Valérie Scarabin-Carré

Sylvie Brailly-Tabard

Marie-Laure Ancelin

Cécilia Maubaret

Anne Guiochon-Mantel

Marianne Canonico

Pierre-Yves Scarabin
email: pierre-yves.scarabin@inserm.fr

M.D. Valerie Scarabin-Carre

MD Marie-Laure Sylvie Brailly-Tabard

PhD Cécilia Ancelin

Anne Maubaret

MD, PhD Marianne Guiochon-Mantel

PhD Pierre-Yves Canonico

MD Scarabin

Elizabeth Barett-Connor
email: ebarrettconnor@ucsd.edu

Kathryn M Rexrode
email: krexrode@partners.org

Dr Valérie Scarabin

Paul Vaillant Couturier

Plasma estrogen levels, estrogen receptor gene variation, and ischemic arterial disease in postmenopausal women: the three

Keywords: Plasma estradiol, estrogen receptor gene variation Ischemic arterial disease, Estradiol, Estrogen receptor polymorphisms, Postmenopausal women

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.

ABSTRACT:

Background: In older postmenopausal women, high levels of endogenous estrogen have been related to adverse health outcomes including ischemic arterial disease (IAD). Whether estrogen receptor alpha (ESR1) and beta (ESR2) polymorphisms modulate the effects of estradiol on IAD has not been investigated.

Methods:

In the Three-City prospective cohort study among subjects over 65 years, we used a casecohort design in which plasma levels of 17β-estradiol were measured. After exclusion of postmenopausal women using hormone therapy, a random subcohort of 533 women and 105 incident cases of first IAD events over 4-year of follow-up were analyzed. Five common polymorphisms of ESR1 and ESR2 were genotyped. Hazard ratios (HRs) of IAD for 1-standard deviation increase in estradiol levels by genotypes were estimated from Cox models after adjustment for cardiovascular risk factors and correction for multiple testing. We also investigated the role of haemostatis and inflammation as potential mediators.

Results: Neither estradiol nor IAD risk were significantly associated with estrogen receptor polymorphisms. Overall, IAD risk increased with estradiol (HR:1.40, 95%CI:1.11-1.77). Stratified analysis by genotypes showed that estradiol was positively related to IAD risk in women with ESR1 rs9340799-AA genotype but not in women with AG/GG genotype (HR:1.62, 95%CI:1.22-2.17 and HR:1.03, 95%CI:0.81-1.30, respectively; p for interaction<0.05). Additional adjustment for haemostatic variables reduced the HR by about one third in women carrying rs9340799-AA genotype (HR:1.41, 95%CI:1.06-1.90).

Conclusion:

ESR1 rs9340799 genotype may modify IAD risk related to high endogenous estradiol levels in older postmenopausal women. Hypercoagulability may act as a mediator.

INTRODUCTION

Few epidemiologic studies have been conducted to assess the association between circulating levels of endogenous estradiol and the risk of chronic diseases in postmenopausal women [START_REF] Rosner | Challenges to the Measurement of Estradiol: An Endocrine Society Position Statement[END_REF]. Despite an important estrogen deficiency in postmenopausal women, high plasma estradiol levels have been related to several adverse health outcomes including breast cancer [START_REF] Key | Endogenous sex hormones and breast cancer in postmenopausal women: reanalysis of nine prospective studies[END_REF], dementia [START_REF] Ravaglia | Endogenous sex hormones as risk factors for dementia in elderly men and women[END_REF], frailty (4) and allcause mortality [START_REF] Maggio | Relationship between higher estradiol levels and 9-year mortality in older women: the Invecchiare in Chianti study[END_REF]. In addition, previous data reported a positive relation of endogenous estrogens with coronary heart disease (CHD) [START_REF] Rexrode | Sex hormone levels and risk of cardiovascular events in postmenopausal women[END_REF][START_REF] Chen | Endogenous hormones and coronary heart disease in postmenopausal women[END_REF] and stroke (8) but these associations were not independent of traditional cardiovascular risk factors such as diabetes and body mass index (BMI). In a recent study, we found that high plasma level of endogenous estradiol was an independent predictor of ischemic arterial disease (IAD) in older postmenopausal women [START_REF] Scarabin-Carre | High level of plasma estradiol as a new predictor of ischemic arterial disease in older postmenopausal women: the three-city cohort study[END_REF].

Estrogens exert their actions via two distinct types of estrogen receptors (ER): ER-α and ER-β, encoded by the estrogen receptor α gene (ESR1) located on chromosome 6 and the estrogen receptor β gene (ESR2) located on chromosome 14, respectively. ERs are expressed in many tissues especially in vascular endothelial and smooth muscle cells of cerebral and coronary arteries and may play a role in the development of cardiovascular disease [START_REF] Mendelsohn | The protective effects of estrogen on the cardiovascular system[END_REF][START_REF] Gruber | Mechanisms of disease -Production and actions of estrogens[END_REF]. Previous studies suggested that the rs2234693 and rs9340799 single nucleotide polymorphism might influence the expression of ESR1 [START_REF] Herrington | Estrogen-receptor polymorphisms and effects of estrogen replacement on high-density lipoprotein cholesterol in women with coronary disease[END_REF] and affect the function of estrogen on arterial disease including CHD and stroke [START_REF] Deroo | Estrogen receptors and human disease[END_REF][START_REF] Saltiki | Coronary heart disease in postmenopausal women; the role of endogenous estrogens and their receptors[END_REF]. However, a recent metaanalysis concluded to a lack of association between ESR1 polymorphisms and CHD [START_REF] Lluis-Ganella | Qualitative assessment of previous evidence and an updated meta-analysis confirms lack of association between the ESR1 rs2234693 (PvuII) variant and coronary heart disease in men and women[END_REF]. Conflicting results about the association of ESR1 polymorphisms with the risk of stroke have been also reported [START_REF] Molvarec | Estrogen receptor alpha (ESR1) PvuII and XbaI gene polymorphisms in ischemic stroke in a Hungarian population[END_REF][START_REF] Munshi | Estrogen receptor alpha genetic variants and the risk of stroke in a South Indian population from Andhra Pradesh[END_REF]. Similarly, data on association of ESR2 polymorphisms (including rs1256049 and rs1271572) with the risk of CHD or stroke have not been consistent [START_REF] Rexrode | Polymorphisms and haplotypes of the estrogen receptor-beta gene (ESR2) and cardiovascular disease in men and women[END_REF][START_REF] Markoula | Associations of ESR2 Alul (G/A) polymorphism with ischemic stroke in Caucasians[END_REF].

Despite the potential role of estrogens and their receptors in the development of IAD, no study has evaluated whether ER polymorphisms could modulate the effects of estradiol on IAD. Therefore, we investigated the risk of CHD and ischemic stroke related to plasma estradiol levels by ESR1 and ESR2 polymorphisms in a cohort study among postmenopausal women over 65 years, who did not use hormone therapy. In addition, since estradiol is known to be associated with haemostatic and inflammation parameters [START_REF] Canonico | Endogenous oestradiol as a positive correlate of plasma fibrinogen among older postmenopausal women: a population-based study (the Three-City cohort study)[END_REF][START_REF] Maggio | SHBG, Sex Hormones, and Inflammatory Markers in Older Women[END_REF], their role was evaluated as potential mediators in the association of both estradiol and ER polymorphisms with IAD risk.

METHODS

Population study

The Three-City (3C) study is a large ongoing French prospective cohort designed to evaluate the risk of dementia, CHD and stroke, in subjects over 65 years. The study was approved by the Ethics Committee of the University Hospital of Kremlin-Bicêtre and a written informed consent was obtained for all participants. A detailed methodology of the study has been previously described [START_REF] Alperovitch | Vascular factors and risk of dementia: Design of the three-city study and baseline characteristics of the study population[END_REF]. Briefly, 3,649 men and 5,645 women, not institutionalized, registered on electoral rolls in 3 French cities (Bordeaux, Dijon and Montpellier), were recruited between 1999 and 2001. Baseline data were collected for each participant by trained psychologists or nurses using standardized questionnaires during a face-to-face interview. Moreover, each subject underwent a clinical examination to measure blood pressure, weight and height.

Baseline covariates

Information on sociodemographic characteristics, education, medical history, medication use, smoking status and consumption of alcohol were systematically collected at baseline. Women were classified as current hormone therapy users if they used hormone therapy at any time during the 3 months before the inclusion. BMI was calculated as weight in kilograms divided by height in meters squared. Hypertension status was defined as a high blood pressure measurement (systolic blood pressure ≥140mmHg and/or diastolic blood pressure ≥90mm Hg) or antihypertensive treatment at inclusion. Participants were categorized as diabetic if their fasting blood glucose level exceeded 1.26g/L (or 7mmol/L) or if they used current treatment for diabetes at baseline. Hypercholesterolemia was considered present if the fasting blood total cholesterol level was above 2.40g/L or if the subjects were treated for hypercholesterolemia. Smoking status was studied in three categories (never, past and current).

Follow-up and event ascertainment

Every 2 years after inclusion, the participants have been reexamined for the detection of dementia and IAD events. For this study, we focused on data collected over the 4-year follow-up. IAD consisted of either CHD or ischemic stroke during the follow-up. These events were adjudicated within an independent group of experts using medical documentation. CHD was defined as a hospitalization for either stable or unstable angina pectoris, coronary dilatation, artery by-pass, myocardial infarction, or CHD death. Non-fatal CHD were ascertained using hospital charts and practitioners' reports. CHD deaths were validated by reviewing hospital records, medical data obtained from family physicians or specialists and proxy interviews (coded I210 to 219, I251 to 259, I461 and R960 according to 10th version of the International Classification Disease) as described [START_REF] Alperovitch | Do we really know the cause of death of the very old? Comparison between official mortality statistics and cohort study classification[END_REF].

Stroke events were defined as a rapid onset of a neurological deficit lasting more than 24 hours and confirmed by a lesion compatible with an acute stroke on computed tomography or magnetic resonance imaging of the brain. Ischemic or hemorrhagic stroke events were classified by a review of brain imaging. Our study focused on IAD and hemorrhagic stroke events were therefore excluded. For subjects who presented with both CHD and ischemic stroke during follow-up, we used the first cardiovascular event that occurred.

Case-cohort study

A case-cohort study was designed from the 3C study to investigate the association of blood biomarkers with cardiovascular risk and dementia [START_REF] Carcaillon | Increased Thrombin Generation Is Associated With Acute Ischemic Stroke but Not With Coronary Heart Disease in the Elderly The Three-City Cohort Study[END_REF]. The case-cohort study design was described firstly by Prentice [START_REF] Prentice | On the design of synthetic case-control studies[END_REF] and consists of a random sample of the original cohort together with all incidents cases of this cohort. In practice, after exclusion of men (n=1,264), current users of hormone therapy (n=120), women with a personal history of CHD or stroke at baseline (n=86) and lost for follow-up (n=16), the subcohort included 537 women (522 non-cases and 15 cases) to which 91 incident cases of IAD outside the subcohort were added. The detailed flowchart has been described [START_REF] Scarabin-Carre | High level of plasma estradiol as a new predictor of ischemic arterial disease in older postmenopausal women: the three-city cohort study[END_REF]. Data on all ER polymorphisms were missing for 5 subjects. The final sample therefore consisted of 623 women, 518 non-cases and 105 incident cases of a first IAD event including 67 CHD and 38 ischemic strokes.

Blood collection and laboratory methods

At baseline, blood samples were collected for more than 90% of the full cohort. Plasma samples were available for all the subjects included in the case-cohort study. EDTA plasmas were obtained after one centrifugation at 3,000g and immediately stored at -80°C in 1-mL plastic tubes.

Plasma total estradiol was measured with a sensitive direct radioimmunoassay (RIA) using an Orion Diagnostica device (Spectria, Espoo, Finland). The minimum detectable concentration was 2pg/mL (7.3pmol/L). The intraassay and interassay coefficient of variation (CV) were 17.6% and 18.1% respectively, for total estradiol concentrations of 3.2pg/mL (12pmol/L) and were 2.8% and 5.8% respectively, for total estradiol concentrations of 24pg/mL (88pmol/L).

DNA was extracted from white blood cells (Puregene Kit, Qiagen, France) and stored at-80°C.

Genotyping of ER polymorphisms was performed by Kbiosciences (Hoddesdon Herts, UK) using their competitive allele specific polymerase chain reaction (PCR) single-nucleotide polymorphism (SNP) genotyping system (KASPar). Fluorescence scanning in a BMG Labtech Pherastar scanner analyzed the amplified PCR products and the results were interpreted with KlusterCaller 1.1 software. The error rate for the KASPar assay system is less than 0.3%. The two most commonly studied ESR1 polymorphisms were investigated: rs2234693 and rs9340799 (otherwise known as PvuII and XbaI), which are located at position 397 and 351 of intron 1, respectively. Three ESR2 polymorphisms were genotyped: rs1256049 (otherwise known as RsaI), rs4986938 (otherwise known as AluI) and rs1271572, which are located in position 1082 of exon 5, in position 1730 of the 3'-untranslated region of exon 8 and in the promoter region, respectively. The selection of these polymorphisms was based on previously published associations with risk of CHD and stroke [START_REF] Lluis-Ganella | Qualitative assessment of previous evidence and an updated meta-analysis confirms lack of association between the ESR1 rs2234693 (PvuII) variant and coronary heart disease in men and women[END_REF][START_REF] Munshi | Estrogen receptor alpha genetic variants and the risk of stroke in a South Indian population from Andhra Pradesh[END_REF][START_REF] Rexrode | Polymorphisms and haplotypes of the estrogen receptor-beta gene (ESR2) and cardiovascular disease in men and women[END_REF] and possible functional significance [START_REF] Herrington | Estrogen-receptor polymorphisms and effects of estrogen replacement on high-density lipoprotein cholesterol in women with coronary disease[END_REF][START_REF] Rosenkranz | Systematic mutation screening of the estrogen receptor beta gene in probands of different weight extremes: Identification of several genetic variants[END_REF][START_REF] Jeng | Estrogen receptor expression and function in long-term estrogen-deprived human breast cancer cells[END_REF].

Laboratory methods for haemostatic variables and CRP have been described [START_REF] Canonico | Endogenous oestradiol as a positive correlate of plasma fibrinogen among older postmenopausal women: a population-based study (the Three-City cohort study)[END_REF][START_REF] Carcaillon | Increased Thrombin Generation Is Associated With Acute Ischemic Stroke but Not With Coronary Heart Disease in the Elderly The Three-City Cohort Study[END_REF][START_REF] Carcaillon | Elevated plasma fibrin D-dimer as a risk factor for vascular dementia: the Three-City cohort study[END_REF][START_REF] Straczek | Higher level of systemic C-reactive protein is independently predictive of coronary heart disease in older community-dwelling adults: the three-city study[END_REF].

Briefly, fibrinogen was measured in citrated plasmas by the kinetic method of Clauss and von Willebrand factor and fibrin D-dimer by ELISAs. Thrombin generation was measured by the calibrated automated thrombography. We used peak height (highest value of thrombin generated), and endogenous thrombin potential (ETP; total quantity of thrombin generated) in our analyses. Highsensitivity serum C-reactive protein (hs-CRP) was measured using a particle-enhanced turbidimetric immunoassay.

Statistical analyses

Chi-square tests were used to compare the distribution of ER genotypes with those predicted under the Hardy-Weinberg equilibrium in the subcohort. Pairwise linkage disequilibrium between the different polymorphisms was analyzed by using Thesias software in the subcohort [START_REF] Tregouet | A new JAVA interface implementation of THESIAS: testing haplotype effects in association studies[END_REF].

Baseline characteristics of all subjects in the subcohort are presented as frequencies for categorical variables and arithmetic means with standard deviations for continuous variables that presented a normal distribution. Variables with a positive skewed distribution were log-transformed and values were expressed as geometric means and interquartile ranges. Baseline characteristics of subjects in the subcohort were compared by rs9340799 genotypes using χ2 tests and 2-tailed Student's t-tests. Mean levels of total estradiol were compared by ER polymorphisms in women of the subcohort using ANOVA tests adjusted for study center and traditional cardiovascular risk factors including BMI, diabetes, hypertension, hypercholesterolemia and smoking status. In addition, Pearson's correlations were estimated between haemostatic variables and estradiol by ER genotype in the subcohort.

The association of both estradiol levels and ER polymorphisms with IAD risk and their interactions were investigated using weighted Cox proportional-hazards models adapted for the casecohort design by the method of Barlow (31,[START_REF] Barlow | Analysis of case-cohort designs[END_REF]. Because age is sharply associated with IAD risk, age as time-scale was used as recommended [START_REF] Korn | Time-to-event analysis of longitudinal follow-up of a survey: choice of the time-scale[END_REF]. The proportional hazards assumption was checked for each model. Additive, dominant and recessive models were initially examined to determine which genetic model best described the data. Therefore, results are presented assuming a genotype model in dominant model with a 2-level categorical variable. The hazard ratios (HRs) and 95% confidence intervals (95%CI) by ER genotypes were estimated for 1-standard deviation increase in the logtransformed estradiol distribution. Estradiol x ER genotypes interaction terms were introduced into statistical models. The HRs for IAD were adjusted for study center and traditional cardiovascular risk factors including BMI, diabetes, hypertension, hypercholesterolemia and smoking status. In addition, given that five SNPs were investigated, Bonferroni correction for multiple comparisons was used. The HRs for IAD were further adjusted for haemostatic and inflammation markers including fibrinogen, thrombin generation, von Willebrand factor, fibrin D-dimer and hs-CRP, to evaluate the part of the excess risk explained by these variables. Of note, data on haemostatic and inflammation variables were missing for 25 subjects.

For each ER polymorphism, the risk of IAD was also investigated by tertiles of estradiol distribution and the low tertile was chosen as the reference group. Tests for linear trend across the 3 categories of estradiol levels were used to investigate the significance of the variables, after having evaluated the linearity of the associations. To assess the linearity of the relation of estradiol levels with IAD risk, we used tests based on the difference in the log-likelihood between two models of prediction (one with 2 dummy variables corresponding to the tertiles of the estradiol levels and the other including the qualitative ordinal variable in 3 categories). All tests were non-significant and we did not reject the hypothesis of linearity.

RESULTS

Baseline characteristics are described for 533 women in the whole subcohort and according to rs9340799 genotype (table 1). The distribution of ESR1 rs9340799 polymorphisms in the subcohort was similar to those expected in Caucasian subjects, as follows: 45.6%, 42.9%, and 11.5% for AA, AG and GG respectively. No significant difference was detected among traditional cardiovascular risk factors between women with rs9340799-AA genotype and those with rs9340799-AG/GG genotype.

Mean levels of total estradiol were similar across rs9340799 genotypes. There was no significant association between estradiol levels and other ER polymorphisms (data not shown).

The genotypic frequencies of ER polymorphisms were in agreement with the Hardy-Weinberg equilibrium. The two ESR1 polymorphisms were in strong linkage disequilibrium and so were the three ESR2 polymorphisms (all D' ranged from 0.90 to 1.00).

No significant association was found between IAD risk and the different ER polymorphisms (data not shown). After adjustment for traditional cardiovascular risk factors, plasma estradiol levels were positively associated with IAD risk in the whole population sample (HR:1.40 for 1-SD log estradiol change, 95%CI:1.11-1.77). Adjusted HR for IAD events and 95% CI in relation to estradiol levels by ER polymorphisms are given in table 2 before and after Bonferroni correction. With regard to ESR1 rs9340799 polymorphism, the risk of IAD was positively associated with total estradiol in women with AA genotype but not in women with AG/GG genotype (HR:1.62, 95% CI:1.22-2.17 and HR:1.03, 95%CI:0.81-1.30, respectively; p for interaction<0.05). In women with AA genotype, high levels of estradiol increased significantly the risk of IAD compared to the lowest estradiol levels (HR: 3.78, 95%CI:1.59-8.99 for the higher tertile vs the lower tertile, p for linear trend<0.01). After Bonferroni correction for multiple testing, the estradiol x rs9340799 genotype interaction remained significant. Similar associations were observed for rs2234693 polymorphism, although the interaction between estradiol levels and rs2234693 polymorphism was not significant. No significant interaction was detected between estradiol levels and ER-β polymorphisms on IAD risk.

Estradiol was positively correlated to fibrinogen (r=0.21, p<0.01), peak height of thrombin generation (r=0.10, p=0.13) and hs-CRP (r=0.38, p<0.01) in women with rs9340799-AA genotype.

After additional adjustment for haemostatic variables, the HR for IAD risk in women with AA genotype (HR:1.58 for 1-SD log estradiol change, 95%CI:1.21-2.05) was reduced to 1.41 (95%CI:1.06-1.90), suggesting that hypercoagulability explained 29 % of the excess risk of IAD.

Adjustment for hs-CRP alone or combined with haemostatic variables made no substantial change to the results (data not shown).

When the analyses were stratified by type of arterial events, total estradiol was positively associated with CHD risk in women with rs9340799-AA genotype, but not in women with rs9340799-AG/GG genotype (adjusted and corrected HR: 1.93, 95% CI: 1.28-2.91 and HR: 1.01, 95% CI: 0.76-1.35, respectively; p for interaction<0.05). No significant interaction was found between rs9340799 genotype and estradiol for the risk of ischemic stroke.

DISCUSSION

In this prospective study, neither estradiol levels nor IAD risk were significantly associated with ER polymorphisms in older postmenopausal women. However, we found that genetic variations in ESR1 modified the risk of IAD related to high endogenous estradiol levels. Plasma estradiol levels were positively associated with IAD risk in women carrying rs9340799-AA genotype but not in women carrying rs9340799-AG/GG genotype. The excess risk of IAD in women with AA genotype was partially explained by hypercoagulability. No interaction between estradiol levels and other ER polymorphisms was observed in relation with the risk of IAD.

Many studies have investigated the association of ER polymorphisms with the risk of IAD but previous data led to conflicting results. The reasons for such discrepancies include differences in study population, design and analysis, together with a strong heterogeneity in quality of investigations [START_REF] Lluis-Ganella | Qualitative assessment of previous evidence and an updated meta-analysis confirms lack of association between the ESR1 rs2234693 (PvuII) variant and coronary heart disease in men and women[END_REF]. Importantly, while the effect of ER polymorphisms on IAD may be different for women and men, few data were stratified by sex. Furthermore, use of hormone therapy and/or menopause status were not taken into account in most studies among women and ultimately, only few studies focused on postmenopausal women. A population-based prospective cohort study including 3,488 older postmenopausal women showed a positive association of ESR1 rs2234693-T/rs9340799-A haplotype with the risk of myocardial infarction [START_REF] Schuit | Estrogen receptor alpha gene polymorphisms and risk of myocardial infarction[END_REF]. However, although the results were adjusted for use of hormone therapy, no data were given among women not using estrogens. Consistently, another study excluding women using hormone therapy, reported an increased risk of stroke in women carrying ESR1 rs2234693-TT [START_REF] Munshi | Estrogen receptor alpha genetic variants and the risk of stroke in a South Indian population from Andhra Pradesh[END_REF]. By contrast, a Japanese case-control study including highly selected postmenopausal women reported that the ESR1 rs2234693-CC and rs9340799-GG genotypes were more common in women with coronary artery disease than in controls [START_REF] Lu | Association of estrogen receptor-alpha gene polymorphisms with coronary artery disease in patients with familial hypercholesterolemia[END_REF].With regard to ESR2 polymorphisms, the Women's Health Study showed that rs1256049-G and rs1271572-T alleles increased CHD risk but not stroke risk, whereas rs4986938 polymorphism was associated with neither CHD nor stroke [START_REF] Rexrode | Polymorphisms and haplotypes of the estrogen receptor-beta gene (ESR2) and cardiovascular disease in men and women[END_REF]. Most other investigations among postmenopausal women failed to detect an association of either CHD or stroke risk with ESR1 and ESR2 polymorphisms [START_REF] Molvarec | Estrogen receptor alpha (ESR1) PvuII and XbaI gene polymorphisms in ischemic stroke in a Hungarian population[END_REF][START_REF] Markoula | Associations of ESR2 Alul (G/A) polymorphism with ischemic stroke in Caucasians[END_REF][START_REF] Matsubara | Genotype distribution of estrogen receptor polymorphisms in men and postmenopausal women from healthy and coronary populations and its relation to serum lipid levels[END_REF][START_REF] Kjaergaard | Estrogen receptor alpha polymorphism and risk of cardiovascular disease, cancer, and hip fracture -Cross-sectional, cohort, and case-control studies and a meta-analysis[END_REF][START_REF] Rossouw | Estrogen Receptor Polymorphisms and the Vascular Effects of Hormone Therapy[END_REF].

Therefore, our data are consistent with these null findings which are also supported by a meta-analysis [START_REF] Lluis-Ganella | Qualitative assessment of previous evidence and an updated meta-analysis confirms lack of association between the ESR1 rs2234693 (PvuII) variant and coronary heart disease in men and women[END_REF].

Few studies investigated the interaction between estradiol and ER polymorphisms in relation to health outcomes in postmenopausal women. Interestingly, a dutch case-cohort study showed that the positive association between estradiol and breast cancer risk was more pronounced among women with rs2234693-CT/ TT genotype than among those with rs2234693-CC genotype [START_REF] Onland-Moret | The estrogen receptor alpha gene and breast cancer risk (The Netherlands)[END_REF]. This result may be relevant to our finding because both rs2234693 and rs9340799 are in linkage disequilibrium.

To our knowledge, the 3C study is the first to show that ESR1 polymorphisms may modulate the association between plasma estradiol levels and IAD risk. As previously described, plasma estradiol levels were positively associated with IAD risk in the whole population irrespective of ER genotypes [START_REF] Scarabin-Carre | High level of plasma estradiol as a new predictor of ischemic arterial disease in older postmenopausal women: the three-city cohort study[END_REF]. Adjustment for traditional cardiovascular risk factors yielded similar results suggesting no major mediator role of obesity, diabetes, hypercholesterolemia, hypertension and smoking status. Therefore, we can hypothesize that the relation between estradiol an IAD risk among women with rs9340799-AA genotype could be driven by other mechanisms involved in atherothrombosis such as inflammation and hypercoagulability. Both estradiol levels and IAD risk are known to be positively associated with CRP in postmenopausal women [START_REF] Maggio | SHBG, Sex Hormones, and Inflammatory Markers in Older Women[END_REF][START_REF] Straczek | Higher level of systemic C-reactive protein is independently predictive of coronary heart disease in older community-dwelling adults: the three-city study[END_REF][START_REF] Stork | Endogenous sex hormones and Creactive protein in healthy postmenopausal women[END_REF]. Moreover, one study reported that the rs2234693-T allele carriers exhibited an enhanced inflammatory response compared to the CC homozygotous [START_REF] Mysliwska | Inflammatory response of coronary artery disease postmenopausal women is associated with the IVS1-397T > C estrogen receptor alpha polymorphism[END_REF]. Of note, while rs2234693 and rs9340799 polymorphisms are in linkage disequilibrium, inflammation could be similarly increased in women with rs9340799-AA genotype as those with rs2234693-TT genotype. Nevertheless, in our study, the additional adjustment for hs-CRP did not change the results, suggesting that the inflammation did not explain the excess of IAD risk. Alternatively, given that high estradiol levels and IAD risk are known to be associated with hypercoagulability [START_REF] Canonico | Endogenous oestradiol as a positive correlate of plasma fibrinogen among older postmenopausal women: a population-based study (the Three-City cohort study)[END_REF][START_REF] Carcaillon | Increased Thrombin Generation Is Associated With Acute Ischemic Stroke but Not With Coronary Heart Disease in the Elderly The Three-City Cohort Study[END_REF][START_REF] Carcaillon | Elevated plasma fibrin D-dimer as a risk factor for vascular dementia: the Three-City cohort study[END_REF][START_REF] Danesh | Plasma fibrinogen level and the risk of major cardiovascular diseases and nonvascular mortality: an individual participant meta-analysis[END_REF], the association between estradiol and IAD risk could also be mediated through haemostatic variables.

Interestingly, a nested case-control study in the Women's Health Initiative trials reported an increased response of plasmin-antiplasmin to hormone therapy in women with rs9340799-AA genotype compared to women with rs9340799-AG or rs9340799-GG genotypes [START_REF] Rossouw | Estrogen Receptor Polymorphisms and the Vascular Effects of Hormone Therapy[END_REF]. Although exogenous and endogenous estrogens might have different metabolic and vascular effects, it can be suggested that high endogenous estradiol levels play a role in the thrombotic component of IAD through blood coagulation and fibrinolysis activation. In our study, hypercoagulability explained a part of the relation between estradiol and IAD risk in women with rs9340799-AA genotype. Further adjustment for hs-CRP did not change the results, suggesting that changes in coagulation pathway play a more important role in the development of IAD than inflammation. Other unmeasured haemostatic variables could also be involved in the association of IAD risk with estradiol in women with rs9340799-AA genotype and further data on clotting factors are required.

Increased IAD risk in women with elevated estradiol levels and carrying rs9340799-AA genotype does not necessarily imply that relationship is causal. First, our findings could be due to the chance. Second, studied genetic variants may be highly correlated with other variants within ESR1 or nearby genes that are themselves "causal" in the development of IAD, suggesting that the ER polymorphisms are not the only factor that determines the effect of estrogen on IAD. Few studies support the functional importance of ESR1 polymorphisms altering the quantity or the quality of ER-α transcripts or resulting proteins and the underlying mechanisms related to a direct effect of ER polymorphism in vascular biology remain to be clarified [START_REF] Herrington | Estrogen-receptor polymorphisms and effects of estrogen replacement on high-density lipoprotein cholesterol in women with coronary disease[END_REF][START_REF] Jeng | Estrogen receptor expression and function in long-term estrogen-deprived human breast cancer cells[END_REF][START_REF] Herrington | Common estrogen receptor polymorphism augments effects of hormone replacement therapy on E-selectin but not C-reactive protein[END_REF].

The strengths of our study include the prospective population-based and multicenter cohort design with a high participation rate during the 4 years of follow-up. Moreover, baseline data were collected by a direct interview and high-quality methods of ascertainment of cardiovascular risk factors and disease outcome were used. In addition, estradiol measurements and genotyping were conducted without knowledge of the case or non-case status, using validated methodology. Furthermore, our genetic-association study cannot be influenced by stratification population or heterogeneity because most participants were Caucasian.

Our study has several limitations. Firstly, the small number of incident cases may result in a lack of statistical power, especially for subgroup analyses by CHD or stroke event. In addition, multiple comparisons by different polymorphisms could result in falsely positive findings. However, our results remained significant after Bonferroni correction for multiple testing. Secondly, our population study included older women who were aged 73 years on average and mostly Caucasian.

Our data cannot therefore be generalized to younger postmenopausal women or other ethnics. With regard to the sex steroid hormones assays, especially at low levels of estradiol in postmenopausal women, conventional RIAs with preceding purification steps would provide more reliable and accurate measurements of plasma estradiol as compared with direct RIA [START_REF] Stanczyk | Limitations of direct immunoassays for measuring circulating estradiol levels in postmenopausal women and men in epidemiologic studies[END_REF]. However, measurement error related to direct RIA would bias our analysis toward the null hypothesis, resulting in a potential underestimation of the true associations [START_REF] Rosner | Challenges to the Measurement of Estradiol: An Endocrine Society Position Statement[END_REF]. On the other hand, the blood concentration of estrogens does not necessarily reflect the biologically active forms at the tissue level, as they are dependent on the local enzyme activity and the binding on the protein transporters such as sex hormone binding globulin.

In conclusion, ESR1 rs9340799-AA genotype may increase IAD risk related to high endogenous estradiol levels in older postmenopausal women and hypercoagulability may explain a part of this excess of risk. These innovative results have the potential to improve the stratification of IAD risk in postmenopausal women whose IAD risk may depend upon both plasma estradiol levels and ESR1 genotype and their interaction. However, further investigations with larger sample size are needed to replicate these findings and to assess the interaction between estradiol levels and ESR1 genetics polymorphism on CHD and stroke risk separately.

SOURCES OF FUNDING:

The 3C Study is conducted under a partnership agreement between the Institut National de la

2 KEYWORDS:

 2 Ischemic arterial disease  Estradiol  Estrogen receptor polymorphisms  Postmenopausal women DISCLOSURE STATEMENT: The authors have nothing to disclose.

Finally, a separate 2 (

 2 analysis was performed for CHD and ischemic stroke, including the first arterial event. Similarly to analyses on IAD risk, the HRs of CHD and ischemic stroke in relation to estradiol levels were estimated by ER polymorphisms with a multivariate Cox model. Statistical analyses were performed with the Statistical Analysis System software version 9.SAS Institute Inc, Cary, NC).

  Santé et de la Recherche Médicale (Inserm), the Victor Segalen-Bordeaux II University, and Sanofi-Aventis. The Fondation pour la Recherche Médicale funded preparation and initiation of the study. The 3C Study is also supported by the Caisse Nationale d'Assurance Maladie des Travailleurs Salariés, Direction Générale de la Santé, Mutuelle Générale de l'Education Nationale, Institut de la Longévité, Conseils Régionaux of Aquitaine and Bourgogne, Fondation de France, and Ministry of Research-Institut National Santé Et Recherche Médicale (Inserm) Programme "Cohortes et collections de données biologiques." The experiments comply with the current laws of the country in which they were performed. Biological assays for hemostatic and hormone parameters were supported by a grant from the Agence Nationale de la Recherche (ANR 2007-LVIE-005-01).

Table legends :Table 1 .

 legends1 Baseline characteristics of participants in subcohort of 3C study by ESR1 rs9340799 genotype

Table 2 .

 2 Hazard Ratios of IAD events in relation to 1 SD log increase of estradiol levels by ER polymorphisms among 623 postmenopausal women of 3C case-cohort study

Table

  Click here to download Table:Tables.docx

Table 1 . Baseline characteristics of participants in subcohort of 3C study by ESR1 rs9340799 genotype

 1 p value obtained from t-tests or χ² tests for all characteristics except for total estradiol (ANOVA adjusted for study center, BMI, diabetes, hypertension, hypercholesterolemia and smoking status )

	p value*

*

Table 2 . Hazard Ratios of IAD events in relation to 1 SD log increase of estradiol levels by ER 13 polymorphisms among 623 postmenopausal women of 3C case-cohort study 14 15 16

 2

				Ischemic Arterial Disease** (n=623)
		No. of Events	HR (95% CI)	Marginal p †	Corrected p λ	No. of Events	HR (95% CI)	Marginal p †	Corrected p λ	Marginal p interaction	Corrected p interaction	λ
	rs2234693*			TT (n=190)				TC/CC (n=421)
	Total Estradiol, pg/mL
	For 1 SD log	29	1.52 (1.06-2.18)	0.02	0.11	74	1.15 (0.94-1.42)	0.18	0.91	0.13	0.65
	T1 < 4.21	4		1 [reference]	0.04	0.22	20	1 [reference]	0.44	1.00
	T2 [4.21-7.27[	13	3.39 (1.02-11.29)			28	1.61 (0.90-2.89)
	T3 ≥ 7.27	12	3.09 (0.98-9.82)			26	1.25 (0.65-2.38)
	ESR1
	rs9340799*			AA (n=280)				AG/GG (n=338)
	Total Estradiol, pg/mL
	For 1 SD log	47	1.62 (1.22-2.17)	<0.01	<0.05	56	1.03 (0.81-1.30)	0.84	1.00	0.01	<0.05
	T1 < 4.21	7		1 [reference]	<0.01	<0.05	18	1	0.54	1.00
	T2 [4.21-7.27[	19	3.14 (1.33-7.45)			21	1.22 (0.65-2.27)
	T3 ≥ 7.27	21	3.78 (1.59-8.99)			17	0.76 (0.36-1.61)
	rs1256049*			GG (n=559)				AG/AA (n=56)
	Total Estradiol, pg/mL
	For 1 SD log	100	1.22 (1.01-1.48)	0.04	0.20	5	3.06 (0.53-17.76)	0.21	1.00	0.30	1.00
	T1 < 4.21	23	1	[reference]	0.10	0.50	3	1
	T2 [4.21-7.27[	40	1.79 (1.06-3.02)			1	NA
	T3 ≥ 7.27	37	1.60 (0.91-2.82)			1	NA
	rs4986938*			AA (n=100)				AG/GG (n=516)
	Total Estradiol, pg/mL
	For 1 SD log	21	1.85 (1.17-2.94)	<0.01	<0.05	84	1.09 (0.88-1.34)	0.42	1.00	0.10	0.50
	ESR2
	T1 < 4.21	1		1	<0.01	<0.05	25	1	0.75	1.00
	T2 [4.21-7.27[	12	22.47 (2.20-229.87)			29	1.03 (0.60-1.76)
	T3 ≥ 7.27	8	9.65 (0.91-102.43)			30	1.10 (0.62-1.95)
	rs1271572*			GG (n=206)				GT/TT (n=404)
	Total Estradiol, pg/mL
	For 1 SD log	36	1.36 (0.95-1.94)	0.09	0.47	67	1.20 (0.96-1.51)	0.11	0.54	0.68	1.00
	T1 < 4.21	8		1	0.22	1.00	16	1	0.37	1.00
	T2 [4.21-7.27[	14	1.96 (0.85-4.51)			27	1.57 (0.82-2.99)
	T3 ≥ 7.27	14	1.74 (0.68-4.44)			24	1.37 (0.69-2.73)
	* 12 missed values for rs2234693, 5 for rs9340799, 8 for rs1256049, 7 for rs4986938 and 13 for rs1271572
	** Including 67 CHD and 39 stroke events
	† P value for continuous variable and p for trend for variable in tertiles
	λ P value after Bonferroni correction
	Model adjusted for study center, BMI, diabetes, hypertension, hypercholesterolemia and smoking status

Plasma estradiol levels, estrogen receptor polymorphisms and ischemic arterial disease in postmenopausal women


Jean-Pierre Massat

Christophe Laurent

Jean-Philippe Bianchi

Etienne Balmès

Pantograph catenary dynamic optimisation based on advanced multibody and finite element co-simulation tools

Keywords: pantograph catenary interaction, co-simulation process, multibody, finite element, innovative design, infrastructure-rolling stock interaction

This paper presents recent developments undertaken by SNCF Innovation & Research Department on numerical modelling of pantograph catenary interaction. It aims at describing an efficient co-simulation process between Finite Element (FE) and Multibody (MB) modelling methods. FE catenary models are coupled with a full flexible MB representation with pneumatic actuation of pantograph. These advanced functionalities allow new kind of numerical analyses such as dynamic improvements based on innovative pneumatic suspensions or assessment of crash risks crossing areas that demonstrate the powerful capabilities of this computing approach.

Introduction

The performance of railway systems was historically improved by inline tests.

Considering the constant traffic increase and the need to cut costs, new assessment methods have to propose higher expertise level at lower prices. Numerical solutions are the most promising way to achieve this goal particularly with tools getting closer from track conditions, while cutting down the computation time. In railways, the development of efficient simulation approaches becomes mandatory to design new components and to optimize maintenance. Various modelling strategies can be used to find the best compromise as it can be illustrated on pantograph catenary dynamic interaction researches (see [START_REF] Collina | Numerical simulation of pantograph-overhead equipment interaction[END_REF], [START_REF] Poetsch | Pantograph/catenary dynamics and control[END_REF], [START_REF] Drugge | Modelling and simulation of catenarypantograph interaction[END_REF], [START_REF] Poetsch | Pantograph/catenary dynamics and control[END_REF] and [START_REF] Yagi | Simulation and visualistaion of the dynamic behaviour of an overhead power system with contact breaking[END_REF]). OSCAR (Outil de Simulation du CAptage pour la Reconnaissance des défauts) has been developed by SNCF for nearly ten years [START_REF] Massat | Pantograph-catenary dynamic simulation[END_REF][7] [START_REF] Massat | Modélisation du comportement dynamique du couple pantographecaténaire, Application à la détection de défauts dans la caténaire[END_REF] and certified against the EN50318 European Standard [START_REF]Railway applications. Current collection systems. Validation of simulation of the dynamic interaction between pantograph and overhead contact line, European standard[END_REF] since 2007. It proposes efficient pantograph catenary dynamic analysis tools based on the Structural Dynamics Toolbox for Matlab. Catenaries are modelled using a three-dimensional geometry interacting with simplified lumped mass pantograph model or special purpose multibody pantograph models [START_REF] Rauter | Pantograph-catenary interaction using flexible multibody dynamics methodology[END_REF] [START_REF] Labergri | Modelisation du comportement dynamique du systeme pantographecatenaire[END_REF]. Several studies showed a really good agreement between simulation results and inline measurements for many catenary designs in Europe [START_REF] Massat | Simulation Tools for Virtual Homologation of Pantographs[END_REF] [START_REF] Bobillot | Pantograph-Catenary: a High-Speed European couple[END_REF] .

In order to allow very general pantograph models, using specialized software is a necessity but implies the need to use separate strategies for time integration. A cosimulation strategy was introduced to connect the FE model with multi-body solutions provided by MSC Software, in order to take into account realistic pantograph geometry, large kinematic displacements of flexible components, pneumatic actuation and joint non linearities in suspensions and dampers. Section 2 first discusses the FE model. Section 3 then discusses the multi-disciplinary model of a French high speed pantograph describing the structural and pneumatic control components. Section 4 then discusses the strategy retained for co-simulation and associated validations based on comparisons for lumped mass pantograph models.

The paper finally addresses two applications. Section 5 presents an optimisation process to demonstrate the large improvements that could be foreseen on current collection quality using an enhanced passive pantograph head suspension with innovative pneumatic functionalities. Section 6, finally details a strategy to assess and improve risky catenary sections such as railway switch. This last study is focused on consequences of critical positioning of the Contact Wire (CW) leading to pantograph lateral horn straddling.

Finite element catenary modelling

The three dimensional catenary is modelled using OSCAR software. The model is mostly composed of pre-tensioned Euler-Bernoulli Finite Elements but also allows masses, bars, springs, etc. This allows every kind of catenary geometries: conventional or high speed designs, DC or AC lines with one or several contact wires, with or without stitch wires, etc. Several catenary sections can be considered including overlap sections where pantographs run under several contact wires. The pantograph considers lumped masses with possible bumpstops and friction elements in the pantograph. Typical non linearities are dropper compression and pantograph/contact wire contact. In the latter case, shape functions of the contact wire beams and a mass or flexible beam representation of the friction band are used to compute penetration at the moving interface and generate a contact force using unilateral linear contact stiffness. The coupling of these flexible structures was studied in the literature, especially about load moving on a FE mesh [START_REF] Verichev | Instability of vibrations of a mass that moves uniformly along a beam on a periodically inhomogeneous foundation[END_REF][15][16] [START_REF] Dahlberg | Moving force on an axially loaded beam -with applications to a railway overhead contact wire[END_REF]. OSCAR has been deeply validated against inline measurements and the catenary model is considered as stable and efficient Erreur ! Source du renvoi introuvable.. Simulation cases in this paper will be focused on the French high speed line between Paris and Tours, named LGV-A, for pneumatic suspension optimisation in section 5 and on simplified pre-tensioned wires for straddling studies in section 6.

Multibody pantograph modelling

Lumped mass models do not allow the representation of fully realistic mechanical features such as large displacement, joint bushing, realistic actuation system with pneumatic control or even advanced tools to apply external excitations such as aerodynamic loads or car body displacements. In initial OSCAR developments, the focus was on describing catenary behaviour and a FE model for the pantograph allowed fast computations. For complex pantograph optimization, it is thus desirable to use multi-body software capable of representing all features. This section details the multidisciplinary pantograph model that was developed for this purpose [START_REF] Dahlberg | Moving force on an axially loaded beam -with applications to a railway overhead contact wire[END_REF].

Mechanical model

The choice was made to represent the pantograph geometry with high detail as shown in Figure 2. The main frame of the pantograph, composed of arms and rods, reproduces large displacements. It is actuated by an air spring that applies a torque on the lower arm through a cam-cable link. The shape description of the cam is significant because its design ensures a nearly constant mean contact load whatever the deployment is. In the same way, non-linear dampers on the main frame can be introduced in the model. The upper part, named bow, defines the interoperability capability and the aerodynamic sensitivity of the pantograph and its weight strongly impacts the dynamic interaction quality with the overhead line. As shown in Figure 2, the MB bow is made of friction bands and lateral horns. The rigid MB model represents only the two first vertical modes of the pantograph and amplitudes are highly underestimated. On the contrary, the partially flexible model without bushing slightly overestimates amplitudes. Joint bushing induces a better matching of amplitudes with the full flexible pantograph. Consequences of this modelling level on dynamic interaction with catenary are studied in Table 2.

Control system for pneumatic actuation

The considered pantograph is deployed by a pneumatic actuator controlled by a pressure related to train speed. The control device is supplied by the general air supply network of the train and delivers compressed air using a pneumatic adjustment system. It is made of two control loops: an open-loop control to establish the pressure target depending on train speed and a closed-loop control to compensate pressure variations in the air spring due to pantograph dynamic movements.

In the model illustrated in Figure 4, the open loop target is computed based on train speed provided by OSCAR. For the closed loop, the mechanical piston displacements is sent by the MB model to the control system that returns the pneumatic load applied on piston surface. The closed loop for pressure regulation is modeled by a PID controller implemented as a second co-simulation process. The objective of co-simulation is to allow the combined use of detailed models for pantograph and catenary. The performance of each model implies the use of different integration strategies. The FE uses large fixed time steps and an implicit Newmark scheme, while the MB uses variable time steps based on Gear time integration method. Since detailed contact modelling is desired at the contact wire/friction band interface, Hertz contact with Coulomb friction is retained. Integration of such contact and verification of further constraints of impenetrability, gap between bodies, and energy conservation requires low time steps and must thus be done in the MB model.

A key contribution is thus the introduction in the process of short rigid contact wire segments, called communication entities. These segments have their positions enforced by the FE model and account for contact wire deflection and train speed. Interpolation is used to estimate their motion at the shorter time steps of the MB model. The MB solver then computes resulting forces on the two segment end nodes and these are applied as contact loads to the FE model at its time steps as shown in Figure 5. Static positioning is a key aspect, so communication of the CW positions in the catenary static state is needed for the pantograph static adjustment before launching the iterative co-simulation process.

Figure 5 -Co-simulation process between FE catenary and MB pantograph model

A co-simulation process generally may introduce some difficulties [START_REF] González | On the effect of multirate co-simulation techniques in the efficiency and accuracy of multibody system dynamics[END_REF] [START_REF] Prescott | Techniques to incorporate multibody solvers into multiphysics applications, 1ST International Conference on Innovations[END_REF]. Motion interpolation between different time schemes can lead to incorrect responses. Comparable simulations will be shown next to give nearly identical results, so this issue is not important here. Moreover, the computation time can be strongly impacted because of additional time required to exchange data between software and this will be discussed in section 4.4.

Verification in comparable cases

The deviations introduced by the co-simulation process need to be numerically validated quantifying possible deviations from current FE solutions that are certified against standards. For this objective multibody co-simulation and classical lumped mass pantographs are modelled with the same rheological values. A first comparison over a simple pre-tensioned wire composed of 200 Euler-Bernoulli beams is made to avoid modifications due to full catenary modelling aspects. A time simulation is performed over 1 second (100m at 100m/s). Statistical deviations are obtained on the average, standard deviation and maximum values of the contact load and given on Table 1. Since every criterion is below 1% of relative difference, no significant deviation is observed.

Unfiltered Fm [N] σ [N] Fmax [N]

OSCAR lumped mass 64. A zoom on one meter of simulation is displayed in Figure 6 and illustrates that element discretization do not introduce any artificial perturbation. The very low difference between the two results establishes the validity of the proposed co-simulation.

Influence of the pantograph model

After this first validation step, one can go through the second part of the validation process that aims at quantifying the deviations linked with detail level of the pantograph model: three lumped mass model, rigid multibody, partial and full flexible model and pantograph with pneumatic actuation. These four modelling levels of multibody pantograph are assessed against the reference case of a native lumped mass model. A French high speed catenary is used for the evaluation.

The proposed procedure is composed of three main steps described in Figure 7: dynamic impedance calculation, lumped mass identification and co-simulation comparisons over catenary case. First, a dynamic analysis is performed on the full flexible MB pantograph using imposed displacements. Dynamic impedance is obtained on three positions (friction bands, upper arm, and knee). Second, the simplified three lumped mass model is identified with a Non Gradient Optimisation method (NGO) by fitting the computed Frequency Response Functions. The rheological parameters are obtained after an optimisation process through a genetic algorithm for global optimum and a simplex algorithm to find the local one. Third, the co-simulation over 400m of the French LGV-A catenary is performed and analyzed. Table 2 gives results for the different pantograph modelling levels. Average F m , standard deviation σ and maximum values F max of the contact load are computed and used as criteria. The contact load average is a simulation input, therefore the same value is applied for each simulation in order to keep the same basis of comparison to study impact of pantograph modelling level. The classical FE simulation is taken as the reference case. This gives information about assessment of hypotheses and values chosen for contact coupling, time step size necessary for convergence or also on communication entities geometry (length, diameter) to guarantee proper data exchanged with the FE. The three lumped mass shows a perfect agreement with the classical FE run since less than 1% deviation is observed for each of the statistical criteria. This further validates co-simulation.

For a full rigid pantograph, the maximum change is obtained for the maximum contact load with a -3.9% difference. These changes are attributed to differences in the model: only two degrees of freedom are represented (vertical displacement) and the real cam geometry (see Figure 2), non-linear suspension of the curved friction bands are taken into account. This demonstrates that co-simulation strategies as well as contact management remain very efficient to be used with more complex and realistic pantograph models under a realistic catenary simulation case.

When flexible bodies are used in the numerical pantograph model, changes become more significant: -3.6% on standard deviation of contact load and -4.6% on the maximum contact load. Those discrepancies illustrate the influence of flexibility on dynamics even if the lumped mass model rather accurately represents vertical behaviour in [0-20] Hz frequency domain. For instance, the upper arm flexion may interact with catenary resonances and minimize or increase contact wire displacements. Moreover, the contact management becomes more complex because of discretized contact strips modelling.

It is important to note that mechanical piston without pneumatic actuation gives a good approximation. The last comparison is made with the full flexible pantograph model including pneumatic actuation of pantograph air spring. The statistical results, respectively standard deviation and maximum contact load, attain a relative difference of -8.3% and -9.0% compared to a three lumped mass model without co-simulation. The pneumatic regulation has a non-negligible impact on pantograph catenary interaction, but deviation remains relatively small.

Computation efficiency

The pantograph catenary co-simulation process requires a strong-coupling to exchange data at each time step. To achieve this objective, the implementation used memory mapped files so that all data is efficiently exchanged through the Random Access Memory (RAM). This section gives some figures to illustrate computational times.

The reference simulation run is 400m under the French LGV-A catenary at 300km/h corresponding to 6 seconds real time. The four multibody models defined in the previous section are assessed through the co-simulation process to study simulation time evolution according to pantograph modelling level. Table 3 gives the computation time and its increase ratio compared to reference. There are two kinds of ratio, first against results without co-simulation and then against the previous model level.

The MB lumped mass model is used with and without co-simulation. In this case, the assessment is focused on the lag introduced by the numerical exchanges during a co-simulation process and the time lost because catenary solver and pantograph solver work sequentially. We can see in Table 3 that 30% total duration increase is observed.

For a fully rigid multibody pantograph, computation time is doubled. This increase can be explained by large displacements taken into account as well as nonlinearities such as cam definition, joints bushing, contact management on incurved friction bands. Introducing flexible elements, that significantly improve the dynamic representation of the model, simulation time is very slightly increased. Only 32% simulation duration is added to the case of a rigid multibody pantograph. Thus, those simulation times remain in a very acceptable range for parametric analysis.

Finally, the pneumatic system requires an integration time step ten times smaller to avoid divergence and ensure a good precision on results. Besides, there is a second co-simulation process between the MB and the pneumatic system solvers. This explains the large time duration increase for this case. However, efficiency is kept since simulations last less than ten times the full flexible case.

5

Head suspension optimisation based on pneumatic systems

Mechanical and pneumatic head suspensions

Pantographs are generally made of two suspension levels: the main frame and the head. They are adjusted to filter respectively large displacements at low frequencies (mast passing and wind gust) and small displacements at high frequencies especially to reduce dynamic interaction with catenary. This second level is located between the main frame and the bow as illustrated on the Figure 2. The current system is made of mechanical springs guided by a ball-bearing to reduce friction damping. The design gives a piecewise linear stiffness, but in operating conditions, the working spring position is associated with a linear behavior shown as k 0 in Figure 8. This stiffness is meant to compensate the mean contact load with catenary.

It has been shown in a previous study [START_REF] Bobillot | Design of pantograph-catenary by simulations[END_REF] that decreasing drastically this suspension stiffness could lead to substantial improvements of pantograph catenary dynamic interaction. But limits arise from mechanical suspensions since decreasing the stiffness value requires an increased spring length because of preload adjustments.

Thus, it has been proposed to take benefit from air supply network available on pantograph and use pneumatic suspensions. The innovative solution developed by SNCF in a patent [START_REF] Bobillot | Design of pantograph-catenary by simulations[END_REF] is assessed using the multidisciplinary software. The design constraints are to keep the same size as the current system and only use pneumatic energy. The system is made of a passive double effect pneumatic actuator (with two chambers supplied by the same source) and two compression springs without pre-stress, as shown on the upper part of the right side of Figure 8. The mean contact load is therefore driven by the section ratio between the piston rod and piston head. Pneumatic damping can be controlled both by a flow valve and the designed piston/box clearance. The resulting stiffness behaviour is illustrated on the lower part of the right side of Figure 8. One can see an ideal system with a nearly 0N/m stiffness in working position.

Figure 8 -Current mechanical suspension scheme and its non linear stiffness (left) -Pneumatic device concept and its associated non linear stiffness (right)

The pneumatic solution allows to design a non linear stiffness with a better decoupling of dynamic displacements between the pantograph main frame and its head. The length clearance may lead to instabilities and thus is reduced to minimum. Four distinct slopes can be defined by designers: the first corresponds to the lower spring stiffness, the middle one to the operating aera, the third one to the upper stiffness and the last one to the upper pneumatic actuator hard stop. The pneumatic control developed with multidisciplinary software reproduces the expected behaviour for the response to a triangular input (see Figure 9). This detailed model highlights a hysteresis phenomenon due to the clearance area.

Parametric analysis based on multi-disciplinary models

A parametric analysis was performed first with this co-simulation process to compare mechanical or pneumatic head suspensions first using a simplified three lumped mass model with two friction bands (see Table 4), then with the full MB pantograph (see Table 5). The catenary is the French LGV-A section, with post-processing distance of 400m, and comparisons are based on statistical contact load analyses. The mean contact load is imposed at 169N for the three lumped mass and 157N for the full pantograph model. It is carefully checked that pneumatic piston displacements remain in the operational area avoiding hard stop contact. Spring stiffness added to pneumatic device is 10 times lower than the nominal one.

Table 4 describes the parametric comparison of pneumatic systems to the reference mechanical system (Case 1). The pneumatic system with nominal stiffness (Case 2) has a very slight impact on the head suspension dynamic behaviour (<1%). However, dividing spring stiffness by 10 (Case 3) leads to 18% decrease of standard deviation values and 21% decrease of maximum contact load.

The introduction of a clearance (Case 4) increases standard deviation and maximum values. This parameter leads to unstable behaviour and has thus to be avoided. Further calculations, in cases 5 & 6, show the robustness of the system to additive mass of the bow. An increase of the bow mass by 10%, then 50%, reduces the standard deviation improvement to 7%, but remains better than the current system with a lighter mass. This study was reproduced using a full flexible multibody pantograph. Results show that a large improvement of 14% is reached for standard deviation of the contact load and 17% for the maximum contact load value (see Table 5). The impact of pneumatic suspension is decreased compared with the case of lumped mass models. It can be explained by differences in modelling details (see §3.1) and the fact that the full multibody pantograph is mounted with four bow suspensions instead of only one for the simplified lumped mass model. Relative difference [%] -3% -14% -17%

Table 5 -Statistical results for a comparison between mechanical and pneumatic actuator mounted on full flexible MB pantograph

This preliminary study is very promising for future advanced design optimisation analysis using a pneumatic head suspension. It shows that the detail of MB pantograph models allow designs studies.

Reproducing railway switch

This section deals modelling of with risky areas where a contact wire comes from a side track and may lead to failure because of horn straddling. A full analysis of pantograph/catenary adjustment is carried out and underlines the benefits of a detailed geometrical modelling of pantograph.

Crossing lines and straddling

This study is focused on a pantograph design developed for French high speed lines. The bow described in Figure 11 is connected to the main frame through the crossbar.

There are primary and secondary horns respectively at each extremity of the two independent friction bands and the crossbar. These horns are designed to avoid any straddling phenomenon.

Figure 10 -Full multibody pantograph bow description with two independent contact strips

The railway switch is characterised by a main track that encounters a secondary track at a crossing point. The main track is the current train running line. The secondary track comes from pantograph side and impacts the bow at the landing point as detailed in Figure 10. The height and the lateral position of the landing point on the pantograph horns are particularly critical because it can occur below the horn depending on the horizontal and vertical contact wire incident angle. Those parameters are defined by national maintenance rules. Usually, no crash happens because lateral horns are designed to guide contact wire on the top of friction bands. However, some configurations allow crash situations called straddling as illustrated in the Figure 11. The following general methodology is introduced to study such configurations. On the FE side, the main catenary is modelled as usual and the secondary CW is modelled using simple FE pre-tensioned wire. The secondary CW incident angles and landing point positions are parameterized. On the MB side, three communication entities are modelled. Each of them is coupled with a specific pantograph body for contact definition: front and rear communication entities are coupled with friction bands and their primary horns, the middle one to the cross bar and its secondary horn as described in Figure 12. The MB solver then manages possible contacts with these entities. The pantograph model is a partially flexible multibody model: all components are flexible bodies except the pantograph basis. The static load on friction bands depends on pressure defined in the pneumatic actuator.

For the simulation, the pneumatic actuator is adjusted to provide a 80N static load for a train running at 30 km/h. In the simulation, the primary CW applies a vertical load on the bow leading to a slight inclination of the friction bands and, as a result, a displacement of the primary horn extremity. Moreover, the bow suspension preload is considered to position the two friction bands vertically. The contact wire of the secondary track is composed of a simple FE pretensioned (20kN) wire of 1000m. This length reproduces a typical catenary section distance taking into account wave reflections that may influence horn straddling. A local wire refinement is applied to improve wire displacement computation accuracy at landing position and optimize co-simulation time. Gravity is not applied to the secondary contact wire to avoid deflection and to better control impact position on secondary horn. This computation case is relevant because of the quasi static state of the simulation.

Left side of Figure 13 shows a case where the secondary contact wire is normally guided by the lateral horns until the top of the friction bands. One can see the deformation of the upper arm because of load on lateral horns. On the right, a case with critical angles is shown. The contact load applied on the secondary horn pushes down the crossing bar and as a consequence increases the clearance between the primary horn and the secondary horn. The lateral wire can slide under the primary horn and then come below the friction band. This situation systematically leads to system breakage on real track. Several other parameters could be considered to complete this analysis: friction bands displacement due to dynamic interaction with the main contact wire, lateral position of the pantograph due to train dynamics, etc. CW is going to impact the bottom part of the primary front horn leading to straddling effect

Parametric analysis for crash prediction

A parametric study is compulsory to define pertinent crash risk indicators and propose pantograph design and catenary adjustment rules. The work proposed here aims at defining secondary contact wire angles that could lead to horn straddling phenomenon described in section 6.1. The design space is defined with a set of 1000 simulation runs. The reference case uses nominal values of the secondary contact wire angle in a railway switch area: 2° (3.5 10 -2 rad) in XZ plane and 7.5° (13.1 10 -2 rad) in XY plane. Vertical and horizontal angles are independent design parameters randomly selected respectively in the ranges [2°, 6°] and [7°, 14°].

Signal processing is carried out on contact loads to detect horn straddling. Several criteria based on the contact load and contact wire position against friction band position have to be considered. For instance, a zero contact force, which indicates that no contact happened between communication entities and horns, combined to a contact wire position below friction bands means that a straddling occurred. In the same way, a negative vertical contact load indicates a straddling. Several successive phenomena can even be combined and needs to be carefully analysed to succeed in failure case prediction.

Figure 14 displays a lateral force in black and a vertical force in grey in the case of a horn straddling phenomenon. The contact force between contact wire and friction bands keeps a zero value until impact occurs at until 0.14s. Then the vertical contact force becomes negative. At 0.2s, the lateral force also becomes negative. It shows that the communication entity slides under the bottom side of the primary horn. Beyond 0.22s, both contact forces come back to zero stating a contact lost between the communication entity and the friction band meaning that communication entities are under the friction bands. A complete parametric analysis, representing 1000 simulations, is displayed in Figure 15. A cross marker is used to represent each design point. Additional circles are added to identify straddling cases and squares for non-obvious straddling cases, where the crash detection doesn't give a full confidence. Indeed, due to co-simulation configuration and time duration, uncertain cases are detected. For example, it can correspond to a rebound on the primary horn extremity that may lead to friction band damage or even possible break. On Figure 15, a critical area in grey is displayed to define three different domains: no risk of straddling represented by cross markers only, uncertain area of straddling represented by the grey area and an area leading to systematic failure by straddling represented by circle marker.

Conclusion

This paper presented recent developments undertaken in the framework of SNCF Innovation & Research Department projects on pantograph catenary interaction modelling based on finite element simulation of the catenary and advanced multibody simulation of the pantograph including finite element and control system methodologies. This powerful approach, that combines multiphysic computing strategies, brings an answer to growing needs for detailed pantograph catenary analyses reproducing realistic physical behaviour and giving access to a large range of parameters hardly measurable on track or test bench.

The co-simulation is very efficient and do not introduce any significant deviation. The additional cost of co-simulation is marginal for equal pantograph models and acceptable when details are needed.

The influence of flexibility of pantograph components is assessed. It is shown that a full flexible pantograph introduces a marginal deviation with a lumped mass model in [0 -20] Hz frequency range but remains necessary to take into account higher frequencies. As conclusion, each model leads to specific analysis and studies about pantograph catenary dynamics. For instance, a lumped mass model is limited to dynamics studies and provides short computation time although a full flexible MB model is dedicated to pantograph design and needs longer computation time. The goal of each study defines the right complexity level to use.

The co-simulation process in particular allowed the study of a novel pneumatic suspension. This preliminary study is very promising for future advanced design optimisation analysis using a pneumatic head suspension. It shows that the detail of MB pantograph models allow designs studies. A design optimisation process illustrates the possible improvements that can be foreseen using an innovative pneumatic head suspension. The parametric study describes gains obtained from mechanical and pneumatic aspects separately and defines limits in terms of acceptable mass on board.

The case of railway switches and possible straddling was studied next and it was shown that the process could be used to provide design guidelines for switch geometry. The DoE is used to define critical catenary design and pantograph adjustment parameters that could lead to system breakage according to body flexibility and suspension preload of the pantograph. Results show that three dimensional structural considerations are key factors for this kind of expertise.

Additional parameters, such as head suspension preloads, car body roll, pantograph catenary dynamics induced by the main contact wire, its lateral positioning, etc., could be taken into account to perform further parametric analysis and lead to an enhanced definition of maintenance criteria or component design.

The application fields allowed by this numerical approach are extended to new and more complex kinds of engineering studies involving the pantograph system at a very detailed level.

Figure 1 -

 1 Figure 1 -Finite element model for two sections of French High Speed catenary

Figure 2 -

 2 Figure 2 -Pantograph key components for multibody modelling Mechanical and structural parameters for dynamic representation and flexible bodies modelling were fitted from laboratory measurements and a full experimental modal analysis. The resulting model reproduces pantograph dynamic behaviour in three dimensions up to 200Hz [17]. For the pantograph base, the four arms and rods, the cross bar and friction bands, flexible bodies are introduced in the MB model based on the Craig-Bampton reduction that uses static modes at interfaces and fixed interface modes. The usual frequency band of interest for general pantograph/catenary analysis is between 0 and 20Hz. This band contains the three first vertical vibration modes: in phase rigid motion of frame and bow suspension, out-of-phase rigid motion of frame and bow suspension, and out-of-phase first bending mode of upper arm and bow suspension. The pantograph model was adjusted against measurements. The full flexible model is considered as the reference model and accurately reproduces these three different vertical resonances.Figure 3 compares flexibility for a rigid MB model, a partially flexible with bushing joints, a partially flexible without bushing joints and a full flexible pantograph. Partially flexible takes into account upper arm and pantograph head as flexible bodies.

Figure 3

 3 compares flexibility for a rigid MB model, a partially flexible with bushing joints, a partially flexible without bushing joints and a full flexible pantograph. Partially flexible takes into account upper arm and pantograph head as flexible bodies.

Figure 3 -

 3 Figure 3 -Dynamic impedance comparison as a function of pantograph flexible elements in the [0,20Hz] range.

Figure 4 - 4 Co-simulation process and numerical validation 4 . 1

 4441 Figure 4 -Pneumatic control system block diagram and communication process with multibody pantograph

Figure 6 -

 6 Figure 6 -Time history of contact load of three lumped mass under a simple pre-tensioned wire through a FE simulation (grey solid line with circles) and an equivalent co-simulation case (black solid line with rectangles)

Figure 7 -

 7 Figure 7 -Co-simulation numerical validation procedure in three steps. First, dynamic impedance calculation. Second, equivalent three lumped mass model identification. Third, temporal contact load comparison between a classical and MB software co-simulation cases

Figure 9 -

 9 Figure 9 -Pneumatic head suspension non linear stiffness obtained by applied load simulation

Figure 11 -

 11 Figure 11 -Top view of a railway switch (top) and pantograph bow straddling phenomenon description (bottom)

Figure 12 -

 12 Figure 12 -Railway switch modelling. Left: Incident angle on XY plane -Right: Incident angle on the XZ plane

Figure 13 -

 13 Figure 13 -Left: Secondary CW is guided by the lateral horns over the friction bands -Right: Secondary CW is going to impact the bottom part of the primary front horn leading to straddling effect

Figure 14 -

 14 Figure 14 -Time histories of lateral contact load (black solid line) and vertical contact load (grey solid line) over crash test on simple pre-tensioned CW

Figure 15 -

 15 Figure 15 -Parametric analysis on secondary CW inclination angles results. Design space (crosses), uncertain failure cases (rectangles), failure cases (circles)

Table 1 -

 1

		2	Réf.	1.343	Réf.	67.7	Réf.
	COSIM lumped mass	64.2 <<1% 1.363	1%	67.7	<<1%

Contact load statistical results comparison between a classical FE simulation and a cosimulation with a multibody three lumped mass model under a simple pre-tensioned wire

Table 2 -

 2 Contact load statistical results for various models under 400m of the French High Speed Line catenary

	Filtered [0 -20]Hz	F m [N]	σ [N]	F max [N]
	FE lumped mass	177.6 Ref.	60.2	Ref.	382.0	Ref.
	Co-sim lumped mass	175.7	1%	60.2	<1%	382.9	<1%
	Co-sim full rigid	178.1 <1%	59.4	-1.3% 367.0 -3.9%
	Co-sim full flexible	176.2 <1%	58.0	-3.6% 364.6 -4.6%
	Co-sim full flexible + pneumatic	175.9	1%	55.2	-8.3% 347.8 -9.0%

Table 3 -

 3 Computation time comparison between base simulation and four complexity levels of pantograph model in co-simulation cases

		Time step	Computation time	Computation time ratio
	OSCAR lumped mass	1.10 -4 s	187s	Ref.
	Co-sim lumped mass	1.10 -4 s	240s	×1.3	Ref.
	Co-sim full rigid	1.10 -4 s	381s	×2.0	×1.6	Ref.
	Co-sim full flexible	1.10 -4 s	501s	×2.7		×1.3	Ref.
	Co-sim full flexible + pneumatic	1.10 -5 s	4069s	×21.8			×8.1

Table 4 -

 4 Contact load statistical results of a parametric analysis on pneumatic head suspension device using a three lumped mass model

			INPUTS			OUTPUTS
	Case	Suspension	Stiffness k1=k2	Clearance	Bow mass	F mean [N]	σ [N]	F max [N]
	1 Mechanical Nominal	-	Nominal 168.7 Ref	62.8	Ref	426.9	Ref
	2 3		Nominal	0cm	Nominal	168.7 <1% 168.9 <1%	62.1 51.2 -18% 336.4 -21% -1% 415.9 -3%
	4 5 6	Pneumatic	0.1×Nom	2cm 0cm	169.5 <1% 1.1×Nom 168.7 <1% 1.5×Nom 168.6 <1%	52.9 -16% 383.1 -10% 52.7 -16% 340.7 -20% 58.6 -7% 363.0 -15%

Acknowledgements

This paper describes work undertaken by SNCF Research and Innovation Department with the precious support of SNCF Infrastructure and Rolling Stock Engineering Departments as well as MSC Software, SDTools and Vibratec companies. The Authors would like to particularly thank Thierry BERNARD from MSC Software for his contribution on pantograph multi-disciplinary modelling and co-simulation process development.