PhD Hermann Nabi

PhD Mika Kivimäki

MD, PhD Jean Phillipe Empana

PhD Séverine Sabia

PhD Annie Britton

PhD, FFPHM Michael G Marmot

MSc Martin J Shipley

PhD Archana Singh-Manoux

Combined Effects of Depressive Symptoms and Resting Heart Rate on Mortality: The Whitehall II Prospective Cohort Study Running title: Depression, Resting Heart Rate and Mortality

Keywords:

Objective: To examine the combined effects of depressive symptoms and resting heart rate (RHR) on mortality.

Methods: Data come from 5936 participants, aged 61 ±6 years, from the Whitehall II study.

Depressive symptoms were assessed in 2002-2004 using the center-for-epidemiologic-studiesdepression-scale (score ≥16). RHR was measured at the same study phase via electrocardiogram. Participants were assigned to 1 of 6 risk-factor-groups based on depression status (yes/no) and RHR categories (<60, 60 -80, >80 bpm). Mean follow-up for mortality was 5.6 years.

Results:

In mutually adjusted Cox regression models, depression (hazard ratio = 1.93 p<0.001) and RHR>80 bpm (hazard ratio = 1.67, p<0.001) were independent predictors of mortality.

After adjustment for potential confounding and mediating variables, participants with both depression and high RHR had a 3.0-fold higher (p<0.001) risk of death compared to depression-free participants with RHR ranging from 60 to 80 bpm. This risk is particularly marked in participants with prevalent CHD.

Conclusions:

This study provides evidence that the coexistence of depressive symptoms and elevated RHR is associated with substantially increased risk of death compared to those without these two factors. This finding raises the possibility that treatments that improve both depression and RHR might improve survival.

INTRODUCTION

Depression is a major public health issue worldwide [START_REF] Moussavi | Depression, chronic diseases, and decrements in health: results from the World Health Surveys[END_REF] . Projections of the Global Burden of Disease by the WHO suggest that depression will account for 10% of the total disease burden in high-income countries by 2030 [START_REF] Mathers | Projections of global mortality and burden of disease from 2002 to 2030[END_REF] . There is fairly consistent evidence that depression is independently associated with increased risk of mortality [START_REF] Michaud | Burden of disease--implications for future research[END_REF][START_REF] Zheng | Major depression and all-cause mortality among white adults in the United States[END_REF][START_REF] Abas | Depression and mortality in a high-risk population. 11-Year follow-up of the Medical Research Council Elderly Hypertension Trial[END_REF][START_REF] Surtees | Depression and ischemic heart disease mortality: evidence from the EPIC-Norfolk United Kingdom prospective cohort study[END_REF][START_REF] Schiffer | Somatic versus cognitive symptoms of depression as predictors of all-cause mortality and health status in chronic heart failure[END_REF] . For example, a recent meta-analysis of 25 community studies on a total of 106,628 individuals found a 1.8-fold increased risk for allcause mortality in depressive compared to non-depressive subjects [START_REF] Cuijpers | Excess mortality in depression: a meta-analysis of community studies[END_REF] .

Resting heart rate (RHR), an indicator of the autonomic nervous system activity, has also been found to be an independent predictor of mortality [START_REF] Dyer | Heart rate as a prognostic factor for coronary heart disease and mortality: findings in three Chicago epidemiologic studies[END_REF][START_REF] Greenland | Resting heart rate is a risk factor for cardiovascular and noncardiovascular mortality: the Chicago Heart Association Detection Project in Industry[END_REF][START_REF] Kannel | Heart rate and cardiovascular mortality: the Framingham Study[END_REF] . In a recent study of working men without clinically detectable cardiovascular diseases (CVD) at baseline followed up for 23 years, the risk for sudden and non-sudden death from acute myocardial infarction and all-cause mortality increased in a dose-response manner with increasing RHR, after adjustment for biobehavioral risk factors [START_REF] Jouven | Heart-rate profile during exercise as a predictor of sudden death[END_REF] . Another recent study involving a large sample of men and women found elevated RHR to be a long-term predictor for mortality independent of other risk factors in patients with suspected or proven coronary artery disease [START_REF] Diaz | Long-term prognostic value of resting heart rate in patients with suspected or proven coronary artery disease[END_REF] .

Despite the large amount of evidence showing depression and RHR to be predictors of mortality, previous studies have not examined the combined impact of depression and RHR. However, in many individuals depression and elevated RHR are co-morbid [START_REF] Carney | Depression, the autonomic nervous system, and coronary heart disease[END_REF][START_REF] Veith | Sympathetic nervous system activity in major depression. Basal and desipramine-induced alterations in plasma norepinephrine kinetics[END_REF][START_REF] Carney | Major depression, heart rate, and plasma norepinephrine in patients with coronary heart disease[END_REF] and it is possible that they exert a combined effect on mortality. Indeed, several studies found clinically depressed psychiatric patients and CHD patients with depression, as compared with their nondepressed counterparts, to have elevated levels of plasma catecholamines and other markers of altered autonomic nervous system (ANS) activity, including elevated heart rate, low heart rate variability, exaggerated heart rate responses to physical stressors [START_REF] Carney | Depression, the autonomic nervous system, and coronary heart disease[END_REF][START_REF] Veith | Sympathetic nervous system activity in major depression. Basal and desipramine-induced alterations in plasma norepinephrine kinetics[END_REF][START_REF] Carney | Major depression, heart rate, and plasma norepinephrine in patients with coronary heart disease[END_REF][START_REF] Carney | Change in heart rate and heart rate variability during treatment for depression in patients with coronary heart disease[END_REF][START_REF] Lahmeyer | Cardiac regulation and depression[END_REF][START_REF] Dawson | Autonomic correlates of depression and clinical improvement following electroconvulsive shock therapy[END_REF][START_REF] Wyatt | Resting plasma catecholamine concentrations in patients with depression and anxiety[END_REF] . All these indicators of altered ANS function have been found to be associated with increased risks of mortality and cardiac morbidity in patients with CHD [START_REF] Carney | Depression, the autonomic nervous system, and coronary heart disease[END_REF] .

We are aware of no published study that examined mortality risk as a function of both depression status and RHR level. To address this issue, the present study examines the combined effect of depressive symptoms and RHR on mortality in a large cohort of middleaged British adults. (1991-1993), 5 (1997-1999) and 7 (2002-2004)]. The University College London ethics committee approved the study.

MATERIAL & METHODS

Data

Measures

Depressive symptoms

Depressive symptoms were assessed using the Center for Epidemiologic Studies Depression Scale (CES-D, Cronbach"s alpha = 0.83) at phase 7 of the Whitehall II study (2002-2004). The CES-D, a widely used and validated instrument, is a 20-item self-report questionnaire designed to measure depressive symptomatology in community studies [START_REF] Radloff | The CES-D Scale: A Self-Report Depression Scale for Research in the General Population[END_REF] . A score ≥16 from a total possible score of 60 has been used extensively to distinguish depressed from nondepressed subjects [START_REF] Radloff | The CES-D Scale: A Self-Report Depression Scale for Research in the General Population[END_REF] .

Resting Heart Rate

RHR was measured at the phase 7 screening clinic via electrocardiogram (ECG) on participants in the supine position following a standard protocol. The following classification was used to categorize RHR: RHR<60, 60≤RHR≥80, and RHR>80 beats/minute (bpm), based on current guidelines that have defined adequate rate control as a ventricular response between 60 and 80 bpm at rest [START_REF] Fuster | ACC/AHA/ESC guidelines for the management of patients with atrial fibrillation: executive summary. A Report of the American College of Cardiology/ American Heart Association Task Force on Practice Guidelines and the European Society of Cardiology Committee for Practice Guidelines and Policy Conferences (Committee to Develop Guidelines for the Management of Patients With Atrial Fibrillation): developed in Collaboration With the North American Society of Pacing and Electrophysiology[END_REF] .

Vital status

Mortality follow-up was available through the British National Health Services Central Registry until 30 th April 2009. Death certificates were coded using the 10 th revision of the International Classification of Disease (ICD). All-cause mortality was the main outcome in our analysis.

Covariates

Sociodemographic measures

Sociodemographic measures included age, sex, ethnicity, and socioeconomic position (SEP) assessed by British civil service grade of employment taken from the phase 7 questionnaire.

Biobehavioral risk factors

Behavioral risk factors were assessed using response to the phase 7 questionnaire and were categorized as follows: smoking status (never, ex, and current), physical activity (≥1.5 or <1.5 hours of moderate or vigorous exercise/week), alcohol consumption in the previous week was categorized as abstention, moderate (1-14 units for women/1-21 units for men), and high consumption (14+ units for women/21+ units for men). A unit is 10 ml or 8 grams of pure alcohol. The following biological CVD risk factors were measured at phase 7 clinical examination: hypertension (systolic blood pressure >140 mm/Hg or diastolic blood pressure >90 mm/Hg or antihypertensive medications), high total blood cholesterol (≥ 6.2 mmol/l), body mass index (BMI) (<20, 20-24.9, 25-29.9, or ≥30 kg/m 2 ) and diabetes, assessed via glucose tolerance test at the medical screening or self-report of doctor diagnosis.

Medications

Data on antidepressant medications was drawn from the phase 7 questionnaire where participants were asked whether in the last 14 days they had taken antidepressants drugs prescribed by a doctor (yes/no). CVD medications at phase 7 were also drawn from questions on whether in the last 14 days the participant had taken CVD drugs, including diuretics, beta blockers, ACE inhibitors, calcium channel blockers, nitrates, antiplatelets prescribed by a doctor (yes/no). The same question was used to assess whether participants had taken lipidlowering medications.

Prevalent Coronary heart disease (CHD)

CHD status at phase 7 was defined as non-fatal myocardial infarction (MI ) or "definite" angina and was based on clinical examinations at phases 1, 3, 5, and 7 and records obtained from general practitioners and hospitals. Potential non-fatal myocardial infarction was ascertained by questionnaire items on chest pain (the World Health Organisation Rose questionnaire [START_REF] Rose | Cardiovascular survey methods[END_REF] ) and the physician"s diagnosis of heart attack. Confirmation of myocardial infarction according to MONICA [START_REF] Gutzwiller | Monitoring of cardiovascular disease and risk factor trends: experiences from the WHO/MONICA project[END_REF]

Statistical analysis

Differences in depression status and RHR categories as a function of the sample characteristics were assessed using a chi-square test. The associations of depression and RHR with mortality were examined separately using Cox regressions in 4 serially adjusted models.

A resting heart rate between 60-80 bpm was used as the reference category so that the hazard ratios (HRs) of lower RHR (< 60 bpm ) and higher RHR (above 80 bpm) were estimated .In model 1, HRs were adjusted for the following socio-demographic characteristics: sex, age, ethnicity and SEP. Model 2 additionally adjusted the hazard of mortality for smoking, BMI, alcohol consumption, physical activity, hypertension, total blood cholesterol and diabetes. Model 3 was model 1 additionally adjusted for CVD medication (diuretics, beta blockers, ACE inhibitors, calcium channel blockers, nitrates, antiplatelets), antidepressant medication, lipid lowering medication, and history of CHD. Model 4 included all aforementioned variables, depression and RHR categories, in order to estimate their independent effect on mortality.

To examine the combined effect of depression and RHR on mortality, we divided the study sample into six groups based on the cross classification of depression status (depression, CES-D ≥16 vs. no depression, CES-D < 16) and RHR categories (<60, 60 -80, >80 bpm) with non-depressive participants with RHR between 60 and 80 bpm taken as the reference group.

Cox regressions models were used to calculate multivariable-adjusted risk of death for each group compared with the reference group using the adjustment specified in models 1 and 2 above. The proportional hazards assumption was checked graphically by plotting the log of the negative log of the survival function. These curves were essentially parallel, suggesting therefore that the proportional hazard was not violated.

We also examined the additive interaction between depressive symptoms and elevated RHR as defined by Rothman [START_REF] Rothman | Epidemiology: an introduction[END_REF] by calculating the relative excess risk due to interaction (RERI) [START_REF] Ferreri | Planning of a screening programme for cervical cancer in Liguria and evaluation of the attitude of the female population towards cancer detection[END_REF] using the methods outlined by Andersson et al. [START_REF] Andersson | Calculating measures of biological interaction[END_REF] . For example, a RERI of 4.0 would mean that the relative risk of death from all-causes in depressive participants with elevated RHR is increased by 4.0 compared to the relative risk that one would expect if there were no interaction between these two factors. In the absence of an interaction between depressive symptoms and RHR, the RERI will be 0. Probability values and 95% CIs for the RERI were computed by the delta method [START_REF] Hosmer | Confidence interval estimation of interaction[END_REF] .

RESULTS

A total of 5936 participants were included in the analyses. Of them, 170 died during the mean follow-up period of 5.6 years (SD 0.7, range 0.03-6.6). The mean age of the participants at phase 7, the start of the follow-up for our analysis, was 61 years (SD 6.0). The prevalence of depression (CES-D ≥16) was 14.9%. 24% of participants had RHR<60 bpm, 61 % were in the normal range with RHR between 60 and 80 bpm and 15% had RHR >80 bpm. Compared to participants included in this study, those who did not respond to the CES-D questionnaire or did not have data on RHR were more likely to be: women (39.8% vs. 29.1%, p<0.001), nonwhite (15.2% vs. 8.4%, p <0.001), older (19.5% vs. 9.3%, p<0.001), and from lower SEP (34.1% vs. 15.9%, p<0.001).

Table 1 shows the sample characteristics as a function of depression status and RHR categories at phase 7. Participants with depressive symptoms were more likely to be female, younger, from lower SEP, non-white, on medication (antidepressants, nitrates and antiplatelets), current smokers, less physically active, and to have lower BMI and higher prevalence of diabetes and CHD (all p ≤ 0.04). Men were more likely to have low RHR (<60 bpm, p<0.001). Participants with higher RHR (>80 bpm) were more likely to be from lower SEP, less physically active, hypertensive, obese, diabetic, on CVD medication (beta blockers, nitrates, antiplatelets) and lipid-lowering medication, and to have depressive symptoms (all p ≤0.032).

Table 2 presents estimates from Cox regression models for the associations between depressive symptoms, RHR and mortality. In model 1 adjusted for socio-demographic characteristics, depressive participants (CES-D ≥ 16) were at increased risk of death (HR = 2.46, 95% CI 1.74-3.48), when compared to nondepressive participants (CES-D < 16). Using the same adjustments, but with RHR as the predictor, participants with RHR >80 bpm were at increased risk of death from any cause (HR = 1.70, 95% CI 1.18-2.44) compared to those with RHR between 60 and 80 bpm. In model 2 adjusted for CVD biobehavioral risk, the magnitude of the associations was reduced, but participants with depressive symptoms remained at greater risk of mortality. Participants with RHR > 80 bpm were also at greater risk of mortality. In model 3, adjustments for CVD, antidepressant and lipids lowering medication and prevalent CHD did not alter the associations observed in model 1. Inclusion of all of these variables and both depression and RHR in model 4 did not substantially affect these associations; both depressive symptoms (HR=1.93, 95% CI 1.35-2.76) and high RHR (HR=1.67, 95% CI 1.14-2.45) remained independently associated with an increased risk of mortality.

Table 3 shows the associations of combinations of depression status and RHR categories with mortality as the outcome. Model 1, adjusted for sociodemographic characteristics, shows that compared with the reference group (participants without depression and with RHR between 60 and 80 bpm), the hazard of death was higher for depressive participants with RHR between 60 and 80 bpm (2.71, 95% CI 1.73-4.23), for those without depression but with RHR >80 bpm (1.80, 95% CI 1.17-2.76), and for those with both depression and RHR >80 bpm (3.85, 95% CI 2.03-7.31). After further multivariate adjustment for biobehavioral risk factors in model 2, the magnitude of the associations was reduced, but the associations persisted. In model 3, adjustment for CVD, antidepressant and lipid lowering medications, and prevalent CHD did not substantially alter the associations observed in model 1. Finally, after inclusion of all these variables in model 4, the hazard for death was 2.1-fold (p<0.001) higher for participants with depression but with RHR between 60 and 80 bpm, 1.8fold (p<0.001) higher for those without depression but with RHR >80 bpm, and 3-fold (p<0.001) higher for those with both depression and RHR >80 bpm. The RERI between depressive symptoms and elevated RHR was 0.20 (95% CI, -2.17-2.5).

Sensitivity analyses

In order to assess the robustness of the present findings, we repeated the analyses excluding participants with a personal history of CHD. The number of deaths was reduced by 22% (n deaths=133). In fully mutually-adjusted model, depressive symptoms (HR=1.82, p=0.005) and elevated RHR (>80 bpm, HR= 1.63, p=0.03) remained independent predictors of death. The corresponding fully adjusted risk of death was 2.5-fold (p=0.04) higher for participants with both depressive symptoms and RHR > 80 bpm when compared to those without depressive symptoms and with RHR between 60 and 80 bpm. The corresponding RERI was -0.60 (95% CI, -2.90-1.71). Similar patterns of association were observed when the analyses were restricted to participants with prevalent CHD (n = 37). The corresponding fully mutually adjusted HRs were 2.97 (p=0.006) for depressive symptoms and 2.00 (p=0.17) for those with RHR > 80 bpm. Finally, participants with both depressive symptoms and RHR >80 bpm had a 7.5-fold (p=0.005) higher risk of death relative to those without depressive symptoms and with RHR between 60 and 80 bpm. The corresponding RERI was 2.39 (95% CI, -4.13-8.90).

In addition, we repeated the analysis in subgroups of beta blockers users and non-users.

In fully mutually-adjusted model, depressive symptoms (HR=2.14, p<0.001) and elevated RHR (>80 bpm, HR= 1.57, p=0.025) remained independent predictors of death (n=142) among non beta blockers users. The corresponding fully adjusted risk of death was 3.22-fold (p≤0.001) higher for participants with both depressive symptoms and RHR > 80 bpm when compared to those without depressive symptoms and with RHR between 60 and 80 bpm.

Among beta blockers users (n deaths= 28) the corresponding HRs were 0.99 (p=0.99) for depressive symptoms and 2.48 (p=0.26) for elevated RHR. Only two beta blocker users had depressive symptoms and RHR > 80 bpm thus preventing further analysis of this group.

Although the risk of death seems to be lower among beta blocker users, the small number of deaths among this group precludes any definite conclusions regarding these observations.

DISCUSSION

In this study we sought to examine the combined effect of depressive symptoms and RHR on mortality in a large cohort of British adults. We found that depressive symptoms and elevated RHR were independent predictors for death from all-causes over 5 years of follow up.

Concurrently, the study also shows that the coexistence of depression and higher RHR is associated with substantially elevated risk of death from all-causes beyond the effect of having either depression or elevated RHR alone. For instance, after adjustment for relevant biobehavioral risk factors, participants with both depression and RHR >80 bpm were at a 3fold higher risk of death when compared to those without depression and with RHR ranging from 60 to 80 bpm. This risk is particularly marked in participants with prevalent CHD where there was some evidence of an additive interaction between depressive symptoms and elevated RHR.

Findings in context of the literature and possible mechanisms

To our knowledge, this is the first prospective cohort study to compare the effects of depressive symptoms on mortality in individuals as a function of their RHR. Our findings are based on a large well-characterized cohort with depression symptomatology assessed by a validated scale and biological risk factors assessed by clinical examination. We found that both depression and RHR were strong predictors of death independently of biobehavioral risk factors and of each other. This is consistent with previous studies [START_REF] Michaud | Burden of disease--implications for future research[END_REF][START_REF] Zheng | Major depression and all-cause mortality among white adults in the United States[END_REF][START_REF] Abas | Depression and mortality in a high-risk population. 11-Year follow-up of the Medical Research Council Elderly Hypertension Trial[END_REF][START_REF] Dyer | Heart rate as a prognostic factor for coronary heart disease and mortality: findings in three Chicago epidemiologic studies[END_REF][START_REF] Greenland | Resting heart rate is a risk factor for cardiovascular and noncardiovascular mortality: the Chicago Heart Association Detection Project in Industry[END_REF][START_REF] Kannel | Heart rate and cardiovascular mortality: the Framingham Study[END_REF] , even though these studies usually considered depression and RHR as individual predictors and rarely showed mutually adjusted analyses. In comparisons across the six exposure categories, we also found that participants with co-existing depression and elevated RHR (>80 bpm) were more likely to die than were participants in any of the other five combinations. Moreover, participants with depression but with RHR ranging from 60 to 80 bpm were at increased risk of mortality compared to those without depression and RHR > 80 bpm, RHR considered to be elevated. These results suggest that the effect of depression on mortality is strong and it is perhaps a stronger predictor of death than RHR in this cohort of middle-aged men and women.

Although this study did not aim to examine the mechanisms that could explain the current observations, several hypotheses seem possible. The finding showing depression to be associated with increased risk of all-cause mortality suggests that depression may act as an exacerbating factor in the progression of other medical illnesses [START_REF] Alexopoulos | Depression in the elderly[END_REF] . Although depression is thought to be implicated in the development of certain physical illnesses such as CVD [START_REF] Nicholson | Depression as an aetiologic and prognostic factor in coronary heart disease: a meta-analysis of 6362 events among 146 538 participants in 54 observational studies[END_REF] , secondary depression, where a diagnosed or undiagnosed medical illness precedes depression, is also possible. In this case, depression may appear to be a marker of the severity of physical illnesses [START_REF] Frasure-Smith | Depression following myocardial infarction. Impact on 6-month survival[END_REF][START_REF] Goodnick | Treatment of depression in patients with diabetes mellitus[END_REF] . The coexistence of depression with other medical illnesses may impair recovery and increase the risk of mortality by impeding treatment seeking, adherence to pharmacological and behavioral regimens, and adoption of healthy life-styles [START_REF] Penninx | Depressive symptoms and physical decline in community-dwelling older persons[END_REF] .

The association between RHR and mortality is plausible because RHR is a marker of both autonomic nervous system and cardiorespiratory fitness, both of which, when impaired, are associated with the risk of death [START_REF] Myers | Exercise capacity and mortality among men referred for exercise testing[END_REF][START_REF] Schwartz | The autonomic nervous system and sudden death[END_REF] . Although an elevated RHR might be the reflection of poor underlying health status [START_REF] Greenland | Resting heart rate is a risk factor for cardiovascular and noncardiovascular mortality: the Chicago Heart Association Detection Project in Industry[END_REF] , it is primarily an indicator of cardiorespiratory fitness which is related to physical fitness [START_REF] Myers | Exercise capacity and mortality among men referred for exercise testing[END_REF] . Indeed, exercise capacity is a powerful predictor of mortality [START_REF] Myers | Exercise capacity and mortality among men referred for exercise testing[END_REF] and RHR is lower in individuals who undertake vigorous physical activity [START_REF] Black | Secular trends in heart rate in young adults, 1949 to 2004: analyses of cross sectional studies[END_REF] . Depression has been shown to be associated with decreased cardiorespiratory fitness [START_REF] Hollenberg | Depression decreases cardiorespiratory fitness in older women[END_REF] which may be the consequence of a lower engagement of individuals in physical activity. Data from the Established Populations Epidemiologic Studies of the Elderly cohort provide some evidence that physical activity is one of the mechanisms underlying the link between depression and physical decline, as those who were depressed undertook less walking, gardening, and vigorous physical activities [START_REF] Penninx | Depressive symptoms and physical decline in community-dwelling older persons[END_REF] . This may explain why depression has been found to be associated with high RHR, although depression itself could also affect physical fitness and subsequently RHR levels by directly modulating central nervous system pathways [START_REF] Carney | Depression, the autonomic nervous system, and coronary heart disease[END_REF][START_REF] Grippo | Biological mechanisms in the relationship between depression and heart disease[END_REF] . Furthermore, despite the independent effects observed in this study, high RHR and depression may be associated due to partially shared biological processes. Increased RHR in depressive participants could reflect deficits in cardiac vagal control. It is known that cardiac vagal activity when unaltered decreases cardiac activity by reducing RHR and contractility. [START_REF] Reed | Heart rate variability measurements and the prediction of ventricular arrhythmias[END_REF] However, there is also some evidence showing an increased RHR in the absence of reduced vagal tone in depressed patients [START_REF] Moser | Increased heart rate in depressed subjects in spite of unchanged autonomic balance?[END_REF] . Recent studies have shown depression to be associated with low heart rate variability [START_REF] Carney | Association of depression with reduced heart rate variability in coronary artery disease[END_REF][START_REF] Carney | Depression as a risk factor for cardiac mortality and morbidity: a review of potential mechanisms[END_REF] , an index of reduced cardiac vagal activity, which has been found to be a risk factor for all cause and cardiac mortality [START_REF] Tsuji | Reduced heart rate variability and mortality risk in an elderly cohort. The Framingham Heart Study[END_REF][START_REF] Tsuji | Impact of reduced heart rate variability on risk for cardiac events. The Framingham Heart Study[END_REF] .

Considering the plausibility of the influence of depression on RHR via behavioral and pathophysiological mechanisms and their independent link with mortality, it is highly possible that they exert a combined effect on mortality risk. However, the underlying mechanisms, including the vagal mechanism, behind this association need to be examined in future studies.

Study limitations

In interpreting the present results, it is important to note some limitations. First, this cohort of civil servants did not include blue collar workers, unemployed or younger adults; thus it is not representative of the general population of working age, which may limit the generalisability of our findings. Second, we assessed depressive symptoms rather than clinical depression. However, it has been suggested that significant depressive symptomatology could be a risk factor for clinical depression [START_REF] Radloff | The CES-D Scale: A Self-Report Depression Scale for Research in the General Population[END_REF] . Finally, we did not have the power to examine cause specific mortality but the results for all cause mortality are robust. The lack of power may also explain why the confidence interval around the RERI estimating the interaction between depressive symptoms and elevated RHR was large among participants with CHD, but did not reach statistical significance. Although this finding is consistent with the idea that depression and RHR are general rather that specific risk factors of any disease, [START_REF] Greenland | Resting heart rate is a risk factor for cardiovascular and noncardiovascular mortality: the Chicago Heart Association Detection Project in Industry[END_REF][START_REF] Silber | The association of resting heart rate with cardiovascular, cancer and all-cause mortality. Eight year follow-up of 3527 male Israeli employees (the CORDIS Study)[END_REF] further studies should examine whether depression and elevated RHR exert a combined effect on CVD, cancer, and non CVD mortality.

Conclusions and implications of this finding

Despite these potential limitations, depression is increasingly recognized to have an important predictive and prognostic value and this study provides additional evidence that the coexistence of depressive symptoms and elevated RHR is associated with substantially increased risk of death. Our findings raise the possibility that treatments that improve both depression and RHR might improve survival.

  are drawn from the Whitehall II study, established in 1985 as a longitudinal cohort study to examine the socioeconomic gradient in health and disease among 10,308 civil servants (6,895 men and 3,413 women). All civil servants aged 35-55 years in 20 London based departments were invited to participate by letter, and 73% agreed. Baseline screening (Phase 1) took place during 1985-1988, and involved a clinical examination and a self-administered questionnaire. Subsequent phases of data collection have alternated between postal questionnaire alone [Phases 2 (1989-1990), 4 (1995-1996), 6 (2001) and 8 (2006)] and postal questionnaire accompanied by a clinical examination [Phases 3

  criteria (Multinational Monitoring of Trends and Determinants in Cardiovascular Disease) was based on electrocardiograms, markers of myocardial necrosis, and chest pain history from medical records. Angina was assessed based on participant"s reports of symptoms with corroboration in medical records or abnormalities on a resting electrocardiogram, an exercise electrocardiogram, or a coronary angiogram.

Table 1 .

 1 Sample characteristics as a function of Depression and Resting Heart Rate at phase 7

			Depressive symptoms
			(CES-D score ≥16)		Resting Heart Rate categories
	Variables
		N total N (%)	p value	< 60 bpm	60-80 bpm	>80 bpm	p value
					N (%)	N (%)	N (%)
	Sex			< 0.001				< 0.001
	Male	4268	559 (13.1)		1124 (79.2)	2498 (68.8)	646 (73.0)
	Female	1668	326 (19.5)		296 (20.8)	1133 (31.2)	239 (27.0)
	Age in years			< 0.001				0.703
	< 54	1110	212 (19.1)		250 (17.6)	721 (19.9)	139 (15.7)
	54-59	1822	272 (14.9)		421 (29.6)	1139 (31.4)	262 (29.6)
	60-64	1259	163 (12.9)		321 (22.6)	746 (20.5)	192 (21.7)
	65-69	1196	163 (13.6)		275 (19.4)	717 (19.7)	204 (23.1)
	70-74	549	75 (13.7)		153 (10.8)	308 (8.5)	88 (9.9)
	SEP			< 0.001				< 0.001
	High	2040	201 (9.9)		546 (38.5)	1221 (33.6)	273 (30.8)
	Middle	3032	469 (15.5)		717 (50.5)	1831 (50.4)	484 (54.7)
	Low	864	215 (24.9)		157 (11.1)	579 (15.9)	128 (14.5)
	Ethnicity			< 0.001				0.543
	White	5485	743 (13.5)		1320 (93.0)	3347 (92.2)	818 (92.4)
	Other	451	142 (31.5)		100 (7.0)	284 (7.8)	67 (7.6)
	Smoking status			< 0.001				0.479
	Never smoker	2678	377 (14.1)		639 (45.0)	1637 (45.1)	402 (45.4)
	Ex smoker	2282	297 (13.0)		556 (39.2)	1364 (37.6)	362 (40.9)
	Current smoker	680	145 (21.3)		157 (11.1)	437 (12.0)	86 (9.7)
	Missing	296	66 (22.3)		68 (4.8)	193 (5.3)	35 (4.0)
	Alcohol consumption			0.514				0.755
	Abstainers	973	220 (22.9)		206 (14.5)	604 (16.6)	163 (18.4)
	Moderate	3725	484 (13.0)		9439 (66.1)	2286 (63.0)	500 (56.5)
	High	1158	153 (13.2)		254 (17.9)	691 (19)	213 (24.1)
	Missing	80	28 (35.0)		21 (1.5)	50 (1.5)	9 (1.0)
	Exercise			< 0.001				< 0.001
	≥ 1.5 h / week	5152	699 (13.6)		1277 (89.9)	3134 (86.3)	741 (83.7)
	< 1.5 h / week	784	186 (23.7)		143 (10.1)	497 (13.7)	144 (16.3)
	Hypertension			0.315				0.032
	No	3585	521 (14.5)		811 (57.1)	2336 (64.3)	438 (49.5)
	Yes	2351	364 (15.5)		609 (42.9)	1295 (35.7)	447 (50.5)
	BMI (kg/m²)			0.002				< 0.001
	< 20	179	38 (21.2)		53 (3.7)	108 (3.0)	18 (2.0)
	20-24.9	2028	263 (13.0)		570 (40.1)	1242 (34.2)	216 (24.4)
	25-29.9	2606	365 (14.0)		588 (41.4)	1627 (44.8)	391 (44.2)
	≥ 30	1099	214 (19.5)		206 (14.5)	638 (17.6)	255 (28.8)
	Missing	24	5 (20.8)		3 (0.2)	16 (0.4)	5 (0.6)
	Diabetes			< 0.001				< 0.001
	No	5656	816 (14.4)		1371 (96.5)	3470 (95.5)	815 (92.1)
	Yes	281	69 (24.6)		49 (3.5)	162 (4.5)	70 (7.9)
	High blood cholesterol			0.266				< 0.174
	No	3940	599 (15.2)		991 (69.2)	2401 (66.1)	548 (61.9)
	Yes	1886	263 (13.9)		396 (27.9)	1174 (32.2)	316 (35.7)
	Missing	110	23 (20.9)		33 (2.3)	56 (1.5)	21 (2.4)
	Antidepressant drugs			< 0.001				0.842
	No	5728	786 (13.7)		1366 (96.2)	3514 (96.8)	848 (95.8)
	Yes	208	99 (47.9)		54 (3.8)	117 (3.2)	37 (4.2)
	CVD medications (Yes)
	Diuretics	494	76 (15.4)	0.757	135 (9.5)	277 (7.6)	82 (9.3)	0.518
	Beta Blockers	584	91 (15.6)	0.631	345 (24.3)	223 (6.1)	16 (1.8)	< 0.001
	ACE Inhibitors	649	110 (16.9)	0.122	164 (11.5)	356 (9.8)	129 (14.6)	0.113
	Calcium Channel Blockers 420	67 (16.0)	0.533	118 (8.3)	228 (6.3)	74 (8.4)	0.614
	Nitrates	62	18 (29.0)	0.002	27 (1.9)	33 (0.9)	2 (0.2)	< 0.001
	Antiplatelets	584	104 (17.8)	0.038	199 (14.0)	310 (8.5)	75 (8.5)	< 0.001
	Lipid lowering medications			0.242				0.001
	No	5247	772 (14.7)		1207 (85.0)	3253 (89.6)	787 (88.9)
	Yes	689	113 (16.4)		213 (15.0)	378 (10.4)	98 (11.1)
	History of CHD			0.001				< 0.001
	No	5385	777 (14.4)		1229 (86.5)	3348 (92.2)	808 (91.3)
	Yes	551	108 (19.7)		191 (13.5)	283 (7.8)	77 (8.7)

ACKNOWLEDGEMENTS

The Whitehall II study is supported by grants from the Medical Research Council; British Heart Foundation; Health and Safety Executive; Department of Health; National Heart Lung and Blood Institute (R01HL036310), US, NIH: National Institute on Aging (R01AG013196 and R01AG034454), US, NIH; Agency for Health Care Policy Research (HS06516); and the John D and Catherine T MacArthur Foundation Research Networks on Successful Midlife Development and Socio-economic Status and Health. JV and MK are supported by the Academy of Finland (projects 124271, 124322, 129262 and 132944) and MK is additionally supported by the BUPA Foundation, UK, the National Heart, Lung, and Blood Institute and the National Institute on Aging, USA. MJS and AB are supported by a grant from the British Heart Foundation and MGM by a Medical Research Council research professorship. AS-M is supported by a "European Young Investigator Award" from the European Science Foundation.


S Drapier
email: drapier@emse.fr

A Pagot

A Vautrin
email: vautrin@emse.fr

P Henrat

Influence of the stitching density on the transverse permeability of Non-Crimped New Concept (NC2) multiaxial reinforcements : measurements and predictions

Keywords: multiaxial reinforcements, through-thickness stitching, resin infusion, transverse permeability, mesoscopical approach

New manufacturing processes arise for polymer-based composites which involve resin infusion through dry pre-forms. Modelling approaches of these processes require to assess new physical characteristics of the materials. In this paper, the transverse permeability of new multiaxial stitched materials, referred to as NC2, is investigated. First, in the framework of Darcy's flows, this permeability is assessed for various biaxial NC2 using a specific device. Through this approach it is shown that the transverse permeability depends strongly on the stitching density. Then, the results from a simplified FE study carried out at the blanket scale are shown to correlate quite well the experimental measurements and evidences established in the first part.

Introduction

Till the early 90's, high performance organic composite structures were mainly manufactured from pre-impregnated unidirectional plies. Since then, processes involving the resin impregnation in dry pre-forms have become very popular due to their versatility along with the cost reductions that they usually induce. Indeed, valuable cost cuts originate from the handling and storage cost reductions, since only the resin has to be cold-stored. But moreover in these processes thick/heavy multilayered preforms can be easily employed, this in turn induces material costs reductions.

In these manufacturing processes the impregnation stage is a key parameter ( [START_REF] Lam | Numerical simulation of the mould-filling process in resin-transfer moulding[END_REF], [START_REF] Avila | An experimental investigation of the isothermal impregnation of fibrous preforms[END_REF]). Originally, liquid resins were injected through injection gates in molds containing the dry preforms. The most popular of these manufacturing processes, widely used, is the Resin Transfer Molding (RTM). Modelling efforts, still continued, have permitted to optimise for the RTM the injection gates and events placements in the molds ( [START_REF] Kenny | Mathematical modelling of resin transfer molding of composites for automotive applications[END_REF], [12]), in order for the mold to be completely filled and free of any air bubble which may be entrapped [START_REF] Lam | Numerical simulation of the mould-filling process in resin-transfer moulding[END_REF]. This injection takes place mainly in the preform plane and hence involves principally the longitudinal permeabilities properties of the preforms ( [START_REF] Trevino | Analysis of resin injection molding in molds with preplaced fiber mats : Permeability andd compressibility measurements[END_REF], [START_REF] Shih | Effect of fiber architecture on permeability in liquid composite molding[END_REF], [START_REF] Binétruy | Effects of fabrics architectural heterogeneities on effective and satured permeabilities in RTM[END_REF]). Other processes, involving rather resin infusion than resin injection and referred to as Liquid Composite Molding (LCM), have been developed in the very last few years. LCM processes permit to overtake these problems of injection heterogeneities by impregnating the dry preforms over wide surfaces [11]. In this sense, lower pressures are involved, and the transverse permeability properties of the preforms become one of the key parameters to optimize the manufacturing cycles.

One of these processes is the Resin Film Infusion (RFI) process in which films of neat resin are stacked, with dry preforms, in a mold. The use of a movable rigid perforated plate, or molds for more complex shapes, placed on top of the stacking permits to ensure well-finished final surfaces. The whole stacking is then vacuum-bagged and usually placed in an autoclave to undergo a temperature-pressure cycle (Figure 1). It is clear that the filling time and resin heterogeneity distributions in this process will depend mainly on the preform through-thickness permeability. This parameter is very seldom studied, since conversely to the longitudinal permeabilities, the length over which it can be measured is very small, of the order of 1 mm for single standard multiaxial reinforcements.

The present paper is dedicated to the study of the transverse permeability in long-fibre composites, more precisely in new multiaxial semi-products developed by Hexcel Fabrics. These Non-Crimped New Concepts (NC2) multiaxial reinforcements are made up from very homogeneous planes of fibres stitched together through their thickness (see Figure 2). The very high resulting homogeneity, essential to achieve high final mechanical properties, leads to very low permeabilities, much lower than the very few ones measured on other more classical materials. Then, in order to optimize the pressure-temperature cycles, the transverse permeability of single NC2 multiaxial fabrics must be input in some modelings of the impregnation process at the fabric scale.

In the present study, first, based on a quick survey of permeability measurements and fluid propagation in porous media, a specific set-up is designed to measure properly this permeability. This set-up is then used to assess the through-thickness permeability of biaxial NC2. These basic multiaxial fabrics are considered here to isolate the phenomena controlling the permeability. Then some simulations are presented at the blanket scale which focus on the effect of the stitching density onto the permeability. A good correlation is found between experimental measurements and predicted permeabilities regarding the stitching density influence.

The permeability phenomenon in composites

The transverse permeability phenomenon across composite multiaxial fabrics is introduced here, this permits to set up the basis of the principle of measurements. Then, longitudinal and transverse permeability measurements are presented.This yields some ideas for the set-up to be designed for the transverse permeability characterization. Finally, since a modelling approach is proposed in the second part of this paper, some representative models are presented which set the basis for the simulations.

Flow through porous media

The multiaxial fabrics studied here are intrinsically porous media, the pore size of which may be at the fibre level as well as at the stitching level (Figure 2). The basics of flows through porous media can be found for instance in [13]. In these flows, the interconnected porosity is involved which restrains, at the microscopic scale, the fluid progression through 'channel-like' cavities. Hence, at this scale the classical laws of fluid mechanics will rule the flow. The two main laws commonly used are the mass conservation equation and the Navier-Stokes equation, provided the fluid can be assumed as newtonian. When compared to a classical mass conservation equation, the volume fraction of any phase must be accounted for. Let us notice that in a wet fabric, the phases are either fluid for the resin in motion, or solid for the composite which can undergo deformation under the pressure generated by the flow. For this latter, the mechanical response must be determined too.

These two laws permit on their own to describe the fluid flow through the porous medium, where pressure and velocity are the parameters to determine in both phases. However, beyond the modelling efforts required for seeking the solution, the complexity of the porosity architecture does not allow in our case this system to be solved easily. Even numerically, the various porosity shapes which exist at the different scales cannot be easily represented without turning to more refined descriptions such those adopted in [START_REF] Henzel | A standard characterisation of satured and unsatured flow behaviours in porous media[END_REF] or [START_REF] Delerue | New algorithms in 3d image analysis and their application to the measurement of a spatialized pore size disctribution in soils[END_REF] for example. In the present approach, these equations will be solved through fluid mechanics finite element (FE) analysis in a simplified framework, following the experimental evidences demonstrated in the measurements.

Assessing permeabilities from flows in composites

In porous media, such as the fabrics of interest in composites, more convenient approaches can be led at the mesoscopic scale, i.e. the scale where the porous medium is seen as homogeneous. Several approaches exist which are used in the literature to model or to identify the permeability. The most popular approach relies on the Darcy's law, empirically established, which permits to relate in three dimensional cases the flow velocity to the gradient of pressure undergone by the fluid in the porous medium :

v = - K η ∇P ( 1
)
where v is the flow rate vector, K is the second order permeability tensor of the porous medium that usually depends on the fluid flowing through it represented here by its viscosity η, and ∇P is the pressure gradient. However, it must be pointed out that this empirical law has been established in a well defined frame. Indeed, the Darcy's law holds only for stationary regimes, and Reynolds (Re) numbers calculated for porous media must be lower than 1. Beyond this limit, the flow is inertial (1 < Re < 150), and further (300 < Re) turbulent. This Reynolds number maybe somehow hard to evaluate in porous media since it depends on a characteristic length of the medium [13], which in turn depends on the scale of observation considered.

For the experimental measurements the simplistic Darcy's approach is conveniently considered, either for longitudinal ( [START_REF] Adams | Forced in-plane flow of an epoxy resin in fibrous networks[END_REF], [START_REF] Henzel | A standard characterisation of satured and unsatured flow behaviours in porous media[END_REF], ...), transverse ( [START_REF] Trevino | Analysis of resin injection molding in molds with preplaced fiber mats : Permeability andd compressibility measurements[END_REF], [START_REF] Binétruy | Effects of fabrics architectural heterogeneities on effective and satured permeabilities in RTM[END_REF]), or 3D permeability characterization [START_REF] Bréard | Mesure de la perméabilité spatiale d'un renfort tridimensionnel pour matériaux composites à matrice polymère[END_REF]. Along with this flow rule, a usual restriction is made to the second order permeability tensor that is taken to be orthotropic. Moreover, it is assumed that no coupling exists between the permeabilities in the three principal directions. Finally, as a first approximation only three independent constants define the permeability tensor : two in-plane (longitudinal) permeabilities and one (through-thickness) transverse permeability. For uniaxial flows, a simplified form is deduced from Eq. (1) which relates the mean uniaxial velocity of the fluid to the pressure gradient undergone in the flow direction (for instance e 3 ). The pressure gradient is here assumed to be linear, since it is deduced from the discrete measurements of the pressure loss along the flow. Moreover, it is assumed that the transverse direction is, in first approximation, a principal direction. Then, for an orthotropic medium, the uniaxial expression writes for a transverse flow :

D = - K 33 A η ∆P e ( 2
)
where D is the flux, K 33 is the transverse permeability, A is the cross-sectional area of the flow, ∆P is the pressure variation, η is the fluid viscosity, and e is the flow length. All these quantities refer to the flow direction. In our case this approach will be used provided the permeability properties can depend on multiaxial architecture.

As for the NC2 material investigated here, it must be noticed that scientific papers devoted to permeability measurements of multiaxial composites mainly focus on woven or random reinforcements ([3], [START_REF] Henzel | A standard characterisation of satured and unsatured flow behaviours in porous media[END_REF], [START_REF] Caba | Verification of a simulation model for resin film infusion of complex shaped composite structures[END_REF]), [START_REF] Lim | Modelling of void formation during resin transfer molding[END_REF], ...). However, in some points multiaxial NC2 and woven fabrics have a close meso-structure, especially both exhibit an alternance of fibre tows and gaps. This meso-structure is important in setting the channels through which the resin will flow, either in injection or infusion. But this is mostly relevant in longitudinal permeability measurements. For the transverse permeability in NC2 materials, macropores are present due to the stitching. Consequently, the fluid will certainly flow through these channel-like connections and then continue either in the fabric planes or in the closest stitching upstream. This will be assessed in the second part dedicated to the transverse permeability modelling.

Longitudinal and transverse measurements

Permeability measurements can be carried out for either in-plane (for instance [START_REF] Trevino | Analysis of resin injection molding in molds with preplaced fiber mats : Permeability andd compressibility measurements[END_REF], [START_REF] Shih | Effect of fiber architecture on permeability in liquid composite molding[END_REF], [START_REF] Robitaille | Permeability modelling of industrial preforms : simulations and practical aspects[END_REF], [START_REF] Lundström | Inplane permeability measurements : stability, repatability and reproductibility[END_REF], [START_REF] Binétruy | Effects of fabrics architectural heterogeneities on effective and satured permeabilities in RTM[END_REF], ...), transverse ([3] and [START_REF] Trevino | Analysis of resin injection molding in molds with preplaced fiber mats : Permeability andd compressibility measurements[END_REF], ...) or 3D flows ( [START_REF] Bréard | Mesure de la perméabilité spatiale d'un renfort tridimensionnel pour matériaux composites à matrice polymère[END_REF]), in unsteady or steady regimes. The principle of measurement is common for both longitudinal and transverse measurements and is rather simple. A specific device is fed in with fluid under constant flux or pressure. Meanwhile pressure or velocity measurements are made in the dry (downstream) and wet (upstream) regions, on either side of the flow front (Figure 3-a), or specimen location (3-b) in saturated regime. Permeability is then identified, using the Darcy's law (Eq. 2 or 1) or more complex relationships in bidirectional or 3D cases, from the variations of velocity or pressure induced by the displacement of the fluid through the sample tested. For longitudinal measurements, rectangular or circular specimens are cut, respectively for unidirectional and bidirectional measurements, and fitted into a rigid mold.

For transverse measurements there is no such restrictions on the specimen shape, but usually circular cylindrical specimens are more conveniently used. This transverse measurement is very seldom studied ( [START_REF] Trevino | Analysis of resin injection molding in molds with preplaced fiber mats : Permeability andd compressibility measurements[END_REF], [START_REF] Bréard | Mesure de la perméabilité spatiale d'un renfort tridimensionnel pour matériaux composites à matrice polymère[END_REF], [START_REF] Binétruy | Effects of fabrics architectural heterogeneities on effective and satured permeabilities in RTM[END_REF] ... ) but tends to be more and more common due to the use of thicker fabrics. The very key point is in this case to realize the fluid injection while maintaining the specimen to be impregnated, but without disturbing the fluid flow. In [START_REF] Binétruy | Effects of fabrics architectural heterogeneities on effective and satured permeabilities in RTM[END_REF] specimens are maintained on their edges, but this does not allow to control the specimen thickness. Therefore the fibre volume fraction, defined as the ratio of the fibre volume over the tested volume, could vary since the apparent fabric thickness may change. It must be pointed out that in the transverse permeability measurement, the fibre volume fraction is of great importance since it will influence the fabric permeability, i.e. will change the porosity configuration. In [START_REF] Trevino | Analysis of resin injection molding in molds with preplaced fiber mats : Permeability andd compressibility measurements[END_REF], the thickness can be controlled by compacting the specimen between 2 porous rigid plates allowing for the injection. The counterpart of this technological solution is that the pressure loss induced by the plate porosity may be higher than the one induced by the specimen itself, due to the reduced thickness involved. In either case, the measurement takes place in saturated regime since it is not possible to visualise the flow front over such a small length.

Through-thickness permeability predictions

As stated previously, commonly permeability phenomena in composites rely on the treatment of their complex meso/micro-structure. Then idealized geometries are widely used, either to predict permeabilities in basic cases [13], or in an attempt to relate experimental permeabilities to micro, meso and macro scales [START_REF] Shih | Effect of fiber architecture on permeability in liquid composite molding[END_REF]. In more refined approaches, such as the lattice Boltzmann model proposed by [START_REF] Spaid | Lattice boltzmann methods for modeling microscale flow in fibrous porous media[END_REF], phenomena can be represented at the mesoscopical scale whilst dealing with void formation in the tows. Results of transverse flows simulations over circular porous tows are proposed which describe the void entrapment in higher permeability regions for unsaturated flows. In our composite materials, saturated flow will be simulated, and consequently any entrapment will be ignored.

This qualitative analysis [START_REF] Spaid | Lattice boltzmann methods for modeling microscale flow in fibrous porous media[END_REF] applies also to more realistic pore architecture, the complexity of which has to be addressed if quantitative predictions are to be proposed. In the case of composites ( [START_REF] Henzel | A standard characterisation of satured and unsatured flow behaviours in porous media[END_REF], [START_REF] Stavrov | Effect of the structure of a fibrous layer on its permeability for a nonlinearly viscous fluid[END_REF]), starting from micrographs the identification of pores at micro and meso scales is deduced from the probabilistic treatment that a segment of length l fits in a pore in a given direction. For soils [START_REF] Delerue | New algorithms in 3d image analysis and their application to the measurement of a spatialized pore size disctribution in soils[END_REF], the pore network is reconstructed from 3D image analyses, after skeletization and creation of a spatialized local pore size distribution. Then the 'conductivity' of the network is evaluated, especially fluid invasion is shown to be controlled by the connectivity between the largest pores. In our materials, where at least two pore scales exist, such a result reinforces our choice of modelling the flow at the mesoscopical scale where the largest pores are seen.

Eventually, homogenization methods exist which are the most relevant regarding the permeability of media with a regular micro/meso-structure ( [START_REF] Velten | Drag measurement and evaluation in impregnation processes[END_REF], [START_REF] Boutin | Study of the permeability by periodic and self-consistent homogenisation[END_REF]). These methods rely on the behaviour of a representative volume element on which are prescribed boundary conditions ensuring its periodicity. In our case, NC2 fabrics cannot be easily represented through a succession of elementary cells at the microscopical level. However, the idea of using a representative volume element can be adapted to the simulation of transverse permeability at the mesoscopical scale. Eventually, finite element approaches are in our case the most easily suitable for the predictions of transverse permeability using a representative mesoscopical cell, and will be subsequently used.

Assessment of the NC2 transverse permeability

Using the knowledge gained in the previous survey, an apparatus has been designed to measure the transverse permeability of fabrics. This experimental device is presented and then used to assess the NC2 transverse permeability, and further to demonstrate how this permeability varies with the stitching density.

Experimental apparatus

The principle of measuring the pressure loss induced by the flow of the fluid through the specimen is the basis of the permeability measurement. The specific apparatus developed here is based on this principle (Figure 4 and5). Following [START_REF] Trevino | Analysis of resin injection molding in molds with preplaced fiber mats : Permeability andd compressibility measurements[END_REF], aluminium honeycombs are selected to maintain the specimen in the apparatus. Indeed, after some FE simulations, the channels formed naturally by the honeycomb structure were shown to make the flow become steady even for high fluid velocities. Hence, the use of honeycombs will allow for the thickness of the tested volume to be controlled while smoothing the flow. The second key point of the apparatus is the pressure measurement which is realized with two pressure probes. Let us notice that the location of the probes along the flow is optimized such that pressures are measured in steady flow regions before and after the honeycombs (Figure 4-b).

Another very important point, as explained previously, is the porosity volume fraction of the tested medium that will depend on the compression required to maintain the specimen. Conversely to the processes involving resin injection, the reinforcement deformation during impregnation appears very rarely in infusion processes [START_REF] Walsh | Composite auto bumper : design and process evaluation[END_REF]. In our case, the specimen thickness will be controlled during the measurements with integrated verniers, and the porosity will be deduced from the specimen surfacic mass. Furthermore, the paper of [START_REF] Lundström | Inplane permeability measurements : stability, repatability and reproductibility[END_REF], dedicated to the repeatability measurements for longitudinal permeability, states that some discrepancies of the order of 15 % may result from heterogeneities in the material as well as from the material deformability. The deformability of the specimen will especially take place during the cutting. Following this evidence, the specimen cutting is integrated to our apparatus such that specimens will not be handled at all (Figure 4-a and Figure 5-b).

This in-situ cutting implies that the airtightness, required both to prevent the fluid from leaking and to isolate the chambers, has to be mobile. This is achieved in the presented apparatus as shown in Figure (4-b) and Figure (5-a). For further simplifications, the specimens tested were chosen circular, 100 mm in diameter. The specimen diameter was fixed such that for the lowest stitching density (10mm×10mm), statistically at least 96% of the stitching points would be submitted to the flow for any random placement of the specimen.

Eventually, for the impregnating fluid a lubrication oil NEUTRAL was selected, the behaviour of which is newtonian. The oil was chosen such that its viscosity was as close as possible to the resin viscosity encountered in the RFI process, taking into account that the gear-pump used for the feeding (Figure 4-b) would not stand fluid viscosities larger than 10 Pa s. The oil viscosity is perfectly known as a function of temperature, and is given in Annexe 1. The fluid temperature is evaluated through a thermo-couple placed between the pump and the fluid inlet, and any apparent thickness variation is assessed using an LVDT displacement sensor. An interface-card is used for data acquisition on a PC, for pressures, temperature, displacement, and flow rate.

Protocol

Measurements are carried out with the presented apparatus (Figure 5). The flow length related to the fibre volume fraction of the specimen is set by the verniers, close to commonly used values. As for the velocity range, it is rather hard to know exactly the velocities encountered in the manufacturing processes. Hence, in order to cover the wider velocity range, it was chosen to stop to increase the fluid velocity (flux) when the upper actuator used to maintain the upper chamber was no longer able to sustain the pressure induced by the flow across the fabric. The pressure applied for maintaining the system closed is 7.5 bars, similar to the pressure which is used in the industrial RFI process.

The following protocol was used for the measurements. A multiaxial fabric is placed on the lower honeycomb and the upper mobile part comes down in contact with the verniers. The vibrating cutting system is turned on and maintained until the blade has completed the cut (Figures 4-a and5-b). The airtightness mobile system can then move upward to ensure both the absence of air in the fluid flow and leaks out of the chambers (Figures 4b). In the first times of the cycle, a low fluid velocity is prescribed to the servo-gear pump which feeds in the apparatus with fluid. In this stage the lower chamber is filled, and then the fabric is impregnated. Once the second pressure probe can measure the fluid flow, the servo-gear pump is stopped, and then a complete test cycle can be started in which the fluid velocity is increased step by step. Every step is continued until pressures stability is reached.

Assessment of the transverse permeability

Permeability measurement

A typical measurement is presented in Figure 6 for a biaxial [0,90] NC2 made up from 2 × Tenax HTS5131 267 g/m 2 carbon fabrics stitched 10 mm × 10 mm. In this figure the resistance provided by the fabrics against the flow, i.e. the pressure gradient deduced from the pressure loss and flow length e ( ∆ P e ) over the fluid viscosity η, is plotted as a function of the fluid velocity (v). It is verified that the largest Reynolds number of the flow encountered is lower than 1 :

Re max = ρ v max d η = 1.75 • 10 -2 << 1 (3)
with ρ the volumic mass of the oil (ρ=877 kg m -3 ), v max the maximum fluid velocity encountered (v max ≤ 3•10 -3 m.s -1 ), d is the largest characteristic length of the NC2 taken as the largest stitching hole diameter measured from micrographs (d ≤ 0.4 mm) and η=0.06 Pa.s is the fluid viscosity at room temperature. Darcy's approach is then valid for these measurements. Then, simply by using the Darcy's law for uniaxial flows (Eq. 2), the transverse permeability (K 33 ) can be identified from these data.

One will notice that this resistance of the fabric dos not depend linearly on the fluid velocity as one would expect. Conversely, in other more 'rigid' materials tested, such as woven fabrics and metallic lattices, a linear relationship is observed between the resistance and the fluid velocity. Therefore, this non-linearity seems to reflect some intrinsic properties of the NC2 materials. Further studies are currently under progress to clarify this point. However, one wishes to make a productive use of the data given by this first approach of the NC2 transverse permeability. Consequently, the nominal transverse permeability is assessed as the permeability prevailing at the onset of flowing in the NC2 (Figure 6). At that stage the fibre volume fraction is perfectly controlled and the meso-structure is not disturbed. Eventually, for the present study, the nominal apparent permeability will be identified as the inverse of the initial slope (Figure 6).

Measurement repeatability

The assessment of measure repeatability has been achieved for 2 types of biaxial NC2 [0,90], made up of identical UD Tenax fabrics 267 g/m 2 (HTS 5131 / 24k tows), but with different stitching pattern. The first biaxial was stitched with a 10mm×10mm pattern and the other one with a 5mm×5mm pattern, both were stitched with PA 6.6 78 tex stitching yarn. The largest discrepancies are for the 10mm×10mm stitching pattern. The secant apparent permeability, deduced from the current slope or a given point on the resistance curve, reach about 20 % of variation (Figure 7) for the fluid velocity tested. However, one must point out that the work of [START_REF] Lundström | Inplane permeability measurements : stability, repatability and reproductibility[END_REF], dedicated to the repeatability measurements for longitudinal permeability reports some discrepancies of the order of 15 %, but for longitudinal flows over several hundreds of millimeters (300 mm). In our case, transverse measurements are made over some lengths of the order of one millimeter or less. Moreover, transverse permeabilities are of the order of 10 -13 m 2 , whereas longitudinal permeabilities are at least one decade higher, of the order of 10 -12 m 2 .

Influence of the stitching density

The transverse permeability of NC2 is assessed with the presented dedicated apparatus, using the protocol introduced. Essentially, biaxial materials are tested, all of them made up from the same Tenax HTS 5131 UD dry fabrics. The stitching, when reported, is realized with a PA 6.6 78 tex stitching yarn. This kind of biaxial material permit to reveal many specificities of NC2 multiaxial fabrics without involving too much complexity related to tricky stacking sequences or architectures.

Assessing the influence of the stitching onto the transverse permeability is the main issue of the present work. To achieve this, 6 types of biaxial fabrics were tested. First [0] 2 and [0,90] fabrics, both unstitched, were tested. Then, biaxial [0,90] NC2, made up of the same fabrics were manufactured but with 3 different balanced stitching patterns of 10mm×mm, 5mm×5mm, and 2.5mm×2.5mm, corresponding respectively to stitching densities of 10 4 , 4.10 4 , and 16.10 4 stitches per m 2 . Eventually, biaxial [+45,-45] NC2 with a 5mm×10mm stitching pattern were tested. Since the same UD blankets are used, the fibre volume fraction is set to 0.65 for all the materials tested.

First, permeabilities for the [0] 2 and [0,90] unstitched biaxial are very close (Figure 6). Unfortunately, the very low permeability (of the order of 2 • 10 -14 m 2 ) of these UD fabrics may, under a 7.5 bars closure pressure, cause leaks in the apparatus even for a moderate flux. Therefore, only few flow rates can be tested but which are sufficient to draw some clear trends about these measurements. The curves obtained for both unstitched materials tend to coincide. The similarity between these material responses demonstrates that the resulting transverse permeability does not depend at all on the stacking sequence. At the opposite, the introduction of stitching (10mm×10mm) seems to increase greatly the permeability which jumps from 0.24 • 10 -13 m 2 to 1.1 • 10 -13 m 2 .

This strong influence is confirmed by the curves for the other material tested (Figure 8) which clearly show that the permeability largely depends upon the stitching. But first, it must be pointed out that the differences between theses experimental results are much higher than the repeatability of the measures themselves. Therefore, these variations can be interpreted as intrinsically related to the material tested. More precisely, this permeability can even be related directly to the stitching density only since actually the independence of the transverse permeability upon the stacking sequence is again confirmed by the [+45,-45] NC2 measurement (Table 1). Indeed, in that material stitched 5mm×10mm, only the stitch density seems to control the permeability comprised between the permeabilities for the biaxials [0,90] stitched 10mm×10mm and 5mm×5mm.

The stitching density seems to control the transverse permeability, this is clearly illustrated in Figure 9 where the permeability is shown to vary, linearly in first approximation, with the stitching density. In fact, mesoscopical measurements of the fabric geometry re-veal that only the holes left around the stitching pitches are open pores, the size of which are quite comparable for the various fabrics tested (∼ 0.4 mm). In first approximation this suggests that mainly these spaces will allow for the fluid to pass through. It can be easily reckoned that permeability depends on the amount of surface spaces for the fluid to flow, directly related to the stitching density. One will notice that, although the gap geometry is not exactly the same for the [+45,-45] biaxial NC2 as for [0,90] (see in Figures 2-a From these results, it can be concluded that the stitching density is of prime importance regarding the transverse permeability of NC2. Although this stitching is introduced mainly to improve the handability and the mechanical properties of the resulting structural component, it appears to be also very helpful in increasing the permeability. Indeed, with a stitching density of 10 4 pts.m -2 , the transverse permeability is increased by a factor of 5 with respect to the same unstitched biaxial. By increasing further the stitching density by 16 (from 10×10mm to 2.5mm×2.5mm), a similar increase is reached for the permeability. Regarding the very low permeability of unstitched materials, this increase of the permeability is essential in achieving proper manufacturings. There is obviously a limit in increasing the stitching density since the mechanical counterpart is that a decrease in the material properties is expected due to the geometrical imperfections resulting from the introduction of stitches, as it can be observed at larger amplitudes in NCF materials ( [START_REF] Drapier | Finite-element investigation of the compressive strength of non-crimp-fabric-based composites[END_REF], [START_REF] Drapier | Finite-element investigation of the interlaminar shear strength of non-crimp-fabric-based composites[END_REF]).

Permeability predictions

The aim of this simulation is to model the influence of the stitching density onto the transverse permeability. The Ansys FE package is used to model the permeability response at the mesoscopical level, on a representative volume element of the biaxial [0,90] fabric tested previously.

Representative volume element

FE simulations are carried out on the biaxial NC2 characterized experimentally. In order to avoid very demanding computations, we use the principle of homogenization techniques based on repeating representative volume elements (RVE). It is assumed that the response of this volume element is representative of the response of the entire medium, provided proper boundary conditions are prescribed on its edges to represent neighbouring volume elements.

For the modelling, the scale of observation has to be chosen first. The choice of this scale must permit to grasp the main features which may influence the permeability. For this choice, first one can notice that there is the formation of inter-tow spaces (gaps) (Figure 2), independently on the direction of the stitching with respect to the fibre orientation. These gaps are similar to the ones developing in NCF manufactured with the Liba process for instance, but with a minor amplitude. Secondly, the other main features which may influence the transverse permeability are the stitches that were shown to strongly control the permeability (Figure 9). Lastly, as saturated flow simulations are considered here, any air entrapment in the tows can be neglected. Consequently, it seems natural to set up the model at the mesoscopical scale where gaps and stitches can be accounted for, and where tows are seen as homogeneous porous media. Therefore, in our biaxial material a RVE is easily extracted, the planar dimensions of which are equal to the stitching pattern used (Figure 10) and its thickness corresponds to the fabric thickness. By applying proper boundary conditions, detailed below, the permeability of the equivalent infinite fabric can be computed.

Computations

For the sake of simplicity, the chosen RVE has been idealized. By symmetry, only a quarter of this RVE must be represented. Also, gaps between the tows induced by the stitching yarns (see Figure 2) are represented as parallelepipeds (Figure 11-a), resulting from the space left between the planes standing for the 0 and 90 • tows (Figure 11-b). For the stitching, a space is considered as the union of the space left by the circular cylindrical stitching and the gap between the tows (Figure 11-a). Stitching densities are represented by varying the cell dimensions (p 1 ,p 2 ) corresponding to the stitching pitch respectively along e 1 and e 2 directions.

The inter-tow gaps and the stitch hole are modeled with fluidic elements in which the Navier-Stokes equation prevail. For modelling tows, i.e. the porous medium, the Darcy's law is employed instead of the previous laws. Both media are meshed with quadratic isoparametric finite elements. Let us notice that in every article where permeability is simulated for a reinforcement, tows are supposed not to be permeable. However, due to the fabric homogeneity, in our case macropores are much less numerous. It is then possible that flow takes place through the tows as it can be observed in the RTM process [START_REF] Binétruy | Effects of fabrics architectural heterogeneities on effective and satured permeabilities in RTM[END_REF]. Tow permeability is defined through a diagonal tensor. This is what prevented us from computing the [+45,-45] biaxial NC2 permeability. The transverse permeability of the tows is the one assessed for a UD fabric (2.25 10 -14 m 2 ), and in the fibre direction it is taken equal to 10 -12 m 2 following the estimations from [START_REF] Lundström | Inplane permeability measurements : stability, repatability and reproductibility[END_REF]. As for the fluid viscosity, it is equal to the viscosity of the lubrication oil used for experiments measured at room temperature (η=0.06 Pa.s) .

As can be seen in Figure 11 the stitch hole is not represented, it is instead modeled with zero normal flux conditions, i.e. no fluid can penetrate the stitching yarn but the flow along this yarn is allowed. Indeed, implicitly it is assumed that the stitching yarn induces a hole, the diameter of which (0.3 mm) corresponds exactly to the yarn diameter deduced from its linear mass and its density. The other boundary conditions are zero normal flux conditions on the lateral faces of the cell. To represent the pressure drop induced by the flow through the fabric, a 1 bar pressure is applied on the upper face of the RVE while on the lower face the pressure is null. Permeability is calculated through the Darcy's law (Eq. 2) from both the pressure differential prescribed and the mean fluid velocity deduced from the massic flux computed.

Results -Comparison with experiments

Permeabilities are computed for [0,90] fabrics considering the 3 stitching densities tested.

The results reported in Table 2 are also plotted in Figure 12 where can be seen the good correlation between the predicted permeabilities and the ones measured. The maximum discrepancy of about 25 % is reached for the highest stitching densities (4 and 16.10 4 pts.m -2 ), whereas for the lowest density it is 8% (1•10 4 pts.m -2 ).

The most important effect confirmed by these computations is the effect of the stitching density on the permeability. The simulations reveal that the fluid flows through the fabric (Figure 13) only across the stitching holes. Indeed, whatever the stitching density simulated, the flow rate of fluid across the tows remains low. The tows are so little permeable that the fluid cannot flow across and passes almost in totality through the stitching holes. This is illustrated by the distribution of the transverse fluid velocity plotted in Figure 13.

Transverse velocities in the tows are 2 decades lower than the transverse velocities in the stitching hole. More particularly the fluid circulate in the narrow region between the gaps and the stitching yarn.

Assuming that the stitching pitches remain large enough, the interaction between flows in the stitching cylinders is negligible. Then, one can propose a very simple relationship that would relate the transverse permeability for a given stitching density d 1 (K d1 33 ) to the permeability of the same fabric but with a stitching density d 2 (K d2 33 ) (Eq. 4). Predictions with this very basic relationship compare well with the FE results (Table 2).

K d1 33 = K d2 33 d 1 d 2 (4)
As a conclusion, both experimentally and theoretically, it is established that the fluid flows almost exclusively through the stitching holes. Some discrepancies exist between predicted and measured permeabilities, however regarding the very low permeabilities identified these moderate differences are acceptable for current industrial applications. Then, as a rule of thumb, assuming that the stitching hole geometry and the gap size will not depend on the stitching density, a linear relationship exist between the transverse permeability and the stitching density. For industrial applications, stitching densities are at least 10000 pts.m -2 but will usually not exceed 40000 pts.m -2 . This ensures that flow across the tows may be negligible, and that in turn this linear approximation will hold.

Conclusion

The first study of the influence of the stitching density on the transverse permeability of NC2 was carried out. The main mechanisms which control the flow of a fluid across NC2 were assessed. Eventually, predictions were shown to compare well with experimental results.

First, a specific apparatus was designed to measure the transverse permeability in multiaxial fabrics. The key point of this system is to maintain properly the specimen, using aluminium honeycombs, while ensuring the fibre volume fraction control. Also, the specimen cutting is integrated to the apparatus which ensures that the fabric deformability will not yield any meso-structure variations. This apparatus allows to evaluate the transverse permeability through the uniaxial Darcy's law, knowing both pressure loss induced by the specimen resistance to the fluid flow, and fluid velocity.

Experiments were carried out on 6 different fabrics, both unstitched and stitched, and with several stacking sequences and stitching patterns. Experimentally it was demonstrated that neither the stacking sequence nor the stitching pattern would influence the transverse permeability. Conversely, the stitching density was shown to control greatly the permeability. Indeed, changing the stitching pitch from 10mm×10mm to 2.5mm×2.5mm, i.e. increasing by 16 the stitching density, permits to increase the permeability by about the same amount, from 1.1 • 10 -13 m 2 to 15.1 • 10 -13 m 2 . From a manufacturing point of view, this improvement of the transverse permeability ensures a good fibre impregnation, and consequently optimum final mechanical characteristics.

This main result was found also by the FE simulations carried out at the mesoscopical scale on a representative volume element of [0,90] biaxial fabrics. Permeabilities were assessed by measuring the flux as a response to a differential of pressure applied to the fluid crossing the porous media standing for the tows. It was established that mainly the fluid flowed along the stitching yarn, in the stitching holes. Then, in first approximation, it is the surfacic ratio of spaces left by the stitching points which controls the permeability. This provides a clear explanation to the experimental dependence of the transverse permeability upon the stitching density. Eventually, as a first approximation, the permeability for any admissible stitching density can be extrapolated linearly from a single permeability known for a given stitching density.

Based on the knowledge gained here, this permeability study should be extended to tri and quadri-axial NC2. For the measurements, these materials will be tested with the apparatus developed here. As for the simulations, some problem may arise due to the non-diagonal terms of the permeability tensor which will appear for non cross-plies.

Annexe : fluid viscosity

The fluid used, a lubrication oil (NEUTRAL), appeared to vary in viscosity with the ambient temperature. The characterization of this viscosity over a wide range of temperatures yields the following results (Table An.

List of Tables

  and 2-b), the effective (open pores) surface spaces may depend essentially on the stitching yarn itself.

Viscosity (η in 10 - 3

 103 Figure An. 1 : Variation of the oil viscosity vs. temperature.

Figure 1 :

 1 Figure 1: Schematic of the Resin Film Infusion process tooling.

Figure 2 :

 2 Figure 2: Picture of a quadriaxial NC2 ([-45,0,45,90]) made up of dry carbon UD fabrics (Tenax HTS 5131/24k tows 150 g/m 2 ), stitching pitch 5mm×5mm : (a) -45 • face and (b) 90 • face.

Figure 3 : 29 Figure 4 :

 3294 Figure 3: Schematic of (a) longitudinal, and (b) transverse permeability measurements.

Figure 5 :

 5 Figure 5: Apparatus designed for transverse permeability measurements : (a) description, (b) cutting stage prior to measurements .

Figure 6 :Figure 7 :

 67 Figure 6: Resistance of fabrics to the fluid flow versus the fluid velocity for fabrics 2 × 267 g/m 2 : [0] 2 unstitched, [0,90] unstitched, and [0,90] stitched 10mm×10 mm

Figure 8 :

 8 Figure 8: Resistance to the fluid flow versus the fluid velocity for fabrics 2 × 267 g/m 2 : [0] 2 unstitched, biaxial [0,90] unstitched and stitched 10mm×10mm, 5mm×5mm, and 2.5mm×2.5mm.

Figure 9 :

 9 Figure 9: Permeability of the materials tested vs their stitching density.

Figure 10 :

 10 Figure 10: Representative Volume Element for the biaxial NC2 permeability simulation.

Figure 11 :

 11 Figure 11: RVE mesh used for FE simulations : (a) mesh of the gaps with fluidic elements, (b) mesh of the tows with solid porous elements, and (c) complete mesh of the RVE.

Figure 12 :

 12 Figure 12: Permeability predicted and measured, for the materials tested, vs their stitching density.

Figure 13 :

 13 Figure 13: Distribution of the fluid velocity (V 3 ) in m.s -1 for the [0,90] NC2 5mm×5mm stitching pitch.

1

  Transverse permeability measurements for the 6 materials tested. . . . . . 24 2 Transverse permeability predicted and measured for the 4 stitched biaxial materials tested. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

	Material	[0] 2	[0,90]	[0,90]	[0,90]	[0,90]	[±45]
		unst.	unst.	10 × 10	5 × 5	2.5× 2.5	5×10
	Stitching density (10 4 pts.m -2 ) -	-	1	4	16	2
	K 33 measured (10 -13 m 2 )	0.21	0.24	1.1	6.37	15.1	2.47

Table 1 :

 1 Transverse permeability measurements for the 6 materials tested.

	Material	[0,90] 10×10	[±45] 5×10	[0,90] 5×5	[0,90] 2.5×2.5
	Stitching density (10 4 pts.m -2 )	1	2	4	16
	K 33 computed (10 -13 m 2 )	1.19	-	4.75	19.1
	Predictions/Measurements	-8%	-	-25%	27%
	K 33 analytical (Eq. 4) (10 -13 m 2 ) 1.19	2.38	4.76	19.1

Table 2 :

 2 Transverse permeability predicted and measured for the 4 stitched biaxial materials tested.

Acknowledgements

The authors wish to acknowledge the Rhône-Alpes Region for its support to this work through the programme 'Thématique Prioritaire 2000-2002'.

List of Figures