Manon Pruvost-Couvreur

Bruno Le Bizec

Camille Béchaux

Gilles Rivière
email: gilles.riviere@anses.fr

Physiologically Based Toxicokinetic), PBTK-TD (Physiologically Based Toxicokinetic and Toxicodynamic) A METHOD TO ASSESS LIFETIME DIETARY RISK: EXAMPLE OF CADMIUM EXPOSURE

Keywords: ADME (Absorption, Distribution, Metabolism, Excretion), AIC (Akaike Lifetime dietary risk, cadmium, toxicokinetic modelling, risk assessment

Usually health risk related to food contaminants is assessed based on consumption data collected on a few days. Consequently, this approach considers neither the evolution of exposures over time nor the potential accumulation of the substance.

The aim of the present study was to develop a method to assess lifetime dietary risk due to cadmium exposure.

Three methods were compared, respectively based on age, dietary pattern and sociodemographic characteristics. Additionally, exposure trajectories were converted into cadmium body burden trajectories using a PBTK-TD model ultimately predicting the occurrence of renal effects.

It was shown that dietary exposures to cadmium, as well as exceedances of health based guidance values, greatly vary with age and individual profiles.

The developed methods allowed identifying parameters affecting dietary exposure to cadmium and distinguishing at-risk subpopulations. Furthermore, this study demonstrated that it is necessary to consider individual changes through life and kinetic of the substance to assess risk properly.

Table of contents

Introduction

Food may expose to many chemicals (ATSDR, 2000;EFSA, 2009a[START_REF] Efsa | Scientific opinion on the risks to public health related to the presence of bisphenol A (BPA) in foodstuffs[END_REF]. Due to potential adverse effects of these chemicals, it is critical to properly assess the amount of contaminant ingested daily, as well as the health risk associated with this exposure.

Usually, the risk is assessed by comparing dietary exposures to critical thresholds. Exposure assessment is performed by recording food consumption of a representative part of the population during a few days (around 1 to 7 days) (FAO/ WHO, 2009;[START_REF] Thompson | Dietary Assessment Methodology[END_REF]. Consumed foods are then analysed to measure the concentration of the chemical present in the food. To estimate dietary exposure, consumption data and actual contaminant concentrations are multiplied and adjusted to individual body weight. This dietary exposure is then compared with a chronic healthbased guidance value (HBGV), a dose below which lifetime exposure to the chemical does not lead to health risk for the consumer.

However, this classic method does not allow the consideration of changes in dietary habits throughout life or changes in food contamination over time. It is known that dietary exposures varies by age [START_REF] Who | Principles for evaluating health risks in children associated with exposure to chemicals[END_REF] and generation because of changes in food consumption, variation in human activity and regulations on the production and the use of chemicals over time [START_REF] Ledoux | Comparaison des contaminations et des expositions alimentaires des années 1970, 2000 et 2010[END_REF].

In this study, we were interested in the impact of changes through life on conclusions of risk assessment. To this end, we applied three different methods to assess lifetime dietary exposure trajectories (i.e. curves representing the dietary exposure according to age, from birth to the end of life) and proposed different interpretations of lifetime trajectories in terms of health risk. The three methods were applied on the example of dietary exposures to cadmium, a heavy metal which bioaccumulates over lifetime exposures and which induces numerous adverse effects such as developmental effect, nephrotoxicity or skeletal effects (ATSDR, 2012;EFSA, 2009a). Lifetime dietary exposure trajectories simulated with each method were compared. In order to assess long-term impact, these were converted into body burden trajectories. Finally, the nephrotoxic effects induced by lifetime exposures to cadmium were assessed using the dose-response curve derived by EFSA (2009a) and linking urinary cadmium concentrations with urinary beta-2-microglobulin (β2M) levels.

This document is divided in three parts: the first part presents the methodology developed in order to model lifetime external and internal exposure trajectories for a food contaminant while taking the evolution of food consumption and contamination over time into account. The second part presents the application of the developed methodology to the case of cadmium as well as several interpretations in terms of risk assessment. The third part discusses about limits and advantages of the methodology and presents interpretations of lifetime trajectories in terms of risk assessment.

Part I: Methodology to assess lifetime dietary exposure trajectories and associated health risks 1. Simulation of dietary lifetime exposure trajectories 1.1. Method 1: Juxtaposition of measured exposures according to the age Individual exposure trajectories can be simulated by juxtaposing dietary exposures of infants, children, adolescents and adults, according to their age.

The first method presented here requires knowledge of only age and dietary exposure to the considered substance, for a sample population (ideally representative of the general population). Such data may be generated through total diet studies. If the sample size of the surveys are insufficient, dietary exposures may be grouped according to age.

The exposure trajectory of a virtual individual is simulated in a stepwise fashion. At each step, from birth to the end of life, an exposure value is randomly selected within the available exposures of the corresponding age group. To select diversified but credible exposures, distributions may be fitted to dietary exposures for each age group. Then, exposure values are drawn at each step within the exposure distribution of the corresponding age group, instead of among measured exposures (Figure 1). This process is repeated 10,000 times to simulate a virtual population.

The main advantage of this method is that it allows accounting changes in food consumption according to age. The drawback is that it does not allow consideration of individual consumer profiles. Dietary exposure of any children may be juxtaposed with those of any adolescent and any adult, without considering dietary habits or individual characteristics.

Method 2: Study of dietary patterns

The second method addresses one of the limitations of the first, taking into consideration individual profiles by identifying groups of consumers from consumption surveys according to their dietary patterns. For example, a cluster analysis coupled with a principal component analysis or a nonnegative factorization matrix method could be used [START_REF] Bertin | Dietary patterns of French adults: associations with demographic, socio-economic and behavioural factors[END_REF][START_REF] Gazan | Dietary patterns in the French adult population: a study from the second French national cross-sectional dietary survey (INCA2) (2006-2007)[END_REF][START_REF] Marques-Vidal | Twenty-year trends in dietary patterns in French-speaking Switzerland: toward healthier eating[END_REF]. In this method, however, it is assumed that an individual keeps the same dietary pattern throughout his/her life. This assumption is not the most probable because it was shown that consumption evolves with age, even in adulthood [START_REF] Chen | Four major dietary patterns identified for a target-population of adults residing in Newfoundland and Labrador, Canada[END_REF][START_REF] Dekker | A spatial analysis of dietary patterns in a large representative population in the north of The Netherlands -the Lifelines cohort study[END_REF][START_REF] Gazan | Dietary patterns in the French adult population: a study from the second French national cross-sectional dietary survey (INCA2) (2006-2007)[END_REF][START_REF] Kriaucioniene | Dietary patterns and their association with sociodemographic factors in Lithuanian adult population[END_REF][START_REF] Wakimoto | Dietary intake, dietary patterns, and changes with age: an epidemiological perspective[END_REF]. However, this assumption allows studying lifetime impact of specific dietary patterns on exposure trajectories.

Once dietary patterns are identified, the method to simulate exposure trajectories is the same as the one presented previously. For each age group and dietary pattern, a distribution is fitted to the exposures. Then, for each individual, exposure values can be randomly drawn within the corresponding exposure distribution, according to dietary pattern and age (Figure 1). This process is repeated 1,000 times for each dietary pattern. This second method is mostly advantageous for studying the lifetime impact of some dietary patterns while taking into account the evolution of exposure with age. However, this method does not take into consideration individual characteristics over time.

Method 3: Study of sociodemographic and physical parameters

The third method aims to model individual profiles based on sociodemographic parameters and to predict the dietary exposure from individual characteristics. It is based on the hypothesis that dietary exposures are correlated with sociodemographic individual characteristics [START_REF] Bertin | Dietary patterns of French adults: associations with demographic, socio-economic and behavioural factors[END_REF][START_REF] Chen | Four major dietary patterns identified for a target-population of adults residing in Newfoundland and Labrador, Canada[END_REF][START_REF] Dekker | A spatial analysis of dietary patterns in a large representative population in the north of The Netherlands -the Lifelines cohort study[END_REF][START_REF] Gazan | Dietary patterns in the French adult population: a study from the second French national cross-sectional dietary survey (INCA2) (2006-2007)[END_REF][START_REF] Kriaucioniene | Dietary patterns and their association with sociodemographic factors in Lithuanian adult population[END_REF].

First, sociodemographic parameters which may potentially explain a part of the dietary exposure by age are identified through the literature. Once this list of parameters of interest is generated, a linear regression is performed to study the influence of each parameter on dietary exposure for quantitative parameters, and an analysis of variance is used for qualitative parameters. If the distribution of exposure is not normal, a transformation may be applied (e.g. logarithm transformation). Regressions must be stratified by age group to account for potential correlations between parameters and exposures extant during each life stage.

A combination of parameters is then selected among significant parameters by Akaike information criterion (AIC) with a backward stepwise process, for each age group. AIC is an estimator of the quality of a statistical model, with lower AIC values indicating better model fit. At each step of this process, an AIC is calculated using the combination of all predictors, and again after removing one of the predictors. If the AIC obtained after removing one predictor is lower than the AIC obtained with all predictors, this predictor is removed permanently and the process is repeated for the remaining parameters until it is no longer possible to decrease the AIC. In this way, only the combination of predictors that best explains the dietary exposure is kept, without over-fitting. The remaining parameters are known as "stratification parameters".

Next, a stratification trajectory is simulated for each stratification parameter: an evolution of the parameter is assessed from birth to age 80, for each virtual individual. Because some stratification parameters may be dependent on one other, correlations must also be taken into consideration. The correlation between two quantitative parameters is calculated using a Spearman coefficient. The correlation between two qualitative parameters is determined by a Cramer's V calculation and the correlation between a quantitative and a qualitative parameter is calculated by a correlation ratio, which compares the variance of the quantitative parameter in each class of the qualitative parameter.

Once all stratification trajectories of a virtual individual are built, the dietary exposure trajectory is simulated using a stepwise approach. A 95% prediction interval of the transformed exposure at time is predicted by regression from values of the stratification parameters at time . Then, a transformed exposure value is randomly drawn in a normal distribution with the 2.5 th and 97.5 th percentiles as the lower and upper bounds of the prediction interval. The final exposure of the virtual individual at time is the back-transformation of the drawn exposure (Figure 1). This process is repeated for life stage of each virtual individual in the virtual population.

Evolution of food contamination over time

In addition to the three methods presented above, the evolution of dietary exposures over time for each substance must also be considered. In fact, for some contaminants, exposures have evolved over time because of changes in dietary habits, bioaccumulation of the substance in the environment, developments in the production of the contaminant, regulations limiting its use or the development of new substitute substances. Methods presented here, however, consider dietary exposures computed at the same date, and thus assume constant food consumption and contamination over time.

If dietary exposure data over time are available, a correction function may be applied to exposure trajectories according to the virtual individual's date of birth.

If dietary exposures data over time are not available, it is possible to consider body burdens or environmental concentrations data as indicators. This information allows the determination of the evolution of dietary exposures using kinetics modelling. In fact, if the behaviour of the substance in the body or in the environment is known, it is possible to simulate dietary exposures which contributed to the observed body burdens or which resulted from the observed environment contaminations.

Let us consider that the body burden of an individual fits the equation:

1 ∆ , ∀ ∈ 1; 80 (1)
where is the body burden at age with 0 supposed to be equal to 0. is the elimination parameter of the considered substance at age , ∆ is the step time between 1 and , is the dietary intake measured nowadays for the age and is the correction factor of dietary exposure, depending on the generation and the age.

Therefore, if body burdens are known over time for a sufficient number of individuals for whom age and birth year are known, it is possible to determine the value of the correction function . With data, the system of equations is:

! , ! " ! , ! , 0 … $ , $ " $ , $ , 0 (2)
where is a body burden measured at for an individual born in the and is available in the literature. " is the body burden simulated according to the equation (1), using the correction function .

The function can then be determined by minimisation of the sum of squared of equations of the system (2) with the L-BFGS-B (extended Limited-memory Broyden-Fletcher-Goldfarb-Shanno)

algorithm. This algorithm of minimisation under constraints uses a limited computer memory and allows fast calculations. A possibility to approximate the function is to suppose that is a spline.

For example, if a cubic spline with 4 knots is selected, is thus a function of 4 parameters which can be determined by minimisation. This spline parametrisation allows numerous different shapes for the function and constraints could be imposed to the 4 parameters in order to have a plausible positive function .

Once the function is calculated, it is applied to exposure trajectories according to the virtual individual's birth year, to account for the evolution of food consumption and contamination.

Risk assessment from dietary exposure trajectories

health risk due to dietary exposure is typically assessed by comparing an exposure to a health based guidance value (HBGV), which is a conservative value derived to be protective of the most sensitive individuals in the general population. It is specific to substance, route of exposure and duration of exposure. If exposure is below HBGV during the considered period, the health risk may be considered unimportant. Otherwise, the health risk cannot be overlooked.

Because lifetime exposure trajectories are composed of numerous and various exposures, several comparisons with the HBGV are possible.

Mean exposures over life

A fluctuating exposure trajectory can be compared with the chronic HBGV by comparing the mean value of the trajectory over the life course with the HBGV value. This corresponds to comparing the area under the exposure trajectory with the area under the constant HBGV, (i.e. comparing the cumulative sum of the exposure trajectory with the HBGV multiplied by the lifetime).

However, averaging a lifetime exposure trajectory induces loss of information on the variability of exposure through life and on punctual exceedances of the HBGV. Indeed, even if the mean exposure through life is lower than the HBGV, this does not mean that there are not instances where the trajectory exceeds the HBGV. On the other hand, the mean trajectory may be higher than the HBGV because of few exceptionally large daily or weekly exposures, while almost all exposures are below the HBGV.

Exceedances of HBGV

In addition to the study of mean trajectories, the duration of exceedance of the HBGV by exposure trajectories must be analysed. This analysis can focus on consecutive periods, during periods of interest (e.g. developmental periods) or during the entire life (for accumulative substances).

Amplitude of exceedances of the HBGV may also be studied, in conjunction or not with the duration of exceedance.

The problem is then to determine the critical duration of exceedance, below which exceedances of the HBGV are not meaningful for consumer health. This critical duration depends on the kinetics of the chemical of interest and on data and method used to derive the HBGV. The interpretation of lifetime exposure trajectories in terms of risk assessment must thus be done on a case by case basis, for each substance.

Conversion

Interpretation of body burden trajectories

Health risk from body burden trajectories is assessed by comparing critical concentration values (CCVs), which represent the body burden value associated with an adverse effect [START_REF] Aylward | Integration of biomonitoring data into risk assessment[END_REF][START_REF] Who | Characterization and application of Physiologically Based Pharmacokinetic models in risk assessment[END_REF]. Mean body burdens through life may be compared with the CCV, with the same limitations as for the comparison between mean exposure and HBGV. Durations of exceedance of the CCV or the age at which the exceedances occurred can be studied. In fact, the study of body burden trajectories, as well as exposure trajectories, takes into consideration the specific periods of vulnerability (e.g. early childhood or pregnancy) during which chemicals may affect the development of the child in utero or during early life.

However, CCVs are often concentrations related to an incidence of an adverse effect. For cumulative substances like cadmium, because of the long elimination half-life, we consider that one exceedance of the CCV can induce an adverse effect, especially if the exceedance occurs during a specific period of vulnerability. If the body burden trajectory reaches the CCV, it is unlikely to quickly decrease.

Part II: Application to cadmium dietary exposure

Cadmium is a ubiquitous heavy metal naturally present in the earth's crust and is used widely in industry. For non-smokers, the main route of cadmium exposure is food (EFSA, 2009a). In the human body, it can trigger numerous adverse effects, such as kidney diseases, skeletal damages and cancers.

As a heavy metal, it bioaccumulates over an individual's lifetime, with a biological half-life between 10 and 30 years.

Simulation of lifetime exposure trajectories to cadmium

Cadmium lifetime trajectories were simulated from dietary exposures from two studies: the French , 2009;[START_REF] Fantino | Nutrient intakes in 2005 by non-breast fed French children of less than 36 months[END_REF].

Cadmium exposure trajectories were simulated using the three aforementioned methods, considering the middle bound censoring scenario; non-detected contamination values were considered equal to the half of the limit of detection and non-quantified contamination values were considered equal to the half of the limit of quantification.

Individuals were partitioned into age groups, with different dietary habits and social behaviours as defined by TDSs. The three first years of life were divided in 4 groups [START_REF] Jean | Dietary exposure to cadmium and health risk assessment in children -Results of the French infant total diet study[END_REF]:

-1 to 4 months: Children consuming first age infant formulae.

-5 to 6 months: Children consuming second age infant formulae.

-7 to 12 months: Children consuming infant formulae and beginning the food diversification with introduction of dairy products, fruits, vegetables, potatoes, meat, fish, eggs and added fats.

-13 to 36 months: Children consuming in addition to formula milk, chopped fruits and vegetables, dried vegetables and salt.

Children over the age of 3 were divided in 3 groups (ANSES, 2011):

-3 to 10 years: Children consuming more milk, dairy products, pastries and cakes and mashed and cooked fruits than adolescents. They attend to nursery and elementary schools.

-11 to 14 years: Adolescents consuming more dairy products, fruit compotes, biscuits and breakfast cereals decreases. They attend to secondary school.

-15 to 17 years: Adolescents consuming more savory snacks and alcoholic drinks increases.

They attend to high school.

Adults were divided in 5 groups: 18-24 years, 25-34 years, 35-49 years, 50-64 years and 65-79 years.

Method 1

Using Method 1, the only required information were age and weekly dietary exposure to cadmium for a sample of the general population. Exposures by age group were fitted to distributions to allow for larger variability of drawn exposures. Distributions were lognormal and random draws were restricted to the interval between zero and twice the maximum exposure measured in the TDS for the corresponding age group. Distributions of cadmium exposure by age group are provided in supplementary material (Part 1). Fittings were performed with the function fitdist() of the package fitdistrplus 1.0-9 in R.

Method 2

Method 2 required to know age, weekly food consumption and dietary exposure to cadmium for a sample of the general population. Dietary patterns used in this study were previously established for adults and children [START_REF] Gazan | Dietary patterns in the French adult population: a study from the second French national cross-sectional dietary survey (INCA2) (2006-2007)[END_REF] Among the seven dietary patterns determined in the adult population, and the six dietary patterns determined in the child population, five were common to both populations:

-"Mediterranean": Higher consumption of vegetables, oil, herbs, condiments and fish than the national average.

-"Sweet and processed": Higher consumption of milk, fruit juice, cereals, chocolate, pastries and yogurts than the national average.

-"Traditional": Higher consumption of potatoes, meat, charcuterie, alcoholic beverages, bread and coffee than the national average.

-"Snacker": Higher consumption of sandwiches, pizzas, sodas, crackers, rice and pasta than the national average.

-"Small eater": Consumption different of the rest of the population due to smaller consumed quantities but not because of the variability of consumed foods.

Because of the relative homogeneity of consumption of children under the age of 3, dietary patterns

were not identified for this age range in simulations. Virtual individuals were assumed to keep the same dietary pattern among the five patterns presented overhead from the age of 3 to the age of 80.

After the age of 3, dietary exposures were drawn according to the age and the dietary pattern,

similarly to what was performed for Method 1 but considering five populations with specific dietary habits.

Method 3

Method 3 required data on age, dietary exposure to cadmium and individual sociodemographic characteristics for a sample of the general population. In the present work, the different sociodemographic parameters studied were:

-Region of residence for children under the age of 3.

-Gender, body mass index (BMI), region of residence, household income, frequency of canteen meals and educational level of the head of the household, for children over the age of 3.

-Gender, BMI, region of residence, household income, marital status and educational level for adults.

Correlation tests between sociodemographic parameters showed that the gender and the BMI were correlated parameters for each age group older than 3 years, as well as the household income and the educational level.

Different considerations were made to construct trajectories of stratification parameters:

-Reference gender was randomly drawn with a probability of 0.5 to be female.

-Trajectories of region of residence and BMI were respectively simulated from the region and the BMI at the age of reference. Reference age was chosen to be the age for which the surveyed population was closest to the general population, in terms of sociodemographic parameters. In this study, reference age was 40 years old.

- for children under 3 because of its lack of significance in early childhood. Once BMI was computed, it was smoothed from 3 to 80 years old by the least squares method.

-Household income was assumed to be the same throughout childhood and throughout adulthood. Because the household income is not available for children under 3, it was considered starting at 3 years old. Income during childhood was drawn considering the distribution of household incomes in INCA2 for children. The income during adulthood was drawn considering the distribution of household incomes in INCA2 for adults.

-Educational level of the head of the household was considered for children over the age of 3.

It was assumed to be constant during childhood and was drawn according to the distribution of the different levels in INCA2 for children. Because household income and educational level were correlated parameters, the educational level of the head of the household was drawn according to the value of the household income during childhood in the household income trajectory.

-Educational level of the individual in adulthood was considered constant and was drawn according to the distribution of the different levels in the study INCA2 for adults. Because household income and educational level were correlated parameters, educational level of the individual was drawn according to the value of the household income during adulthood in the household income trajectory.

- were given dependently of gender or when only interval of exposure was given, the mean exposure was calculated. If the year of sampling was not available, the year of publication was considered and if sampling lasted several years, the sampling period was represented by a segment around the median year of sampling. Several differences were observed in cadmium intake with the European population over time (Figure 2). The first hypothesis to explain these observed differences is variability in the analytical methods used to quantify cadmium in food. Secondly, consumption surveys (i.e. food frequency questionnaires, 24-hour recalls, 7 days diaries, duplicate meal studies, etc.) varied from one study to another. Lastly, studied populations were not the same in all studies (e.g. age groups, genders, region of residence, socioeconomic class).

Despite the variability of cadmium exposures in Europe, exposures did not appear to vary with time.

The Spearman correlation coefficient was -0.42, which indicates a poor relation between the cadmium exposure and the year of sampling. Consequently, for this study, dietary exposures to cadmium were assumed constant over time and equal to those measured in the iTDS and the TDS2.

This assumption is supported by several studies that did not observed any temporal trend in blood cadmium concentrations from the 1980's to the 2000's (EFSA, 2009a).

Interpretation of exposure trajectories to cadmium

Mean exposures through life

Mean exposures through life were on average 1.23 μg/kg bw/week for both Methods 1 and 3 but with greater variability with Method 3 (Table 1).

Populations simulated with the second method were not comparable with the two other since they do not represent the general population. Five different populations (one for each dietary pattern)

were simulated. Differences of mean exposures through life were observed according to dietary patterns. On average, mean exposures were 1.07 μg/kg bw/week for individuals with the "small eater" pattern, and 1.25 μg/kg bw/week for individuals with "Mediterranean" or "traditional" dietary patterns (Table 1).

Exceedances of HBGVs

Exceedances of the chronic HBGV of 2.5 μg/kg bw/week were analysed (EFSA CONTAM Panel, 2011).

With the first method, durations of exceedance were on average 3.4 years, varying between 2.5 and 4.2 years. With the third method, durations were on average 3.0 years, varying between 0.2 and 9.4 years. Both methods led to similar mean durations of exceedance of the chronic HBGV. However, the variability was higher with Method 3 (Table 1).

Concerning dietary patterns, there were slight differences between durations of exceedance of the chronic HBGV. "Small eater" pattern individuals had on average exposure trajectories exceeding the HBGV during almost 2.2 years through life whereas "Mediterranean" pattern individuals had exposures exceeding the HBGV during an average of 3.6 years (Table 1). Durations of exceedance ranged from 1.6 years ("small eater" pattern) to 4.5 years ("Mediterranean" pattern).

Based on the literature, several threshold durations may be studied for exceedances of the chronic HBGV of 2.5 μg/kg bw/week:

- On the other hand, lifetime durations of exceedances of the subchronic HBGV of 0.5 μg/kg bw/day (ATSDR, 2012) were studied. On average, these durations were equal to 40 weeks with the first method of simulation of trajectories and 34 weeks with the third method.

Durations of exceedance of the subchronic HBGV had almost the same distribution regardless the dietary pattern, except for the "small eater" population (Table 1). They were around 41 weeks on average, and varying between 20 and 65 weeks. Population of "small eaters" had shorter lifetime exceedances of the subchronic HBGV: 26 weeks on average (from 8 to 43 weeks).

Several threshold durations may be studied for exceedances of the subchronic HBGV of 0.5 μg/kg bw/day:

-15 days, which corresponds to the definition of subchronicity for ATSDR and ANSES (ANSES, 2017b; ATSDR, 2017) -30 days, which is the definition of the duration of a long-term HBGV for US EPA (US EPA, 2011)

-23.3 years, which corresponds to the experimental duration of 12 months in rats, adjusting on the life span (i.e 3 years for rats and 70 years for humans). Even if time scaling between species is approximate because of the difference of developmental periods durations [START_REF] Sengupta | The Laboratory Rat: Relating Its Age With Human's[END_REF], this duration of exposure in rats highlight the gap between agencies definition of subchronicity and durations of experiments.

Populations with exposure trajectories simulated with Methods 1 and 2 had trajectories exceeding the subchronic HBGV during at least 30 days but during less than 23.3 years. 99.70% of the population simulated with the third method have exposure trajectories exceeding during at least 15 days, 98.87% during at least 30 days and 0.58% during at least 23.3 years. Depending on the considered critical duration of exceedance, conclusions in terms of health risk are very different.

Assessment of body burden trajectories

Parametrisation of the model

To convert dietary exposure trajectories into body burden trajectories, the PBTK model developed by [START_REF] Kjellström | A kinetic model of cadmium metabolism in the human being[END_REF] was used, with modifications by [START_REF] Choudhury | Urinary cadmium elimination as a biomarker of exposure for evaluating a cadmium dietary exposure--biokinetics model[END_REF] for the differences of absorption of ingested cadmium according to the gender.

In our model, cadmium intakes were those from exposure trajectories, multiplied at each time by the body weight. For trajectories simulated with Method 3, body weight was determined from the BMI trajectory used to simulate the corresponding exposure trajectory, as well as age and gender.

Because BMI was not pertinent for individuals under 3 years of age, body weights for those children To assess cadmium concentration in urinary creatinine, an equation estimating the weekly creatinine excretion according to age was added to the model (personal communication, Béchaux C.).

Simulation of body burden trajectories

A trajectory of cadmium concentration in the urinary creatinine was calculated for each individual of virtual populations simulated by all three methods. To consider inter-individual physiological variability, each parameter was randomly drawn for each simulation. Draws were performed in triangular distributions, where minima and maxima were bounds of ranges given by [START_REF] Kjellström | A kinetic model of cadmium metabolism in the human being[END_REF] and [START_REF] Choudhury | Urinary cadmium elimination as a biomarker of exposure for evaluating a cadmium dietary exposure--biokinetics model[END_REF], and modes were given fitting values. An additional coefficient of variation was added to the prediction of body weight to allow variations around the value obtained from the equation presented above. This coefficient was drawn in a normal distribution with a mean equal to 1, with 95% of values between 0.8 and 1.2. The coefficient was supposed to remain constant through life to avoid unrealistic body weight oscillations.

Sensitivity analysis

A global sensitivity analysis was performed to identify parameters that most influenced outputs of the model. The extended-FAST method [START_REF] Hsieh | Applying a Global Sensitivity Analysis Workflow to Improve the Computational Efficiencies in Physiologically-Based Pharmacokinetic Modeling[END_REF] was used to estimate the variation of the cadmium urinary creatinine concentration at the age of 40 explained by each input parameter, independently or in interaction with other parameters. The sensitivity analysis was performed using the function fast99() of the sensitivity package in R. This method generates 7

sets of parameters where 7 is the number of parameters analysed and is the length of the discretization of the space ( 100 . Moreover, to study the influence of the gender, the exposure trajectory and the BMI trajectory on the modelled cadmiuria, different scenarios were considered for the sensitivity analysis.

Sensitivity analyses were consistent across scenarios (i.e. using female or male, using mean, worst case or best case exposure trajectory). Input parameters influencing the most the cadmium urinary concentration at 40 were the fraction of cadmium intake retained in the intestinal walls (C5), followed by the age-specific rate constant for transfer of cadmium from kidneys to urine (C19) and the rate of transfer of cadmium from plasma to liver (C12). When C5, C12 and C19 increased, the cadmium urinary concentration increased as well. The detail of the sensitivity analyses is provided in supplementary materials (Part 7).

Validation of the model

The PBTK model was validated using cadmium concentrations from the ENNS study. The ENNS study measured the cadmium urinary concentration of 1939 adults in France, including 913 non-smokers, between 2006and 2007[START_REF] Fréry | Exposition de la population française aux substances de l'environnement -Tome 1[END_REF]. For each of these individuals, age, gender and BMI were known, in addition to the cadmium urinary concentration (personal communication). In order to validate our model, 10 exposures trajectories simulated with Method 3 were randomly allocated to each non-smoker individual of the ENNS study to simulate 10 individual body burden trajectories. Because gender and BMI were the only two variables filled out for lifetime trajectories and individuals of the ENNS study, exposure trajectories were allocated according to gender and BMI. For example, if one individual of the ENNS study was 40-year-old male with a BMI equal to 25 kg/m², exposure trajectories had to be simulated for a male for whom the BMI at the age of 40 was equal to 25 kg/m², more or less 5%.

The distribution of cadmium urinary concentrations simulated with the PBTK model fits well with concentrations measured in the ENNS study for the population of non-smoker adults (Figure 3). The PBTK model of [START_REF] Kjellström | A kinetic model of cadmium metabolism in the human being[END_REF] was previously validated with several cadmium concentration records (ATSDR, 2012;[START_REF] Choudhury | Urinary cadmium elimination as a biomarker of exposure for evaluating a cadmium dietary exposure--biokinetics model[END_REF][START_REF] Ruiz | Interpreting NHANES biomonitoring data, cadmium[END_REF]. Simulations of body burden trajectories for individuals of the ENNS study allowed validating changes made to the model (i.e. the equation of the body weight according to age, gender and BMI). In addition, these simulations also validated exposure trajectories simulated with Method 3 and the assumption that cadmium exposure remained constant over the past decades.

Interpretation

Mean lifetime evolutions of cadmium urinary concentrations

Mean lifetime evolutions of cadmium urinary concentrations are presented in Figure 4. Mean evolutions were very similar, regardless of the method used to simulate exposure trajectories. Upper curves represent a worst case body burden and were computed by considering the 97.5 th percentile of cadmium urinary concentrations in the simulated population at each step time. Lower curves represent a best case cadmium body burden and were computed by considering the 2.5 th percentile of urinary concentrations in the simulated population at each step time.

Maximum urinary concentrations

Distributions of the maximum lifetime cadmium urinary concentration were also similar across methods (Table 2). Maximum urinary concentrations were on average 0.51 μg/g creatinine with Method 1 and 0.48 μg/g creatinine with Method 3. With Method 2, maximum concentrations were on average 0.43 μg/g creatinine for individuals with a "small eater" dietary pattern and 0.50 μg/g creatinine for individuals with a "Mediterranean" or a "traditional" dietary pattern.

Mean age of virtual individuals at peak of urinary concentration was 74 according to Methods 1 and 3 and varied between 65 and 75 years old according to the dietary pattern with Method 2. Few individuals had a peak of cadmium urinary concentration between birth and the age of 2. This could be explained by the fact that dietary exposures were on average higher for children under 3 than for the rest of the population, due to the high ratio between food intake and body weight in the first year of life. Moreover, individuals with a peak of cadmium urinary concentration before 2 had significantly higher mean and maximum dietary exposures than the rest of the population between birth and the age of 2, partly due to their region of residence.

Exceedances of the critical concentration

Exceedances of the critical concentration of 1 μg/g creatinine were studied. This CCV is the lower confidence limit of the benchmark dose considered by EFSA to derive the chronic HBGV of 2.52 µg/kg bw/week (EFSA, 2009a).

Between 2.9% and 5.3% of the virtual population had a urinary concentration higher than 1 μg/g creatinine at least one week during their life, depending on the method used to simulate exposure trajectories.

For people having a body burden trajectory exceeding the critical concentration, the mean duration of exceedance was on average 14 years for Methods 1 and 3, with exceedances between 1 week and 47 years.

For populations simulated according to the dietary pattern, distributions of durations of exceedance of the CCV were more variable. For individuals with body burden trajectories exceeding the CCV of 1 µg Cd/g creatinine having a "Mediterranean" or a "snacker" pattern, the median duration of exceedance was around 12 years, with a maximum exceedance lasting 40 years. Individuals with a "traditional" or a "sweet and processed" pattern had a median duration of exceedance around 13 years, but the maximum duration of exceedance is 54.3 years for individuals with a "traditional" pattern, whereas it was 37.8 years for individuals with a "sweet and processed" pattern. Individuals with a "small eater" pattern had a lower duration of exceedance of the CCV compared to others (median duration of 10.8 years).

Regardless of the method used to simulate exposure trajectories, age at first exceedance of the CCV varied dramatically. Apart from some rare exceptions, the first exceedance of the 1 μg/g creatinine value did not occur before the age of 40. According to the virtual population, 66% to 89% of the first exceedances occurred after the age of 50, according to the virtual population.

Dose-response curve

The dose-response curve developed by EFSA (2009b) was used to make the connection between body burden trajectories and health risk. It links the concentration of cadmium in urinary creatinine with the level of β2M in urine.

Using the average dose-response curve, as well as the 95 th percentile of the interval around the curve, β2M trajectories of virtual individuals were simulated, especially for individuals with a body burden exceeding the critical cadmium concentration at least one week during their live. One example of cadmium urinary concentration trajectory and its corresponding β2M urinary concentration trajectory using the P95 dose-response curve is provided in supplementary materials (Part 8).

With Method 1, 5.2% of the population had cadmium concentrations higher than 1 μg/g creatinine at least one week in their lives (Table 2). The maximum β2M urinary concentration of these individuals varied between 81 and 1 150 μg/g creatinine, with a mean of 88 μg/g creatinine, when β2M levels were simulated using the mean dose-response curve. Using the P95 curve, maximum β2M concentrations ranged from 100 to 3 574 μg/g creatinine, with a mean of 138 μg/g creatinine (Table 3).

With Method 2, between 2.9% and 5.3% of the population had concentrations higher than 1 μg/g creatinine at least one week in their live, according to the dietary pattern (Table 1). Maximum lifetime β2M urinary concentrations of these individuals varied between 81 and 99 μg/g creatinine for individuals with a "small eater" dietary pattern, and between 81 and 3 424 μg/g creatinine for individuals with a "traditional" dietary pattern, when simulated using the mean dose-response curve.

On average, maximum β2M concentrations ranged from 107 to 243 μg/g creatinine according to the dietary pattern, when simulated using the P95 dose-response curve (Table 3).

With Method 3, 3.7% of the population had cadmium concentrations higher than 1 μg/g creatinine at least one week in their live (Table 1). Maximum lifetime β2M urinary concentration of these individuals varied between 81 and 2412 μg/g creatinine, with a mean of 95 μg/g creatinine, when β2M levels were simulated using the mean dose-response curve. Using the P95 curve, maximum β2M concentrations varied between 100 and 4826 μg/g creatinine, with a mean of 143 μg/g creatinine (Table 3). Different thresholds of β2M concentration were studied:

-Below 300 μg β2M/g creatinine which is a normal value, -Between 300 and 1 000 μg β2M/g creatinine for which tubulopathy may appear but may be reversible if the cadmium concentration decreases enough, -Between 1 000 and 10 000 μg β2M/g creatinine for which an irreversible tubulopathy may appear [START_REF] Bernard | Renal dysfunction induced by cadmium: biomarkers of critical effects[END_REF].

Considering the mean dose-response curve, with Method 1, 0.04% and 0.01% of the population had a maximum lifetime β2M urinary concentration higher than 300 μg β2M/g creatinine and 1 000 μg β2M/g creatinine, respectively. With Method 3, these percentages were 0.03% and 0.02%.

Considering the P95 dose-response curve, with Method 1, 0.14% and 0.06% of the population had a maximum lifetime β2M urinary concentration higher than 300 μg β2M/g creatinine and 1 000 μg β2M/g creatinine, respectively. With Method 3, these percentages were 0.12% and 0.03%.

With Method 2, only one individual over 1 000 with a "traditional" dietary pattern had a maximum β2M urinary concentration higher than 300 and 1000 μg β2M/g creatinine, considering the mean dose-response curve. Considering the P95 dose-response curve, one individual over 1 000 in each subpopulation except "small eaters" had a maximum β2M concentration higher than 300 μg β2M/g creatinine, and only one individual in subpopulations with "Mediterranean", "traditional" and "snacker" dietary patterns had a maximum β2M level higher than 1 000 μg/g creatinine.

Part III: Discussion and perspectives 1. Interpretation of lifetime trajectories in terms of risk assessment

Only a few HBGVs have been selected here for the risk assessment but numerous HBGVs have been developed to assess the health risk related to dietary exposure to cadmium (supplementary materials, Part 9).

Because health effects of cadmium are due to bioaccumulation in organs and tissues, they are more related to body burden than to external exposure. Moreover, external HBGVs have been derived

from CCVs, by assuming constant exposures through life and by using toxicokinetic models.

the age group over 18, durations of exceedances of the HBGV through adulthood could be under-or over-estimated.

Considering sociodemographic trajectories, several assumptions were made:

-Marital status was considered constant in each age group and was limited to five over adulthood. Moreover, the repartition of the different marital statuses in each age group was determined from the INCA2 study and was supposed to be constant through time. However, the rate of marriage has decreased by half and the age of first marriage has increased between 1970 and 2017 in France (INSEE, 2018).

-The probability of moving to another region at the end of each year was considered depending on the current region of residence and the age group, according to information about relocations in France between [START_REF] Sengupta | The Laboratory Rat: Relating Its Age With Human's[END_REF][START_REF] Serafino | Intergenerational transmission of disadvantage in the UK and EU[END_REF](INSEE, 2017)). Even if annual mobility rates have increased between 1970 and 2006, changes in region have remained relatively constant. The variation observed is mainly due to local moves which were not considered in trajectory simulations [START_REF] Donzeau | Residential mobility trends in France, 1973-2006[END_REF]. However, at the level of age groups, the mobility rate has changed, with more interregional moves for younger people and less mobility for older people. At the level of regions, mobility is complex, with regions that have become more attractive over time and others less. For instance, Paris area records increasing rate of departures, except amongst individuals ages 20-24 [START_REF] Baccaïni | Les flux migratoires interrégionaux en France depuis cinquante ans[END_REF]. Interregional mobility depends on age and generation, and cannot be accurately assessed due to lack of data and the evolution of data collection methods.

-Household incomes and educational levels were assumed to be constant during childhood and adulthood, with no link between situations during childhood and adulthood. However, it is possible to change socio-professional category over life and there is often an intergenerational correlation between educational and income levels [START_REF] Chusseau | Education, Intergenerational Mobility and Inequality[END_REF][START_REF] Serafino | Intergenerational transmission of disadvantage in the UK and EU[END_REF]. Nevertheless, the assumption of constant household income and educational level allows the study of the long-term impact of these parameters on dietary exposure.

-Between 3 and 17 years old, the frequency of canteen meals was assumed to be constant in each age group, and a potential between-age-group correlation was not considered due to lack of information. Even if changes in the frequency of canteen meals across age groups were known, the frequency is likely to be constant because each age group during childhood corresponds to one different school institution in France.

-Available sociodemographic and physical variables studied here did not completely explained the variability of exposure. However, because simulated exposures were drawn in prediction intervals, the non-explained variability of dietary exposure to Cd was considered.

It is also difficult to accurately estimate the evolution of exposure over time. It is known that dietary habits varied in last decades, at a global and a regional level, and will continue to change (Garcia- [START_REF] Garcia-Closas | Changes in food supply in Mediterranean countries from 1961 to 2001[END_REF][START_REF] Kearney | Food consumption trends and drivers[END_REF]. However, the diversity of diets and changes in consumption patterns makes assessment of this evolution very complex. Considering chemical exposures, a great variability in daily cadmium intakes was observed in the literature, within the same country, at a given period (Figure 2). This variability can be explained by differences in methodology in different studies, but this does not help in the assessment of the evolution of cadmium intake over time. Furthermore, the literature review on the evolution of cadmium intakes may not have been exhaustive as it was not a systematic review. So it is possible that there are other studies assessing cadmium intakes that were not included in this work.

Closas

Dietary exposures to cadmium through breastfeeding were not studied here. However, levels of cadmium found in breast milk were relatively low (5-10% of levels found in maternal blood) (ATSDR, 2012). Moreover, infant formulae contain more cadmium than breast milk (EFSA, 2009a), therefore the study of formula-fed infants is more protective.

In this study, only non-smoker individuals were assessed, to focus on the impact of dietary exposure.

However, smoking is a known important source of cadmium exposure. Body burdens of smokers would thus be higher than those simulated for non-smokers. Results computed here cannot therefore be applied to a general population, because nearly 32% of French adults declared smoking at least occasionally in 2017 [START_REF] Pasquereau | La consommation de tabac en France : premiers résultats du Baromètre santé 2017 [Tobacco consumption in France: preliminary results from the 2017 health Barometer[END_REF].

Simulated PBTK urinary concentration distributions fit better with measured concentrations for nonsmoking men than for non-smoking women ( In the study of β2M trajectories, the dose-response curve set by EFSA was applied without considering age. However, data used by EFSA came from people aged over 50. The relation between β2M and cadmium urinary concentrations may be different for infants, children and young adults.

Capabilities of methods for simulating lifetime trajectories

Method 2 can be used to study the lifetime impact of dietary pattern on exposure and body burden.

Thus, an individual with a "Mediterranean" dietary pattern exceeded the chronic HBGV on average 1.6 times longer than an individual with a "small eater" dietary pattern. Individuals with a "Mediterranean" or a "traditional" dietary pattern were those with higher mean lifetime exposures and longer durations of HBGV exceedances. This may be due to the fact that individuals with a "Mediterranean" dietary pattern consume more vegetables and that individuals with a "traditional" dietary pattern consume more potatoes than the rest of the population. For adults and children over 1 year old, vegetables and potatoes are foods that highly contribute to the global dietary exposure to cadmium (ANSES, 2011(ANSES, , 2016a)). Because individuals with a "small eater" dietary pattern eat all kinds of foods but in smaller quantities, this may explain their lower mean lifetime exposures and their shorter durations of HBGV exceedances.

Method 3 studies individual profiles, inducing more variability in exposure trajectories than Method 1. Some people simulated with Method 3 had higher or lower exposures than the rest of the population during long periods, due to their sociodemographic characteristics. This method may potentially identify at-risk subpopulations. According to regressions on the relation between cadmium dietary exposures and individual characteristics, parameters strongly associated with exposures were BMI, gender and region of residence. Individuals with higher BMI had lower exposures, men had higher exposures than women and individuals living in the region Ile-de-France had lower exposures than the rest of the population. More specifically, a man had a trajectory exceeding the chronic HBGV on average during 3.4 years, whereas this duration was 2.7 years for a woman. Similarly, an increase of 6 years of the time spent in Ile-de-France decreased the duration of exceedance of the chronic HBGV of one month on average through life. Moreover, even if it is not possible to validate the adequacy between simulate and real exposure trajectories, the validation of body burden trajectories proves that Method 3 adequately predicts exposure trajectories from individual characteristics.

Method 1 has not much added value compared with punctual assessment of exposures realised in TDSs. It allows the consideration of evolution of exposure with age but simulates lifetime trajectories which that do not correspond to any real individual profile.

For a bioaccumulative substance such as cadmium, the conversion of exposure trajectories into body burden trajectories allows us to assess the long-term impact of dietary exposures on urinary concentrations and renal activity. However, this risk assessment is dependent on the selected critical value. Considering the representative population simulated by Method 3, less than 0.2% of individuals had a β2M urinary concentration at a level reflecting a renal injury, but 3.7% exceeded the CCV of 1.0 µg Cd/g creatinine and 36.5% exceeded the CCV of 0.5 µg Cd/g creatinine.

Conclusions

Three methods to simulate lifetime dietary exposure trajectories were developed and applied to the case of cadmium, a bioaccumulative heavy metal with severe health implications. It was found that these simulations, considering individual profiles, were able to generate more variability of exposure trajectories than the classical approach and also identify factors influencing exposure. Whereas the classical risk assessment approach allows the identification of critical food contamination levels that may have an impact on regulation, modelling lifetime exposure trajectories provides information on individual characteristics impacting the exposure, and allows the assessment of the lifelong effects of specific behaviours on dietary exposure. Moreover, the lifetime approach allows estimating past as well as future exposures (considering some hypotheses), in contrast to the classical approach based on present data. Both approaches bringing useful information, they are both of interest in the context of public safety.

Different interpretations of lifetime exposure trajectories were proposed in terms of risk assessment leading to various conclusions. The most relevant seemed to be the internal approach using cadmium urinary concentration trajectories or β2M trajectories due to cadmium's bioaccumulative nature.

It is evident from the results of this study that a health risk due to exposure to cadmium in the general non-smoker population cannot be excluded.

In conclusion, the three simulation methods presented in this paper offer a more comprehensive way to assess dietary risk considering changes in eating habits with age, demographic and socioeconomic characteristics. Methods 1 and 3 were comparable because they refer to a virtual general population, whereas populations simulated with Method 2 were subpopulations with specific lifetime dietary habits.

Figure and table captions

Regardless of the method, a large part of virtual populations was exposed to levels of PCBs above the chronic HBGV of 2.5 µg/kg bw/week during several years and above the subchronic HBGV of 0.5 µg/kg bw/day during several months. Regardless of the method used to simulate lifetime exposure trajectories, critical urinary thresholds of β2M were rarely reached, even for individuals with cadmiuria above the critical concentration of 1.0 µg Cd/g creatinine.

  Abstract ...................................................................................................................................................

Figure 1 :

 1 Figure 1: Diagram of the trajectory construction mechanism for the three developed methods, based on the example of an age group

  infant Total Diet Study (iTDS) (ANSES, 2016b) and the French second Total Diet Study (TDS2)(ANSES, 2011). The iTDS was conducted by ANSES between 2010 and 2016 and focused on the dietary exposures to 500 substances including cadmium of non-breastfed children under the age of 3. The TDS2 focused on the dietary exposures to more than 400 substances including cadmium, between 2006 and 2011, for the French population over 3. Exposures were estimated over one week in the TDS2 and over 3 consecutive days in the iTDS. The consumption surveys used to estimate exposure in the TDSs reported age, gender, body weight and height, and several additional sociodemographic characteristics (e.g. region household income, marital status, number of children in the household, etc.) (AFSSA

  using a non-negative-matrix factorisation method coupled with a cluster analysis on food consumption data from study INCA2 (i.e. the consumption study used in the TDS2) which recorded consumption of 1 455 children and 2 624 adults in France during seven consecutive days between 2005 and 2007 (AFSSA, 2009).

Figure 2 :

 2 Figure 2: Evolution of European dietary cadmium intakes over time

  1 year, which corresponds to the definition of chronicity for ATSDR and ANSES (ANSES, 2015; ATSDR, 2017) -7 years, which is the definition of chronicity of US EPA and corresponds to 10% of the human lifetime (US EPA, 2011) -50 years, which is the duration of exposure considered for the derivation of the HBGV from the critical concentration of 1 μg/g urinary creatinine based on effects on the β2microglobuline level (EFSA CONTAM Panel, 2011).Because the maximum duration of exceedance of the HBGV was 4.2 years with Method 1, 4.5 years with Method 2 for individuals with a "Mediterranean" dietary pattern and 9.4 years with Method 3, no individual had an exposure trajectory exceeding the chronic HBGV during at least 50 years. Only 2% of the population simulated with Method 3 had exposures exceeding the HBGV during at least 7 years, and no individual with other methods. With Methods 1 and 2, the entire studied population had lifetime exceedances longer than 1 year and 93% of the population with Method 3.

  were computed from age and gender. The equation was obtained from body weights defined in the growth standard curves assessed by the WHO Multicentre Growth Reference StudyGroup (2006) and was validated on the population of the iTDS. After age 3, the equation between body weight and BMI, age and gender was obtained by regression from a population simulated with the software PopGen (McNally, Cotton, Hogg, & Loizou, 2015) and validated on the population of the TDS2. With this regression, 95% of simulated body weights were within a 20% margin of error of true measured body weights. Because the BMI was not involved in the simulation of exposure trajectories with Methods 1 and 2, an equation of mean body weight according to age and gender was used, instead of the equation presented previously. This equation was obtained by polynomial regression from individuals from TDS2, with an equation for children and another for adults. Ages of change of equation were determined to have the better fitting at intersections. Equations of body weight for the different methods are provided as supplementary materials (Parts 5 and 6).

  Simulated and measured geometric means were, respectively, equal to 0.270 [0.265; 0.273] and 0.27 [0.26; 0.28] μg/g creatinine. Simulated and measured 95 th percentiles were respectively equal to 0.70 [0.68; 0.73] and 0.79 [0.69; 0.89] μg/g creatinine. (All intervals provided in this paragraph are 95% confidence intervals).

Figure 3 :

 3 Figure 3: Distributions of measured and simulated cadmium urinary concentrations in the non-smoking ENNS population

Figure 4 :

 4 Figure 4: Mean evolutions of cadmium urinary concentrations through life according to the method used to simulate lifetime exposure trajectories (A) and according to the dietary pattern (B)

Figure 1 :Figure 2 :

 12 Figure 1: Diagram of the trajectory construction mechanism for the three developed methods, based

Figure 3 :

 3 Figure 3: Distributions of measured and simulated cadmium urinary concentrations in the non-

Figure 4 :

 4 Figure 4: Mean evolutions of cadmium urinary concentrations through life according to the method

  in a region, knowing the current region and age. Region of residence was considered only once a year. The region at reference age was randomly drawn according to the distribution of regions of residence in INCA2 for the age group 35-49 years old. Then, regions of residence at the age of 39 and 41 years old were drawn, knowing the probability to move in each region, according to region of residence at the age of 40 years. This Markov chain process was repeated from birth to 80 years old, with a different probability matrix for each age group. Probability matrices are provided in supplementary materials (Part 2).-BMI at reference age was drawn in the distribution of BMI in the INCA2 study for the age group 35-49 years old, according to gender. The BMI on week %&' 1 was drawn in the distribution of BMI of the corresponding age group and gender, in such a way that quantile

	of BMI at %&' 1 was in the interval ()*	+, -./0 123 4 0.01 ; )*	+, -./0 123 4

Considering region of residence, data on relocations between 2013 and 2014, according to the age and the starting region, were used

(INSEE, 2017)

. It was possible to determine the probability of moving 0.016. Similarly, the BMI at week %&' 1 was drawn in the distribution of BMI of the corresponding age group and gender, in such a way that quantile of BMI at %&' 1 was in the interval ()* +, -./0 123 4 0.01 ; )* +, -./0 123 4 0.016. This process avoids creating unrealistic oscillations of BMI in consecutive weeks. The process was applied for each week up to the age of 80 years old and the age of 3 years old. BMI was not considered

  and 64 years old if he/she was not married, in couple, divorced or separated between 35 and 49 years old (supplementary materials, Part 3). The same process was repeated for marital status from 18 to 24 and from 65 to 80 years old.1.4. Determination of the shape of food contamination over timeA review of several studies evaluating dietary cadmium exposure was performed. Studies in non-European countries were excluded because of the high differences in food consumption and in food cadmium contamination. Moreover, studies assessing the cadmium exposure of children or elderly people were excluded because of specific food consumptions. After this selection, 38 articles were studied, recording 56 different values of cadmium dietary exposures in different countries, at different dates. The list of articles is provided in supplementary materials (Part 4). Results in terms of daily cadmium intakes were illustrated in Figure 2. When cadmium exposures adjusted by body weight were available, values were multiplied by a mean body weight of 70 kg. When exposures

The frequency of canteen meals was considered by age group because groups 3-10 years old, 11-14 years old and 15-17 years old correspond to three different types of French educational institutions. For each age group, the frequency was drawn according to the distribution of the different frequency in the study INCA2 and in the corresponding age group.

-Marital status by age group was considered for adults. The marital status from 35 to 49 years old was drawn according to the distribution of the different status in the INCA2 study for the age group 39-45 years old. Marital status from 25 to 34 and from 50 to 64 years old were drawn according to the respective distributions of marital status in the study INCA2 for these two age groups, with logic rules. For example, an individual could not be divorced or separated between 50

Table 1 :

 1 Distribution of cadmium exposure and exceedances of the different HBGVs according to the method used to simulate exposure trajectories Intervals provided in the Table1correspond to minimum and maximum values. Results from Methods 1 and 3 were comparable because they refer to a virtual general population, whereas populations simulated with Method 2 were subpopulations with specific lifetime dietary habits. Regardless of the method, a large part of virtual populations was exposed to levels of PCBs above the chronic HBGV of 2.5 µg/kg bw/week during several years and above the subchronic HBGV of 0.5 µg/kg bw/day during several months.

		Method 1 Method 3	Method 2: Mediterra nean	Method 2: Small eater	Method 2: Snacker	Method 2: Sweet and processed	Method 2: Traditiona l
	Mean exposure through life (µg/kg/week)	1.24 [1.21 ; 1.28]	1.23 [0.83 ; 1.64]	1.25 [1.22 ; 1.27]	1.07 [1.05 ; 1.10]	1.18 [1.16 ; 1.20]	1.20 [1.18 ; 1.22]	1.25 [1.23 ; 1.27]
	Duration of
	exceedances of	3.35 [2.54	2.97 [0.25	3.55 [2.67	2.22 [1.58	3.35 [2.69	3.10 [2.37	3.18 [2.48
	the chronic	; 4.17]	; 9.39]	; 4.54]	; 2.81]	; 4.02]	; 3.85]	; 3.87]
	HBGV (year)
	Percentage
	exceeding the
	chronic HBGV	100	93.10	100	100	100	100	100
	at least 1 year
	(%)
	Percentage
	exceeding the
	chronic HBGV	0	2.13	0	0	0	0	0
	at least 7 years
	(%)
	Percentage
	exceeding the
	chronic HBGV	0	0	0	0	0	0	0
	at least 50
	years (%)
	Duration of
	exceedances of	40.25 [20	33.52 [0 ;	40.65 [22	26.24 [8 ;	40.13 [20	42.32 [26	42.80 [20
	the subchronic	; 64]	164]	; 61]	43]	; 63]	; 65]	; 64]
	HBGV (week)
	Percentage
	exceeding the
	subchronic	94.01	84.77	94.10	87.60	94.20	96.40	95.10
	HBGV at least
	15 days (%)
	Percentage
	exceeding the
	subchronic	3.09	7.46	3.00	3.20	2.20	4.50	2.50
	HBGV at least
	30 days (%)

Table 2 :

 2 Distribution of cadmium in urine according to the method used to simulate exposure trajectories Intervals provided in the Table 2 correspond to minimum and maximum values. Regardless of the method used to simulate

		of body burden trajectories
	4.1. Mean cadmium urinary concentrations through life
	Mean lifetime cadmium urinary concentrations were 0.27 μg/g creatinine, varying in [0.033; 1.37]
	with Method 1, 0.25 μg/g creatinine [0.034; 1.46] with Method 3 and between 0.23 and 0.27 μg/g
	creatinine [0.039; 2.18] with Method 2, according to dietary pattern (Table 2).
		Method 1 Method 3	Method 2: Mediterra nean	Method 2: Small eater	Method 2: Snacker	Method 2: Sweet and processed	Method 2: Traditiona l
	Mean cadmiuria through life (µg/g creat)	0.27 [0.033 ; 1.37]	0.25 [0.034 ; 1.46]	0.26 [0.044 ; 1.05]	0.23 [0.048 ; 0.99]	0.25 [0.039 ; 1.13]	0.26 [0.049 ; 1.00]	0.27 [0.064 ; 2.18]
	Maximum cadmiuria through life (µg/g creat)	0.51 [0.075 ; 2.51]	0.48 [0.072 ; 2.79]	0.50 [0.093 ; 2.16]	0.43 [0.091 ; 1.87]	0.45 [0.077 ; 2.15]	0.47 [0.093 ; 1.92]	0.50 [0.13 ; 4.61]
	Percentage
	exceeding the	5.22	3.70	5.30	3.00	2.90	3.80	4.10
	CCV (%)

exposure trajectories, lifetime concentrations of cadmium in urine were very close. For a part of simulated populations, the critical concentration of 1.0 µg Cd/g creatinine was reached at least once in a lifetime.

Table 3 :

 3 Distribution of β2M level in urine for individuals exceeding the CCV of 1 µg Cd/g creatinine at least one week

	through life
	Intervals provided in the Table 3 correspond to minimum and maximum values Results concerning Methods 1 and 3 were
	comparable because they refer to a virtual general population, whereas populations simulated with Method 2 were
	subpopulations with specific lifetime dietary habits. Regardless of the method used to simulate lifetime exposure
	trajectories, critical urinary thresholds of β2M were rarely reached, even for individuals with cadmiuria above the critical
	concentration of 1.0 µg Cd/g creatinine.

  Table4). For women, despite the fit in median concentrations between simulated and measured values, distribution of simulated concentrations was skewed slightly less to the right compared to measured concentrations in the ENNS study. This may be due to, among other things, a lack of sufficient variability of female parameters of the PBTK model.At the age group level, cadmium urinary concentrations of 18 to 39-year-old individuals were overall under-estimated. For 40 to 59 and 60 to 74-year-old individuals, lowest concentrations were slightly over-estimated and highest concentrations were under-estimated (Table4). The under-estimation of body burden of young people and the over-estimation of older people could be partly explained by the fact that absorption of cadmium may decrease with age (EFSA, 2009a), whereas it was considered constant in the model. However, even if the distributions of simulated concentrations were not identical to those measured, they were close enough for validating the robustness of the model to predict cadmium body burden.

	40-59-year-old	0.31 [0.30 ; 0.31] 0.31 [0.30 ; 0.33] 0.67 [0.63 ; 0.71] 0.79 [0.63 ; 0.95]
	60-74-year-old	0.40 [0.38 ; 0.41] 0.40 [0.36 ; 0.44] 0.87 [0.80 ; 0.95] 1.04 [0.87 ; 1.21]
		Simulated	Measured	Simulated	95 th	Measured	95 th
		geometric mean	geometric mean	percentile		percentile
	Women	0.31 [0.31 ; 0.32] 0.33 [0.32 ; 0.35] 0.74 [0.72 ; 0.78] 0.95 [0.85 ; 1.05]
	Men	0.18 [0.17 ; 0.19] 0.20 [0.18 ; 0.21] 0.44 [0.41 ; 0.47] 0.47 [0.40 ; 0.54]
	18-39-year-old	0.15 [0.14 ; 0.16] 0.19 [0.18 ; 0.20] 0.35 [0.33 ; 0.37] 0.44 [0.40 ; 0.48]

Table 4 :

 4 Distributions of simulated and mean cadmium urinary concentrations in the non-smoking ENNS study according to the gender and the age groupIntervals provided in the Table4correspond to 95% confidence intervals of the different geometric means and 95 th percentiles. Urinary concentrations of cadmium were higher for women than for men and increased with age. On average, simulated cadmiuria were similar to those measured in the ENNS study, whereas the model failed to predict the highest body burdens.

Table 1 :

 1 Distribution of cadmium exposure and exceedances of the different HBGVs according to the method used to simulate exposure trajectories Intervals provided in the Table 1 correspond to minimum and maximum values Results from

Table 3 :

 3 Distribution of β2M level in urine for individuals exceeding the CCV of 1 µg Cd/g creatinine at least one week through life Intervals provided in the Table3correspond to minimum and maximum values. Results concerning Methods 1 and 3 were comparable because they refer to a virtual general population, whereas populations simulated with Method 2 were subpopulations with specific lifetime dietary habits.

Table 4 :

 4 Distributions of simulated and mean cadmium urinary concentrations in the non-smoking ENNS study according to the gender and the age group Intervals provided in the Table4correspond to 95% confidence intervals of the different geometric means and 95 th percentiles. Urinary concentrations of cadmium were higher for women than for men and increased with age. On average, simulated cadmiuria were similar to those measured in the ENNS study, whereas the model failed to predict the highest body burdens.

Acknowledgements

We would like to thank Komodo Matta for providing language help during the writing process.

Fundings

This work was supported by Anses (CRD Anses / Oniris n°2017-CRD-09) and INRA (thesis scholarship co-financing agreement).

Consequently, considering CCVs instead of HBGVs addresses modelling limitations and does not necessitate assumptions on exposure scenarios. Therefore, it seems to be more relevant to assess the risk by using an internal approach: comparing body burden trajectories with CCVs.

The Human Biomonitoring (HBM) Commission ( 2011) has proposed a conservative concentration of 0.5 µg Cd/L urine for children and 1.0 µg Cd/L urine for adults as a protective value below which risk to health can be excluded. This value falls within the same order of magnitude as other CCVs and can be used in the same capacity.

For the population simulated from sociodemographic parameters, 3.7% of the population had a body burden trajectory exceeding the CCV of 1.0 µg Cd/g creatinine set by EFSA (2009a) but 36.5% of the population exceeded the CCV of 0.5 µg Cd/g creatinine set by ATSDR (2012) and ANSES (2017a).

Conclusions in terms of risk assessment thus varied markedly according to the considered CCV.

However, these results showed that body burdens of the population were within the same order of magnitude as the different CCVs and that dietary cadmium exposures should be reduced.

Limits of methods to simulate lifetime trajectories

This work presents three methods to simulate lifetime dietary exposure trajectories and proposes different interpretations of these trajectories in terms of health risk.

As for all modellings, however, these methods have biases and uncertainties that must be considered.

All random draws were performed in theoretical distributions, fitted to measured exposure data. In the case of cadmium, the chronic HBGV (=2.5 ng/kg bw/week) is at the end of the tail of the exposure distribution for adults. Consequently, if tails of exposure distributions are not well fitted for In summary, the advantages of using Methods 2 and 3 are that they allow us to identify the longterm impact of dietary patterns and sociodemographic profiles on dietary exposures and associated health risk.

Conflicts of interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.