic current in-field practices were the footbaths usage is reduced during the summer season. Therefore, additional studies are necessary to clarify the relation between the intensity of footbathing, the influence of seasons, and the effectiveness of such measures. Moreover, as noted in a previous investigation, future studies must implement standardized footbath dimensions to ensure the optimal performance of the disinfectant products studied and to enable reliable and comparable results [START_REF] Solano | Effectiveness of a standardized footbath protocol for prevention of digital dermatitis[END_REF].

An association between footbathing practices and a reduced risk of bDD occurrence was not evidenced in this trial. The lack of effectiveness of both footbathing regimens to delay the occurrence of bDD lesions might be related to the weak effect of the footbath solution, which was probably below what was expected when the sample size necessary for the trial was calculated. Likewise, as the correlation between feet was unknown before this trial, the current sample size was probably inferior to that needed to evidence small effects on bDD occurrence. Additionally, in this trial all of the feet were cleaned for the scoring at each visit, and therefore every healthy foot periodically received what can be perceived as a prophylactic intervention. Consequently, the disinfectant efficacy of a solution over an already cleaned foot might be imperceptible, in other words, the effectiveness of disinfectants on delaying the occurrence of bDD lesions might be roughly equivalent to regular cleaning with water [START_REF] Nielsen | A study of the dynamics of digital dermatitis in 742 lactating dairy cows[END_REF]. Despite the evidenced lack of effectiveness on delaying the occurrence of bDD lesions, the time to healing was enhanced in inactive lesions compared to active lesions, and footbathing practices thus might act as a potential protective measure, controlling bDD reservoirs and the recrudescence of their lesions. One of the important limitations of this trial was related to the bias produced by the absence of investigator blinding during the follow-up. While this bias could be avoided by using a colored solution instead of an empty bath, the split-bath design implemented in this trial restrained this approach for practical reasons and for the risk of invert the solutions during their preparation. Although an objective methodology was implemented to score the lesions, investigators could not be blinded to the footbath allocation of feet due to the distinctive pink color of the solution studied. Future clinical trials in bDD control should aim to blind the investigators to ensure an objective assessment of the lesions.

Otherwise, the split-body design of this trial might lead to some limitations. Although all of the feet had the same baseline probability of developing or healing a bDD lesion, significant differences between the allocation groups were detected after randomization. The imbalances between the baseline characteristics of the feet groups highlight the importance of considering confounding by adjusting for all potential effect modifiers in the data analysis. Another limitation related to the split-body design is the possible carry across effects within feet. On one hand, the pathogens in untreated feet might have remained undisturbed during the trial and thus may have increased the infection pressure in the environment. On the other hand, the disinfectant effect of footbaths might have reduced to an important degree the densities of environmental pathogens, enhancing as well the healing rates and decreasing the risk of lesion occurrence in untreated feet. In both scenarios, an under-estimation of the true effect of footbaths was expected. However, these methodological limitations inherent to this design might be compensated by the reduced sample size of the design. In this trial, the small random effect at the farm level reflected the homogeneous sample analyzed, being coherent with the strict inclusion parameters applied. Otherwise, the large random effect at the cow level suggests a greater correlation of the survival times for feet belonging to the same cow. This strong correlation was evidenced, for example, by the reduced risk of bDD healing in cows which have contralateral lesions. Future studies implementing the split-body design must consider the implications of this choice, such as establishing an appropriate data analysis and including a smaller number of farms or just one farm but with a large herd.

The individual treatment of active lesions was rare in the data set. Although their effectiveness is supported by scientific literature [START_REF] Apley | Clinical Evidence for Individual Animal Therapy for Papillomatous Digital Dermatitis (Hairy Heel Wart) and Infectious Bovine Pododermatitis (Foot Rot)[END_REF], in this trial the time to healing was not improved by individual treatments. A possible explanation may lie in how the farmer's decision to treat was altered by the trial environment which involved a close followup by the veterinarians involved in the trial. Similarly, it may be possible that only the most severe cases of bDD capture the attention of farmers, and such lesions are frequently less responsive to treatment [START_REF] Evans | Association between bovine digital dermatitis treponemes and a range of 'non-healing' bovine hoof disorders[END_REF]. Another explanation for the lack of efficacy of Oxytetracycline treatment involves an incorrect or incomplete implementation of the protocol [START_REF] Sawant | A Survey on Antibiotic Usage in Dairy Herds in Pennsylvania[END_REF]Relun et al., 2013a). Likewise, during the trial, the feet were trimmed mainly for therapeutic reasons instead of prophylactic reasons. Therefore, the healing benefits of trimming might be missed in those severe cases which persisted longer than the trial period. Similarly, the presumed preventive influence of trimming was not evidenced in the trial, probably because the impact of dirty conditions was more important than that of the implementation of prophylactic measures on the farms studied.

As has been consistently noted in other epidemiological studies (Relun et al., 2013b), poor feet hygiene was confirmed as the most important factor influencing bDD lesion occurrence at both the cow and farm levels. However, although previous studies have suggested that poor feet hygiene might delay the healing of bDD lesions [START_REF] Relun | Effectiveness of different regimens of a collective topical treatment using a solution of copper and zinc chelates in the cure of digital dermatitis in dairy farms under field conditions[END_REF], we were unable to identify a relation between feet cleanliness and time to bDD healing. Experimental studies have confirmed that dirty and wet environmental conditions are the main determinants for the occurrence of bDD lesions [START_REF] Gomez | An experimental infection model to induce digital dermatitis infection in cattle[END_REF]. Similarly, field studies have identified different factors which may alter environmental hygiene and thereby increase the risk of bDD, such as housing in cubicles, grooved concrete floors, and reduced manure scraping rates [START_REF] Somers | Risk factors for digital dermatitis in dairy cows kept in cubicle houses in The Netherlands[END_REF][START_REF] Barker | Risk factors for increased rates of sole ulcers, white line disease, and digital dermatitis in dairy cattle from twenty-seven farms in England and Wales[END_REF][START_REF] Oliveira | Associations between biosecurity practices and bovine digital dermatitis in Danish dairy herds[END_REF]. In practice, feet hygiene is a measure of the impact of several factors that condition the farming environment in which cows stand. Therefore, as the bDD lesions and the treatments implemented were centered at the foot level, focusing cleanliness observations on the foot rather than the leg might improve the precision concerning the association of the different factors which may affect feet hygiene and bDD lesions [START_REF] Guatteo | Elaboration of a scoring grid to assess feet cleanliness in dairy cattle and identification of risk factors in the winter period[END_REF]. Otherwise, other studies have reported an important seasonal effect on the risk of bDD [START_REF] Argaez-Rodriguez | Papillomatous digital dermatitis on a commercial dairy farm in Mexicali, Mexico: incidence and effect on reproduction and milk production[END_REF] and other feet disorders [START_REF] Murray | Epidemiology of lameness in dairy cattle: Description and analysis of foot lesions[END_REF]. Although this factor is mostly related to a limited access to pasture, this association was not evidenced in the present study in relation to grazing practices or their impact on feet cleanliness and bDD healing or occurrence.

Another limitation of this trial is related to the potential selection bias on the allocation process due that the footbath frequency regimen (MR or IR) was assigned base on the willingness of the farmers. Farmers who accepted to participate only if included in the IR were likely more conscientious of the disease problem than those opting for the MR and the involvement of the farmers on the trial could therefore be different. Beyond the potential impact of different farm characteristics and farm management factors recorded during the trial, the heterogeneity within cows indicates that other factors affecting the bDD dynamics differ between cows and their feet. Further investigation at the cow level therefore might enhance current understanding of bDD, highlighting, for example, the role of skin microbiota or the immune response in the disease outcome.

CONCLUSION

This investigation confirmed that multiple factors interact in the dynamics of bDD lesions determining their occurrence and persistence. Strategies to control the bDD therefore must rely on the simultaneous implementation of multiple measures to improve the environment of feet, and to reduce the severity of lesions and the presence of infected cows. The results of this study revealed the utility of footbathing practices for improving the time to healing of

Finally

  , to limit bDD lesion occurrence, trial findings confirmed the crucial importance of implementing efficient measures to improve feet hygiene. Veterinary Medicine 71, 11-21. Thomsen PT 2015. Short communication: Efficacy of copper sulfate hoof baths against digital dermatitis-Where is the evidence? Journal of Dairy Science 98, 2539-2544. Thomsen PT, Ersbøll AK and Sørensen JT 2012. Short communication: Automatic washing of hooves can help control digital dermatitis in dairy cows. Journal of dairy science 95, 7195-9. Xie T and Waksman J 2003. Design and sample size estimation in clinical trials with clustered survival times as the primary endpoint. Statistics in Medicine 22, 2835-2846.

Figure 1 .

 1 Figure 1. Scoring grid to assess feet cleanliness at the cow and farm level (Guatteo et al., 2013).

Figure 2 .

 2 Figure 2. Flow diagram of the feet included in the clinical trial. From enrollment until the final analyses.

Figure 3 .

 3 Figure 3. The effect of footbath regimen on delaying the first occurrence of digital dermatitis (bDD) lesion adjusted for herd, feet, and cow characteristics in the nested survival model including observations on 743 hind feet from 468 cows from 10 French dairy herds involved in a clinical trial.

Figure 4 .

 4 Figure 4. The healing effect of footbath regimen adjusted for herd, cow, and feet characteristics on the healing of digital dermatitis (bDD) lesions in the nested survival model of the observations of 807 hind feet from 508 cows from 10 French dairy herds involved in a clinical trial.

Table 2 .

 2 Main farms characteristics before side randomization

	Allocation	Farm ID	Lactating Cows	Heifers	Initial bDD prevalence (%) a	Housing system	Global feet hygiene b	Grazing period	Milking system	Preventive hoof trimming practices	Number of feet included in the healing outcome	Number of feet included in the occurrence outcome
		1	45	14	36	Cubicles 2.00	Yes	Conventio nal	Yes	59	26
		2	115	37	18	Cubicles 2.42	No	Conventio nal	Yes	75	118
	Moderate Regimen	3	47	13	47	Cubicles 2.00	Yes	Conventio nal	Yes	32	21
		4	78	26	33	Cubicles 2.38	Yes	Conventio nal	Yes	75	43
		5	57	22	21	Loose housing	2.30	Yes	Conventio nal	No	20	41
		6	85	33	40	Cubicles 2.31	Yes	Conventio nal	Yes	99	45
		7	145	49	59	Cubicles 2.18	Yes	Rotary	Yes	180	99
	Intensive Regimen	8	105	35	30	Cubicles 2.11	Yes	Conventio nal	Yes	81	123
		9	123	38	31	Cubicles 2.02	Yes	Rotary	Yes	103	138
		10	99	37	20	Cubicles 2.03	Yes	Conventio nal	No	83	89
						Cubicles
	Summary c 10 899 (90) 304 (30) 34 % d	=9 Loose housing	2.17 d	Yes=9 No=1	Conventio nal=8 Rotary =2	Yes=8 No=2	807	743
						=1
	Total average

a Prevalence of cows with active lesions at the pre-study visit b Average feet hygiene score (1-3) among the animals recorded at the pre-study visit c Total count and mean proportion in parenthesis, unless otherwise specified. d

Table 3 .

 3 Feet baseline characteristics according to the allocation group, the covariates recorded and the outcomes of interest.

				Healing outcome				Occurrence outcome
	Covariates	Group	Control (%)	Intensive (%)	Moderate (%)	Total	p-value	Control (%)	Intensive (%)	Moderate (%)	Total	p-value
	Initial score	M4 -3	214 (53) 135 (49) 73 (57)	422	0.25	-	-	-	-	-
			M1-M2-M4.1 186 (47) 143 (51) 56 (43)	385
			0-1	115 (28) 83 (30)	36 (28)	234		189 (50) 124 (50) 60 (49)	373
	Cow parity	2	103 (29) 68 (25)	42 (33)	213	0.50	83 (22) 49 (20)	29 (24)	161	0.88
			≥ 3	182 (45) 127 (45) 51 (39)	360		102 (27) 74 (30)	33 (27)	209
			Low (<36.4) 101 (26) 63 (23)	42 (34)	206		132 (35) 77 (31)	46 (38)	255
	Milk potential	yield	Moderate (36.4-42.2)	157 (41) 120 (45) 49 (40)	326	0.21	112 (30) 78 (32)	30 (25)	220	0.56
			High (>42.2) 126 (33) 86 (32)	32 (26)	244		130 (35) 92 (37)	46 (37)	268
			DIM <90	109 (27) 77 (28)	37 (29)	223		143 (39) 93 (38)	43 (35)	279
	Lactation stage	DIM 90-150 85 (21)	58 (21)	20 (15)	163	0.70	61 (16) 45 (18)	20 (16)	126	0.90
			DIM ≥150	206 (52) 143 (51) 72 (56)	421		168 (45) 107 (44) 59 (48)	334
	Cow hygiene	feet	Fair (< 2) Poor (≥ 2)	315 (78) 215 (77) 103 (80) 633 85 (22) 63 (23) 26 (20) 174	0.82	283 (76) 206 (83) 78 (64) 91 (24) 41 (17) 44 (36)	567 176	≤0.001
	Preventive hoof-trimming	Yes No	328 (82) 240 (86) 97 (75) 72 (18) 38 (14) 32 (25)	665 142	≤0.05	318 (85) 200 (81) 110 (90) 628 56 (15) 47 (19) 12 (10) 115	0.06
			< 25	93 (23)	38 (14)	47 (36)	178		123 (33) 47 (19)	78 (64)	248
	Initial prevalence	25-35	128 (32) 95 (34)	36 (28)	259	≤0.001	154 (41) 127 (51) 23 (19)	304	≤0.001
			>35	179 (45) 145 (52) 46 (36)	370		97 (26) 73 (30)	21 (17)	191
	Proportion of < 33%	131 (33) 55 (20)	83 (64)	269	≤0.001	156 (42) 66 (27)	81 (66)	303	≤0.001

a LC=Lactating cows

ACKNOWLEDGMENTS

The authors acknowledge the farmers and veterinarians who have contributed to this study.

Additionally, we thank G. Puel (Oniris, Nantes, France) and Y. Quenet (INRA, Nantes, France) for helpful participation as investigators, for their time and motivation.

Funding: This study was supported as part of a Ph.D. studentship by Qalian (Neovia group, Segré, France) and the "Association Nationale de la Recherche et de la Technologie" (ANRT, Paris, France).

* Time-dependent covariates; "number of feet" are transitions between categories during the follow-up trial period.


Caroline Toffolon-Masclet

Laure Martinelli

Clara Desgranges

Paul Lafaye

Jean-Christophe Brachet

Fabrice Legendre

Jean-Claude Crivello

Jean-Marc Joubert

Daniel Monceau

J.-C Brachet

J-C Crivello

J-M Joubert

Development of thermokinetic tools for phase transformation studies of Zr alloys in service and LOCA conditions

Keywords: Thermodynamic, kinetic, Zr-base alloys, ab-initio calculations, corrosion

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

Introduction

Multi-alloying and processing are important factors influencing microstructural evolutions and phase transformations in industrial Zirconium alloys. In operating or in accidental conditions in nuclear power plant, the microstructure of these alloys is modified. Thus, tools enabling the determination of phase transformation temperatures, chemical compositions and volume fractions of phases taking into account several alloying elements, are of high interest. In this context, computational thermodynamics and kinetics represent powerful tools for industrial applications.

These last years, a couple of thermodynamic databases for Zr alloys have been developed using the CALPHAD modelling method [START_REF] Dupin | Thermodynamic database for zirconium alloys[END_REF] [START_REF] Barberis | Microstructure and phase control in Zr-Fe-Cr-Ni alloys: Thermodynamic and kinetic aspects[END_REF]. The formalism used within the CALPHAD method enforces the description of end-members. In the former databases, the metastable end-members were given arbitrary values for the formation enthalpy, since they were not measurable experimentally. Density Funstional Theory (DFT) calculations enabled the determination of these formation enthalpy. Thus, a new thermodynamic database for zirconium alloys has been created, including a systematic use of DFT calculations for the determination of formation enthalpies of metastable phases.

High temperature (HT) oxidation and its influence on the mechanical behavior of cladding tubes is a subject of matter as well. Indeed, during some hypothetical Pressurized Water Reactor (PWR) accidental scenario, like Loss of Coolant Accident (LOCA), the oxidation phenomena is accelerated, leading to the formation and growth of two brittle phases: ZrO2 and Zr enriched in oxygen, from the parent Zr ductile phase. Thus, once the whole system is quenched down to room temperature, the only ductile phase is the Zr phase. It has been demonstrated that the ductility of this quenched Zr phase depends upon the O content: for oxygen contents superior to 0.4wt.%, this phase becomes brittle [START_REF] Brachet | Hydrogen content, Preoxidation, and Cooling Scenario Effects on Post-Quench Microstructure and Mechanical Properties of Zircaloy-4 and M5 Alloys in LOCA Conditions[END_REF]. A tool has been developed, Ekinox-Zr [4]- [START_REF] Mazères | Modeling Two-and Three-Stage Oxygen Tracer Experiments during High-Temperature Oxidation of Metals with a High Oxygen Solubility[END_REF], able to calculate the O concentration profiles in the three successive layers, ZrO2, Zr and Zr, and the growth of these layers as a function of time at a given temperature [START_REF] Corvalan-Moya | Numerical modeling of oxygen diffusion in the wall thickness of Low-Tin Zircaloy-4 fuel cladding tube during high temperature (1100-1250 °C) steam oxidation[END_REF]. This tool, linked to the Zircobase database and the Thermo-Calc software, has already demonstrated its ability to forecast high temperature isothermal oxidation of Zr alloys [START_REF] Toffolon-Masclet | Simulation of the β→α(O) Phase Transformation due to Oxygen Diffusion during High Temperature Oxidation of Zirconium Alloys[END_REF]- [START_REF] Mazères | Modeling Two-and Three-Stage Oxygen Tracer Experiments during High-Temperature Oxidation of Metals with a High Oxygen Solubility[END_REF].

A first part of this article is dedicated to the description of the new thermodynamic database containing the following elements: Cr, Fe, Nb, Sn, Zr. Two of the 20 binary and ternary systems constituting this database, Fe-Nb and Fe-Nb-Zr, are more specifically described. Then application examples are presented illustrating the performance of the database.

The second part of this paper deals with the modification of the Ekinox-Zr code in order to simulate anisothermal oxidation transients and its linkage to the OCASI interface of the OpenCalphad software (free software for multicomponent equilibrium calculations).

Thermodynamic tool

METHODOLOGY

Calphad methodology

The Gibbs energy of each phase is described considering the sublattice model chosen and using the Compound Energy Formalism (CEF) [START_REF] Hillert | The compound energy formalism[END_REF].

The total molar Gibbs energy of a given  phase is expressed as follows:

= - +
where is the Gibbs energy surface of reference and represents the site occupancy weighted average molar Gibbs energy of the ordered structure.

is the configurational entropy of the α phase and is based on the number of possible arrangements of the constituents of the phase.

represents the excess Gibbs energy of mixing allowing to represent a deviation from ideality.

The crystallography of the different phases is respected, as much as possible, in the sublattice model chosen for the different phases. Furthermore, in order to give account of the existence of a homogeneity range for a given phase, all elements are allowed to enter all sublattices to reflect substitution mechanisms. Thus, the model adopted will generate so called end-members i.e.

stoichiometric compounds corresponding to all the possible combinations with each sublattice occupied by a single element. Among them, only one corresponds to a stable phase and can be evaluated experimentally, the other ones are metastable or not stable and cannot be derived from experimental data. However, the Gibbs energies of formation of all of them appear in the expression of the total molar Gibbs energy of the phase. Thus, the formation enthalpies of the metastable or unstable phases can be calculated by ab initio methods.

DFT calculations

DFT calculations were performed using the Vienna Ab-Initio Simulation Package (VASP) code [START_REF] Kresse | Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set[END_REF], [START_REF] Kresse | From ultrasoft pseudopotentials to the projector augmentedwave method[END_REF]. The calculations were done using the generalized gradient approximation (GGA) with the Perdew-Burke-Ernzerhof (PBE) [START_REF] Perdew | Generalized gradient approximation made simple[END_REF] functional and with projector augmented wave (PAW) pseudo potentials (PP).

The formation enthalpy is obtained by subtracting the total energy of the structure calculated by DFT to the molar fraction weighted sum of the energies of the pure elements in their Stable Element Reference (SER).

Mixing enthalpies were also determined for solid solutions using the SQS method [START_REF] Zunger | Special Quasi Random Structures[END_REF]. It consists in generating a series of "special" configurations that reproduce the random disorder of a solid solution at a given composition with a limited number of atoms per unit cell. The quality of the "special" configuration is evaluated by comparison to its correlation function relative to those of a perfectly disordered state. The mixing enthalpy is calculated by subtracting the total energy of the SQS structure calculated by DFT to the molar fraction weighted sum of the energies of the pure elements in to the solid solution structure.

Results

THERMODYNAMIC ASSESSMENT

Among the binary and ternary systems included in the newly created thermodynamic database, the Fe-Nb-Zr ternary system and its three constitutive binary systems , Nb-Zr, Fe-Zr and Fe-Nb, will be presented hereafter.

The Nb-Zr system

The reference assessment for this system is the one of Guillermet [START_REF] Guillermet | Thermodynamic Analysis of the Stable Phases in the Zr-Nb System and Calculation of the Phase-Diagram[END_REF]. All the available experimental and calculated data available for this system have been considered for our new assessment [START_REF] Lafaye | Experimental investigations and thermodynamic modelling of the Cr-Nb-Sn-Zr system[END_REF].

This new description of the Nb-Zr system is presented in FIG. 1. It shows a slightly better agreement of the monotectoid temperature, 596°C, with experimental data, and consequently, the miscibility gap is better described.

FIG. 1Calculated Nb-Zr system calculated from [START_REF] Lafaye | Experimental investigations and thermodynamic modelling of the Cr-Nb-Sn-Zr system[END_REF].

The Fe-Zr binary system

The Fe-Zr system has been assessed several times using the CALPHAD method [START_REF] Servant | Experimental and thermodynamic assessment of the Fe-Zr system[END_REF]- [START_REF] Yang | Thermodynamic modeling and experimental study of the Fe-Cr-Zr system[END_REF].

The result of our assessment is detailed in [START_REF] Lafaye | New experimental study, first-principles calculations and thermodynamic modelling of the ternary Fe-Sn-Zr system[END_REF] and the obtained phase diagram is presented in FIG.

2. Four intermetallic phases have been considered: two Fe2Zr Laves phases C36 and C15, FeZr2 and FeZr3.

FIG. 2 Fe-Zr phase diagram calculated from [START_REF] Lafaye | New experimental study, first-principles calculations and thermodynamic modelling of the ternary Fe-Sn-Zr system[END_REF] This new assessment shows a very good agreement of the calculated solidus and solvus with experimental data in the Zr rich part of the system. The invariant reactions are also very well described in this part of the diagram.

The Fe-Nb binary system

Many experimental studies have been dedicated to this system [START_REF] Voronov | N[END_REF]- [START_REF] Drys | Phase equilibira in the niobium-gallium-iron system at 1000°C[END_REF]. Two intermetallic phases are present: Fe2Nb (C14) and Fe7Nb6 (µ) phases.

The DFT calculations, performed at 0K, confirm the stability of the Fe2Nb and Fe7Nb6 phases.

Indeed the calculated ground state is in good agreement with the experimental diagram (FIG. 3).

FIG. 3Fe-Nb system: Calculated formation enthalpies of the intermetallic phases compared to experimental data (Meschel06 [START_REF] Meschel | Standard enthalpies of formation of some 3d, 4d and 5d transition-metal stannides by direct synthesis calorimetry[END_REF] and Syutkin06 [START_REF] Syutkin | Thermochimica Acta Experimental determination of the thermodynamic properties of the Laves phases in the Cr -Fe -Nb system[END_REF]) and calculated ones (Liu12 [START_REF] Liu | CALPHAD : Computer Coupling of Phase Diagrams and Thermochemistry Ab initio calculations and thermodynamic modeling for the Fe -Mn -Nb system[END_REF], Mathon09 [START_REF] Mathon | CALPHAD : Computer Coupling of Phase Diagrams and Thermochemistry Calphad-type assessment of the Fe -Nb -Ni ternary system[END_REF] and Ladines15 [START_REF] Ladines | Intermetallics Structural stability of Fe-based topologically close-packed phases[END_REF]).

The calculated data are in good agreement with the data from Liu et al. [START_REF] Liu | CALPHAD : Computer Coupling of Phase Diagrams and Thermochemistry Ab initio calculations and thermodynamic modeling for the Fe -Mn -Nb system[END_REF], Mathon et al. [START_REF] Mathon | CALPHAD : Computer Coupling of Phase Diagrams and Thermochemistry Calphad-type assessment of the Fe -Nb -Ni ternary system[END_REF] and Ladines et al. [START_REF] Ladines | Intermetallics Structural stability of Fe-based topologically close-packed phases[END_REF], and the experimental one from Syutkin et al. [START_REF] Syutkin | Thermochimica Acta Experimental determination of the thermodynamic properties of the Laves phases in the Cr -Fe -Nb system[END_REF] as well. The experimental data from Meschel et al. [START_REF] Meschel | Standard enthalpies of formation of some 3d, 4d and 5d transition-metal stannides by direct synthesis calorimetry[END_REF] show strong disagreement. The optimised ground-state is calculated from our assesment. It also shows very good agreement with the calculated one.

The calculated mixing enthalpies of the Fe solid solution (fcc) and Fe and Nb rich solid solutions (bcc) are represented in FIG. 4 and compared to optimized data from literature and from these calculations.

FIG. 4Fe-Nb system : mixing enthalpies of the fcc and bcc solid solutions compared to optimised data from Khvan13 [START_REF] Khvan | CALPHAD : Computer Coupling of Phase Diagrams and Thermochemistry Thermodynamic description of the Fe -Mn -Nb -C system[END_REF] and Liu12 [START_REF] Liu | CALPHAD : Computer Coupling of Phase Diagrams and Thermochemistry Ab initio calculations and thermodynamic modeling for the Fe -Mn -Nb system[END_REF] For fcc phase, our optimized mixing enthalpy show a good agreement with the data from Khvan et al. [START_REF] Khvan | CALPHAD : Computer Coupling of Phase Diagrams and Thermochemistry Thermodynamic description of the Fe -Mn -Nb -C system[END_REF], and a reasonable agreement with our SQS calculations. On the contrary, the data from Liu et al. [START_REF] Liu | CALPHAD : Computer Coupling of Phase Diagrams and Thermochemistry Ab initio calculations and thermodynamic modeling for the Fe -Mn -Nb system[END_REF] show a complete disagreement. For the bcc phase, our optimized mixing enthalpy is in good agreement with the optimized data from [START_REF] Khvan | CALPHAD : Computer Coupling of Phase Diagrams and Thermochemistry Thermodynamic description of the Fe -Mn -Nb -C system[END_REF] as well. It shows attractive interaction and an assymetrical shape on the Fe rich side. Strong disagreement still exist with the data from Liu et al. [START_REF] Liu | CALPHAD : Computer Coupling of Phase Diagrams and Thermochemistry Ab initio calculations and thermodynamic modeling for the Fe -Mn -Nb system[END_REF].

FIG. 5Calculated Fe-Nb phase diagram compared to data from Eggers38 [23], Genders39 [30], Ferrier64 [START_REF] Ferrier | Etude du diagramme Fer-Niobium entre 0 et 12 at % de niobium dans l'intervalle 1200-1535 °C[END_REF], Fisher70 [START_REF] Fischer | Examination of a gamma transformation in very pure binary alloys of iron with molybdenum, vanadium, tungsten, niobium, tantalum, zirconium and cobalt[END_REF], Abrahamson66 [START_REF] Abrahamson | The lattice parameters and solubility limits of alpha iron as affected by some binary transition-element additions[END_REF], Gibson61 [32], Voronov37 [START_REF] Voronov | N[END_REF], Bejarano91-93 [START_REF] Bejarano | On the existence of the Fe2Nb3 phase in the Fe-Nb system[END_REF], [START_REF] Bejarano | the iron-niobium phase[END_REF], Voss11 [START_REF] Voss | Phase Equilibria in the Fe-Nb System[END_REF] Finally, the calculated phase diagram is presented in FIG. 5, showing a good agreement with literature data.

The Fe-Nb-Zr ternary system

Once each binary system of interest is optimized, it is possible to start the optimization of ternary systems. Many studies have been dedicated to the Fe-Nb-Zr system [44]- [START_REF] Toffolon-Masclet | Contribution of Thermodynamic Calculations to Metallurgical Studies of Multi-Component Zirconium Based Alloys[END_REF]. Two ternary intermetallic phases are reported in this system: the hexagonal C14 Laves phase (Fe,Nb)2Zr and the fcc Ti2Ni phase (Nb,Zr)2Fe. A few authors [START_REF] Granovsky | Experimental Investigation of the Zr corner of the Ternary Zr-Nb-Fe Phase Diagram[END_REF], [START_REF] Liang | Contribution on the phase equilibria in Zr-Nb-Fe system[END_REF], [START_REF] Arreguez | Short communication on experimental phase diagram of the Fe corner in the Fe-Nb-Zr system at 800 C[END_REF] report the existence of an additional ternary phase: a hexagonal C36-Laves phase Fe2(Nb,Zr) (FIG. 6).

10

FIG. 6Ternary isothermal section of the FeNbZr system experimentally determined at 800°C by Granovsky et al. [START_REF] Granovsky | Experimental Investigation of the Zr corner of the Ternary Zr-Nb-Fe Phase Diagram[END_REF] The presence of this phase is a matter of debate. Thus, its potential existence has been checked within this work both experimentally and by DFT calculations. The experimental verification consisted in fabricating an alloy at the targeted composition, that is Fe2Nb0,5Zr0,5. This alloy was annealed three weeks at 800°C and analyzed by X-ray diffraction and microprobe. These analyses showed the presence of two phases: Fe2Zr (C15 Laves phase) and Fe2Nb (C14 Laves phase).

The formation enthalpies of the end-members of phases Fe2Nb (C14), Fe2Zr (C15) and Fe2(Nb,Zr) (C36) have been calculated at 0K by means of DFT along the 66 at.% Fe isocomposition as represented in FIG. 7.

FIG. 7Calculated formation enthalpies along the Fe2Nb-Fe2Zr line.

These calculations clearly show the unstability of the Fe2(Nb,Zr) (C36) phase along this line.

The thermodynamic assessment has been done taking into account our DFT calculations and most of the experimental data. Two calculated isothermal sections are presented in FIG. 8 and. 9. They show a good agreement with experimental data from litterature.

FIG. 8Isothermal section of the Fe-Nb-Zr system calculated at 800°C and compared to experimental measurements from Ramos03-07 [START_REF] Ramos | Effects of Nb content on the Zr2Fe Intermetallic stability[END_REF], [START_REF] Ramos | Some new experimental results on the Zr-Nb-Fe system[END_REF] and Granovsky02 [START_REF] Granovsky | Experimental Investigation of the Zr corner of the Ternary Zr-Nb-Fe Phase Diagram[END_REF] FIG. 9Isothermal section of the Fe-Nb-Zr system calculated at 900°C and compared to experimental measurements from Ramos07 [START_REF] Ramos | Some new experimental results on the Zr-Nb-Fe system[END_REF] Discussion A similar methodology has been applied to the ten binary systems and ten ternary systems constituting the quinary Zr-Cr-Fe-Nb-Sn system [START_REF] Lafaye | Experimental investigations and thermodynamic modelling of the Cr-Nb-Sn-Zr system[END_REF], [START_REF] Lafaye | Thermodynamic modelling of the Cr-Nb-Sn system[END_REF] leading to a new thermodynamic database for Zr base alloys. The ten binary systems have been reassessed. Four among the ten ternary systems were completely unknown : Cr-Sn-Zr, Cr-Nb-Sn [START_REF] Lafaye | Experimental investigations and thermodynamic modelling of the Cr-Nb-Sn-Zr system[END_REF], Cr-Fe-Sn and Fe-Nb-Sn and have thus been studied using experiments and calculations.

The accuracy of this new database is illustrated hereafter with two different examples.

The first one comes from [START_REF] Toffolon-Masclet | Contribution of Thermodynamic Calculations to Metallurgical Studies of Multi-Component Zirconium Based Alloys[END_REF]. In this work, three ternary Fe-Nb-Zr, A1, A2 and A3 reported in 13

The chemical composition and the volume fraction of the different phases were determined by microprobe analysis and image analysis. The second example concerns the Zr-0.7Nb-0.3Sn-0.35Fe-0.25Cr quinary alloy that was studied experimentally by Barberis et al. [START_REF] Barberis | Thermodynamics of Zr Alloys: Application to Heterogeneous Materials[END_REF]. In this work, the chemical compositions of the second phase precipitates have been measured by EDS analysis after 2h annealing treatment at 675°C. The authors report the presence of two intermetallic phases identified as Laves C14 phases for both of them. The thermodynamic database used in this work predicted only one intermetallic phase: the Zr(Nb,Fe)2 -C14 phase. The calculations performed with the new thermodynamic database are reported in Table 2 and compared to the experimental measurements and predictions using the Zircobase database [START_REF] Dupin | Thermodynamic database for zirconium alloys[END_REF] TABLE 2 : Comparison between predicted and measured chemical compositions of second phase precipitates in Zr-0,7Nb-0,3Sn-0,35Fe-0,25Cr annealed 2h at 675°C. Phase at.% Zr at.% Nb at.% Fe at.% Cr Réf. Zr(Nb,Fe,Cr)2

(Nb,Fe)2 -C14 34, 33,8 20,2 29,2 16,8 [56] Zr(Fe,Cr)2 33,0 4,6 29,5 32,9 [56] Zr
The Zircobase database predicts the presence of only one C14 Zr(Nb,Fe)2 phase. The experimental measurements detected two intermetallic phases: a Nb enriched and a Nb impoverished one. The authors identified these phases as two C14 phases, only based on EDS measurements.

Crystallographic structure determinations should be done on these samples in order to settle the right ones. Our thermodynamic calculations predict two intermetallic phases: a Zr(Nb,Fe)2 -C14 and a Zr(Fe,Cr)2 -C15. The calculated chemical compositions are in quite good agreement with the experimental ones.

Kinetic tool

METHODOLOGY

Ekinox-Zr

Ekinox-Zr is a numerical tool able to simulate the oxidation of zirconium alloys at high temperature [START_REF] Toffolon-Masclet | Simulation of the β→α(O) Phase Transformation due to Oxygen Diffusion during High Temperature Oxidation of Zirconium Alloys[END_REF], [START_REF] Mazères | Contribution to modeling of hydrogen effect on oxygen diffusion in Zy-4 alloy during high temperature steam oxidation[END_REF], [START_REF] Corvalan-Moya | Numerical modeling of oxygen diffusion in the wall thickness of Low-Tin Zircaloy-4 fuel cladding tube during high temperature (1100-1250 °C) steam oxidation[END_REF]. In this model, the cladding tube is represented as a one-dimensional domain containing the successive layers: ZrO2, Zr(O) and Zr . The diffusion profiles of oxygen are calculated thanks to the numerical resolution of Fick's equations with boundary conditions on moving interfaces (gas/ZrO2, ZrO2/Zr(O) and Zr(O) /Zr). A strong hypothesis of this code is to consider local thermodynamic equilibrium at the 3 different interfaces. Furthermore, in order to obtain accurate concentration values at the different interfaces, the code was linked to the Zircobase database via the TQ interface of Thermo-Calc.

This tool already demonstrated its ability to:

-simulate oxygen diffusion profiles in Zr(O) and Zr in Zr alloys during isothermal oxidation at high temperature [1100-1250°C] [START_REF] Corvalan-Moya | Numerical modeling of oxygen diffusion in the wall thickness of Low-Tin Zircaloy-4 fuel cladding tube during high temperature (1100-1250 °C) steam oxidation[END_REF];

-take into account the influence of hydrogen of HT oxidation [START_REF] Mazères | Contribution to modeling of hydrogen effect on oxygen diffusion in Zy-4 alloy during high temperature steam oxidation[END_REF] -take into account the effect of a pre-oxide layer presence on the oxygen concentration profile during HT oxidation [START_REF] Mazères | Experimental study and numerical simulation of high temperature (1100-1250 °C) oxidation of prior-oxidized zirconium alloy[END_REF] The new development of the Ekinox-Zr code presented hereafter concerned the simulation of anisothermal transients.

Results and discussion

The Ekinox-Zr code has been recently linked to the Zircobase via the OCASI interface of the OpenCalphad software. OpenCalphad is a free software for multicomponent equilibrium calculations similar to Thermo-Calc. Then, the code has been modified in order to be able to calculate anisothermal transients. Anisothermal calculations have been performed and compared to experimental data obtained on Zy-4 alloy.

The experimental oxidations were performed under a mixture containing 60% O2 / 40% He using Thermogravimetric analysis.

The experimental oxidation kinetics obtained for two different heating rates, 2 and 20°C/min between 1100 and 1275°C, are compared to Ekinox-Zr simulations in Figure 13.

For both heating rates, 2 and 20°C/min, the experimental kinetics deviate from the usual parabolic kinetics (Figure 13b andd) after respectively 1300 s and 165 s of oxidation. These oxidation durations correspond to roughly 1144°C and 1155°C respectively. This breakaway oxidation is not reproduced by simulation. It is attributed to the occurrence of the ZrO2 monoclinic to ZrO2 tetragonal phase transformation that leads to micro-cracking of the oxide scale and consequently to the breakaway oxidation. This refinement is not included yet in the Ekinox-Zr code: only a global ZrO2 layer is taken into account. Different studies tend to demonstrate that the tetragonal structure of zirconia is stabilized at temperatures inferior to its existence temperature range, at the metal / oxide interface thanks to the existence of stresses [START_REF] Garvie | Stabilization of the tetragonal structureof zirconia microcrystals[END_REF]- [START_REF] Garvie | Thermodynamics of the tetragonal to monoclinic phase transformation in constrained zirconia microcrystals -Part. 2 In the presence of an applied stress field[END_REF]. Thus, Ekinox-Zr could be modified to take into account two different layers in the zirconia phase. This is one of the development perspective of the code. However, before the breakaway, the Ekinox-Zr code reproduces very well the parabolic oxidation kinetics. This agreement between experiments and calculation shows that the code is now able to forecast oxidation kinetics in anisothermal conditions before the breakaway occurrence. One of the interest of the Ekinox-Zr code is to calculate oxygen concentration profiles in the metallic phases involved in the oxidation process. Such oxygen concentration profiles are represented in Figure 14 for both heating rates (2 and 20°C/min) and two conditions: at T=1133°C (Figure 14a) and after 200 s (Figure 14b) of anisothermal oxidation. The calculated profiles are consistent: at a given temperature, the cladding submitted to the slower heating rate is more oxidized as the thickness of the Zr phase is higher for the alloy heated at 2°C/min compared to the one heated at 20°C/min. The volume fraction of brittle phase is thus superior. However, for an equivalent low time of oxidation (200 s), the concentration profiles are quite similar. The oxygen uptake is similar but slightly higher in the Zr phase for the 2°C/min ramp and slightly higher in the Zr phase for the 20°C/min ramp. This result can be explained by the oxygen concentrations at the Zr/Zr interface that are higher in both phases for the 20°C/min ramp: the higher oxygen concentration in the Zr phase reduces the Zr phase growth, and the higher O flux within the Zr phase induces a higher O flux within the Zr layer.

Conclusions

This study highlights many advances both in Zr alloys thermodynamics and in Zr alloys oxidation kinetics:

 a new thermodynamic database for zirconium alloys, containing the Cr-Fe-Nb-Sn-Zr elements, has been developed, implying the systematic use of DFT calculation for the determination of specific parameters for formation enthalpies of metastable phases.

 The ten binary and ten ternary systems constituting this database have been reassessed

implying experimental verification for some of them. Hence, the non-stability of the C36-Laves in the Fe-Nb-Zr system has been demonstrated.

 The use of this database for thermodynamic computations show very good agreement with experimental data. These agreements demonstrate the consistency of the new thermodynamic database.

 The Ekinox-Zr numerical code enabling the calculation of oxidation kinetics and oxygen concentration profiles in Zr alloys during high temperature oxidation has been improved

to allow anisothermal calculations.

FIG. 10

 10 FIG.10shows a comparison of the experimental and calculated volume fractions in the three alloys

FIG. 13Anisothermal oxidations

  FIG. 13Anisothermal oxidations of Zy-4 alloy at 2°C/min (a) and 20°C/min (c) between 1100 and 1275°C. (b) and (d) represent the corresponding weight gain as a function of the square root of time.

FIG. 14Calculated concentration

  FIG. 14Calculated concentration profiles in Zy-4 alloy for anisothermal oxidation at two different heating rates: 2 and 20°C/min and for two different conditions: at T=1133°C (a) and after 200 s of oxidation (b).

TABLE 1 ,

 1 were fabricated and annealed at different temperatures.

TABLE 1 :

 1 Nominal chemical composition of the Fe-Nb-Zr alloys from[START_REF] Toffolon-Masclet | Contribution of Thermodynamic Calculations to Metallurgical Studies of Multi-Component Zirconium Based Alloys[END_REF]

	Alloy	wt.% Zr	wt.% Nb	wt.%Fe	at.%Zr	at.%Nb	at.%Fe
	A1	29	51	20	26	45	29
	A2	62	21	17	56	19	25
	A3	73	6	21	65	5	30


Cédric Baudrit

Patrice Buche

Nadine Leconte

Christophe Fernandez

Maëllis Belna

Geneviève Gésan-Guiziou

Towards decision support system for the agri-food sector using heterogeneous scientific data annotated with an ontology and Bayesian networks: a proof of concept applied to milk microfiltration

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

  Titre de la présentation Date / information / nom de l'auteur Cédric Baudrit, Patrice Buche, Nadine Leconte, Christophe Fernandez, Maëllis Belna, Geneviève Gésan-Guiziou UMR IATE Montpellier, I2M Bordeaux, STLO Rennes CATI DIISCICO Towards decision support system for the agrifood sector using heterogeneous scientific data annotated with an ontology and Bayesian networks: a proof of concept applied to milk microfiltration Decision tasks based on the scientific literature in the agri-food sector (here milk microfiltration) because: • Key role in the sector (here dairy sector) • Need to improve prediction of unit operation performances and optimize plant design (here microfiltration) • Existing models only available on restricted operating conditions Issues • Scientific data heterogeneously structured, available in textual format • Data uncertainty due to processes involving biological material • Data reliability due to the way experiments have been conducted p. 3 Titre de la présentation Date / information / nom de l'auteur Séminaire Sète Patrice Buche Proposal A Decision Support System (DSS) based on ontology and Bayesian networks which deals with the preceeding issues in order to: • structure and integrate heterogeneous experimental data sources by using ontologies • provide open access to annotated data • assess data source reliability • learn Bayesian networks using uncertain data taking into account data reliability

p. 15