Anna Cabanes

Roberto Pastor-Barriuso

Milagros García-López

Carmen Pedraz-Pingarrón

Carmen Sánchez-Contador

Jose Antonio

Vázquez Carrete

María Pilar Moreno

Carmen Vidal

Dolores Salas

Josefa Miranda-García

Jose Antonio Vázquez

Mercé Peris

Pilar Moreo

María Carmen Santamariña

Francisca Collado-García

Isabel González

Nieves Ascunce

Marina Pollan
email: mpollan@isciii.es

Virginia Lope

Beatriz Pérez-Gómez

Nuria Aragonés

Gonzalo López-Abente

Juana Vidán

Francisco Casanova

Montserrat Corujo

Ana Belén Fernández

Soledad Abad

Francisco Ruiz-Perales

Maria Soledad Laso

Manuela Alcaraz

Marina Pollán

Alcohol, tobacco, and mammographic density: a population-based study

Keywords: mammographic density, alcohol, smoking, breast cancer, ordinal logistic models Mammographic density FFQ: Food frequency questionnaire BMI: Body mass index HRT: Hormone replacement therapy E2: Estradiol IGF-1: Insulin-like growth factor 1

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ABSTRACT

Mammographic density (MD), or the proportion of the breast with respect to its overall area that is composed of dense tissue, is a strong risk factor for breast cancer. Studies support a positive association of mammographic density and alcohol drinking. This was a cross-sectional multicenter study based on 3584 women, aged 45 to 68 years, recruited from seven screening centers within the Spanish Breast Cancer Screening Program network. The association between MD, alcohol consumption and tobacco use was evaluated by using ordinal logistic models with random center-specific intercepts.

We found a weak positive association between current alcohol intake and higher MD, with current alcohol consumption increasing the odds of high MD by 13% (OR=1.13; 95% CI 0.99-1.28) and high daily grams of alcohol being positively associated with increased MD (p for trend=0.045). There were no statistically significant differences in MD between smokers and non-smokers. Nevertheless, increased number of daily cigarettes and increased number of accumulated lifetime cigarettes were negatively associated with high MD (p for trend 0.017 and 0.021). The effect of alcohol on MD was modified by menopausal status and tobacco smoking: whereas alcohol consumption and daily grams of alcohol were positively associated with higher MD in postmenopausal women and in women who were not currently smoking, alcohol consumption had no effect on MD in premenopausal women and current smokers.

INTRODUCTION

Mammographic density (MD), or the proportion of the breast with respect to its overall breast area that is composed of dense tissue, is a strong risk factor for breast cancer.

Over 40 studies have assessed this association and the majority have reported a 2-to 6-fold increased risk of breast cancer for the highest to lowest density categories [START_REF] Mccormack | Breast density and parenchymal patterns as markers of breast cancer risk: a meta-analysis[END_REF].

Breast density is also associated with reproductive and anthropometric risk factors for breast cancer [START_REF] Titus-Ernstoff | Breast cancer risk factors in relation to breast density (United States)[END_REF][START_REF] Butler | Menstrual and reproductive factors in relation to mammographic density: the Study of Women's Health Across the Nation (SWAN)[END_REF][START_REF] Johansson | Relationships between circulating hormone levels, mammographic percent density and breast cancer risk factors in postmenopausal women[END_REF][START_REF] Yong | Associations between endogenous sex hormone levels and mammographic and bone densities in premenopausal women[END_REF][START_REF] Walker | Premenopausal mammographic density in relation to cyclic variations in endogenous sex hormone levels, prolactin, and insulin-like growth factors[END_REF](7)(8)(9)(10)(11)(12)(13). However, the association between MD and breast cancer appears to be independent, and usually persists after adjustment for these factors. In addition, there is strong evidence of a genetic determinant of MD [START_REF] Vachon | Strong evidence of a genetic determinant for mammographic density, a major risk factor for breast cancer[END_REF].

Although relatively few studies have examined the association between alcohol consumption and breast density, most nonetheless report higher MD among alcohol drinkers than abstainers [START_REF] Vachon | Association of diet and mammographic breast density in the Minnesota breast cancer family cohort[END_REF][START_REF] Brisson | Diet, mammographic features of breast tissue, and breast cancer risk[END_REF][START_REF] Maskarinec | Alcohol consumption and mammographic density in a multiethnic population[END_REF][START_REF] Masala | Dietary and lifestyle determinants of mammographic breast density. A longitudinal study in a Mediterranean population[END_REF][START_REF] Flom | Alcohol intake over the life course and mammographic density[END_REF]. Whereas some of these studies support a weak, albeit significant, positive association between current alcohol intake and MD in both pre-and postmenopausal women, there is more limited and inconclusive data on the association between the timing of initiation of alcohol intake and MD [START_REF] Flom | Alcohol intake over the life course and mammographic density[END_REF][START_REF] Vachon | Alcohol intake in adolescence and mammographic density[END_REF].

Even less information is available on the effects of tobacco smoking on breast density. Some studies consistently report an inverse relationship between current smoking and MD (7, [START_REF] Vachon | Association of diet and mammographic breast density in the Minnesota breast cancer family cohort[END_REF][START_REF] Jeffreys | Life course breast cancer risk factors and adult breast density (United Kingdom)[END_REF][START_REF] Butler | Active, but not passive cigarette smoking was inversely associated with mammographic density[END_REF], attributed to an antiestrogenic effect of tobacco smoke; others, in contrast, fail to observe any association [START_REF] Gapstur | Associations of breast cancer risk factors with breast density in Hispanic women[END_REF][START_REF] Roubidoux | Relationship of mammographic parenchymal patterns to breast cancer risk factors and smoking in Alaska Native women[END_REF]. Accordingly, we decided to investigate the association between alcohol consumption, smoking and adult MD using data from food frequency questionnaires (FFQs), risk factor data, and breast density measures from the Determinants of Mammographic Density in Spain study (DDM-Spain).

MATERIALS AND METHODS

Study population

This was a cross-sectional multicenter study based on 3584 women, aged 45 to 68 years, recruited from seven specific screening centers within the Spanish Breast Cancer Screening Program network. All women aged 50-65 years, regardless of nationality or legal status, are screened under these government-sponsored programs every two years, with the exception of women carrying BRCA1 or BRCA2 mutations who are generally screened by specific units. In some regions, women between 45-49 years of age are also included. Furthermore, the age range in all regional programs is currently being extended to cover women up to the age of 70 years.

Sampling procedure and data-collection

A minimum of 500 women per screening center were recruited from October 7, 2007 to July 14, 2008. Women previously diagnosed with breast cancer or some other malignant disease (except basal cell epitheliomas) were excluded, as were women who failed to respond to the questionnaire or presented with some physical inability that prevented a mammography from being performed. The DDM-Spain study protocol was formally approved by the Institutional Review Board at the Carlos III Institute of Health.

Women were interviewed at the screening center by purpose-trained interviewers. The questionnaire collected demographic information relating to the following: childhood and youth; family and personal background; gynecologic, obstetric and occupational history; household activities; current and lifetime alcohol consumption; current and lifetime tobacco use; current and past physical activity; and diet during the preceding year. Women's height and weight were measured twice by the interviewer, with a third measurement being taken if the first two were in any way dissimilar. Average values were used to compute BMI.

The dietary section of the questionnaire ascertained the frequency of consumption and usual portion size of 117 food items (including alcoholic beverages), and was used to estimate daily intake of alcohol and calories. The standard servings of red wine [30ml], and brandy, gin, rum, whisky and vodka [40ml], were estimated to contain 13.25g, 12.63g, 6.15g, 3.06g, 7.80g, 7.40g, and 14.25g of ethanol, respectively. Daily calorie intake was estimated from a nutrient database developed by Vioque et al [START_REF] Vioque | Validez de la evaluación de la ingesta dietética[END_REF].

The folate intake values comprised dietary sources and vitamin supplements.

Estimation of percent breast density

We measured MD from the craniocaudal mammogram of the left breast using Boyd's semiquantitative scale, a visual scale that rates density in 6 categories, namely: A (0%); B (<10%); C (10-25%); D (25-50%); E (50-75%); and F (>75%). Mammographic density was assessed on a blind, anonymous basis by a single, experienced radiologist.

Statistical analysis

The association between MD, alcohol consumption and tobacco use was evaluated by using ordinal logistic models with random center-specific intercepts [START_REF] Gelman | Data Analysis using Regression and Multilevel/ Hierarchical Models[END_REF]. The main exposure variables, as well as the remaining adjustment factors, were regarded as fixed effects, so that their associated ORs were deemed to be the same for women at all screening centers. In addition, the ordinal logistic models included a random, centerspecific intercept term that accounted for unexplained variations in the baseline odds of higher MDs across screening centers.

The Brant test was used to verify the proportional odds assumption. This assumption held for the effects of alcohol consumption and tobacco use in all fitted models, after the two lowest categories (A and B) of Boyd's classification had been combined. These categories are fairly similar in terms of reduced percentage of dense breast tissue (0 and <10%), and there were only 4.2% of women in the "no dense tissue" category.

Hence, all logistic models included MD as an ordinal response variable with five categories (A+B, C, D, E, and F).

The main exposures of interest linked to alcohol consumption were: (a) current alcohol intake (yes or no); (b) lifetime alcohol drinking (never, past, or current drinker); (c) average alcohol intake during preceding year as reported in the FFQ (grams/day); and (d) age at which regular drinking had been initiated. Insofar as tobacco use was concerned, the exposures of interest were: (e) current smoking (yes or no); (f) lifetime tobacco smoking (never, past, or current smoker); (g) daily amount of cigarettes; (h) accumulated amount of cigarettes; and (i) age at which smoking had been initiated. All these exposures were analyzed as categorical variables, except for daily grams of alcohol, daily and accumulated amount of cigarettes, and age of initiation of alcohol and tobacco use, which were modeled both as predetermined categorical and continuous variables.

To further explore the association between amount of alcohol intake and MD without assuming a linear dose-response relationship, we used restricted quadratic splines for log-transformed alcohol intakes, with knots at 0.09, 3.3, and 33.1 g/day, corresponding to the 5 th , 50 th and 95 th percentiles of alcohol consumption among drinkers, respectively. These spline models require the same number of parameters as the categorical analysis but can accommodate a wide variety of smoothed risk trends [START_REF] Greenland | Dose-response and trend analysis in epidemiology: alternatives to categorical analysis[END_REF].

In addition, the above models were fitted with increasing levels of adjustment. First, we fitted a simple model adjusted for strong determinants of MD, i.e., age at mammography (continuous), BMI (restricted quadratic spline), and menopausal status.

Second, we fitted an extended model, further adjusted for variables associated both with lifestyle and MD, including number of live births (continuous), current HRT use, current alcohol intake, and current smoking. Separate simple and extended models were constructed for pre-and postmenopausal women. Furthermore, the effect of alcohol consumption was separately assessed in current and noncurrent smokers.

All analyses were performed in Stata (StataCorp LP, College Station, TX), using the gllamm function to fit random-intercept ordinal logistic models [START_REF] Rabe-Hesketh | Generalized Linear Latent and Mixed Models[END_REF], and R statistical software (R Foundation for Statistical Computing, Vienna, Austria).

RESULTS

Of the three thousand, five hundred, eighty-four (3584) women recruited and interviewed, MD assessment was completed for 3568. The average participation rate was 74.5% (64.7-84.0%). Women who developed breast cancer within 6 months of mammography were excluded from the analysis (n=10). Daily calorie intake below 800 calories or above 4000 was considered unrealistic, and the women concerned were also excluded (n=8) along with one woman who was being fed intravenously.

The overall proportion of Boyd mammographic density categories in the study population was as follows: A, n=150 (4.2%); B, n=722 (20.3%); C, n=732 (20.7%); D, n=1135 (32%); E, n=623 (17.5%); and F, n=187 (5.3%). Twenty-one percent of women were pre-or perimenopausal, and 79% were postmenopausal. With respect to alcohol consumption, 41.6% were abstainers, 41.1% currently drank up to 10g of alcohol/day, and only 17.3% consumed more than 10g of alcohol/day. In the case of tobacco use, 57.8% of participants had never smoked, 24.3% currently smoked, and 17.9% were exsmokers.

In a simple analysis adjusted for age, BMI, menopausal status and screening program, higher MD was positively associated with never being pregnant, older age at first live birth, larger daily caloric intake and more years of education (Table 1). In contrast, higher MD was negatively associated with increased age; younger age at menopause, increased number of live births; being postmenopausal; having osteoporosis; and being very active between the ages of 36 and 50 years. Age at menarche, HRT use, folic acid intake and tobacco smoking were considered potential confounders, but in our study were not associated with MD.

After an extended analysis adjusted for age, screening program, BMI, menopausal status, number of live births, HRT use, current alcohol consumption and current tobacco use, osteoporosis and high levels of physical activity remained associated with decreased odds of being in high MD groups (OR=0.71; 95% CI 0.59-0.86 and OR=0.86; 95% CI 0.75-0.98, respectively), and daily calorie intake was associated with increased odds of being in high-density categories (highest versus lowest calorie intake OR=1.33; 95% CI 1.11-1.59; p for trend=0.003)(Table 1).

Alcohol was positively related with MD (Table 1). In the extended model, current alcohol drinking increased the odds of high MD by 13% (OR=1.13; 95% CI 0.99-1.28), with high daily grams of alcohol being positively associated with increased MD (p for trend=0.045; Table 1). Among drinkers, older age of initiation of alcohol consumption was only slightly associated with a higher probability of being in high MD categories, though the statistical test was not significant at p<0.05 (Table 1). In contrast, women who started drinking before menarche had a lower probability of being in higher density categories than did other women who also consumed alcohol. Further adjustment for daily calorie intake, physical activity levels, and osteoporosis failed to change the magnitude of the associations (data not shown) and so these variables were not included in the final analysis. There were no statistically significant differences in MD between smokers and nonsmokers. Nevertheless, increased number of daily cigarettes and increased number of accumulated lifetime cigarettes were negatively associated with high MD in the extended adjusted model (p for trend 0.008 and 0.004, respectively). Age of smoking initiation had no influence on MD (Table 1).

Although formal testing showed no statistical interactions between menopausal status and variables linked to alcohol consumption and tobacco use (likelihood ratio test; p>0.05), in view of the strong influence of ovarian hormones on MD and the reported estrogenic or antiestrogenic effects of alcohol and tobacco on the breast, extended models were constructed separately for pre-and postmenopausal women (Table 2).

In peri-and premenopausal women, alcohol consumption was not associated with MD and the dose-response curve was almost flat (Fig. 1). Increased age of initiation of alcohol consumption seemed to be associated with higher MD, though the number of women in the older age groups was small. Among postmenopausal women, in contrast, alcohol consumption increased the odds of being in high MD categories by 15% relative to abstainers (OR=1.15; 95% CI 1.00-1.32). Raising daily alcohol consumption resulted in a dose-dependent increase in the likelihood of being in a high MD group (p for trend=0.022). In comparison with abstaining, drinking more than 10g of alcohol/day increased the probability of having MD by 26% (OR=1.26; 95% CI 1.03-1.53). Using restricted quadratic splines, we observed increased odds of being in high MD groups with increasing amounts of alcohol but the relationship was not linear. Whereas moderate daily intake of alcohol (less than one glass of red wine) increased mammographic density, higher alcohol intake led to a lower probability of having high MD (Fig. 1).

Postmenopausal women displayed a negative association between the number of cigarettes -both current and accumulated over a lifetime-and the odds of being in high MD groups. Women who smoked more than 15 cigarettes/day were 32% less likely to be in high MD categories than were women who smoked 0-5 cigarettes/day (OR=0.68; 95% CI 0.46-0.99; p for trend=0.046); and similarly, women who had smoked more than 700 cigarettes in their lifetime were 30% less likely to be in high MD categories than were women who had smoked fewer than 300 cigarettes (OR=0.70; 95% CI 0.51-0.96; p for trend=0.053).

We found that an interaction test between alcohol and tobacco use with respect to their influence on mammographic density approached statistical significance (likelihood ratio test p=0.075). The effects of increasing tobacco consumption on MD were different depending on the level of alcohol intake. In the highest alcohol consumption group (women who drank more than 10g of alcohol/day), the odds of being in high MD categories decreased by 17% for every increase of 10 cigarettes/day (p=0.037) compared to women that do not drink. In women who drank less than 10g/day, however, the increased number of daily cigarettes showed no association with lower MD (p=0.976). Moreover, alcohol consumption and smoking are interrelated, in that heavy drinkers tend to smoke more than do light drinkers or abstainers. In the DDM-Spain study, while only 4% of abstainers smoked over 20 cigarettes a day, 9% of women in the highest alcohol intake levels (>20 g/day) smoked over 20 cigarettes a day.

Given the strong antiestrogenic effects reported for tobacco smoking, extended models for alcohol consumption were separately fitted for current and noncurrent smokers (Table 3). There was a positive association between increased daily grams of alcohol and high MD among noncurrent smokers (women who drank more than 10g of alcohol/day versus abstainers OR=1.25; 95% CI 1.02-1.53; p for trend 0.029).

Increasing the amount of alcohol consumed raised the odds of being in a higher density group (p for trend=0.029). Whereas older age of alcohol initiation increased the probability of being in higher MD groups, starting to drink alcohol before menarche decreased the odds of being in high MD categories by 50% (OR=0.50; 95% CI 0.29-0.85). Among current smokers, in contrast, no association was observed between drinking alcohol, increased alcohol consumption or age of initiation into alcohol drinking and MD. The effects of alcohol on MD were observed solely for women who were not current smokers.

DISCUSSION

This paper reports a positive association between current alcohol intake and higher MD. The effect of alcohol on MD was mainly observed among postmenopausal women. Furthermore, whereas alcohol consumption and daily grams of alcohol were positively associated with higher MD among women who were not current smokers, alcohol consumption failed to show any effect on MD among current smokers.

In general, the positive association observed for current drinking is in line with much of the literature on alcohol and MD [START_REF] Vachon | Association of diet and mammographic breast density in the Minnesota breast cancer family cohort[END_REF][START_REF] Maskarinec | Alcohol consumption and mammographic density in a multiethnic population[END_REF][START_REF] Masala | Dietary and lifestyle determinants of mammographic breast density. A longitudinal study in a Mediterranean population[END_REF][START_REF] Flom | Alcohol intake over the life course and mammographic density[END_REF][START_REF] Vachon | Alcohol intake in adolescence and mammographic density[END_REF][START_REF] Boyd | Plasma lipids, lipoproteins, and mammographic densities[END_REF][START_REF] Herrinton | Do alcohol intake and mammographic densities interact in regard to the risk of breast cancer?[END_REF]. Even though the interaction test between menopausal status and alcohol consumption was not statistically significant in our study, a different effect in pre-versus postmenopausal women has been described elsewhere [START_REF] Vachon | Association of diet and mammographic breast density in the Minnesota breast cancer family cohort[END_REF][START_REF] Maskarinec | Alcohol consumption and mammographic density in a multiethnic population[END_REF]. To our knowledge, no other study has yet reported an opposite effect of smoking and alcohol drinking on MD.

We failed to find a consistent association between age at which women started consuming alcohol and MD. However, our results suggest that the timing of exposure to alcohol affected MD in several different ways. First, later age of initiation of alcohol consumption was positively related (although not statistically significant) with a higher probability of being in high-density categories in premenopausal women versus women who started drinking at early ages. Conversely, women who started drinking alcohol before menarche were half as likely to be in high MD groups as women who started drinking after menarche. This is in agreement with reports showing that prepubertal estrogenic exposures reduce MD [START_REF] Cabanes | Prepubertal estradiol and genistein exposures up-regulate BRCA1 mRNA and reduce mammary tumorigenesis[END_REF][START_REF] Jordan | Influence of high-dose estrogen exposure during adolescence on mammographic density for age in adulthood[END_REF] while estrogenic exposures during adulthood increase it [START_REF] Titus-Ernstoff | Breast cancer risk factors in relation to breast density (United States)[END_REF][START_REF] Mctiernan | Estrogen-plus-progestin use and mammographic density in postmenopausal women: Women's Health Initiative randomized trial[END_REF][START_REF] Mctiernan | No effect of aspirin on mammographic density in a randomized controlled clinical trial[END_REF][START_REF] Marchesoni | Postmenopausal hormone therapy and mammographic breast density[END_REF].

Thus, alcohol may have different effects on MD, depending on the time of exposure, i.e., whereas starting to drink during peripubertal years reduces the odds of being in high mammographic density groups, starting to drink during adulthood has no effect on MD unless it occurs close to the date of mammography. This agrees both with reports suggesting that drinking alcohol before age 21 years is inversely associated with mammary density [START_REF] Vachon | Alcohol intake in adolescence and mammographic density[END_REF], and with others showing that current rather than lifetime alcohol intake is more strongly associated with MD [START_REF] Flom | Alcohol intake over the life course and mammographic density[END_REF]. In this regard, we created a variable representing the time elapsed between initiation of alcohol consumption and mammography, and found that the likelihood of being in a higher Boyd category of MD increased as initiation approached mammography, which suggests that starting to drink increases MD but that the initial effect of alcohol wanes over time. This is not the only estrogenic exposure with this paradoxical effect: one study has found that the effects of estrogen-plus-progestin therapy on MD persist but are attenuated after 2 years of treatment [START_REF] Mctiernan | Estrogen-plus-progestin use and mammographic density in postmenopausal women: Women's Health Initiative randomized trial[END_REF].

Our finding of a weak, negative association between current smoking and MD supports most (7, [START_REF] Jeffreys | Life course breast cancer risk factors and adult breast density (United Kingdom)[END_REF][START_REF] Butler | Active, but not passive cigarette smoking was inversely associated with mammographic density[END_REF] but not all [START_REF] Gapstur | Associations of breast cancer risk factors with breast density in Hispanic women[END_REF][START_REF] Roubidoux | Relationship of mammographic parenchymal patterns to breast cancer risk factors and smoking in Alaska Native women[END_REF][START_REF] Vachon | Association of mammographically defined percent breast density with epidemiologic risk factors for breast cancer (United States)[END_REF] prior published reports, and is consistent with an antiestrogenic effect of cigarette smoking on breast tissue. While MD and daily number of cigarettes smoked were found to have an inverse relationship, neither age at initiation nor smoking duration displayed an association.

According to our results, the effects of both exposures -alcohol and tobacco-on MD may work in opposite directions, which could explain why the OR of the effect of alcohol consumption on MD among smokers was close to one and why there was a decrease in risk of high MD with increased number of daily cigarettes among heavy drinkers. An antagonistic effect would also explain the unexpected decline at the end of the dose-response curve of alcohol intake and MD in postmenopausal women. Alcohol consumption and smoking are interrelated, in that heavy drinkers tend to smoke more than do light drinkers or abstainers. However, women in the highest alcohol consumption group may have been different in other lifestyle aspects, and so residual confounding by unknown factors at high alcohol intake levels cannot be ruled out.

One potential limitation of this study is the error inherent in dietary assessment in such a large epidemiologic study. However, the semiquantitative FFQ was adapted from Willett et al. [START_REF] Willett | Reproducibility and validity of a semiquantitative food frequency questionnaire[END_REF] for the Spanish population, and has demonstrated reasonable levels of reliability and validity in other studies [START_REF] Vioque | Validez de la evaluación de la ingesta dietética[END_REF]. Further, we found that the association of MD with general reproductive variables such as age at first birth, number of live births, age at menarche and menopause (2,3), etc, as well as osteoporosis [START_REF] Crandall | The association between mammographic breast density and bone mineral density in the study of women's health across the nation[END_REF], level of physical activity [START_REF] Masala | Physical activity and mammographic breast density in a Mediterranean population: the EPIC Florence longitudinal study[END_REF][START_REF] Oestreicher | Physical activity and mammographic density in a cohort of midlife women[END_REF] or daily caloric intake [START_REF] Mishra | Body weight through adult life and risk of urinary incontinence in middle-aged women: results from a British prospective cohort[END_REF] were consistent with what is known about MD. These observed findings provide additional support for the validity of the questionnaire that was used in this study.

Low alcohol consumption and low prevalence of regular adolescent drinking among the study population constitute two further possible drawbacks of our study: only 17% of the women drank more than 10g of alcohol/day, and less than 19% of the women started drinking at age 18 years or before. Another potential limitation resides in the length of time between adolescence and recall of alcohol consumption later in life.

Even though other studies have shown good reliability of reporting past alcohol consumption [START_REF] Longnecker | The reliability of self-reported alcohol consumption in the remote past[END_REF], recall of exposures during adolescence is likely to be imprecise and could result in attenuation of estimates.

Similarly, the measure of breast density was subjectively determined by only one radiologist. Nevertheless, the intra-observer reproducibility of the Boyd scale was good in our study, with a concordance between the first and second reading of 0.92 [START_REF] Garrido | Evaluation of mammographic density patterns: reproducibility and concordance among scales[END_REF].

Indeed, all disagreements corresponded to differences in only one category.

In summary, our results provide further support for an association between recent alcohol consumption and high mammographic density, characterized by a modest increase in risk at low levels of current consumption and a decrease in risk among heavier drinkers. Our study also suggests that the effects of alcohol in the breast can be modified by other factors, such as smoking. Yet, to what precise degree tobacco use may explain the lack of increased MD among women who drink alcoholic beverages daily is difficult to establish. Alcohol drinking is a modifiable behavior, and since moderate alcohol consumption is associated with a reduced risk of cardiovascular mortality and overall mortality among women, studies such as ours, which address the link between alcohol consumption and breast cancer risk, are critical for ascertaining the cost-benefit ratio of alcohol intake.

FIGURE LEGENDS Figure 1

Odds ratio of higher mammographic density (MD) according to alcohol intake in premenopausal (top) and postmenopausal women (bottom). Curves depict adjusted odds ratios (solid lines) and their 95% confidence intervals (dashed lines), based on restricted quadratic splines for log-transformed alcohol intakes with knots at 5 th , 50 th , and 95 th percentiles among drinkers. The reference value (OR = 1) was set at 0.01 g/day (abstainers). Odds ratios were obtained from an ordinal logistic model with random program-specific intercepts, adjusted for age, BMI, current smoking status, number of live births, and current use of HRT (only for postmenopausal women). Bars represent the frequency distribution of alcohol intake among pre-and postmenopausal women.

[

  125ml], white wine [125ml], beer [200ml], sherry [50ml], hard cider [125ml], spirits

( 7 )

 7 Bremnes Y, Ursin G, Bjurstam N, Gram IT. Different measures of smoking exposure and mammographic density in postmenopausal Norwegian women: a cross-sectional study. Breast Cancer Res 2007; 9(5):R73. (8) Noh JJ, Maskarinec G, Pagano I, Cheung LW, Stanczyk FZ. Mammographic densities and circulating hormones: a cross-sectional study in premenopausal women. Breast 2006; 15(1):20-28. (9) Verheus M, Peeters PH, van Noord PA, van der Schouw YT, Grobbee DE, van Gils CH. No relationship between circulating levels of sex steroids and mammographic breast density: the Prospect-EPIC cohort. Breast Cancer Res 2007; 9(4):R53. (10) Tamimi RM, Hankinson SE, Colditz GA, Byrne C. Endogenous sex hormone levels and mammographic density among postmenopausal women. Cancer Epidemiol Biomarkers Prev 2005; 14(11 Pt 1):2641-2647. (11) Diorio C, Pollak M, Byrne C, Masse B, Hebert-Croteau N, Yaffe M et al. Insulinlike growth factor-I, IGF-binding protein-3, and mammographic breast density. Cancer Epidemiol Biomarkers Prev 2005; 14(5):1065-1073. (12) Byrne C, Colditz GA, Willett WC, Speizer FE, Pollak M, Hankinson SE. Plasma insulin-like growth factor (IGF) I, IGF-binding protein 3, and mammographic density. Cancer Res 2000; 60(14):3744-3748. (13) Boyd NF, Stone J, Martin LJ, Jong R, Fishell E, Yaffe M et al. The association of breast mitogens with mammographic densities. Br J Cancer 2002; 87(8):876-882.

TABLE 1 .

 1 Characteristics of study population according to Boyd' mammographic density categoriese, associated ORs and 95% CIs for a higher Bo category. Simple model adjusted for age at mammography, BMI, menopausal status, and screening program.2 Extended model adjusted for age at mammog BMI, menopausal status, and screening program, plus number of live births, HRT use, current smoker, and current alcohol drinker status.*To calcula trends, variables were modeled as continuous variables; a Variables linked to age of alcohol and smoking initiation were analyzed only in drinkers an smokers/ex-smokers.

				Boyd Scale (%)				Simple Model 1			Extended Model 2
	VARIABLES	N	A+B <10%	C 10-25%	D 25-50%	E 50-75%	F >75%	OR	95% CI	p	p for trend*	OR	95% CI	p
	Age (y)
	< 50 y	547	10	13	35	31	11	1.00				1.00
	50-54 y	968	20	19	33	22	7	0.81 0.65-1.02 0.071		0.83 0.66-1.04	0.119
	55-59 y	1000	25	25	33	14	4	0.68 0.53-0.87 0.002		0.72 0.55-0.93	0.011
	60-64 y	939	37	22	29	10	2	0.45 0.35-0.58 <0.001		0.49 0.37-0.64 <0.001
	>65 y	95	38	23	24	12	3	0.41 0.26-0.63 <0.001 <0.001	0.44 0.28-0.68 <0.001
	BMI (kg/m2)
	<25	977	10	14	35	29	11	1.00				1.00
	25-30	1516	22	23	33	18	4	0.48 0.41-0.56 <0.001		0.49 0.42-0.57 <0.001
	>30	1056	42	23	27	6	2	0.18 0.16-0.22 <0.001 <0.001	0.20 0.17-0.24 <0.001
	Number of live births
	1	543	17	17	33	27	6	1.00				1.00
	2	1701	24	21	33	17	5	0.72 0.61-0.86 <0.001		0.77 0.64-0.92	0.004
	3	715	29	24	29	14	4	0.65 0.53-0.80 <0.001		0.73 0.59-0.90	0.003
	≥4	272	42	26	26	3	2	0.40 0.31-0.53 <0.001		0.48 0.36-0.63 <0.001
	Nulliparous	318	15	15	35	23	12	1.33 1.03-1.72 0.029 <0.001	1.40 1.08-1.81	0.010
	Age at 1st birth (y)
	<20	155	26	30	23	16	5	1.00				1.00
	20-24	1340	29	23	30	15	4	0.96 0.71-1.29 0.771		0.88 0.65-1.20	0.422

TABLE 2 .

 2 Associated ORs and 95% CIs for a higher Boyd category.In pre-and perimenopausal women, the model was adjusted for age at mammography, BMI, menopausal status, and screening program, plus number of live births, and current smoker status.2 In postmenopausal women, the model was adjusted for the same variables as well as HRT use.*To calculate p trends, variables were modeled as continuous variables; a Variables linked to age of alcohol and smoking initiation were only analyzed in drinkers and smokers/ex-smokers.

			PRE & PERIMENOPAUSAL 1			POSTMENENOPAUSAL 2
	VARIABLES	N	OR	95% CI	p	p for trend	N	OR	95% CI	p	p for trend
	ALCOHOL DRINKING
	Current drinker
	No	301	1.00				1174	1.00
	Yes	499	1.04	0.79-1.36	0.801		1573	1.15 1.00-1.32	0.058
										0.058
	Daily g alcohol
	0 (non-drinker)	301	1.00				1174	1.00
	0-less than 10	373	1.07	0.80-1.42	0.656		1087	1.10 0.94-1.29	0.223
	10 or more	126	0.95	0.65-1.40	0.790	0.925	486	1.26 1.03-1.53	0.023	0.022
	Lifetime alcohol use
	Never	263	1.00				1047	1.00
	Ex-drinker	38	0.65	0.35-1.23	0.185		127	1.13 0.81-1.58	0.470
	Current	499	0.98	0.74-1.30	0.887		1573	1.16 1.00-1.35	0.043
	Age of alcohol initiation a
	≤18 years old	225	1.00				378	1.00
	19-24	123	1.03 0.69-1.55	0.870		417	1.10 0.85-1.42	0.477
	25-40	101	1.03 0.67-1.57	0.893		407	1.13 0.87-1.46	0.366
	>40 years old	21	2.57 1.06-6.26	0.038	0.258	125	1.12 0.78-1.62	0.534	0.381
	Before/at 18 years old	245	1.00				949	1.00
	After 18 years old	225	0.91 0.65-1.26	0.564		378	0.90 0.72-1.12	0.336
									760	1
	After menarche Before/at menarche	451 20	1.00 0.49 0.21-1.14	0.098		1283 48	363 0.70 0.41-1.19 1.00	1.12 0.89-1.41 0.189
	Before/at first pregn	300	1.00				760	1.00
	After first pregnancy	100	1.04 0.68-1.59	0.853		363	1.12 0.89-1.41	0.342
	SMOKING
	Current smoker
	No	549	1.00				2141	1.00
	Yes	251	0.86	0.65-1.13	0.278		606	0.93 0.79-1.10	0.415
										0.415
	Daily cigarettes
	0-5	73	1.00				178	1.00
	6-15	92	1.01	0.57-1.79	0.970		223	0.81 0.56-1.19	0.285
	>15	86	0.80	0.45-1.42	0.442	0.434	205	0.68 0.46-0.99	0.046	0.046
	Lifetime tobacco
	Never	342	1.00				1712	1.00
	Ex-smoker	207	1.06	0.77-1.47	0.721		429	1.10 0.90-1.34	0.366
	Current	251	0.88	0.65-1.19	0.398		606	0.95 0.80-1.13	0.579
	Accumulated cigarettes life
	≤300	215	1.00				391	1.00
	301-500	106	0.88	0.57-1.35	0.555		202	0.73 0.53-1.01	0.054
	501-700	87	0.82	0.52-1.30	0.400		157	0.92 0.65-1.29	0.628
	>700	37	0.72	0.37-1.40	0.337	0.238	193	0.70 0.51-0.96	0.028	0.053
	Age of smoking initiation a
	≤18 years old	350	1.00				519	1.00
	19-24	70	0.66	0.40-1.08	0.098		247	0.92 0.69-1.22	0.557
	25-40 (or ≥25 in prem.)	26	0.81	0.37-1.66	0.590	0.177	153	0.96 0.67-1.37	0.824
	>40 years old						29	1.36 0.67-2.80	0.396	0.920
	Before/at 18 years old	350	1.00				519	1.00
	After 18 years old	76	0.71	0.46-1.09	0.119		429	0.95 0.74-1.22	0.700
	After menarche	411	1.00				919	1.00
	Before/at menarche	36	1.36	0.73-2.53	0.333		36	1.00 0.55-1.83	0.992

TABLE 3 .

 3 Associated OR and 95% CI for a higher Boyd category in non current smokers and current smokers 1 .

		NON CURRENT SMOKERS (N=2691)			CURRENT SMOKERS (N=858)
	VARIABLES	N	OR	95% CI	p	p for trend	N	OR	95% CI	p	p for trend
	Current drinker
	No	1169	1.00				308	1.00
	Yes	1522	1.15	0.99-1.32	0.063		550	1.06	0.82-1.37	0.672
	Daily g alcohol
	0 (non-drinker)	1169	1.00				308	1.00
	0-less than 10	1079	1.11	0.95-1.29	0.207		381	1.09	0.82-1.44	0.562
	10 or more	443	1.25	1.02-1.53	0.034 0.029	169	1.00	0.70-1.41	0.984 0.916
	Lifetime alcohol use
	Never	1058	1.00				254	1.00
	Ex-drinker	111	0.92	0.64-1.32	0.650		54	1.15	0.67-1.97	0.601
	Current	1522	1.14	0.98-1.32	0.089		550	1.09	0.82-1.43	0.562
	Age of alcohol initiation a
	≤18 years old	426	1.00				177	1.00

ACKNOWLEDGMENTS

We should like to thank the participants in the DDM-Spain study for their contribution to breast cancer research.

This study was supported by: Research Grant FIS PI060386 from Spain's Health Research Fund (Fondo de Investigación Sanitaria); the EPY 1306/06 Collaboration Agreement between Astra-Zeneca and the Carlos III Institute of Health (Instituto de Salud Carlos III); and a grant from the Spanish Federation of Breast Cancer.


A Mechraoui
email: amine.mechraoui@gipsa-lab.inpg.fr

F Djohor
email: faris.djohor@lsis.org.

J-M Thiriet
email: jean-marc.thiriet@gipsa-lab.inpg.fr

S Gentil

A Co-design Distributed Bayesian Approach for Decision and Scheduling of WNCS

Keywords: Wireless Networked Control Systems, Co-design, Bayesian Network, Scheduling, Decision-making, Mobile robot

This paper deals with the problem of co-design of Wireless Networked Control systems (WNCS). The integration of the Wireless Network (WN) in the control loop influences the Quality of Control (QoC) of the system in terms of the Quality of Service (QoS) of the WN. We present a co-design approach for WNCS based on distributed Bayesian Network (BN) and we illustrate it with Khepera III robot. The proposed BN is constructed from the robot experimental data. This approach allows to make decisions to ensure a good QoC for the robot and also ensure that the QoS is always sufficient to maintain a good QoC. Keeping a sufficient QoS depends on the scheduling method used and therefore the proposed approach aims also to determine the proper scheduling method to keep the system's performance. Finally a comparison is performed with the classical time-triggered scheduling. The results obtained with BN scheduling are better in terms of QoS and QoC for WNCS.

INTRODUCTION

Wireless Networked Control Systems (WNCS) are distributed systems in which the information between the node controller and node system are exchanged via a wireless communication network. Compared with traditionally known controlled systems, the Quality of control (QoC) in the WNCS depends mainly on the Quality of Service (QoS) of the used Wireless Network (WN). Using a WN to interconnect different nodes of a distributed system brings many benefits. One of the advantages of WNCS is to reduce complexity in terms of installation. The weight and the limited space of WNCS may be one of the criteria for selecting such systems. The simplicity of maintenance also proves a great advantage for these systems. These benefits can also increase system flexibility. Therefore, the WNCS have found applications in various fields such as mobile sensor networks [START_REF] Leonard | Collective motion, sensor networks, and ocean sampling[END_REF], robotics and mobile robotics [START_REF] Arzen | A component-based approach to the design of networked control systems[END_REF][START_REF] Cremean | Alice: An information-rich autonomous vehicle for high-speed desert navigation[END_REF], Unmanned Aerial Vehicles UAV [START_REF] Berbra | Hybrid priority scheme for networked control quadrotor[END_REF] etc. . However, the integration of the WN in the control loop introduces some difficult problems to solve. Traditionally known Controlled Systems are based on the assumption that all transmitted information is received without loss and delay, which means that the link between the various components of the system is considered as "perfect". However, in Networked Control Systems (NCS), the network either wired or wireless is "imperfect", and the modeling and analysis of such NCS are more complex [START_REF] Hespanha | A survey of recent results in networked control systems[END_REF]. The network influence on the QoC of the system can be due to sampling, delay, packets loss and the rate of the WN. A lot of works have been done recently on these topics. According to various aspects of the analysis and design of the NCS, existing works can be broadly divided into four categories: stability analysis [START_REF] Hespanha | A survey of recent results in networked control systems[END_REF][START_REF] Liu | Stability analysis of networked control systems with time-varying sampling periods[END_REF][START_REF] Xiaomei | Stochastic stability of networked control systems with network-induced delay and data dropout[END_REF], state estimation [START_REF] Giorgiev | Packet-based control: The H 2 -optimal solution[END_REF]Tilbury, 2006, Sinopoli et al., 2004], control synthesis [START_REF] Varsakelis | LQG control of networked control systems with access constraints and delays[END_REF][START_REF] Guo | A new networked predictive control approach for systems with random network delay in the forward channel[END_REF][START_REF] Fu | Mixed H 2 /H ∞ control for networked control systems (NCSs) with markovian packet-loss[END_REF] and co-design of control and communication [START_REF] Aubrun | Co-design Approaches for Dependable Networked Control Systems[END_REF][START_REF] Branicky | Scheduling and feedback co-design for networked control systems[END_REF][START_REF] Branicky | Networked control system co-simulation for co-design[END_REF]. Co-design approach is a new research domain. In such approach, problems due to the network such as delays, packet loss and jitter (QoS) are considered simultaneously with the control problems such as stability and performance of the controller (QoC). Generally, NCS has to be assigned to a schedule of transmission for each transmission entity (sensor, controller) based on a scheduling algorithm. Usually, the control system design and network scheduling are studied separately. This separation allowed the automatic community to focus on this particular field without taking into account the scheduling. But with the growing use of NCS, the need to address simultaneously the problem of scheduling and control encouraged the researchers to work on a so-called problem of co-design (adapt the network to the dynamic needs of the control and vice-versa) Fig. 1. Therefore, understanding the impact of scheduling on the stability and performance of the control has become crucial. Indeed, recent years have allowed the automatic community to study the communication network [START_REF] Branicky | Scheduling and feedback co-design for networked control systems[END_REF][START_REF] Cervin | Control-scheduling codesign of realtime systems: The control server approach[END_REF][START_REF] Branicky | Networked control system co-simulation for co-design[END_REF]. All these works are focused on NCS and less works have been done till now on WNCS. This paper proposes a novel approach of Co-design of WNCS.

The causality between the different parameters of the WN and the QoS and the QoC permits to use the graph theory to model the system. The probability theory can also be used according to the stochastic aspect of WN. Hence, we propose in this paper to use Bayesian Network (BN) [START_REF] Pearl | Probabilistic reasoning in intelligent systems: Networks of plausible inference[END_REF], [START_REF] Naim | Rseaux baysiens[END_REF] to model the QoS and the QoC of the WNCS as it brings graph theory and probability theory together. BN is used in this paper to schedule the information and to make on-line decision to avoid both degradation of the QoS and the QoC. The reconfiguration of the WN is required to fulfill the need of control in the case of degradation of the QoC. The adaptation of control is required too in the case of the degradation of the QoS of the WN. To illustrate our proposals, the communication architecture for two mobile robots moving with obstacle avoidance strategy in a 2D space with fixed control station is considered. According to the information delivered by the proposed BN, the reconfiguration of both the communication architecture (Dynamic priority) and the strategy of control is possible by using different methods of tasks scheduling. The paper is organized as follows. Section 2 presents the co-design problem and describes the proposed BN approach. The qualitative and the quantitative approach to model the proposed distributed BN using the experimental results are presented. The decision and scheduling approach using distributed BN are discussed in section 3. Section 4 demonstrates the effectiveness of the approach using simulated results for two robots and two scenario are studied and compared. Section 5 gives conclusion and some perspectives.

CO-DESIGN PROBLEM

Distributed systems generally incorporate communication resources (such as networks and wireless networks) to connect their different subsystems. This category of systems requires appropriate scheduling taking into account stochastic phenomena and decision to ensure the reconfiguration of the communication resource to maintain an acceptable QoC for the system, and also to ensure the adaptation of the control strategy to maintain a good QoS of the network. To solve this co-design problem, we need also to locate on-line the source of degradation of the QoC and QoS. We propose Bayesian networks to come through these tasks and to achieve scheduling and decision making of the system.

The system considered in this paper is KHEPERA III mobile robot. The modeling methodology of the robot and the strategy of communication of two robots is presented in [START_REF] Mechraoui | On-line distributed bayesian decision and diagnosis of wireless networked mobile robots[END_REF][START_REF] Mechraoui | Codesign for wireless networked control of an intelligent mobile robot[END_REF]. For this robot, two missions are described (reach a target and avoid obstacles).

Definition of Bayesian network

Formally, BNs are directed acyclic graphs whose nodes represent random variables in the Bayesian meaning: they may be observable quantities, latent variables, unknown parameters or hypotheses. Edges represent causal relationships; nodes which are not connected represent variables which are conditionally independent from each other. Each node is associated with a probability function that takes as input a particular set of values for the node's parent variables and gives the probability of the variable represented by the node. Efficient algorithms exist that perform inference and learning (structure and parameter) in BN (see [START_REF] Naim | Rseaux baysiens[END_REF] for more details). Many definition of BN exist in the literature. For what follows, let G = (V, E) be a directed acyclic graph, and let x = (x v ) v∈V be a set of random variables indexed by V .

x is a BN with respect to G if its joint probability density function can be written as a product of the individual density function, conditional on their parent variables:

p(x) = v∈V p(x v |x pa(v) ) (1)
Where pa(v) is the set of parents of v.

Distributed Bayesian Networks

The modeling of a system using Bayesian networks (BN) takes two important steps: qualitative approach and quantitative approach. The first consists of determining the structure of the BN (i.e. causal relationships between nodes), the second consists of finding for each node X, the probability conditional distribution upon X's parents. In the simplest case, a BN can be specified by an expert and is then used to perform inference. In other applications defining the network is too complex for humans. In this case, the structure and the parameters of the local distributions must be learned from data (see [START_REF] Naim | Rseaux baysiens[END_REF] for more details). However, in distributed systems, nodes might not be physically connected. In our application, which consists of controlling a group of robots via a WN, the idea of distributing the BN comes out from the fact that some of the nodes are aboard the robots, some are in the control station. In addition to that, the complexity of a BN render impossible embedding all of it in a robot, due to memory and energy consumption constraints [START_REF] Mechraoui | Codesign for wireless networked control of an intelligent mobile robot[END_REF]. That led us to imagine a distribution strategy that can handle those constraints, and simplify as possible the complexity of the BN. For our application, the structural modeling can be done, based on graph theory, by analyzing influence between the nodes. On the other hand, the quantitative approach will be performed by parameter learning of the BN, due to it's relative complexity, using BayesiaLab. Qualitative approach The QoC is mainly influenced by three parameters: the network's QoS, the mission the robot M and the state of the robot R. Referring to [START_REF] Hespanha | A survey of recent results in networked control systems[END_REF] and [START_REF] Li | Control and communication synthesis in networked control systems[END_REF] Quantitative approach Here we're looking for finding the probability distributions based on available data from a real robot. Two simple methods will be described here to perform this task. When all the variables are observable the simplest method is the statistical estimation which consists of estimating the probability of an event by the frequency of appearance of this event in a database constructed from series of tests on the real system. The estimator is then given by: Where N i,j,k is the number of events in database for which the variable X i is in the state x k and its parents are in the configuration x j . The statistical learning is chosen here over other methods for its simplicity. Database is constructed from series of tests on the real system and was obtained based on two criteria for such systems (robot unicycle and a WN). These criteria are proposed to quantify the QoS and the QoC.

P (X i = x k |pa(X i ) = x j ) = θLH i,j,k = N i,j,k k N i,j,k (2)
As stated above, the QoS is particularly influenced by packet loss and also the delay. To construct the database, we need to quantify the QoS for this system, and then qualify by ranges of values to define the modes (or states) of QoS. For this, we propose the following criterion:

QoS = max( (1 -P L) * (nT s -∆ t ) nT s , 0) (3)
P L is the probability of packet loss, it is defined by tests on the real system. ∆ T is the delay between the sensor and the controller. T s is the sampling period. n is a constant that characterizes the maximum number of lost samples that can be tolerated in which the system works perfectly. the QoC is influenced mainly by three parameters, namely QoS, the state of the robot and the system's mission. This leads us to propose the following criterion:

QoC = QoS * κ j * i (4)
κ j is a variable that depends on the state j of the robot such that j ∈{Good, degraded or bad} and κ good > κ deg > κ bad , in our case we took: κ good = 1,κ deg = 0.5 and κ bad = 0. i is a variable that depends on the mission i of the robot (i ∈ {obstacle, target}) as obstacle < target ( target = 1 and obstacle = 0.5). Fig. 3 shows the variation of the QoC depending on the QoS in two different cases ("Reach a target" and "Avoid obstacle"). We note that the robot needs more QoS in the case of obstacle avoidance. The decreasing of the QoS is caused by the number of nodes that communicates.

DISTRIBUTED BAYESIAN NETWORK FOR SCHEDULING AND DECISION

After proposing a distributed BN model Fig. 2 and performing parameter learning (using BayesiaLab) to define the probability distribution for every node, this BN is used for scheduling, and also making on-line decision to maintain an acceptable QoC and/or QoS. However, to perform this task, the BN needs information and knowledge about the robot's QoC. A criterion designed to evaluate online QoC is used (Algorithm 1). This algorithm gives the : communication, : stop communication.

Using information about all the measured variables, the BN provides a probabilistic estimation of the QoC and the QoS. Based on this estimation, the robot can make decision to change the scheduling strategy. The objective is to keep the better possible QoC for each robot and the better possible network's QoS.

According to the state of the QoC of the robot (delivered by Algorithm 1) and the state of the QoS (delivered by the BN knowing the state of the QoC), the system changes the scheduling strategy. Thus, with probability delivered by the BN (Algorithm 2) and Algorithm 1, the values of the conditional probability P (QoS|QoC, D, Col, M ) triggers the sensor task. With only Algorithme 1, the state of the QoC triggers the sensor task of each robot.

RESULTS

To verify the efficiency of the proposed BN to schedule and to make decision, two scenarios are presented. In each scenario, the BN and Algorithm 1 are tested and compared with the system without the proposed approach. The use of Algorithm 1 without BN to schedule is also compared with the other strategies (see Table 3). To perform the comparison, five criteria are considered.

(1) The first criterion (Eq. 5) is the Use Request Factor (URF) which represents the frame rate requested to the MAC layer [START_REF] Juanole | Qos in real time distributed systems and process control applications[END_REF]. It influences directly the QoS.

U RF = N i=1 ξ i Γ * T i s (5)
ξ i is the length of the frame of task i. Γ is the throughput of the WN. N is the number of tasks.

(2) The second criterion concerns also the rate of packet loss. It is calculated as follow:

Φ = P r P s (6)
P s is the number of packets sent and P r the number of received packets.

(3) The third criterion concerns the QoC. It is the Integral of the Absolute Error (IAE) (see Eq.7).

IAE = p k=0 x (k) 2 + y (k) 2 (7)
x and y are errors between the reference trajectories (at 0% of network load) and other trajectory (depending on the network load rate) with respect to X -axis and Y -axis respectively computed with p points representing each trajectory. (4) The fourth criterion is the fact that the robot reaches the target or not. (5) The last criterion is the collision between the obstacle and the robot.

Scenario 1

In the first scenario, we suppose that the two robots communicate with one control station. The initial position of the robot 1 is (x 0 , y 0 , θ 0 ) = (0, 0, 0) and the position of the target is (x d , y d ) = (1, 1). The two robots are always within the coverage area of the station. Hence, the probability P (D < D T hreshold ) = 1 for each robot.

To limit the resource of the WN and to study the network limits, the throughput is set to 8000bits/s. With this throughput and the sensor tasks of R1 and R2 and the controller tasks, the U RF = 64% in the case of non application of the proposed methods of scheduling (BN and Algorithm1). In this case, the robot reaches the target but it cannot avoid the obstacle. When Algorithm 1 is applied to control the sending of sensor measurements to controllers, it provides the current state of the QoC to the robot. Taking into account this state, a boolean signal for scheduling is generated; "0" starts the communication and "1" stops it. We note that after applying Algorithm 1, URF decreases from 64% to 34%, the QoS becomes good but the IAE increases from 0.13 to 0.89 for Robot 1 and 0.42 to 1.36 for Robot 2 (see Table 3). However, despite the increasing value of IAE, the application of this algorithm has slightly influenced the trajectory and the two robots reach their targets (see Fig. 4) and avoid the obstacle. However, applying the scheduling based on the results of BN, we notice that we have the same performance as with Algorithm 1 except that the IAE drops to zero. This can be explained by the fact that the BN has taken into account the state of the QoS and as it is sufficient to send periodic measurements, the two sensor tasks remain time-triggered. We can conclude that the proposed method is efficient because it takes into account both the QoS and the QoC to make decision and scheduling.

Scenario 2

In this scenario, the same situation as in first scenario is kept but the throughput of the WN is set to 3000bits/s, which means that U RF = 170% in the case of non application of the proposed methods of scheduling. The IAE is increased from 0.13 to 66.35. Packet losses have increased from 0 to 90 and thus the robot cannot reach the target (Fig. 4) and cannot avoid the obstacle (see Table 3). Now Algorithm 1 is applied to control the sensor task flow.

The IAE is decreased from 170% to 82%. Packet losses are increased but still reasonable. In fact, the robot can reach a target (see Fig. 4) but it cannot avoid the obstacle. Fig. 5 shows the delay with and without the proposed approach.

It is clear that the delay with BN is less than the delay without BN. Using results provided from the BN, and with the same scenario, the robot can reach its target (see Fig. 4) and avoid the obstacle. This scenario shows that, the proposed approach is efficient and solves the co-design problem.

CONCLUSION

In this paper, a novel distributed BN based approach has been proposed to model the QoS and the QoC of WNCS. This model combines all parameters or variables that influence the Quality of Service of the WN and the Quality of Control of the robot. The BN is designed using statistical learning of experimental data acquired from Khepera III robot. The use of the BN is justified by the stochastic behavior of the WN. The main objective of the BN is to make decisions and to control the sensor task flow. According to the situation, the scheduling strategy is applied to guarantee a good QoC of the robot and also to keep a sufficient QoS to send the critical information.

The proposed model achieves the desired objectives in terms of scheduling and decision-making. In this paper, the communication architecture for two mobile robots of Robot1 with and without BN moving in a 2D space with fixed control station has been considered as an illustrative example. According to the information delivered by the proposed BN, the strategy of controlling the sensor flow is applied. It aims to keep a good QoC in when the robot has to reach a target and avoid obstacle and also to ensure a sufficient QoS. Finally a comparison of the proposed BN scheduling with the classical time-triggered scheduling is performed and the results obtained with BN scheduling are better in terms of QoS and QoC for WNCS. In the future work, the degradation of the QoC and the QoS of WNCS can be avoided by adding some dynamic nodes in two time slices. The probability of the QoC and the QoS in time slice t+1 knowing their states in time slice t can help predict the degradation of the QoC.

  Fig. 1. Co-design problem

  Fig. 2. Distributed Bayesian network

Fig. 3 .

 3 Fig. 3. QoC depending on QoS with two missions: reach a target and avoid abstacle

Algorithm 2

 2 Scheduling using BN P 1 = P (QoS = good|QoC, D, Col, M ) P 2 = P (QoS = degraded|QoC, D, Col, M ) P 3 = P (QoS = bad|QoC, D, Col, M ) if (P 1 > P 2 ) and (P 1 > P 3 ) then sensor controller else Execute Algorithm 1 end if

Fig. 4 .Fig. 5 .

 45 Fig. 4. Comparison between the trajectory of Robot1 with and without BN

Table 1 .

 1 Signification of different nodes of the BN

	Nodes	Signification
	QoC	Quality of Control
	QoS	Quality of Service
	R	State of the robot
	PL	Packet loss
	RSSI	Request Signal Strength Indicator
	∆t	Delay
	Obst	Obstacle
	D	Distance between the station and the robot
	Col	Collision
	N	Number of communicating nodes
	M	Mission

  , the QoS is influenced by the delay ∆ t between transmission and reception, and by the rate of packet loss P L. The signal strength represented by the Request Signal Strength Indicator (RSSI ) influences the packet loss. The RSSI is affected directly by the distance D and obstacles Obst between the robot and the control station. The delay ∆ t is influenced by the probability of collisions Col between sources (robots or other applications) sending information via the network. The node Col is affected by the number N of robots communicating with the control station (see Fig.2, Tab.2 and Tab.1).

			RSSI	i
	QoS	i	i PL
	i QoC		i
			t

Table 2 .

 2 Node modes of BN

	Nodes	Modes
	QoC	Good, Degraded, Bad
	QoS	Good, Degraded, Bad
	R	Good, Degraded, Faulty
	PL	0% ≤ P L < 24%, 24% ≤ P L < 46%,
		46% ≤ P L < 74%,74% ≤ P L < 100%
	RSSI	(≤ -48, > -40, -48 < RSSI ≤ -40)dBm
	∆t	∆t < T threshold ,T threshold ≤ ∆t < Ts, ∆t ≥ Ts
	Obst	Yes, No
	D	D < D1, D1 ≤ D < D2, D ≥ D2
	Col	yes, N o
	N	Number of nodes
	M	Reach target, Obstacle avoidance

Table 3 .

 3 Comparison between the classical approach and the proposed one

				Scenario1 Scenario2
		U RF	64%	170%
			R1	0%	91%
	BN	Φ	R2	0%	96%
	Algo1		S	0%	91%
			R1	0.13	66.35
		IAE	R2	0.42	49.97
		Reach target	Yes	No
		Collision	Yes	Yes
		U RF	34%	82%
			R1	0%	32%
	BN	Φ	R2	0%	33%
	Algo1		S	0%	64%
			R1	0.89	1.31
		IAE	R2	1.36	1.76
		Reach target	Yes	Yes
		Collision	No	Yes
		U RF	64%	79%
			R1	0%	33%
	BN	Φ	R2	0%	30%
	Algo1		S	0%	56%
			R1	0.21	0.87
		IAE	R2	0.59	1.02
		Reach target	Yes	Yes
		Collision	No	No

Table 4 .

 4 Signification of the used abbreviations

	Abbreviation	Signification
	R1	Robot number 1
	R2	Robot number 2
	S	Control Station
	Φ	Packet loss rate
	IAE	Integral of the Absolute Error
	BN	Without BN Approach
	Algo1	Without Algorithm 1
	BN	With BN approach
	Algo1	With Algorithm 1


Najatte Harouiya
email: najatte.harouiya@cemagref.fr

Stéphanie Prost-Boucle
email: stephanie.prost-boucle@cemagref.fr

Catherine Morlay
email: catherine.morlay@univ-lyon1.fr

Dirk Esser
email: dirk.esser@sint.fr

Samuel Martin Ruel

Pascal Molle
email: pascal.molle@cemagref.fr

Performances evaluation of phosphorus removal by apatite in constructed wetlands treating domestic wastewater: Column and pilot experiments

Keywords: constructed wetlands, phosphorus removal, apatite, experiments scale, sustainable treatment

In constructed wetlands (CWs) treating domestic wastewater, good treatment performances are obtained on mains parameters except phosphorus (P) which can cause eutrophication problems. In order to improve P removal from wastewater with a low specific filter surface per people equivalent (p. e.), different materials have been tested: man-made and natural materials, industrial by-products, and a mixture of these materials. The P removal by natural apatite have been studied by a very few works. Despite apatite materials appears to possess high and long-term retention capacity, a better knowledge is needed to precise the quality of apatite to be used and the P removal evolution with time and water quality. In this work the P retention kinetics have been studied in two different scales (lab-experiments and pilots) on different apatite qualities. Retention rate in pilots is smaller than the one found in labexperiments and the results suggested that a security coefficient might be applied while designing apatite filter.

Introduction

In constructed wetlands phosphorus can be assimilated by biomass and incorporated by organic matter [1]. But in such systems it's not possible to remove the sludge and P is released back into water after organic matter mineralization [2]. On the other hand phosphorus is used by reeds [3], however the quantity removed by plant assimilation can be neglected when using small surfaces (30 to 150 kg.m -2 .year -1 ) [4]. To avoid eutrophication problems in surface waters many researches have been done to use specific materials in CWs.

In the previous works several materials were tested as iron, aluminium and calcium rich materials [5][START_REF] Brix | Proceedings, 7th International Conference on Wetlands systems for water pollution control[END_REF][7][8][9][10][11][12][13][14][15][START_REF] Vohla | Ecological Engineering[END_REF].

The P removal by these materials is based on adsorption and/or precipitation mechanisms onto particle surface. Recently researches have focused on the use of apatite to promote irreversible sorption onto the material surface. Nevertheless, in the few works done on P removal by apatite [START_REF] Jang | [END_REF][18][19][START_REF] Chazarenc | Proceedings, 11th International conference on Wetlands Systems for Water Pollution Control[END_REF], the materials have been only evaluated in lab-scale experiments (batch and/or column) under controlled conditions. Apatite minerals are known to have a great stability and the particular crystalline structure allows substitutions of different elements [START_REF] Kreidler | [END_REF][22][START_REF] Roy | In phase diagrams, material sciences and technology 6[END_REF][START_REF] Elliott | [END_REF]. This material has been proposed as an effective means for retaining metals and radionuclides [START_REF] Lindsay | [END_REF][START_REF] Gauglitz | [END_REF][27][28][29]. For these reasons in this work besides the evaluation of apatite capacity to remove P in CWs, the materials have been characterized for metal content.

In this study five different apatite materials have been tested in column and pilot experiments.

In lab-scale columns, the objectives were to precise retention kinetics versus apatite qualities and influence of water ionic composition. In pilots, fed with treated wastewaters in hydraulic controlled conditions, the objectives were to point out the retention rate evolution with time, scale transition effect and exhibit the reed effect on P removal. Other objectives were also sought as:

-Evaluation of the process sustainability and design optimization.

-The capability of column experiments to predict P retention.

Material and methods

Apatites tested

P retention experiments were performed in the present study using five sedimentary apatites from Morocco and Algeria (Table 1). Particle size distribution was determined using drysieving techniques [START_REF]Tests for geometrical properties of aggregates -Part 1: Determination of particle size distribution -sieving method[END_REF], to calculate d 10 , d 60 (mesh diameter allowing, respectively, 10 or 60% of the material mass to pass through), and the uniformity coefficient (UC= d 60 /d 10 ). Porosity was determined from the amount of water needed to saturate a known volume of component (replicate number n=3) and the bulk density was measured by the volume of water displaced by a known mass of medium (n=3). Geometric surface areas in the present study were estimated from the particle size distribution, assuming spherical grains, according to:

( ) ∑ - = + ⋅ + ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ = 1 1 1 12 1 n i i i i M m d d S ε (1)
Where d i represents the sphere diameter, ε stands for the sample density, m i correspond to the mass passing across d i diameter, and M to the total mass of sample.

Physical, chemical and mineralogical properties of materials used are shown in Tables 1,2 and 3. Materials tested contain 40 % to 95 % of apatite associated with other impurities. In this paper the term "quality of apatite" will be used to mean % content of apatite mineral. A good quality of material is one with a high percent of apatite mineral. (4) 82.1 40.1 (4) limit of quantification

Column experiments

The apatites materials have been tested in vertical downward flow columns of 9 cm of inner diameter (Fig. 1a). All columns consist of 20 cm high layers of apatite, equipped with five sampling ports to study P removal evolution into the media and to have better model fitting.

The columns were fed with synthetic solution (table 4) with known P concentration (inlet P concentrations ranged from 1 to 16 mg. l -1 ) and maintained in hydraulic saturation conditions as in horizontal flow constructed wetlands (HFCW). The inlet pH of all synthetic solutions was 7.6±0.2. The columns samples are taken regularly and analyzed for calcium, phosphorus, alkalinity, and pH to observe the temporal evolution of effluent composition. Experiments have lasted 3 months for each material.

Pilots

Pilot-scale description

BT and HT 2 materials have been tested in three similar pilot-scale (HFCW) at Bagnols plant (Rhône, France). The pilots consist of 1.5m² tanks and 40 cm in depth filled up with apatite.

The pilot units were fed with treated wastewater (except for P, table 5) from the outlet of Bagnols plant (trickling filter) (Fig. 1b). One apatite pilot (HT+r) is planted with Phragmites australis to study the reeds effect on P retention.

Results and discussion

P removal in column experiments

As example, the evolution of P removal by AM apatite is shown in the figure 2. The P concentration is presented as a function of time at the inlet and the outlet of the column

Outlet P Inlet P

Step 1

Step 2

Fig. 2. Evolution of P concentrations as a function of the time during the AM column experiment

Two steps can be noted:

Step 1: For 70 days 99% of phosphorus was removed and the P outlet concentration did not exceed 0.1mg. l -1 . The adsorption seems to be the predominant mechanism as proved by other previous studies [START_REF] Harouiya | Proceedings, 11th International conference on Wetlands Systems for Water Pollution Control[END_REF].

Step2: The outlet P concentration increased to reach lower but stable P retention kinetic. With AM, this period starts after a storage level of about 5 g of P. kg -1 of apatite as found by Molle et al. [18]. The precipitation becomes the predominant phenomenon of P retention in this step.

This points out how experiment duration is important to predict long term removal with such material.

k-C* model and removal rates evolution

Using the internal sampling system, the P concentration in the apatite was modeled using k-C* model [2]. The model has been chosen because it's a simple way to model pollutant removal in HFCW. The P concentration (C) at time t can be obtained by the following expression:

( ) The comparison of retention rate evolution for all materials tested in this study as given by the figure 4.b show that the retention rate k decreases systematically as adsorption mechanism reduces until it reaches a steady state once precipitation becomes the major mechanism involved in P removal. The stabilised k is about 0.9±0.1 h -1 and 0.3±0.1 h -1 for AM and BT materials respectively. Indeed, the retention rates are different between materials used and the differences observed could be related to material quality. This difference in k value is of great importance in determination of the surface needed for P removal.

* exp *) ( 0 C kt C C C + - - = (

Surface observations

The AM apatite surface before and after column experiments was observed using an Environmental Scanning Electron Microscopy (ESEM) equipped with a microanalysis instrument EDS (Energy Dispersive X-ray System). the Zn content is included as substitution of Calcium in the precipitate formed, the molar ratio ((Ca +Zn)/P) increase to 1.51±0.04. This composition obtained suggests a formation of tricalcium phosphate (TCP) and the precipitate could be considered as a precursor for hydroxyapatite (HAP) phase. The formation of TCP as precursor of HAP precipitate could have an effect on the evolution of P removal rates as observed in 3.2.

Hydraulic and treatment performances in pilots

The pilots were fed since April 2008 with residence time measured of about 2 days in the whole pilots. The mean hydraulic and organic loads received by Bagnols pilots and inlet wastewater characteristics are given in the table 5. Removal performances are similar in all pilots and achieve about 70% and 98% for COD and SS respectively.

(a) (b)

effect of reeds on phosphorus removal was observed in pilot experiments because the quantity removed by reeds is very negligible compared to P loads applied on the HT+r pilot (30 to 150 kg. ha -1 . year -1 [4]).

Scale transition effect

BT and HT 2 materials have been tested in pilot system in order to evaluate the scale factor effect and the biomass development on P retention rate. As presented in table 6, the retention rates obtained in lab-experiments are different from those measured in pilots mostly for HT 2 material. The differences might be caused by the hydraulic conditions. In pilots, hydrodynamic is less controlled than in lab experiment. In another and longer study on BT apatite carried out in real scale HFCW at Evieu plant [START_REF] Harouiya | Proceedings, 11th International conference on Wetlands Systems for Water Pollution Control[END_REF], k value decreases to 0.07±0.02 h -1 after two years of experiments. Stabilised k value for all materials might be smaller than the one stated in table 6 and in figure 3.b. Therefore designers have to be aware of it and apply security coefficient while designing apatite filter. In real conditions the stabilised k values could be estimated two to three times less than values in lab-scale experiments.

Design recommendations

To evaluate the process sustainability and optimize the design of apatite filter. In the figure 5 is given the surfaces needed per p.e. to respect 2 or 1 mg P.l -1 for the two extreme apatites studied in this work (AM and BT). In this figure the surfaces are calculated for an inlet P concentration of 10 mgP.l -1 and a retention rates of 0.9±0.1 h -1 and 0.3±0.1 h -1 for AM and BT materials respectively. Using AM material a surface of 0.2 m²/p.e is sufficient to achieve 1 mgP.l -1 in the effluent.

However, due to hydraulic short-cutting it is not secure to use smaller surfaces and the best window in term of application is to use about 0.5 m².p.e -1 . It means that apatite materials like BT with poor quality are not suitable. The use of 0.5 m².p.e -1 have also an important role to delay final saturation of the filter. The actual storage level reached for AM material in labexperiments is about 7 g of P. kg -1 of apatite. As presented by grey curve, if the filter accumulates 1g of P. kg -1 of apatite per year using a surface of 0.5 m².p.e -1 , this level would be reached after 7 years and the filter could work at least 7 years with high P retention kinetics. The use of smaller filter surfaces would lead to earlier final saturation.

Conclusions

Main conclusion, except confirmation of the good P removal potential of apatite in constructed wetlands, is the importance of apatite quality on long-term P removal. A better insight of processes in term of adsorption/precipitation, precipitate formed, impact of reeds and experiments scale allow to consolidate the design of apatite filters and its sustainability.

This work provides data in lab-scale experiments and in pilots for P removal by apatite.

Apatite materials have a high retention capacity and the results of lab-scale experiments could be used to predict P removal in full-scale taking into account others factors as hydraulic conditions. A decrease in retention rates with time was observed for all materials and the apatite quality appears to be very important for sustainable P treatment. Using a good quality of apatite the surface needed for P treatment is about 0.5 m² to respect 1 mgP.l -1 in the effluent.

Fig. 1 .

 1 Fig. 1. Schematic representation of: (a) column experiments and (b) pilots at Bagnols

(

  residence time =3.3 hours in that case). A slight change of pH is observed (pH inlet =7.6±0.2 and pH outlet =7.4±0.3).

2 )Fig. 3 .

 23 Fig. 3. (a) Variation of the phosphorus concentration with the reaction time for AM apatite. The symbols designate the P experimental data, the curves drawn through this data represent the P concentrations calculated from k-C* model and (b) Evolution of retention rates for all apatite materials studied as a function of P storage level per kilograms of apatite

Fig. 4 .

 4 Fig. 4. Surface observation: (a) ESEM of AM apatite before experiment and (b) after experiment Comparison of the photomicrographs illustrated in Figs. 4a and 4b shows a formation of precipitate at the apatite surface. Precipitate formed are rich in Ca and P with Ca/P molar ratio of 1.35±0.06. A presence of Zn in the precipitate was also observed and confirmed by water analyze performed in column experiments (about 99% of Zn was retained by AM apatite). If

Fig. 5 .

 5 Fig. 5. Effect of apatite quality on surface needed for P treatment and on final saturation of the apatite filter

FIGURESFig. 1 .Fig. 2 .Fig. 3 .Fig. 4 .

 1234 FIGURES

Table 1

 1 Physical characteristics of tested materials

							Geometric
			Particle size		Porosity Density	surface area
		d 10 (mm) d 60 (mm) UC (d 60 /d 10 )	%	kg.m -3	m 2 .kg -1
	BT	1.27	4.02	3.15	50	2414	0.73
	HT 1 HT 2	4.44 0.19	9.21 9.21	2.09 47.54 (1)	46 53	2160 2243	0.17 1.48
	AM	0.37	2.79	7.46	58	2392	1.76
	AT 2	2.14	3.85	1.80	54	2447	0.33
							size distribution is
	modified and real grain distribution is masked. In reality we observe apatite grains of 0.1 -0.3 µm and coarser grains with impurities.

(1)

HT 2 material contains 30 % of fine particles of clay that can be bonded to larger particles. As a consequence, particle

Table 2 Mineralogical characteristics of materials Mineralogical composition % (W/W) of materials Apatite Calcite Quartz Ankerite (2) Dolomite Clay BT

 2

		41.8	50.4	4.8	n.d (3)	3.0	0.0
	HT 1 60.2 HT 2 46.3 AM 95.4	35.1 39.5 3.2	0.0 10.1 1.3	n.d (3) n.d (3) n.d (3)	4.7 2.5 0.0	0.0 1.5 0.0
	AT 2 58.1	0.0	0.2	41.7	0.0	0.0
	(2) CaFe (CO 3 ) 2 and	(3) not determined

Table 3

 3 Chemical composition of materials

	(a) Major constituents
	% Mass	Ca	P	Si	Mg	Fe	Al
	BT	36.3	8.4	3.1	0.5	0.3	0.4
	HT 1	35.3	10.1	3.3	0.2	0.3	0.2
	HT 2	32.3	8.2	6.5	0.5	0.6	1.0
	AM	38.2	13.2	1.1	0.2	0.2	0.2

Table 4

 4 Inlet water characteristics and hydraulic loads tested in column experiments

		Water	Flow rate/ cross section
			m.d -1
	BT Tap water and wastewater	0.80-1.60
	HT 1	Tap water	0.85
	HT 2 Tap water and wastewater	0.80-1.60
	AM	Tap water	0.80-1.15
	AT 2	Tap water	0.80-1.15

Table 5

 5 Mean hydraulic and organic loads applied on the pilots and inlet wastewater characteristics.

	Values for parameters are means/ (SD: standard deviation) of 34 samples
	HL (m/d)		COD	SS	KN	TN	TP
		Inlet wastewater (mg. l -1 ) 67.8/(31.2) 19.7/(16.1) 6.2/(4.3) 21.8/(8.0) 4.2/(1.7)
	0.18/(0.08) HT+ r (g. m -2 . d -1 )/(SD) 11.6/(5.7) 3.1/(1.9) 1.0/(0.9) 3.6/(2.8) 0.7/(0.4)
	0.18/(0.07)	HT (g. m -2 . d -1 )/(SD)	11.8/(5.3) 3.0/(2.2) 1.1/(0.8) 4.0/(2.3) 0.7/(0.4)
	0.13/(0.05)	BT (g. m -2 . d -1 )/(SD)	8.3/(3.8)	2.2/(1.3) 0.7/(0.5) 2.5/(1.6) 0.5/(0.3)
	Conversely total nitrogen removal in the pilots is low (<40%) and this result could be related

to the longer time needed for nitrifying bacteria to develop in the beginning of experiments and insufficient amounts of organic carbon available for denitrifying bacteria. The total phosphorus removal is approximately 80% for HT 2 material and 98% for BT material. No

Table 6

 6 Comparison of retention rates between column experiments and pilots

	Materials k (h -1 ) in column-scale k (h -1 ) in pilot-scale
	BT	0.3	0.3
	HT 2	0.6	0.3

Table 1

 1 Physical characteristics of tested materials HT 2 material contains 30 % of fine particles of clay that can be bonded to larger particles. As a consequence, particle size distribution is modified and real grain distribution is masked. In reality we observe apatite grains of 0.1 -0.3 µm and coarser grains with impurities.

							Geometric
			Particle size		Porosity Density	surface area
		d 10 (mm) d 60 (mm) UC (d 60 /d 10 )	%	kg.m -3	m 2 .kg -1
	BT	1.27	4.02	3.15	50	2414	0.73
	HT 1 HT 2	4.44 0.19	9.21 9.21	2.09 47.54 (1)	46 53	2160 2243	0.17 1.48
	AM	0.37	2.79	7.46	58	2392	1.76
	AT 2	2.14	3.85	1.80	54	2447	0.33
	(1)

Table 2

 2 Mineralogical characteristics of materials

		Mineralogical composition % (W/W) of materials
		Apatite Calcite Quartz Ankerite (2) Dolomite Clay
	BT	41.8	50.4	4.8	n.d (3)	3.0	0.0
	HT 1 60.2 HT 2 46.3 AM 95.4	35.1 39.5 3.2	0.0 10.1 1.3	n.d (3) n.d (3) n.d (3)	4.7 2.5 0.0	0.0 1.5 0.0
	AT 2 58.1	0.0	0.2	41.7	0.0	0.0
	(2) CaFe (CO 3 ) 2 and	(3) not determined

Table 3

 3 Chemical composition of materials

	(a) Major constituents
	% Mass	Ca	P	Si	Mg	Fe	Al
	BT	36.3	8.4	3.1	0.5	0.3	0.4
	HT 1	35.3	10.1	3.3	0.2	0.3	0.2
	HT 2	32.3	8.2	6.5	0.5	0.6	1.0
	AM	38.2	13.2	1.1	0.2	0.2	0.2
	AT 2	31.9	9.6	2.2	1.7	0.4	0.5
	(b) Trace elements
	mg.kg -1	As	Cd	Cr	Cu	Pb	Se	V	Zn	U
	BT	11.4	76.8	182.1	6.4	2.3	3.2	115.5	109.9	61.5
	HT 1 HT 2	11.6 9.5	34.5 31.5	196.0 321.0	18.9 21.3	3.3 3.8	<DL (4) <DL (4)	152.0 242.0	196.0 237.0	106.0 78.9
	AM	13.3	14.4	257.0	22.9	3.8	1.9	130.0	181.0	131.0
	AT 2	4.0	11.9	210.0	5.1	3.2	21.3	<DL (4)	82.1	40.1
	(4) Detection limit

Table 4

 4 Inlet water characteristics in column experiments

		Water	Flow rate/ cross section
			m.d -1
	BT Tap water and wastewater	0.80-1.60
	HT 1	Tap water	0.85
	HT 2 Tap water and wastewater	0.80-1.60
	AM	Tap water	0.80-1.15
	AT 2	Tap water	0.80-1.15

Table 5

 5 Mean hydraulic and organic loads applied on the pilots and inlet wastewater characteristics. Values for parameters are means/ (SD: standard deviation) of 34 samples

Table 6

 6 Comparison of retention rates between column experiments and pilots mg. l -1 ) 67.8/(31.2) 19.7/(16.1) 6.2/(4.3) 21.8/(8.0) 4.2/(1.7) 0.18/(0.08) HT+ r (g. m -2 . d -1 )/(SD) 11.6/(5.7) 3.1/(1.9) 1.0/(0.9) 3.6/(2.8) 0.7/(0.4) 0.18/(0.07) HT (g. m -2 . d -1 )/(SD) 11.8/(5.3) 3.0/(2.2) 1.1/(0.8) 4.0/(2.3) 0.7/(0.4) 0.13/(0.05) BT (g. m -2 . d -1 )/(SD) 8.3/(3.8) 2.2/(1.3) 0.7/(0.5) 2.5/(1.6) 0.5/(0.3)

	HL (m/d)	COD	SS	KN	TN	TP
	Inlet wastewater (
	Materials k (h -1 ) in column-scale k (h -1 ) in pilot-scale
	BT	0.3	0.3
	HT 2	0.6	0.3

Acknowledgements: the Authors would like to thank the Rhône-Alpes Chemicals and Environment competitiveness cluster "Axelera" in which this project takes place. We thank CERPHOS and FERPHOS groups for providing the apatite used in this study.