PharmD Marie Allard
email: marie.allard3@gmail.com

PharmD Alicja Puszkiel
email: alicjapuszkiel@gmail.com

MD, PhD Filomena Conti
email: filomena.conti@aphp.fr

PharmD, PhD Lucie Chevillard
email: luciechevillard@gmail.com

MD, PhD Nassim Kamar
email: kamar.n@chu-toulouse.fr

PharmD Gaëlle Noé
email: gaelle.noe@aphp.fr

PhD Mélanie White-Koning
email: melanie.white-koning@univ-tlse3.fr

PharmD Audrey Thomas-Schoemann

MD, PhD Tabassome Simon
email: tabassome.simon@aphp.fr

PharmD Michel Vidal
email: michel.vidal@aphp.fr

MD, PhD Yvon Calmus
email: yvon.calmus@aphp.fr

PharmD Benoit Blanchet
email: benoit.blanchet@aphp.fr

Pharmacokinetics and Pharmacodynamics of Once-daily Prolonged-release Tacrolimus in Liver Transplant Recipients

Keywords: ClinicalTrials.gov Registration identification NCT02105155 liver transplantation, prolonged-release tacrolimus, pharmacokinetics, calcineurin activity

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

1

Abstract

Purpose

There is limited published data regarding the pharmacokinetics (PK) and pharmacodynamics (PD) of prolonged-release tacrolimus (PRT) after liver transplant. We aimed to compare PK and PD of PRT in early and stable liver transplant recipients by developing a population PK model of PRT and investigating the profile of calcineurin activity (CNA) in the peripheral blood mononuclear cells.

Methods

A conversion from twice-daily immediate-release tacrolimus (IRT) to once-daily PRT based on one-to-one daily dose was performed at day 7 (D7) and D90 post-transplantation in groups A (n = 12) and B (n = 12), respectively. Extensive PK samplings including whole blood tacrolimus (TAC) concentration and CNA assessment were performed at D14 and D104 in groups A and B, respectively. TAC concentration-time data (n = 221) were analyzed using non-linear mixed effects modeling.

Findings

A two-compartment model with linear elimination and a delayed first order absorption characterized by two transit compartments best described PK data. Model-predicted dosenormalized (6.0 mg/day) area under the TAC concentration-time curve over the dosing interval (AUCTAC) in groups A and B were similar (geometric mean 235.6 ng/mL.h [CI95% = 139.6 -598.7] vs 224.6 ng/mL.h [117. 6 -421.5], respectively, p = 0.94). Area under the CNA versus time curve over the dosing interval (AUCCNA) were not different between both groups (4897 ± 3437 and 4079 ± 1008 pmol/min/10 6 cells, respectively, p = 0.50). In group A, trough CNA at D14 post-transplantation was statistically higher than that measured just before the switch to PRT (i.e D7 post-transplantation) (198 ± 92 vs 124 ± 72 pmol/min/10 6 cells, n = 8, respectively, p = 0.048), while no statistical difference in TAC concentration was observed (p = 0.11). In group B, no statistical difference between D90 and D104 was observed in either trough CNA (149 ± 78 vs 172 ± 82 pmol/min/10 6 cells, respectively, n = 6, p = 0.18) or TAC concentration (p = 0.17). No graft rejection was observed in either of the groups.

Introduction

Tacrolimus (TAC) is a key immunosuppressive agent for the prevention and treatment of allograft rejection in liver transplantation [START_REF] Association | European Organisation For Research And Treatment Of Cancer. EASL-EORTC clinical practice guidelines: management of hepatocellular carcinoma[END_REF] . TAC binds with high affinity to FK-binding protein 12 [START_REF] Bram | Identification of the immunophilins capable of mediating inhibition of signal transduction by cyclosporin A and FK506: roles of calcineurin binding and cellular location[END_REF] . The drug-receptor complex specifically and competitively binds to and inhibits calcineurin, a calcium-and calmodulin-dependent phosphatase. This process inhibits the translocation of a family of transcription factors (NF-AT), leading to reduced transcriptional activation of cytokine genes such as interleukin (IL)-2 and thereby to a reduction of T-cell proliferation [START_REF] Schreiber | The mechanism of action of cyclosporin A and FK506[END_REF] . TAC has a narrow therapeutic range and a significant between-subject variability (BSV), and thus a close monitoring of whole blood trough concentrations is required to avoid under-or over-exposure [START_REF] Wallemacq | Opportunities to optimize tacrolimus therapy in solid organ transplantation: report of the European consensus conference[END_REF] . Hence, therapeutic drug monitoring of TAC in liver transplant recipients is the benchmark method in this indication 1 . However, some liver transplant recipients with sufficient exposure to TAC nonetheless experience graft rejection [START_REF] Capron | Intra-cellular immunosuppressive drugs monitoring: A step forward towards better therapeutic efficacy after organ transplantation?[END_REF][START_REF] Fukudo | Pharmacodynamic analysis of tacrolimus and cyclosporine in living-donor liver transplant patients[END_REF] , suggesting that whole blood trough concentration may not be the most appropriate surrogate marker of pharmacodynamics (PD) in these patients. Different approaches such as evaluation of TAC intracellular concentration in peripheral blood mononuclear cells (PBMC) [START_REF] Lemaitre | Pharmacokinetics and pharmacodynamics of tacrolimus in liver transplant recipients: inside the white blood cells[END_REF] or calcineurin activity (CNA) in PBMC [START_REF] Fukudo | Pharmacodynamic analysis of tacrolimus and cyclosporine in living-donor liver transplant patients[END_REF][START_REF] Lemaitre | Pharmacokinetics and pharmacodynamics of tacrolimus in liver transplant recipients: inside the white blood cells[END_REF][START_REF] Blanchet | Pharmacokinetic-pharmacodynamic assessment of tacrolimus in liver-transplant recipients during the early post-transplantation period[END_REF][START_REF] Yano | Significance of trough monitoring for tacrolimus blood concentration and calcineurin activity in adult patients undergoing primary living-donor liver transplantation[END_REF] could be helpful to overcome this issue in those patients. However, they are not currently used for the clinical management of liver transplant recipients in daily clinical practice.

Liver transplant recipients are usually treated with twice-daily immediate-release tacrolimus (IRT) (Prograf®). Non-adherence to treatment has been found to be a significant factor associated with graft rejection and graft loss [START_REF] Muduma | Budget impact of switching from an immediate-release to a prolonged-release formulation of tacrolimus in renal transplant recipients in the UK based on differences in adherence[END_REF] . A once-daily prolonged-release tacrolimus (PRT) (Advagraf®) has been developed to improve treatment adherence. The phase III trial conducted in de novo liver transplant recipients showed that both efficacy and safety profiles were similar between twice-daily IRT and once-daily PRT [START_REF] Trunečka | Once-daily prolonged-release tacrolimus (ADVAGRAF) versus twice-daily tacrolimus (PROGRAF) in liver transplantation[END_REF] . The twice-daily dosage of IRT usually shifts to once-daily PRT based on a one-to-one conversion (i.e. same daily dose for IRT and PRT). The narrow therapeutic range and the significant BSV in the pharmacokinetics (PK) of TAC, could result in significant variations in PD in some patients, possibly leading to acute graft rejection within the early post-transplantation period. In this context, exploring both PK and PD of once-daily PRT at the time of conversion becomes mandatory. However, the PK data of once-daily PRT in liver transplant recipients are very sparse. A single population PK study was conducted to investigate once-daily PRT PK in stable liver transplant recipients [START_REF] Moes | Population pharmacokinetics and pharmacogenetics of once daily tacrolimus formulation in stable liver transplant recipients[END_REF] , while another study using a standard noncompartmental approach characterized its PK during the early post-transplantation period [START_REF] Ericzon | Pharmacokinetics of prolonged-release tacrolimus versus immediate-release tacrolimus in de novo liver transplantation: A randomized phase III substudy[END_REF] . In this context, a population PK study including data from the early and late posttransplantation period could be interesting to better characterize the PK/PD relationship of once-daily PRT in liver transplant recipients. Finally, as far as we know, the profile of CNA has not been investigated in PBMC from liver transplant recipients treated with once-daily PRT.

The aim of this study was to describe the PK of once-daily PRT using a population approach and to characterize the CNA profile in PBMC in liver transplant recipients treated with oncedaily PRT and included in the CONVERSION® trial.

Patients and Methods

Study population and treatment

The CONVERSION® trial (ClinicalTrials.gov Registration identification NCT02105155) is a prospective, randomized, multicenter trial aiming to prove the non-inferiority of the early conversion from IRT to PRT versus the conversion at three months after liver transplantation. Eligible patients (>18 years) underwent liver transplantation at day 1 (D1) and started treatment with IRT (Prograf ® ). A conversion from IRT to PRT (Advagraf ® ) was performed at D7 and D90 after transplantation in groups A and B, respectively (Figure 1).

The dosage of twice-daily IRT shifted to once-daily PRT based on a one-to-one conversion (i.e same daily dose for IRT and PRT). After conversion, daily dosing was adjusted according to TAC whole blood trough concentration with a therapeutic range of 6 -10 ng/mL 1 . All patients provided written informed consent. The protocol was approved by the Committee for the Protection of Persons and the French National Agency for Medicines and Health Products Safety.

Two hundred and fifty liver transplant recipients were supposed to be included in the CONVERSION® trial, and 40 of them in the PK/PD study (n = 20 in each group). However, only 90 patients were included in the CONVERSION® trial because of numerous simultaneous clinical trials. Furthermore, many patients refused to participate in the PK/PD study because of the lack of personal gain. In this context, PK and PD data come from 24 patients included in the CONVERSION® trial.

PK data collection

Extensive PK sampling was performed at D14 post-transplantation (i.e. at D7 postconversion) in group A and at D104 post-transplantation (i.e. at D14 post-conversion) in group B (Figure 1). Blood samples (7 mL) were drawn before next administration (at trough), 0.33, 0.66, 1, 2, 3, 4, 6, 8 and 24 hours after drug intake. Blood samples were also collected right before next drug intake (trough concentration) at D5, D7, D14, D30, D90 and D180 post-transplantation in group A and at D90, D104 and D180 post-transplantation in group B (Figure 1). Whole blood TAC concentrations were assayed using an ECLIA method [START_REF] Shipkova | Multi-center analytical evaluation of a novel automated tacrolimus immunoassay[END_REF] on Cobas 8000 (Roche Diagnostics, Meylan, France). The calibration range of the ECLIA method was 1 -40 ng/mL with a limit of detection of 0.5 ng/mL. The intermediate precision and accuracy of the ECLIA method were below 8.1% and 5.1%, respectively, at three levels of concentrations (2.5, 10.4 and 19.8 ng/mL) [START_REF] Shipkova | Multi-center analytical evaluation of a novel automated tacrolimus immunoassay[END_REF] . The accuracy of our method was ensured by our participation in the TAC Proficiency Testing Scheme provided by the Cardiac and Vascular Sciences Analytic Unit of St. George's Hospital Medical School (D. Holt, London, United Kingdom).

At each follow-up visit, body composition and biological parameters were collected: body weight (BW), lean body mass (LBM), hematocrit (HT), glomerular filtration rate (GFR) estimated by Cockcroft-Gault formula, alanine aminotransferase (ALT), aspartate aminotransferase (AST), albumin (ALB), bilirubin (BIL). LBM was estimated according to the McLeay et al. formula [START_REF] Mcleay | The relationship between drug clearance and body size: systematic review and meta-analysis of the literature published from 2000 to 2007[END_REF] .

Calcineurin activity in PBMC

Trough CNA in PBMC (just before drug intake) was assayed immediately before the switch to PRT (i.e. at D7 and D90 post-transplant for groups A and B, respectively, Figure 1). Furthermore, CNA was assayed on the blood samples from extensive PK sampling (D14 for group A and D104 for group B) before next administration (at trough), 0.33, 0.66, 1, 2, 3, 4, 6, 8 and 24 hours after drug intake. For each blood sample, PBMC isolation was performed within 24 hours after blood collection [START_REF] Blanchet | Determination of serine/threonine protein phosphatase type 2B PP2B in lymphocytes by HPLC[END_REF] . First, granulocyte depletion was performed to prevent the influence of granulocytes on CNA [START_REF] Blanchet | Distribution of calcineurin activity in blood cell fractions and impact of tacrolimus inhibition[END_REF] . For this purpose, the RosettSep ® kit was used according to the manufacturer's instructions (StemCell Technologies, Grenoble, France). Second, PBMC were isolated by Ficoll density-gradient centrifugation (Unisep Ficolltubes, Abcys, Jerusalem, Israel), then washed and counted with Xn-9000 (Sysmex, Villepinte, France). Each sample including 10 6 PBMC was dried and frozen at -80°C up to analysis. CNA assay was run in duplicate as previously described [START_REF] Blanchet | Determination of serine/threonine protein phosphatase type 2B PP2B in lymphocytes by HPLC[END_REF] . Briefly, PBMC lysates were incubated for 15 minutes at 30°C in analysis buffer including 50 mM Tris-HCl, pH 7.0, 0.1 M Ethylene glycol-bis(2-aminoethylether)-N,N,N',N'-tetraacetic acid (EGTA), 0.5 mM dithiothreitol, 1 mM MnCl2, 0.3 mg/mL bovine serum albumin, 0.1 mM EGTA, 1 mM CaCl2, 0.1 µM calmodulin and 500 nM okadaic acid. The reaction was initiated by adding a 19 amino-acid phosphopeptide (DLDVPIPGRFDRRVSVAAE, Bachem, Voisin, France). Aliquots were sampled at 5 and 10 minutes. The reaction was stopped with 0.5% perchloric acid. Dephosphorylated peptide concentrations were determined using high-performance liquid chromatography coupled with UV detection. The chromatography system consisted of Dionex Ultimate 300 equipped with a gradient pump with degas option and gradient mixer, a UV-visible detector, an autosampler, and a Chromeleon® chromatography workstation (Dionex Corporation, Sunnyvale, CA, USA). The within-day precision of this method was 13.3% including all the steps from blood collection to CNA assay [START_REF] Blanchet | Determination of serine/threonine protein phosphatase type 2B PP2B in lymphocytes by HPLC[END_REF] . CNA was expressed as picomole of formed dephosphorylated peptide per minute per 10 6 PBMC (pmol/min/10 6 cells).

Non-compartmental Pharmacokinetic Analysis

Whole blood concentrations of TAC from extensive PK sampling were used to calculate the area under the TAC concentration-time curve over the dosing interval (AUCTAC) using the trapezoidal rule.

Population Pharmacokinetic Analysis

TAC concentration-time data were analyzed by nonlinear mixed effects modeling using NONMEM® software (version 7.4, ICON Development Solutions, Ellicott City, MD, USA) with Piraña® (version 2.9.7) and PsN toolkit (version 4.7.0). Analyses were carried out with first order conditional estimation method with interaction (FOCE-I). Data processing and plots were performed in R (version 3.4.2). Several structural models were used to fit the concentration-time data. First, one and two compartment models with first order absorption and elimination were tested. Since TAC was administered as a prolonged-release formulation, a first order process with either a lag time or transit compartments with an identical transfer rate constant (ktr) were tested to account for the delay in the absorption phase. The inclusion of BSV and between-occasion variability (BOV) defined as OCC1 ≤ D28 and OCC2 > D28 for group A and OCC1 ≤ D105 and OCC2 > D105 for group B was tested on all PK parameters according to an exponential model:

ϴi = ϴµ • exp(ƞi + ƞ1iOCC1 + ƞ2iOCC2)
where ϴi is the estimate of the parameter for the ith subject, ϴµ is the population mean estimate of the PK parameter, ƞi is the deviation from the mean for the ith subject with zero mean and variance ω 2 , ƞ1i and ƞ2i is the deviation from the mean for the first (OCC1) and second (OCC2) occasion for the ith subject, respectively. Correlation between ƞ of PK parameters was tested using a ω block structure. The residual unexplained variability was described using a proportional error model. Model selection was based on the objective function value (OFV = -2loglikelihood), using the likelihood ratio test to test for significant differences in goodness-of-fit (GOF) between nested models. A drop of at least 3.84 (χ² test, α = 5%, degree of freedom = 1) between hierarchical models was considered statistically significant. Additionally, the plausibility of parameter estimates with their precision (expressed by relative standard error, %RSE), ƞ-shrinkage value and model stability were considered.

Covariate analysis

The individual parameter estimates of the base model were used to investigate the correlations with biological and demographic variables. The following covariates were tested for their influence on clearance (CL): age, sex (0 for male and 1 for female), BW, LBM, HT, GFR, AST, ALT, ALB, BIL and study group (GRP). As PK data come from a large time period, different values of a covariate for the same patient were included in the data. Continuous covariates were tested according to the linear function:

CL = ϴCL x (1+ ϴcov x (cov -covmean))
where ϴCL is the typical value of CL in the population, cov is the individual covariate value, covmean is the mean value of a covariate in the studied population, ϴcov is the fractional change in CL from the mean value of the covariate. Categorical covariates (sex, study group) were tested according to the following equation:

CL = ϴCL x ϴcov COV
where ϴcov is the estimated influential factor for a covariate and cov is 1 or 0. In the forward procedure, covariates were tested one by one and a covariate was considered significantly associated with a PK parameter if its inclusion resulted in a drop in OFV of at least 3.84 points (χ² test, α = 5%, df = 1). In the backward procedure, a full covariate model including the covariates significant in the forward procedure was built. A covariate remained in the final model if its removal resulted in an increase of at least 6.63 points (χ² test, α = 1%, df = 1) compared to the full covariate model.

Model evaluation

Diagnostic plots including population predictions (PRED) versus observed concentrations (DV), individual predictions (IPRED) versus DV, conditional weighted residuals (CWRES) versus PRED and time after dose were generated. Since patients were treated with different doses of TAC, the model validation was performed with a prediction-corrected visual predictive check (pcVPC) based on 1000 replicates of the original data set and presented as concentrations versus time after dose and stratified on study group to facilitate interpretation. Finally, 500 bootstrap analyses with resampling using the final model were performed.

Analysis of the individual PK parameters

The individual CL values obtained in NONMEM were used to calculate AUCTAC according to the following formula in the model input file:

AUCij = DOSEi x F/CLij
where AUCij is the area under the concentration-time curve over the dosing interval for the ith subject and jth occasion, DOSEi is the administered dose for the ith subject, CLij is the individual clearance value for the ith subject and jth occasion and F is the oral bioavailability of TAC (fixed in the model to 0.23 based on the literature) [START_REF] Scholten | AUC-guided dosing of tacrolimus prevents progressive systemic overexposure in renal transplant recipients[END_REF] .

Statistical Analysis

The demographic and biological characteristics of the study cohort are presented as median [interquartile range]. PK data are expressed as geometric mean [95% confidence interval, CI95%] and PD data are expressed as mean ± SD. The individual AUCTAC values obtained by non-compartmental analysis and population approach were normalized by the median daily dose which was administered prior to extensive PK sampling. Individual AUCTAC obtained in the non-compartmental analysis were compared with model-predicted AUCTAC for group A and B using non-parametric Wilcoxon paired sample test. AUCTAC obtained by both noncompartmental analysis and population approach were compared between group A and B using a Wilcoxon unpaired samples test. Since the number of patients per each study group is low, the ratio of the geometric means of AUCTAC group A over AUCTAC group B as well as its CI90% was calculated in addition to the non-parametric statistical tests to compare AUCTAC between groups A and B.

From data of extensive PK sampling, individual 24-hour area under the calcineurin activity versus time curve (AUCCNA) was calculated using the trapezoidal rule. Only PD data from extensive PK sampling were used to investigate the PK/PD relationship. The AUCCNA were compared between groups A and B using a Wilcoxon unpaired samples test. The relationship between AUCTAC and AUCCNA was tested using Spearman's correlation test. All tests were two-sided, and they were considered significant when p-values were <0.05. Computations were performed using R software and SAS V9 statistical package (SAS institute, Cary, NC, USA).

Results

Patients and TAC concentrations

The baseline demographic and biological characteristics of 24 patients (n = 12 patients in each group) included in the study are summarized in Table 1. Overall, 221 blood samples including those from therapeutic drug monitoring were available for the PK analysis. The median number of measurements per individual was 11 (range 1 -13). The sampling time was in the range 0.1 -27 h after drug intake. Four patients who did not have extensive PK sampling (n = 1 in group A and n = 3 in group B) withdrew their informed consent on the day of the analysis as they did not understand that a part of the study included several blood samples drawn throughout the day and required them to stay for a longer time in the medical department. For the remaining patients (n = 20), extensive PK sampling was performed at median 14 days (range 13 -21) and 104 days (95 -109) after transplantation in groups A and B, respectively. Figure 2 presents TAC concentrations versus time after dose at D14 (n = 11) and D104 (n = 9) for groups A and B, respectively (data from extensive PK sampling only).

Non-compartmental Pharmacokinetic Analysis

AUCTAC values were calculated using trapezoidal rule for the 20 patients (n = 11 and n = 9 for groups A and B, respectively) for which extensive PK data were available. The absolute AUCTAC means obtained by the non-compartmental analysis were similar between groups A and B (251.3 ng/mL.h [CI95% = 108.5 -460.7] and 200.7 ng/mL.h [CI95% = 126.0 -302.2], respectively, p = 0.17).

At the time of extensive PK sampling, the median dose of PRT was 7.0 mg/day and 5.0 mg/day in groups A and B, respectively, whereas median dose was 6.0 mg/day regardless of study group. The geometric means of dose-normalized AUCTAC (6.0 mg/day) were similar in groups A and B (234.5 ng/ml.h [CI95% = 130.3 -670.6] and 231.0 ng/ml.h [CI95% = 120.2 -433.4], respectively). The ratio of the geometric means of AUCTAC group A over AUCTAC group B was 1.01 [CI90% = 0.66 -1.56] (Table 2). The dose-normalized AUCTAC obtained by noncompartmental analysis were not statistically different between groups A and B (p = 0.77).

Population Pharmacokinetic Analysis

TAC concentration-time data were described by a two-compartment model with linear elimination and a delayed first order absorption characterized by two transit compartments with an identical ktr. Addition of transit compartments to describe the absorption phase resulted in a significant improvement of the model fit: one transit compartment dropped OFV by 14 points and two transit compartments by 25 points compared to the model without delayed absorption. Further addition of a third transit compartment did not improve the model fit. The PK parameters of the final model were: ktr, clearance (CL), volume of distribution of the central compartment (Vc), inter-compartmental clearance (Q), volume of distribution of the peripheral compartment (Vp). The bioavailability (F) of TAC was fixed to the value previously reported in the literature (F = 0.23) [START_REF] Scholten | AUC-guided dosing of tacrolimus prevents progressive systemic overexposure in renal transplant recipients[END_REF] . Therefore, the PK parameters (CL, Vc, Q, Vp) were reported as absolute values. BSV was included on ktr, CL and Q. BSV could not be reliably estimated on Vc and Vp and inclusion of BSV on F did not improve the model fit, thus BSV was fixed to zero for these three parameters. The addition of covariance between ƞ of the PK parameters did not improve the model fit. Finally, inclusion of BOV on CL resulted in a drop of 86 points in OFV and decreased the residual variability from 27.8% to 19.8%.

Covariate analysis

The covariate analysis was performed on CL only as ƞktr showed significant deviation from a normal distribution (Shapiro-Wilk test, p = 0.02) and ƞQ was associated with shrinkage of 35%. The correlation plots between individual CL of OCC1 and OCC2 and continuous covariates are presented in Supplementary Figure 1. The lack of influence of sex and GRP on CL is presented in Supplementary Figure 2. In the forward analysis, none of the tested covariates was significantly associated with CL (Supplementary Table 1) thus the final model did not include covariates. The estimates of the final model with corresponding %RSE are presented in Table 3.

Evaluation of the final model

GOF plots depicted in Figure 3 show no major bias of the model based on IPRED vs DV plot whereas CWRES vs PRED and time after dose were homogeneously distributed around the zero line although a slight bias at higher PRED values was observed. The pcVPC showed that the 5 th , 95 th percentiles and the median of the simulated data are in good agreement with the 5 th and 95 th percentiles and the median of the observed concentrations for both groups A and B (Figure 4). Finally, the mean estimates of the PK parameters from 500 bootstrap analyses are in accordance with those estimated using the original data set (Table 3).

Analysis of individual PK parameters

Model-predicted absolute AUCTAC at extensive PK sampling (corresponding to OCC1 for both group A and B) was no statistically different between group A and B (252.4 ng/mL.h [CI95% = 111.3 -510.5] vs 195.2 ng/mL.h [CI95% = 124.9 -302.1], respectively, p = 0.17, n = 20).

Table 2 presents model-predicted geometric means of AUCTAC normalized for a median dose of 6.0 mg/day. Dose-normalized AUCTAC were not statistically different between groups A and B (235.6 ng/mL.h [CI95% = 139.6 -598.7] and 224.6 ng/mL.h [CI95% = 117.6 -421.5] ng/mL.h, respectively, p = 0.94) and the ratio of the geometric means of AUCTAC group A over AUCTAC group B was 1.05 [CI90% = 0.70 -1.57] (Table 2). Finally, the comparison of AUCTAC obtained either by non-compartmental analysis or by population approach showed that both values were similar (p = 0.90 and p = 0.25 for groups A and B, respectively) further validating our PK model.

PRT pharmacodynamics

Figure 5 presents individual CNA profile (log scale) over the dosing interval at D14 for group A (n = 11) and D104 for group B (n = 9). The AUCCNA means were not statistically different between groups A and B (4897 ± 3437 and 4079 ± 1008 pmol/min/10 6 cells, Wilcoxon unpaired t-test p = 0.50). However, a larger BSV in AUCCNA was observed in group A (70.2 vs 24.7% for groups A and B, respectively). No relationship was found between AUCCNA and either model-predicted absolute AUCTAC (rho coefficient, ρ = 0.26, [CI95% = -0.20; 0.63]; p = 0.25; Figure 6) or TAC whole blood trough concentration (rho coefficient, ρ = 0.20, [CI95% = -0.27; 0.59], p = 0.39). The mean trough CNA activity (just prior TAC intake) at D14 posttransplantation in group A was statistically higher than that measured just before the switch to PRT (i.e. D7 post-transplantation) (198 ± 92 vs 124 ± 72 pmol/min/10 6 cells, n = 8, respectively; paired t-test, p = 0.048), while no statistical difference was observed for TAC whole blood trough concentration (6.9 ± 2.3 vs 10.1 ± 5.4 ng/mL, respectively; paired t-test, p = 0.11). Finally, no statistical difference between D90 and D104 was observed for either trough CNA (149 ± 78 vs 172 ± 82 pmol/min/10 6 cells, n = 6; paired t-test, p = 0.18) or TAC whole blood trough concentration (8.8 ± 4.6 vs 5.9 ± 2.1 ng/mL, respectively; paired t-test, p = 0.17). Finally, no graft rejection was observed in either group.

Discussion

PRT (Advagraf®) is EMA-approved for use in the context of liver transplants. However, there is limited published data regarding the PK and PD of PRT in this indication. As far as we know, the present study is the first to assess the PK of PRT within the early and late posttransplantation periods using a population approach. Furthermore, it provides new insights about the profile of CNA in PBMC from liver transplant recipients treated with PRT.

In the population PK analysis, blood concentration-time data of once-daily PRT were described by a two-compartment model with delayed absorption characterized by two transit compartments. This is consistent with a previous population PK study reported by Moes et al. in which a two-compartment model with three transit compartments was used to characterize the PK of once-daily PRT in 66 stable liver transplant recipients [START_REF] Moes | Population pharmacokinetics and pharmacogenetics of once daily tacrolimus formulation in stable liver transplant recipients[END_REF] . The mean estimate of CL in our analysis was 5.1 L/h (BSV = 34.7%) which is close to the value reported by Moes et al. (4.77 L/h, BSV = 45.4%). The analysis of the demographic and biological covariates on CL did not allow us to identify any significant correlations. This may be due to small sample size and the small dispersion of the covariates in our study. Nevertheless, in stable liver transplant recipients treated with PRT, Moes et al. did not report any significant influence of the covariates which we tested on total CL [START_REF] Moes | Population pharmacokinetics and pharmacogenetics of once daily tacrolimus formulation in stable liver transplant recipients[END_REF] .

It has been reported that the expression of CYP3A5*1, both in donor and receiver of a liver transplant, significantly increases CL of TAC in patients treated with PRT [START_REF] Moes | Population pharmacokinetics and pharmacogenetics of once daily tacrolimus formulation in stable liver transplant recipients[END_REF] . Other studies conducted in kidney transplant recipients treated with PRT also reported the influence of CYP3A5*1 on CL [START_REF] Woillard | Population pharmacokinetic model and Bayesian estimator for two tacrolimus formulations--twice daily Prograf and once daily Advagraf[END_REF][START_REF] Benkali | Population pharmacokinetics and Bayesian estimation of tacrolimus exposure in renal transplant recipients on a new once-daily formulation[END_REF] . We could not confirm or contradict these results because pharmacogenetic data were not available in our study. It was decided not to conduct an analysis of CYP3A5*1 genotype in the CONVERSION study because the frequency of CYP3A5*1 genotype in the French population is low (13%) [START_REF] Quaranta | Identification by single-strand conformational polymorphism analysis of known and new mutations of the CYP3A5 gene in a French population[END_REF] and as the study included a small number of patients, the statistical power would not have been sufficient to draw any firm conclusion. Similarly, using a mixture model in the PK population analysis to identify the subpopulation carrying the CYP3A5*1 allele would not have been possible. Regarding the genetic polymorphisms of drug transporters such as MDR1, although its influence on TAC PK has been reported, the results still remain controversial [START_REF] Tron | Pharmacogenetics of Membrane Transporters of Tacrolimus in Solid Organ Transplantation[END_REF] . In the same way as for the CYP3A5*1 genotype, our study could not contribute any results regarding the impact of the present study, no relationship was found between AUCTAC and AUCCNA values regardless of the moment of conversion from IRT to PRT, as previously reported [START_REF] Fukudo | Pharmacodynamic analysis of tacrolimus and cyclosporine in living-donor liver transplant patients[END_REF][START_REF] Lemaitre | Pharmacokinetics and pharmacodynamics of tacrolimus in liver transplant recipients: inside the white blood cells[END_REF][START_REF] Blanchet | Pharmacokinetic-pharmacodynamic assessment of tacrolimus in liver-transplant recipients during the early post-transplantation period[END_REF] . Different factors such as the amount of cytosolic FKBP12 [START_REF] Kung | Immunophilins may limit calcineurin inhibition by cyclosporine and tacrolimus at high drug concentrations[END_REF] and FKBP13, FKBP51 acting as a reservoir 2 , the genetic polymorphism of the calcineurin catalytic subunit α [START_REF] Noceti | Tacrolimus pharmacodynamics and pharmacogenetics along the calcineurin pathway in human lymphocytes[END_REF][START_REF] Noceti | Activity of the Calcineurin Pathway in Patients on the Liver Transplantation Waiting List: Factors of Variability and Response to Tacrolimus Inhibition[END_REF] and the etiology of liver disease before transplant [START_REF] Blanchet | Deficiency in calcineurin activity in liver transplantation candidates with alcoholic cirrhosis or hepatocellular carcinoma[END_REF] might significantly influence the CNA in PBMC regardless of the whole blood TAC concentration. Besides, Lemaitre et al. showed that CNA in PBMC was not further associated to intracellular concentration of TAC in liver transplant recipients [START_REF] Lemaitre | Pharmacokinetics and pharmacodynamics of tacrolimus in liver transplant recipients: inside the white blood cells[END_REF] , which supports our result. The BSV in AUCCNA for group A is in accordance with that reported at D7 and D14 post-transplantation in liver transplant recipients treated with twice-daily IRT [START_REF] Fukudo | Pharmacodynamic analysis of tacrolimus and cyclosporine in living-donor liver transplant patients[END_REF][START_REF] Lemaitre | Pharmacokinetics and pharmacodynamics of tacrolimus in liver transplant recipients: inside the white blood cells[END_REF][START_REF] Blanchet | Pharmacokinetic-pharmacodynamic assessment of tacrolimus in liver-transplant recipients during the early post-transplantation period[END_REF] . However, it was 3-fold higher compared to the BSV in AUCCNA for group B (70.2 vs 24.7%, respectively) while AUCCNA means were not statistically different in both groups. In addition, absolute AUCTAC values were similar between groups A and B (p = 0.17) which altogether suggests that factors other than drug exposure contribute to this variability. Although patients' characteristics regarding immunophilins (FKBP12, 13 and 51) were probably different between both groups, the magnitude of immune response during the early posttransplantation period might also contribute to the large BSV in AUCCNA. Besides, our study shows that the conversion from IRT to PRT in a 1:1 ratio based on total mg/day dose could also contribute to this variability. Interestingly, trough CNA at D14 in group A was statistically higher than that measured just before the switch to PRT (p = 0.048), while no difference in TAC whole blood trough concentration was observed. Furthermore, neither trough CNA nor TAC whole blood trough concentration at D90 and D104 was different in group B. Finally, no graft rejection was observed in our PK/PD study regardless of study group. Although the number of patients was limited, these results suggest that the conversion from IRT to PRT during the early post-transplantation period could modify PD profile of calcineurin without causing graft rejection. Further investigations with a larger cohort of patients should be conducted to confirm this result.

In conclusion, we have developed a population PK model for PRT in order to evaluate the PK/PD relationship for TAC in early and stable liver transplant recipients. The results suggest that one-to-one dosage conversion from twice-daily IRT to once-daily PRT during the early post-transplantation period could modify CNA in PBMC which might not be related to TAC PK. The advantage of our study is the PK and PD comparison between early and stable transplant recipients. Using both a non-compartmental analysis and a population approach, we showed that the mean AUCTAC values between group A and B were not statistically significantly different. Therefore, the model we have developed can be used to predict TAC whole blood concentrations in liver transplant recipients under the same conditions and dosing regimen as specified in our study. However, as the sample size in our study is low, our results should first be confirmed in larger cohorts.

Figure 1 .

 1 Figure 1. Design of the pharmacokinetic/pharmacodynamic study in the CONVERSION® trial.

Figure 2

 2 Figure 2 Individual pharmacokinetic profiles of once-daily prolonged-release tacrolimus from extensive sampling day, corresponding to day 14 for group A (n = 11) and day 104 for group B (n = 9).

Figure 3 .

 3 Figure 3. Goodness-of-fit plots of the final model. (PRED, population predictions, IPRED, individual predictions, DV, observed concentrations, CWRES, conditional weighted residuals).

Figure 4 .

 4 Figure 4. Prediction-corrected visual predictive check stratified on study group based on 1000 replicates of the original data set using the final model. Blue lines represent the 5th and 95th percentiles of the observed concentrations, red line represents the median of the observed concentrations, blue areas represent 95% confidence intervals around 5th and 95th percentiles of the simulated concentrations, red area represents 95% confidence interval around the median of the simulated concentrations and black points represent observed concentrations.

Figure 5 .

 5 Figure 5. Individual CNA profile over the dosing interval at day 14 for group A (n = 11) and day 104 for group B (n = 9).

Figure 6 .

 6 Figure 6. Relationship between area under the tacrolimus concentration-time curve over the dosing interval (AUCTAC) and 24-hour area under the calcineurin activity curve (AUCCNA) in liver transplant recipients treated with once-daily prolonged-release tacrolimus. Calcineurin activity (CNA) is expressed for 10 6 cells.

Acknowledgments

The authors are grateful to Dr Laurence Dubel (Astellas Pharma Europe) for her support in the preparation of this clinical trial. The authors thank Juliette Polselli from the Clinical Research Unit of East of Paris (URC-Est), Saint Antoine University Hospital (AP-HP) for study coordination and logistics.

Funding: This study was funded by a grant from Astellas Pharma Europe. The sponsor was Assistance Publique -Hôpitaux de Paris (Clinical Research and Innovation Department).

Astellas Pharma Europe provided financial support to conduct this clinical trial.

genetic polymorphisms of drug transporters on TAC PK because of the lack of statistical power.

To further evaluate the validity of our model, the individual AUCTAC obtained using a population approach were compared with those obtained using a non-compartmental analysis with data from extensive PK sampling. AUCTAC means of groups A and B obtained using either a non-compartmental or a population approach were not statistically different (p = 0.90 and p = 0.25 for groups A and B, respectively). Furthermore, comparison of AUCTAC values obtained by both approaches showed no statistical differences between groups A and B (p = 0.77 and p = 0.94, respectively). Finally, the geometric means of model-predicted dose-normalized AUCTAC in our study (235.6 ng/mL.h [CI95% = 139.6 -598.7] and 224.6 ng/mL.h [CI95% = 117.6 -421.5] for groups A and B, respectively, normalized to median dose of 6.0 mg/day) are close to those previously reported in liver transplant recipients obtained using a non-compartmental approach [START_REF] Florman | Conversion of stable liver transplant recipients from a twice-daily Prograf-based regimen to a once-daily modified release tacrolimus-based regimen[END_REF] . Indeed, Florman et al. reported a mean AUCTAC of 184 ± 63 ng.h/mL at day 28 post-transplantation in liver transplant recipients treated with PRT (mean dose of 5.2 mg/day). Taken together, these results suggest that the developed model satisfyingly describes the TAC concentration-time data. However, the limitation of our PK analysis is the small number of patients. Therefore, our results are not conclusive and need to be confirmed in larger cohorts. Moreover, some individual PK profiles in our study show a second peak of absorption. This was previously observed in liver and kidney transplant recipients treated with a different PRT formulation (Envarsus®) [START_REF] Woillard | Tacrolimus Updated Guidelines through popPK Modeling: How to Benefit More from CYP3A Pre-emptive Genotyping Prior to Kidney Transplantation[END_REF][START_REF] Woillard | Population Pharmacokinetics and Bayesian Estimators for Refined Dose Adjustment of a New Tacrolimus Formulation in Kidney and Liver Transplant Patients[END_REF] and was described by a double-gamma absorption model. In our analysis, the attempts to describe the second absorption peak did not give a reliable estimation of the PK parameters probably due to an insufficient number of samples in the absorption phase or the fact that it was only observed in some patients. In addition, the low number of PK samples in the absorption and distribution phases might be the reason for high BSV on ktr and Q. Although we analyzed the PK data with a model which did not account for the second peak of absorption, the comparison of AUCTAC values obtained with the non-compartmental approach and predicted by the PK model were in good agreement for both study groups which shows that our model accurately described the data.

CNA is a surrogate marker of TAC PD. Different PK/PD studies conducted in liver transplant recipients have suggested that assessment of CNA within the early post-transplantation period could be helpful to predict acute graft rejection in patients well exposed to TAC [START_REF] Fukudo | Pharmacodynamic analysis of tacrolimus and cyclosporine in living-donor liver transplant patients[END_REF][START_REF] Lemaitre | Pharmacokinetics and pharmacodynamics of tacrolimus in liver transplant recipients: inside the white blood cells[END_REF] . In

Supplementary Material

Supplementary Table 1 Results of the covariate analysis using the base model (forward step).

Supplementary Figure 1 (a Supplementary Figure 2 Box-plots for individual absolute clearance (CL) obtained from the population approach and categorical covariates.


N-P Pham

A Toumi
email: toumi@insa-toulouse.fr

A Turatsinze

Evaluating damage of rubberized cement-based composites 1 under aggressive environments 2

Keywords: Rubber aggregates, rubber coating, rubber-cement matrix bond enhancement, acetic acid attack, external sodium sulfate attack, damage variable

Rubberized cement-based composites are suitable for large surface applica-8 tions that require higher strain capacity and lower propensity for cracking owing to length 9 change rather than prioritize strengths. However, bond defects between rubber aggregates 10 and cement matrix affect durability of the composite, especially the sustainability of such 11 materials under aggressive environments. An enhanced rubber-cement matrix bond using 12 a rubber coating solution contributed to a significant improvement in transfer properties.

13

Hence, this study investigated effect of this bond enhancement on resistance of rubberized

Introduction

Incorporation of rubber aggregates (RA) into cementitious mixtures is detrimental to mechanical properties of rubberized cement-based composites (compressive and flexural strengths, and modulus of elasticity) partly due to bond defects between RA and cement matrix [START_REF] Albano | Influence of scrap rubber addition to portland i concrete composites: destructive and non-destructive testing[END_REF][START_REF] Chung | Introductory behavior of rubber concrete[END_REF][START_REF] Eldin | Rubber-tire particles as concrete aggregate[END_REF][START_REF] Khatib | Rubberized portland cement concrete[END_REF][START_REF] Lee | Development of tire added latex concrete[END_REF][START_REF] Turatsinze | Positive synergy between steel-fibres and rubber aggregates: Effect on the resistance of cement-based mortars to shrinkage cracking[END_REF][START_REF] Turki | Microstructure, physical and mechanical properties of mortar-rubber aggregates mixtures[END_REF][START_REF] Thomas | Abrasion resistance of sustainable green concrete containing waste tire rubber particles[END_REF]. Attempts to improve the bond such as washing or soaking RA with water, pre-treating RA with sodium hydroxide (NaOH), partly oxidizing RA, and coating RA with cementitious materials or sand seem not efficient to improve mechanical properties [START_REF] Albano | Influence of scrap rubber addition to portland i concrete composites: destructive and non-destructive testing[END_REF][START_REF] Rashad | A comprehensive overview about recycling rubber as fine aggregate replacement in traditional cementitious materials[END_REF]. As emphasized by Pham et al. [START_REF] Pham | Effect of styrene-butadiene copolymer coating on properties of rubberized cement-based composites[END_REF][START_REF] Pham | Rubber aggregate-cement matrix bond enhancement: Microstructural analysis, effect on transfer properties and on mechanical behaviours of the composite[END_REF], the reduction in strengths can be acceptable owing to low stiffness of RA. Despite strength loss, the composites exhibit high strain capacity and low propensity for cracking due to restrained shrinkage [START_REF] Turatsinze | Positive synergy between steel-fibres and rubber aggregates: Effect on the resistance of cement-based mortars to shrinkage cracking[END_REF][START_REF] Turatsinze | Mechanical characterisation of cementbased mortar incorporating rubber aggregates from recycled worn tyres[END_REF][START_REF] Turatsinze | On the modulus of elasticity and strain capacity of self-compacting concrete incorporating rubber aggregates[END_REF]. Such behaviors make the materials suitable for large surface applications (pavements and thin bonded overlays) where their strength is not a first priority, but higher deformation before macro-cracking localization is required [START_REF] Turatsinze | Mechanical characterisation of cementbased mortar incorporating rubber aggregates from recycled worn tyres[END_REF][START_REF] Nguyen | Mechanical properties of steel fibre reinforced and rubberised cement-based mortars[END_REF][START_REF] Ho | On the potential of rubber aggregates obtained by grinding end-of-life tyres to improve the strain capacity of concrete[END_REF][START_REF] Ho | Effects of rubber aggregates from grinded used tyres on the concrete resistance to cracking[END_REF][START_REF] Turatsinze | Rubberised concrete: from laboratory findings to field experiment validation[END_REF]. Nevertheless, due to bond defects at rubber-cement matrix interface, there are limitations on durability of the materials, such as their resistance to aggressive environments. According to Pham et al. [START_REF] Pham | Effect of styrene-butadiene copolymer coating on properties of rubberized cement-based composites[END_REF], solution to coat RA with copolymer before a slight mixing with premixed cementitious mixture induced an enhanced bond at rubber-cement matrix interface, as illustrated in Fig. 1. This bond enhancement results in a significant improvement in transfer properties, such as lower air permeability of coated rubberized mortar [START_REF] Pham | Effect of styrene-butadiene copolymer coating on properties of rubberized cement-based composites[END_REF][START_REF] Pham | Rubber aggregate-cement matrix bond enhancement: Microstructural analysis, effect on transfer properties and on mechanical behaviours of the composite[END_REF].

As for the durability of rubberized cement-based composites under aggressive environments, few investigations on resistance of such materials to acid attack have been conducted. Thomas et al. [START_REF] Thomas | Performance of high strength rubberized concrete in aggressive environment[END_REF] used RA (size 0-4 mm) as a replacement of natural fine aggregates at different levels (0 to 20%). After acid attack, more losses in mass and in compressive strength were observed in control concrete than rubberized ones. For a comparison of the resistance of control and rubberized mortars to hydrochloric acid (HCl) attack, Segre et al. [START_REF] Segre | Rubber-mortar composites: Effect of composition on properties[END_REF] immersed cylindrical specimens (45 mm in height and 30 mm in diameter) in HCl 5% (1.4 M). In order to obtain the rubberized mortars, the authors pretreated 10% of RA (size 0.2 mm) with saturated NaOH solution for 20 -30 minutes and then incorporated such treated RA in cementitious mixtures as a partial replacement of cement or sand, by weight. The mass of each mortar specimen was measured after several periods of testing time, and the obtained results showed higher resistance of rubberized mortar against HCl compared to the control one in terms of weight loss. On the contrary, Azevedo et al. [START_REF] Azevedo | Properties and durability of hpc with tyre rubber wastes[END_REF] compared the resistance to attack of a 10% of sulphuric acid solution between control and rubberized concrete specimens (150 mm x 150 mm x 150 mm) and reported that increasing rubber contents resulted in a higher degree of mass loss over a 28-day immersion period.

Similarly, few studies are available on the resistance of rubberized cement-based composites exposed to sulfate attack. Yung et al. [START_REF] Yung | A study of the durability properties of waste tire rubber applied to self-compacting concrete[END_REF] investigated anti-sulfate corrosion properties of self-compacting rubberized concrete by comparing weight loss after 5 dryingsoaking cycles in sulfate solution. The authors observed that concrete specimens incorporating 5% waste tire rubber powder (size less than 0.6 mm) exhibited sulfate resistance in comparison with the control one. However, large volume of RA incorporation led to nonresistance to sulfate [START_REF] Yung | A study of the durability properties of waste tire rubber applied to self-compacting concrete[END_REF]. In order to evaluate impacts of magnesium sulfate (MgSO 4 ) (3%) on rubberized concrete, Thomas et al. [START_REF] Thomas | Performance of high strength rubberized concrete in aggressive environment[END_REF] conducted an external sulfate attack test on specimens (100 mm x 100 mm x 100 mm) for 6 months according to ASTM C 1012 standard [START_REF] Astm C ; A | Standard test method for length change of hydrauliccement mortars exposed to a sulfate solution[END_REF]. At a given time after sulfate immersion, the concrete specimens were weighed, compressed, and checked water absorption. As reported, concrete specimens with higher RA content were more damaged than the control one. As a consequence, more losses in compressive strength and mass, as well as higher water absorption were observed. After 91 days of sulfate immersion, for composites with water-cement ratio of 0.4, compressive strength losses of control and rubberized concretes were 2% and 7%, respectively [START_REF] Thomas | Performance of high strength rubberized concrete in aggressive environment[END_REF].

From a brief summary above, one can reveal that RA incorporation into cementitious mixtures may be detrimental to the resistance of cement-based composites against aggressive environments. One of typical reasons of low acid/ sulfate resistance may be related to bond defects between RA and cement matrix. In this regard, this paper focuses on effect of rubber-cement matrix bond enhancement induced by rubber coating, as suggested by Pham et al. [START_REF] Pham | Effect of styrene-butadiene copolymer coating on properties of rubberized cement-based composites[END_REF][START_REF] Pham | Rubber aggregate-cement matrix bond enhancement: Microstructural analysis, effect on transfer properties and on mechanical behaviours of the composite[END_REF], on anti-acid or sulfate corrosion properties of rubberized mortars.

Usually, while some indicators such degraded depth, mass loss, and strength reduction are measured during acid attack, those of the sulfate attack are length gain, mass changes, and strength variations. In this study, damage variable of rubberized mortar specimens under chemical attacks was defined to evaluate effects of rubber incorporation and of copolymer coating. Micro-structural studies using Scanning Electron Microscopy (SEM) were also used to explore any changes at rubber-cement matrix interface in order to explain the durability of rubberized cement-based applications under aggressive environments.

Materials and methods

Materials

RA were incorporated in cementitious mixtures as a replacement of 30% by volume of rounded siliceous sand. Such low stiff aggregates are hydrophobic thus air-entrapment phenomenon happens on the surface of RA when they are in contact with mixing water.

The air bubbles are further partly released into the matrix and such phenomenon results in higher air content of rubberized mixtures. Density and water absorption of sand are 2.62 and 1.9%, respectively. Due to low specific gravity of RA (1.2), viscosity agent made from a high molecular weight synthetic polymer and a polycarboxylate-type superplasticizer were added to prevent segregation phenomenon and to maintain focused workability of fresh rubberized mixtures, respectively. Table 1 presents the studied mortar mix proportions. It should be noted that acronyms UR and CR stand for mixtures incorporating Untreated Rubber and Coated RA, respectively; letter P refers to coPolymer, which is used as a treatment material to improve rubber-cement matrix interface [START_REF] Pham | Effect of styrene-butadiene copolymer coating on properties of rubberized cement-based composites[END_REF][START_REF] Pham | Rubber aggregate-cement matrix bond enhancement: Microstructural analysis, effect on transfer properties and on mechanical behaviours of the composite[END_REF]. For coating procedure, it was followed as recommended by Pham et al. [START_REF] Pham | Rubber aggregate-cement matrix bond enhancement: Microstructural analysis, effect on transfer properties and on mechanical behaviours of the composite[END_REF]. That is, RA were firstly mixed with styrene-butadiene copolymer (2% of RA by mass). The coated-RA were then maintained under room conditions (20 • C temperature and 50% relative humidity) during 1 hour to condense and stabilize copolymer on rubber surface before a short and light mixing with the pre-mixed cementitious mixture.

Cylindrical specimens used for acid and sulfate attack tests are 28 mm and 60 mm in diameter, as well as 60 mm and 120 mm in height, respectively. All mortar specimens were demoulded 24 hours after casting and then placed in a curing room where temperature and relative humidity were fixed at 20 • C and 95%. At the end of this curing period (28 days), the top and bottom surfaces of cylindrical specimens were ground to impose high parallelism and good contact with platens of the loading machine. They were then coated with a layer of impermeable resin to only obtain the radial acid/ sulfate diffusion inside mortar specimens.

Experimental programme

Acetic acid attack

Acid attack test was performed according to ASTM C267-01 standard [START_REF]Standard test methods for chemical resistance of mortars, grouts, and monolithic[END_REF]. In NF EN 206-1/CN standard [START_REF]/CN. Concrete -Specification, performance, production and conformity[END_REF], the XA exposure class classifies the environmental conditions from low (XA1) to high (XA3) risk of chemical attack, depending on the concentration of aggressive substances from natural soils and groundwater. The most unfavorable exposure, the class XA3, corresponds to a case where pH of aggressive conditions is ranged between 4.0 and 4.5. Based on a stability of acetic acid in such pH range [START_REF] Hegyi | Introduction to practical biochemistry[END_REF], such acid with pH of 4.0 was chosen. The acetic acid solution (CH 3 COOH) having concentration of 0.28 M was prepared with a solution to specimen volume ratio in the range of 20 to 30. After stirring distilled water and acetic acid, approximately 2 g/l of NaOH agent was then added to adjust the pH of the obtained solution up to 4. Cylindrical mortar specimens at the end of a 28-day curing period were wiped to eliminate superficial water before immersing in the acid solution. The pH was then checked regularly and maintained at 4 during the whole experimental period by changing the acid solution every 2 days for the first 10 days, and every 1 week until the end of this experiment (7 weeks). The process of preparing mortar specimens and acid immersion is shown in Fig. 2.

External sodium sulfate attack

Sulfate attack test on untreated and coated rubberized mortars was carried out using ASTM C1012/C1012M-18a standard [START_REF] Astm C ; A | Standard test method for length change of hydrauliccement mortars exposed to a sulfate solution[END_REF]. Cylindrical specimens were placed in a tank and immersed by a sodium sulfate solution, as illustrated schematically in Fig. 3. It should be noted that the solution was prepared by adding 50 g of sodium sulfate (N a 2 SO 4 ) to 1L of distilled water. The pH of such solution was maintained between 6 and 8 with the aid of a pH regulator injecting sulfuric acid (H 2 SO 4 ) (0.05 mol/L). The solution in a tank was kept homogeneous by slightly agitating by a mini-pump. The volume ratio between the solution and specimens was maintained between 3.5 and 4.5 according to the recommendations of ASTM C1012 standard [START_REF] Astm C ; A | Standard test method for length change of hydrauliccement mortars exposed to a sulfate solution[END_REF]. The sulfate solution was weekly renewed for the first 2.5 months and then for every 2 weeks until the test end. The sulfate concentration was reported to decrease with time of immersion. Therefore, changing solution shortly will ensure higher sulfate concentration in order to accelerate degradation process [START_REF] Van Tittelboom | Test methods for resistance of concrete to sulfate attack-a critical review[END_REF]. It is one of relevant methods to shorten immersion time of sulfate attack.

Compressive test

Load-bearing capacity of mortars at different time of acid/ sulfate immersion was determined according to NF EN 1015-11 standard [START_REF] Nf En | Methods of test for mortar for masonry[END_REF] using a compressive machine with maximum capacity of 100 kN. The loading rates used for compressive tests on acid/ sulfate attacked specimens were 0.2 kN/s and 0.5 kN/s, respectively. Each value of compressive strength was averaged from 3 tests.

Microstructural analyses

Microstructural studies aim to observe any changes at rubber-cement matrix interface under acid/ sulfate attack. For the case of specimen attacked by acid, fractured samples were used. Whereas, polished specimens were prepared for sulfate-attacked mortars. In order to carry out these analyses, it is important to cut perpendicularly the lateral surface of sulfate-attacked specimens to get samples (10 x 10 x 15 mm 3 ) close to the exposed surface. After air-drying these samples, they were then polished with SiC papers 320, 600, 1200 and 2400 grit for approximately 2 minutes each. The samples were cleaned and then coated by a thin carbon layer right before starting SEM observations.

Results and discussion

Compressive strength

Changes in compressive strengths of acid-attacked mortars are presented in Fig. 4. It can be clearly seen that compressive strengths of mortars decreased with an increase of immersion time, especially a sharp drop of the control mortar compared to rubberized mortars. These findings are in good agreement with conclusions of Thomas et al. [START_REF] Thomas | Recycling of waste tire rubber as aggregate in concrete: durability-related performance[END_REF] who indicated that more loss in compressive strength was observed in control concrete than that of the rubberized concrete. The residual compressive strength of the control mortar was much lower than the one of rubberized mortar, namely 26% after 4 weeks of immersion. The one incorporating coated RA showed a higher residual compressive strength (42%) compared to untreated rubberized mortar (32%).

After a given time of exposing untreated and coated rubberized mortars to sodium sulfate solution, the compressive test was conducted. Fig. 5 shows reduction in compressive strength versus time of sulfate immersion. Such strength loss for the first period was more significant than the later time. It seems that the sulfate diffusion becomes lower as increasing immersion time due to the fact that products formed close the points of entrance.

Damage variable

A scalar damage variable to describe the distress of a material was introduced by Kachanow [29]. This scalar can be calculated based on a property that depends on the damage of the material, such as stiffness e.g. [START_REF] Ho | Effects of rubber aggregates from grinded used tyres on the concrete resistance to cracking[END_REF]. It is a relevant parameter to evaluate distresses due to internal or external loadings. In this study, as for specimens attacked by acetic acid or external sodium sulfate, damage variable (D) is defined and evaluated as a change in load-resisting area, as given in Eq. ( 1). It should be noted that, with regard to chemical attack, mortar samples were laterally damaged and most useful test set-up cannot be implemented.

D = 1 - Ã A ( 1
)
where A is initial cross-sectional area (m 2 ). Ã is an effective cross-sectional area or an equivalent undamaged sectional area of damaged specimen (m 2 ). The equivalent loadresisting area ( Ã) consists of an un-attacked part and chemicals-attacked regions close to undamaged area that can be still resisted to compressive loading. Herein, one keeps in mind that damaged areas exhibit a residual strength that should be taken into account in evaluating Ã. Ã is obtained based on a statement that strength (f t ) of mortar specimen before chemical attack is equal to the one of equivalent undamaged parts of chemical attacked sample, as illustrated in Eq. ( 2).

f t = F A = F * Ã (2)
From Eq. ( 2), Ã is determined as Eq. ( 3), where F and F * are the maximum compressive bearing capacities of a sound specimen and the one having undergone the chemical attack, respectively (kN). F and F * are determined experimentally. All parameters are described in Fig. 6.

à = A. F * F (3)
The evolution of damage variable (D) during acid attack for control mortar and rubberized mortars is represented in Fig. 7. Damage variable increased quickly and differentially between the control mortar and rubberized mortars. Initially, damage variable of the control mortar seemed to be linear-developed during the first four weeks of immersion.

A slight rise of damage variable after its sharp increase for a given time of immersion has demonstrated that acid-attacked area of rubberized mortars can be partly of loading resistance. Damage variable values of coated rubberized mortar (30CR-P) illustrated in Fig. 7 is always lower than that of the untreated one (30UR). Lower damage variable of 30CR-P is attributed to the rubber-cement matrix bond enhancement.

The difference in damage variable (D) under external sodium sulfate attack between untreated rubberized mortar and the one incorporating copolymer-coated RA is presented in Fig. 8. Damage variable was observed to increase with increasing time of sulfate immersion. Moreover, untreated rubberized mortar always exhibited higher damage variable than the coated one and it can be explained by an improved bond at rubber-cement matrix interface that reduces the ingress of damaging agents.

Changes at rubber-cement matrix interface

In degraded areas induced by acid attack, it can be clearly seen that the interface between untreated RA and cement matrix seems to be still porous as it is generally observed in untreated rubberized mortar (Fig. 9a). In case of the one incorporating coated RA, the degraded cement matrix still bonds to the coated RA (Fig. 9b). Such characteristic can result in a decrease of acid diffusion into coated rubberized mortar, leading to reduction in its strength loss.

A general observation on microstructure of rubberized mortars close to the sulfateexposed surface shows micro-cracks in both untreated and coated rubberized mortar specimens (Fig. 10). It is a consequence of tensile stress induced by formation of expansive products such as gypsum or ettringite. As observed in Fig. 10a, the gap around untreated RA appeared to be filled by such crystals more than that of the coated one. It could be attributed to bond defects at untreated rubber-cement matrix interface, leading to high sulfate diffusion into the composite via porosity at the interface. For the case where coated RA were used, no clear difference in sulfur distribution within the interface and other neighboring areas was noticed (Fig. 10b). The enhanced interface and effect of copolymer coating may be responsible for these findings. Interestingly, despite a good interface between sand and cement matrix, expansive products were still generated and the density of sulfur at such interface appeared to be higher (Fig. 10c) than that at coated rubber-cement matrix transition zone (Fig. 10b).

Due to low stiffness of RA, their presence in composites can partly delay cracking phenomena due to expansive crystals at rubber-cement matrix interface more than natural aggregates. Hence, cracks can be more visible at sand-matrix interface than that encountered with RA, especially with the ones coated by copolymer (Fig. 11).

Conclusions

From experiments focusing on the effect of an enhanced rubber-cement matrix interface on the durability of rubberized mortars under aggressive environments, the primary conclusions can be summarized as following:

• Rubberized mortars behave better than the control one in preventing distresses due to acid diffusion into the composite, especially when rubber-cement interface was enhanced by copolymer coating. Such improvement in the durability can be attributed to reduced water capillary absorption of rubberized mortars and especially to lower permeability of the coated one.

• Under external sodium sulfate attack, higher reduction in compressive strength was noticed in untreated rubberized mortar compared to the one incorporating copolymer-coated RA. After an exposure to external sodium sulfate solution, the rubber-cement matrix interface seems still sound.

• To evaluate the resistance of mortar to aggressive environments, damage variable is defined as relative change in equivalent load-resisting area. Based on damage variable values, coated rubberized mortar appeared to be more durable than the one incorporating untreated-RA against chemical attacks.

Figure 1 :

 1 Figure1: Effect of copolymer coating on rubber-cement matrix interface: (a) bond defects in untreated rubberized mortar (UR-Untreated RA), and (b) bond enhancement between coated RA (CR-P) and cement matrix (C)[START_REF] Pham | Rubber aggregate-cement matrix bond enhancement: Microstructural analysis, effect on transfer properties and on mechanical behaviours of the composite[END_REF]

Figure 2 :Figure 3 :Figure 4 :Figure 5 :

 2345 Figure 2: Moulds and specimens (a), grinding specimens (b), coating resin on top and bottom surface of specimens (c), immersing specimens in acid solution (d)

Figure 6 :Figure 8 :Figure 9 :Figure 10 :Figure 11 :

 6891011 Figure 6: Illustration of determination of equivalent load-resisting area ( Ã)

Table 1 :

 1 Mix design and proportioning (values in kg/m 3 )

	Mix	Cement (CEM	Sand	(0-	Water	RA	(0-	Superplasticiser Viscosity
	name	I 52.5R)	4mm)			4mm)			agent
	0R	500	1600		235	-		3.25	0.9
	30UR	500	1120		235	220		3.25	0.9
	30CR-P	500	1120		235	220		3.25	0.9