food additives & contaminants -...
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Food Additives & ContaminantsEDITORS: Prof John Gilbert Prof Timothy Phillips
Department for Environment, Food and Rural Affairs Texas A&M UniversityCentral Science Laboratory College of Veterinary MedicineSand Hutton Department VAPHYork YO41 1LZ Mail stop: 4458 College StationUK TX 77843-4458
USAFAX: +44 (0)1904 462426e-mail: [email protected] [email protected]
Dr O VitracUMR Fractionnement des Agro-Ressources et EmballageINRA 614Moulin de la Housse51687 Reims cedex2FRANCE 7 July 2005
Dear Dr Vitrac
Exposure of consumers to substances from plastic packaging materials: assessment of the contribution of styrene from yoghurt pots – Vitrac et al(Manuscript Ref: 04-JG/FAC/090)
Thank you for returning your revised manuscript and for your responses to the referees comments. I am pleased to inform you that your paper is now accepted for publication. Nevertheless, I still feel that there is too much specialised mathematics in the paper which will be a ’turn-off’ for most FAC readers but will not ask you to make any further revisions.
I have forwarded your paper to the Publishers from who you will receive proofs (sent electronically as a PDF File) in due course, which you will need to check carefully. You will also need to look critically at the Figures when you get the proofs and ensure they are sized appropriately to maintain legibility.
Once typesetting and corrections to your paper has been completed it will be available in electronic form as PReVIEW on the Taylor and Francis web-site
http://www.tandf.co.uk/journals/titles/0265203X.asp
prior to publication in the Journal.
Kind regards
Yours sincerely
Prof John GilbertEditor
Exposure of consumers to substances from plastic packaging materials. 1.
Assessment of the contribution of styrene from yogurt pots.
Olivier Vitrac1, Jean-Charles Leblanc2
1UMR Fractionnement des Agro-Ressources et Emballage, INRA 614, Moulin de la Housse. 51687 Reims cedex
2. France.
Fax. 33-3-26-91-39-16
E-mail: [email protected]
2UR Méthodologies d’analyse du risque alimentaire , INRA, INAP-G, 16 rue Claude Bernard, 75005 Paris,
France
Abstract
A generic methodology for the assessment of consumer exposure to substances migrating
from packaging materials into foodstuffs during storage is presented. Consumer exposure at
household scale is derived from the efficient probabilistic modeling of the contamination of
all packed food product units (e.g. a yogurt pot, a milk bottle…) that are consumed by a given
household during one year. Exposure of given population is finally estimated by gathering the
exposure distributions of individual households respectively to suitable weights (conveniently
household sizes). Tractable calculations are achieved by combining both i) an efficient
resolution of migration models and ii) a methodology combining different sources of
uncertainty and variability. The full procedure is applied on the assessment of consumer
exposure to styrene from yogurt pots based on yearly purchases data of more than 5400
households in France (about 2 millions of yogurt pots) and an initial concentration of styrene
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in yogurt wall pots, which is assumed to be normally distributed with an average value of 500
ppm and a standard deviation of 150 ppm. Results are discussed regarding both the sensitivity
of the migration model to boundary conditions and household practices. By assuming a
partition coefficient of 1 and a Biot number of 100, the estimated median household exposure
to styrene calculated is ranged between 1 and 35 µg⋅day-1⋅person-1 (5th and 95th percentiles)
with a likely value of 12 µg⋅day-1⋅person-1 (50th percentile). It is found that exposure does not
vary independently with the average consumption rate and contact times. Thus, falsely
assuming an uniform contact time equal to the sale-by-date for all yogurts overestimates
significantly the daily exposure (5th and 95th percentiles of 2 and 110 µg⋅day-1⋅person-1
respectively) since high consumers showed quicker turnovers of their stock.
Key words: consumer exposure, packaging, styrene, risk assessment
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Notations
Roman symbols
Bi dimensionless mass Biot number [-]
eqFC concentration in food at thermodynamic equilibrium [mg⋅kg-1]
D diffusion coefficient [m⋅s-2]
kE individual (per capita) consumer exposure [mg⋅day-1⋅pers-1]
2i
it DFol×= dimensionless Fourier number related to the ith yogurt [-]
kN number of consumed yogurts for the kth household [-]
K partition coefficient [-]
F
P
V
V
F
PLρρ= dilution factor [-]
kP size of the kth household [-]
SD sale-by-date [days]
PV volume of the packaging material [m3]
FV yogurt volume [m3]
0c initial concentration in the packaging material [mg⋅kg-1]
i yogurt pot index [-]
k household index [-]
l yogurt pot thickness [m]
Sr safety ratio in assessed exposure (see 3.6) [-]
Vr variability ratio in exposure assessment (see 3.6) [-]
k household index [-]
0cs normalized standard deviation of 0c [-]
Ds normalized standard deviation of ( )log D [-]
it storage time of the ith yogurt [s]
*iv dimensionless migration rate [-]
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Greek symbols
Pr packaging density [kg⋅m-3]
Fr yogurt density [kg⋅m-3]
1. Introduction
Motivation
Over the last decade, chronic exposure to chemicals ingested through diet has exerted an
increasing impact on technical, political and legislative decisions (e.g. regulations, industrial
practices,…). Despite considerable improvements in quantification limits for measuring
substances in food, it is nevertheless currently not possible to identify all potential sources of
intake of a given chemical over lifetime (Lau and Wong 2000). A major difficulty is that large
variations of contaminant concentrations in foodstuffs may occur according to industrial and
household practices (Svensson, 2002).
The contamination of food products through packaging materials illustrates the stakes for both
contamination risk and exposure assessments. The accumulation of contaminants from food
packaging materials in packed food products occurs through a migration process during all
steps of the product life including: during process and distribution , during storage by both
retailers and households. As a result, the final concentration in a packed food product will
depend on factors that are specific to the product (composition, rheology, volume ratio
between food and packaging) but also on its overall history (time, temperature, vibrations,
possible stirring). For products having shelf-lives longer than a few days, the storage time by
consumers may be larger than the time for processing and distribution, so that the
contamination of food products – when they are consumed – may be strongly influenced by
consumer behaviors and practices (Vitrac et al. 2005).
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Typical accumulation kinetics for non equilibrated systems are related to an effect of storage
time ( st ) proportional to stb with 0.5 1b£ £ . When the process responsible for the release of a
given contaminant is controlled by internal diffusion (without limiting effect of the packaging
volume), one gets 12
b = at constant temperature (Cranck 1975). When the limiting process is
either a reaction or an interfacial transport, b is expected to be close to 1 (Treybal 1980,
Vergnaud 1991). These kinetic considerations illustrate that the distribution of storage times
at household scale may modify drastically the range of the contamination of packed food
products. Indeed for a same overall food consumption, it is expected that a household
including high consumers or doing regular purchases consumes less contaminated packed
food than a household doing infrequent purchases. For products regularly consumed, such a
scatter between household practices can be responsible for an inter-household variability in
food contamination, which may be higher than the intra-household variability. Possible
correlations between consumption patterns and storage times, and consequently between
consumption and contamination, imply that a probabilistic approach at house scale should be
preferred to a coarse grained assessment of individual risk assuming that modeling quantities
– contamination and consumption levels – are independent. An additional argument in
supporting detailed description of contamination at the moment of consumption is to analyze
separately the effects of variability and uncertainty on quantitative risk estimates.
The current paper proposes a modular risk assessment model dedicated to the quantitative
assessment of exposure to substances originating from the plastic layer in contact with food
items, which may obey to general principles defined by Huggett et al. (1998). For this
purpose, a full probabilistic modeling driven by the knowledge of both the migration of
assessed substances and of the consumption is devised. Unlike other empirical methods based
on Monte Carlo simulations (Hamey and Harris 1999, Gauchi and Leblanc 2002, Lambe
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2002, Gibney and van der Voet 2003), such an approach would be not as limited by the
availability of contamination data and by strategies used to handle undetectable levels, false-
negative, false-positive results and outliers.
Background
The interest of combining the knowledge of both physical processes and food pathway
conditions to predict the migration of packaging substances was early discussed by Chatwin
and Katan (1989). They suggested that such an approach could partly replace long and
prohibitive surveys of contamination in real food products if the degree of variability in the
migration occurring in real life should be undertaken. The predictability of the contamination
of foodstuffs by substances migrating from plastics in contact is achievable through a physical
formulation of the migration process between and food items (European Commission 2003).
The use of physical models to replace contamination data in exposure assessment was first
proposed by Vermeire et al. (1993) for both occupational and consumer exposure and
specifically by Lickly et al. (1995) for food contact materials. It has been recently proposed to
handle conveniently inherent sources of uncertainty on initial concentration in plastic
materials, physiochemical properties (diffusion and partition coefficients), geometry factors,
contact times, food texture via a stochastic resolution of transport equations (Vitrac and
Hayert 2005). It is worth to notice that this formulation strives for likely or “best” estimators
of modeling quantities (e.g. diffusion coefficients) rather than overestimates as detailed by
Begley et al. (2005). Indeed, the concept of conservatism as it used either in point exposure
estimates or for compliance determination introduces a priori assumptions and choices that
deliberately yield overestimates of chronic exposure and that do not separate the effects of
both variability and uncertainty (Leber 2001, Vitrac 2003).
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The main restrictions for the application of full probabilistic approaches are the lack of food
consumption data including correspondence with packaging formulations (starting substances,
typical concentrations…) and uses (food matrices, geometry…). The proposed dimensionless
formulation detailed in Vitrac and Hayert (2005) provides reliable strategies to handle
incomplete information on packaging usage and food storage.
The first strategy relies on the assumption of the invariance of some distribution shape
parameters related to geometric quantities, contact times, transport properties. As a result,
only likelihood values the main scale parameters are required with enough accuracy.
Important distribution parameters such as contact times can be either measured or
reconstructed. This methodology was applied to estimate the possible risk of contamination of
12 real packed food products by a phenolic antioxidant starting from the yearly purchases of
6,422 households in France (Vitrac et al. 2005).
In this work, we refine the approach by calculating the probability density function (pdf) of
the contamination of all food units that are consumed by a given household during one year.
The probabilistic approach of the contamination of each product unit is here mainly related to
the uncertainty in both the physical quantities that control the migration and in the initial
concentration within the considered packaging materials.
Contribution
The current work focus on the assessment at household scale of the exposure to styrene
related to the consumption of yogurt pots. The exposure to styrene offers a high
methodological concern since the link between the migrating substance (styrene) and its use in
styrene based materials is clearly established. Besides, styrene oxide has been believed to
promote lung tumors in mice and could promote cancer of the forestomach in rats at high
doses (Cohen 2002). The International Agency for Research on Cancer (1994) evaluates the
styrene-7, 8-oxide as “possibly carcinogenic to humans” (group 2B). A provisional maximum
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tolerable daily intake of 40 µg⋅kg-1 bodyweight⋅day-1 has been set by the joint FAO/WHO
Expert Committee on Food Additives (World Health Organization 1984). An accurate
appraisal of exposure to styrene at household scale and focused on both vulnerable and high
consumers of dairy products such as children is therefore also highly desirable.
The contamination of all yogurt pots consumed by 5,473 households during one year is
derived from their yearly volume and frequency of purchases. Individual exposure at
household scale is calculated by weighting results according to household sizes. The assessed
exposure at the scale of tested population is finally compared by gathering the information
available at household scale (proposed strategy) and by crudely combining the sampled
distributions of contamination and consumption at the scale of the tested population
(conventional strategy). With the developed example on styrene, we additionally identify
some important gaps in knowledge and we are able to suggest some risk mitigation strategies
for a specific packed food product of concern.
2. Quantitative methodology for exposure assessment
The granular approach for exposure assessment of households, which is used in this work, is
illustrated in figure 1. This detailed risk scheme assumes that members of a given household
consume only yogurt pots purchased and stored by themselves. It is assumed i) that there is no
interaction between households (no products exchange and no crossed consumption) and ii)
that all purchased yogurts are consumed. Yogurts consumed in institutional catering or fast
food chain are not considered here. As a result of the migration process, the contamination of
yogurts by styrene increases during storage. The contribution of the storage period on
exposure is studied here.
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The concentration in styrene in each yogurt at the date of its consumption is calculated for a
given contact time and a probable distribution of the initial concentration in wall pots. The
exposure at household scale is assumed to be equal to the cumulative amount of styrene that
has migrated into all consumed yogurts.
The time list of purchases of each household is extracted from long marketing national
surveys and is used as input in the risk assessment procedure. Since the date of consumption
of each yogurt is unknown, contact times are reconstructed as point estimates from likely
scenarios of household storage. Due to a significant uncertainty in predicted styrene
concentrations in yogurts, the contamination of each consumed yogurt is calculated via a
probabilistic approach that takes into several sources of uncertainty. The resulting
concentration in each yogurt is known via a distribution of probabilities. Finally, all these
distributions are combined to derive the exposure at household scale. The so-calculated
exposure is also a distribution, which represents both the different sources of uncertainty and
the variability due to different contact times between consumed yogurts.
2.1 Exposure quantification at household scale: kE
Exposure at household scale is expressed in mg⋅day-1⋅pers-1 and inferred from the cumulative
amount of migrant ingested during one year within by the considered household and averaged
over the household size. For a householdk , of size kP , the exposure of the “typical”
consumer, kE , that consumes kN yogurts contained in individual pots of weight 0 iM , is
efficiently calculated by factorizing kE as a sum of independent variables:
( ), , ,*0
1
1365
ki
NFo Bi K Leq
k i F i ik iE M C v
P == × × ×
× å (1)
where the notation iX stands for the quantity X taken for the thi pot (i.e. food product unit).
*v is the migration level, it is ranged between 0 (no migration) and 1 (thermodynamical
equilibrium) and is related to 4 dimensionless numbers: the dimensionless time, Fo , the ratio
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between internal and external resistances to mass transfer (also known as mass Biot number),
Bi , the partition coefficient between food and packaging materials, K , the dilution factor, L ,
defined as the ratio between the mass of packaging and food materials P
F
VV
P
F
Lrr
= . The
quantity eqFC is related to the concentration in yogurt at thermodynamical equilibrium (when
* 1v = ) and is derived from a mass balance in styrene assuming an initial concentration 0c
(weight/weight) in the packaging material:
01 1
eqF
cC
K L
=+ (2)
Equations (1) and (2) are valid for any food, any contaminant and any packaging material. The
only assumptions are that: i) the contamination is controlled by the diffusion of the
contaminant from the packaging material into the food product, ii) the packaging material is
the only source in the considered contaminant, iii) no contaminant losses occur during the
storage. Besides, as previously discussed in Vitrac (2003), equation (1) assumes that K and L
have a much higher effect on eqFC than on *v for similar products with similar packaging. The
effect of possible variations in K and L are thus neglected in *v but are taken into account in
eqF iC via equation (2). Since no information is available of the value of Bi for each food
product unit, a typical value is assumed for all units.
For yogurts sold in France, additional simplifications are possible since most yogurts
packaged in thermoformed polystyrene pots have a same weight of 125 g (volume 120 ml).
This description is still currently valid and was valid at the year of considered purchases
(1998). In addition, according to the French legal definition of yogurts, such labeled products
are only made from coagulated milk resulting from the lactic fermentation by only two strains:
Lactobacillus bulgaricus and Streptococcus thermophilus. From these considerations,
equation (1) is realistically simplified as:
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10
( ), , ,0 *
1365
ki
NeqFo Bi K LF
k ik i
M CE v
P =
×= ×
× å (3)
2.2 Migration model: ( ), , ,* iFo Bi K L
iv
The migration level, *v , also defined by eqF FC C , where FC which is the concentration in food,
is calculated from a general physical model of the migration similar to the one used in Vitrac
et al. (2005). The main assumptions are detailed in Vitrac (2003) and in Vitrac and Hayert
(2005). For plastic materials non-subjected to swelling, the transport of additives in polymer
matrices is assumed to be controlled by a molecular diffusion process. At the interface
between food and packaging materials, the pervious contact between food and packaging is
assumed to be controlled by a generalized Robin boundary condition, which accounts for both
a possible partition effect on both sides of the interface and an external mass transfer
resistance controlled by the texture of the food product. All properties are assumed to be
constant during storage.
As depicted in figure 2, the expected value of *v of a yogurt is expected to vary significantly
with the dimensionless contact time (or Fourier number), 2D tFol×= , and the Biot number,
h lBi
D×= where D is the diffusion coefficient (with SI units in m2·s-1), t is the contact time, l
is the packaging thickness and h is the mass transfer coefficient on the food side of the
packaging-food interface (with SI units in m·s-1). Bi is the mass Biot number expressing the
ratio of mass transfer resistances on both sides of the food-packaging interface. For solid food
products, Bi is expected to be close to 1 whereas it is greater than 1 for liquid food products.
The limit condition Bi ® ¥ corresponds to a situation where only an internal resistance to
mass transfer within the packaging material occurs. For a same Fo value, v * is increasing
with Bi up to a limit curve that depends on K and L values. In particular, for Fo values
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lower than 1 (case of yogurts), the overall migration kinetics change from a variation of v *
proportional to the square root of time to a first order kinetic when the Bi ® ¥ condition is
changing towards 1Bi>® . Consequently, the shape of the distribution of exposure values is
expected to vary in a significant extent with the considered boundary condition. In solid like
food materials (related to low Bi values), the effect of contact time is expected to be higher
than in liquid like food materials (related to high Bi values) and would consequently lead to
more spread values of exposure at household scale.
In the current study, a likely value of D , noted D , is assumed to be available and applied to
all consumed packed products (i.e. yogurts packed in PS pots). By contrast, since few
estimates of h are available for real food products and in realistic conditions of storage, only
magnitude orders of Bi are considered. The true value of D of the considered packaging (i.e.
yogurt pot) remains however unknown since it can vary significantly with the type of
polystyrene (formulation and processing) and the temperature of storage (typically between
2°C and 10°C). The sources of uncertainty in the D value are taking into account via a
stochastic resolution of the migration model discussed in sub-section 2.4. Since the migration
level does not vary regularly with Bi , the uncertainty in the true Bi value due to possible
different food textures (e.g. gelified or stirred yogurts) is tested by comparing results obtained
for a set of typical Bi values.
2.3 Assumptions for the reconstruction of contact times between food and packaging
material: 1..i NkFo
=
Likely dimensionless contact times defined by 1..
1.. 2i Nk
i Nk
D tFo
l=
=
×= , are derived from contact
times, 1..i Nkt= , reconstructed from the frequency and the amount of household purchases as
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recorded in marketing databases. The methodology used to reconstruct 1..i Nkt= related to each
food product unit (i.e. yogurt pot) is similar to the approach described in Vitrac et al. (2005)
and applied to 10 different real food products. The contact time due to household storage is
defined as the time between the date of purchase and consumption. Since only the date of
purchase is known, the date of consumption is estimated assuming a regular consumption
between two consecutive purchases. Two scenarios are considered:
Scenario H1: all yogurts bought at the previous purchase date are consumed by the considered
household before the date of the next purchase of yogurts;
Scenario H2: the number of consumed yogurts between two consecutive purchases cannot
exceed the number of purchased units at the date of the last purchase. According to this
scenario, an accumulation of yogurts is possible between consecutive purchases. They are
consumed in the order “first bought, first consumed” so as to minimize the overall duration of
storage.
Since scenarios H1 and H2 do not take into account the contribution of distribution and
retailing on contact times, an upper bound, noted scenario H3, is provided by assuming that all
products are consumed at the sale-by-date, that is:
1.. 2i Nk
D SDFol=
×= (4)
where SD is the contact time at the sale-by-date.
2.4 Probabilistic description of exposure
The probability density function (pdf) of kE is derived from the pdfs of independent quantities
eqFC and 1 ki Nv = K . The distribution of eq
FC values is only related to the distribution of 0c between
all packaging materials. The main source of residual styrene in the wall of yogurt pots is the
thermal degradation of polystyrene due to partial depolymerization, its residual concentration
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is assumed to be concentrated around a likely value controlled by the processing technology of
polystyrene. Thus, the dimensionless quantity 0 0 0/c c c* = is assumed normally distributed
with an average of 1 and a standard deviation, noted 0cs , where 0c is the likely concentration
in the packaging material. Besides, the distribution of each 1 ki Nv = K is related to the uncertainty
in the corresponding dimensionless contact times 1i NkFo
= K written as:
1 1i Nk i Nk
Fo Fo Fo= =
*= ×K K
(5)
where *Fo D* = is a normalized random variation of contact times mainly related to the
uncertainty inD value. As discussed in sub-section 2.2, this uncertainty includes both the
unknown variability in the PS matrix and possible change in temperature during storage. The
random contribution is assumed to be log-normally distributed as ( )log Norm(1, )DD s* : . This
choice is discussed in Vitrac and Hayert (2005).
Mass balance considerations between food and packaging materials demonstrated that 1 ki Nv = K
are Beta distributed with parameters ( )Beta ,i ia bb b (Vitrac and Hayert 2005). This approach is
illustrated in figure 2 for 3 distributions of Fo values, corresponding to a same prescribed
distribution of *Fo values and 3 different Fo values. It is underlined that the mode of Fo pdfs
coincides with Fo . The Since iab and ibb values vary continuously with Fo for a same Ds
value, they are efficiently non-linearly interpolated from pre-calculated tabulated data.
Since { } 1 ki i Nv * = K are not identically distributed, the sequence 1
kN
iiv *
=å is besides not expected to be
normally distributed even for high consumer patterns with large kN values. The pdf of 1
kN
iiv *
=å is
efficiently calculated as a kN convolution product of independent 1 ki Nv = K densities. As
convolutions are equivalent in Fourier space to simple multiplications with associativity and
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commutativity properties, the final result is efficiently calculated iteratively by partitioning
previously calculated densities in same order as their variance. At each step, this algorithm
aims at calculating two-by-two the convolution of densities with similar variation coefficient.
Each two-by-two convolution product is numerically calculated starting from FFT (Fast
Fourier Transforms) transforms of previously scaled densities. Discrete FFT transforms were
performed with a normalized cut-off frequency of 1/216. Since all calculations can be
effectively calculated in parallel for all households and all packaging units, no Monte Carlo
sampling is required. This approach is therefore particularly conservative of all pertinent
information available at household scale.
Finally, the distribution of product of random normalized quantities 01
kN
ii
c v* *
=
æ ö÷ç ÷× ç ÷ç ÷÷çè øå is inferred
from the distribution of its log-transform written as ( )10 0 101
log logkN
ii
c v* *
=
æ ö÷ç ÷+ ç ÷ç ÷÷çè øå , which is
straightforwardly calculated as the convolution product of ( )10 0log c* and 101
logkN
iiv *
=
æ ö÷ç ÷ç ÷ç ÷÷çè øå
densities.
2.5 Initial assumptions and purchase data
Both contact time and consumption at household scale are based on yearly volume and
frequency of purchases of a panel of 5,473 households (including 14,649 persons) (SECODIP
databases, 1998, France; Combris et al. 2000). Eighty thirteen percents of the French market
of yogurts are estimated to be covered by the present survey (SECODIP sources). All
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households belonging to the tested panel performed more than 8 purchases per year. Only
purchases of yogurt in plastic containers with net weight about 0.125 kg are considered. Such
restrictions ensure that almost packaging materials were made in PS. According to former
conditions, 221,190 purchases including 1,930,257 yogurt pots are analyzed.
The values of parameters involved in the exposure assessment procedure are summarized in
table 1. Thermodynamical and transport properties as well as an initial concentration in
styrene monomer ( 0c ) of 500 ppm are chosen according to our own expertise and accordingly
to values given by EC-DG SANCO D3 (2003). It is emphasized that the chosen value of 0c is
3 times lower than values assessed 29 years ago in polystyrene (Withey, 1976) but is of a
same magnitude order as values found by Murphy et al. (1992). Geometry and mass related
quantities are measured starting from typical yogurt products available on the French market.
Values of distribution shape parameters, 0cs and Ds , are assumed to introduce realistic sources
of variability in the analysis. This choice is discussed in Vitrac and Hayert (2005) and in
Vitrac et al. (2005).
2.6 Distribution of individual exposure at the scale of tested population (5,473 households)
Since equation (3) does not separate children and adults, males and females, the calculated
individual exposure was averaged over the household size. When the size of a given
household varied during the considered year, the maximum size of the household was used.
The likely distribution of individual exposure at the scale of all the 5,473 examined
households is derived by accumulating (gathering) all the corresponding individual exposure
distributions calculated at household scale according to a suitable set of weights. In absence of
pertinent information, weights proportional to household sizes are applied. This approach
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provides likely estimates of the French population exposure to styrene resulting from the
consumption of yogurts.
It is emphasized that the probabilistic estimation of exposure combine two different scales –
food product unit and household scale – and different kind of distributions - delta-
distributions, discrete and continuous ones. At the scale of each food product unit, contact
times are thus delta distributed, whereas concentrations in food are continuously distributed.
At household scale, distributions are either discretely (e.g. contact times) or continuously (e.g.
v * or individual exposure) approximated.
In order to identify trends and deviations between results different strategies relying on the
properties of each explicative variable are used. Contact times, used as explicative variable at
the scale of tested population, are arithmetically averaged over all product units consumed by
each household. Consumption rates and delays between purchases, used as explicative
variable, are averaged over the observed time frame (1 year) utilizing a root mean square
average operator. By contrast, the individual exposure to styrene is mainly discussed
according to either its 50 or 95th percentile values. The 50th percentile defines indeed the likely
individual exposure value and the 95th exposure value defines an upper bound that takes into
account the effects of both “unknown” sources variation and uncertainty (e.g. initial
packaging formulation, material structure, storage conditions).
3. Results and discussion
3.1 Comparison of contact times reconstructed according to H1 and H2 scenarios
Results present first how differ household averaged contact times reconstructed according to
scenarios H1 and H2. Figure 3 compares averaged reconstructed contact times derived from
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scenarios H1 and H2. Scenario H1 leads to values asymmetrically distributed between 2 and 16
days with a likely value of 5 days. On the contrary, scenario H2 yields more widely and
symmetrically distributed values between 3 and 22 days with a likely value of 12 days. Due to
possible stock creation, H2 generates strictly higher values than H1 ones. The discrepancy
between both values varies significantly according to household practices. It rises up to 10
days when the expected contact time increases. Low consumption rates give more particularly
both higher contact times and higher discrepancy between averaged reconstructed values.
3.2 Distributions of individual exposure within a household and between households
Individual exposure distributions are presented for some households belonging to typical
consumption patterns and compared to the weighted distribution that is representative for all
the tested population. The main objective is to identify the possible range of variation of the
individual exposure value due to tested scenarios, differences in consumption, unexplained
variations between households, uncertainty in the amount of styrene that may migrate.
Figure 4 plots the cumulative distributions of individual exposure for households belonging to
a similar consumption pattern for all combinations of tested conditions
( ) ( )1 2 3H ,H ,H 1, 100,Bi Bi Bi´ = = ® ¥ . Three typical patterns are considered, based on the 5th,
50th and 95th percentile values of gathered individual consumption rates. For each pattern, the
cumulative distributions of individual exposure of 20 households – with averaged
consumption rates distributed closest to the targeted value – are plotted. Due to the skewness
the distribution of consumption rates (Vitrac et al. 2005) and the finite size of the household
population, only the two last patterns consist in homogeneous samples. The cumulative
distribution of individual exposure accumulated over all the tested population (called
“gathered” distribution) is also depicted. Typical values are collected in table 2.
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In particular, the conservative combinations ( )3H 1, 100,Bi Bi Bi´ = = ® ¥ illustrate the effect
of the variation in consumption pattern alone on the exposure dispersion. For a given Bi
value, scenario H3 is indeed responsible for an uniform contamination of all consumed
yogurts.
3.2.1 Gathered distributions of exposure: towards an estimation of the exposure of the general
population
The spreading of the exposure “gathered” over all examined households is assessed by the
ratio between the 95th and 5th percentile values. For similar tested conditions, the spreading is
higher when realistic contact times are considered (figures 4a, 4b, 4d, 4e, 4g and 4h) than
when a rough estimation of contact times (i.e. sale by date) is assumed (figures, 4c, 4f and 4i),
with ratios ranged between 1.5 and 2 decades and ranged between 1 and 1.5 decades
respectively. Upper percentile values calculated with scenario H3 are however up to 2 to 5
times higher than those calculated with scenario H1 and H2 (table 2). It is hence concluded that
accounting for contact times between yogurts and their packaging materials at household scale
modifies significantly the estimation of the individual exposure to styrene of the tested
population.
Since all reconstruction scenarios account for similar uncertainties in 0c and D values, the
bias between the “household” approach (i.e. scenarios H1 and H2) and the “global” approach
(i.e. scenario H3) is only related to the variability in storage practices between households. It is
also demonstrated that the introduction of realistic assumptions combined with an additional
source of uncertainty on storage practices (i.e. discrepancy between H1 and H2 scenarios) does
not increase the whole uncertainty but contributes to a more realistic estimate of an upper
bound of the exposure for the whole tested population.
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All 9 “gathered” distributions of exposure have similar shape (asymmetric distributions with a
right decreasing tail) but whose scale values change significantly with the tested condition. At
the scale of the whole tested population, the lowest median exposure, 0.3 µg⋅day-1⋅pers-1, is
obtained with the condition ( )1H 1Bi´ = . The condition ( )3H Bi´ ® ¥ gives the highest
median value, about 35 µg⋅day-1⋅pers-1. As a result, the tested conditions introduce
discrepancies in exposure estimates as high as expected variations within the tested population
(up to 2 decades). The differences between tested conditions will be discussed further but it is
noticeable that assuming unlikely contact times, as scenario H3 does, leads to a positive shift
of exposure values that is higher when Bi values are higher. Such effects illustrate the time
dependence of exposure estimates on the migration process and consequently on household
practices.
3.2.2 Typical distributions of exposure at household scale
Individual exposure distributions at household scale, corresponding to the 5th, 50th and 95th
percentiles of consumption rates, are distributed along the “gathered” exposure scale with
median values that coincide approximatively with the 5th, 50th and 95th percentiles of the
“gathered” exposure values. As a result, individual exposure and consumption rate values
appear highly correlated together. As expected, the dispersion of median individual exposure
is minimal under scenario H3 (figures 4c, 4f and 4i). On the contrary, the dispersion is the
highest for low consumption rates and scenario H2. Results summarized in table 2
demonstrate also that variability between households is higher (up to a factor five) than the
uncertainty (lower than a factor 2) defined by the ratio between the 5th and 95th percentiles
values of the individual exposure. It is consequently demonstrated that other factors, such as
equivalent contact times at a reference temperature, must be taken into account to achieve
realistic exposure estimations to styrene originating from yogurt pots.
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In this study, the effect of time is not concealed by the considered sources of uncertainty:
either initial concentration in the food packaging material or in the diffusion coefficient. In a
similar way, substituting a reconstruction scenario (either H1 or H2) does not modify
dramatically the conclusions. Only the parameter Bi modifies drastically the expected
dynamics of the migration by changing the limiting transport and the corresponding dynamic
of the contamination of packed food materials.
3.3 Dispersion of household-scale estimated exposure values among the tested population
In order to emphasize on variations between household exposures, figure 5 plots the
distributions of the 50th (likely exposure) and 95th (exposure including uncertainty) percentile
values of styrene exposure estimated at household scale among the tested population (5473
households). The effects of all combinations of tested conditions
( ) ( )1 2 3H ,H ,H 1, 100,Bi Bi Bi´ = = ® ¥ are depicted. The corresponding exposure values at the
maximum of probability are gathered in table 3.
Variable contact times (figures 5a, 5b, 5d, 5e, 5g and 5h) yield distributions of 50th and 95th
percentile exposure values with very similar shapes. The distributions are asymmetrical and
exhibit a decreasing tail. They are conveniently approximated by log-normal distributions. By
contrast, scenario H3 (figures 5c, 5f and 5i) generates distributions presenting a left increasing
tail, which cannot be fitted by log-normal distributions. The alike continuous distribution is a
particular form of generalized Beta distributions. This discrepancy in the shape reveals the
additional effect of contact times on exposure estimates. For a same Bi value, assuming a
similar contact times for all yogurts (scenario H3) shifts drastically the distributions towards
higher exposure values. As a result, the mode of the distribution predicted by scenario H3 is
higher than 90 % of values calculated under H1 or H2.
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In details, distributions of either 50th or 95th percentile values are derived from a homothetic
transformation with a factor ranged between 1.2 and 1.6 (see table 3). This ratio is a measure
of the uncertainty in the “likely” exposure value inherent to possible variations in initial
concentration and to the uncertainty in the true diffusion coefficient. By choosing the 95th
percentile exposure value as reference, the likely exposure at household scale varies between
0.4 and 64 µg⋅kg-1⋅pers-1 depending on the tested conditions. Scenarios H2 and H3
overestimates the likely exposure calculated from scenario H1 by a factor ranged between 1.5
and 2.1, and between 2.6 and 4.9, respectively. The overestimation is higher when the effect
of time on yogurt contamination, and therefore on exposure, is almost linear (i.e. when 1Bi>® )
.
The parameter Bi combined with contact times influences significantly the likely exposure.
The exposure is increased by a factor ranged between 35 and 66 when it is increased from 1 to
an infinite value. The case 1Bi = is unlikely as it would assume that the mass transfer
resistance is as high within the yogurt than within the packaging material (from the Bi
definition, it would be stated that the diffusion of styrene in yogurt is only 100 times higher
than in polystyrene). On the opposite, the case Bi ® ¥ is also poorly realistic as it assumes
that the yogurt is a perfectly stirred liquid. It is however realistic to envision different Bi
values between stirred (expected high Bi values) and gelified yogurts (expected lowBi
values), probably about one decade. Since mass transfer coefficients between food and
packaging materials are poorly described in the literature, the choice 100Bi = seems an
acceptable compromise for all cases.
The choice of the partition coefficient, K , is not discussed in this paper as it is an apparent
physicochemical property, which is poorly documented. In addition, it is known to be highly
variable according to the composition of yogurt (mainly due to the fraction of lipid fraction,
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maximum 4% w/w on a wet basis) and the possible separation of gel and liquid phases during
storage of yogurt (exudation, gel dissolution). A value of 1 is assumed as an upper bound of
physically realistic values, but results can be straightforwardly extrapolated to other K values
(i.e. K <1) from algebraic equation (2). As an indication, values of K between crystal
polystyrene and different foods are given by Till et al. (1982). It must be noted that a similar
transformation or correction is not possible with Bi because it acts non-trivially and non-
linearly on the contamination of food products.
3.4 Comparison of calculated values with previously published exposure estimates
Few estimations of lifetime exposure to styrene from dietary intake have been published in the
literature comparatively to the large amounts of available data on the migration of styrene into
food and food simulants. According to the investigations of Tang et al. (2000) conducted in
Germany, if all consumed milk products (average consumption rate about 0.338 kg⋅day-1⋅pers-
1) and fat products (average consumption rate 0.072 kg⋅day-1⋅pers-1) were packed in styrene
materials, causing a contamination in styrene ranged between 5 and 30 µg⋅kg-1, the
corresponding daily intake would reach 2 – 12 µg⋅day-1⋅kg-1. In the particular case of yogurts,
the British Ministry of Agriculture Fisheries and Food (1983 and 1995) reports a broader
range of styrene concentrations in yogurt pots that were sampled on the market, with values
between 1 and 200 µg⋅kg-1. By comparison, simulated contamination of yogurt pots assigned
in the current exposure assessment procedure are ranged between 10 and 350 µg⋅kg-1
(respectively 5th and 95th percentile value) for the likelihood condition H2× 100Bi = (see
Vitrac et al. 2005 for details). Svensson (2002) considers that a styrene intake of 15-30 µg⋅kg⋅
pers-1 due to the contact of food with styrenic materials would be a realistic estimate for highly
exposed consumers. Average exposure would range from 0.2 to 9 µg⋅day-1⋅pers-1.
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As a result, the 95th percentile exposure value predicted by the current full probabilistic
approach, that is 20 µg⋅day-1⋅pers-1, under the likely condition H2× 100Bi = , is realistic and
possibly consistent with previous studies and in particular for high consumers. According to
this last estimation, exposure to styrene caused by the consumption of yogurts in polystyrene
materials would contribute significantly on the total exposure to styrene estimated to be
between 18.2 and 55.2 µg⋅kg⋅pers-1 reported by Tang et al. (2000) From this observation and
for particular consumers, the ingested amount of styrene could have the similar magnitude as
the inhaled amount. In particular, it is worth to notice that the overestimated exposure (95th
percentile of the household-scale estimated exposure) varies significantly between
households. Under the likely condition H2× 100Bi = , 5% of the most exposed households are
exposed to values above 60 µg⋅kg⋅pers-1 (figure 5).
By comparison, the predictive methodology proposed by Lickly et al. (1995), relying on
migration modeling and consumption factors and applied to a wide range of products, leads to
an average styrene exposure values of 9 µg⋅day-1⋅pers-1 for the US population. According to
this study, styrene exposure related to yogurt pots represented 31 % of the total exposure from
polystyrene food packaging. Concentration in yogurts were calculated assuming a hot fill
(leading to a contact of 30 min at 65°C) of containers and followed by long term storage (60
days) at 4°C.
The raw comparison of simulated results with previously estimates of styrene exposure is
difficult in practice. First, because previous studies were not focused on really consumed
yogurts (i.e. sampled in households) and because significant differences in the consumption of
yogurts and therefore in storage practices are expected between Countries, even within the
EU. Differences in the legal definition of yogurt must be also underlined, as the French
definition of yogurts is very restrictive regarding the fermenting strains (see paragraph 2.1).
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Secondly, surveys (Withey 1976, Withey and Collins 1978, Gilbert and Startin 1983, Ministry
of Agriculture, Fisheries and Food, 1983, 1995 and 1999), which collect contamination data,
do not report generally the conditions that make it possible to compare results with similar
mass balances (via equation (2)) and kinetic considerations (see section 2.2). The type of
yogurt (composition, texture, and volume) and packaging (thickness, residual concentration in
containers in styrene and in plasticizers) and the duration of contact are rarely available. In
addition, contrary to the study conducted by Lickly et al. (1995), it is often unclear whether
samples were subjected to hot fill, conservative conditions of storage or not (e.g. storage at
8°C or 10°C during 40 days rather than few days or weeks at temperatures ranged between 2
and 4°C).
The use previously published migration data into food simulants (Davies 1974, Varner S. L.
and Breder 1981, Miltz and Rosen-Doody 1984, Snyder and Breder 1985, Linssen et al. 1991,
Murphy et al. 1992, Lehr et al. 1993, Lickly et al. 1995) as alternative to contamination data
are also questionable. Indeed, migration into oil would be a too severe migrant condition as it
is suspected to plasticize packaging materials in polystyrene and consequently to increase the
apparent diffusion coefficient of styrene (Milz and Rosen-Doody 1984, Linssen et al. 1991).
On the opposite, aqueous or acidic simulants, as low viscous liquids, are not satisfying as they
may generate underestimated K values (too much optimistic scenario) and may drastically
increase the yielded Bi value (too much pessimistic scenario). This effect was experimentally
assessed by Till et al. (1982) using radio labeled styrene monomer. Finally, from equation (2),
one must also notice that migration levels assessed in food simulants for a particular L value
(e.g. 6 dm2 of packaging material in contact 1 kg of food) cannot be introduced “as is” into
exposure assessment procedures and must be corrected to match realistic dilution factors.
Previous comments suggest that it would be preferable to use calculated diffusion and
partition coefficients from the literature instead of raw contamination data that may not
directly related to real cases. The probabilistic approach of the migration developed in Vitrac
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and Hayert (2005) and used in this work can be used to extrapolate the contamination and
therefore the consumer exposure to real conditions of storage ,while taking into account the
inherent uncertainty/variability in published results. As an example of uncertainty, Till et al.
studies (1982 and 1987) demonstrate that the diffusion coefficient of styrene in polystyrene
was independent on the concentration in styrene whereas Miltz and Rosen-Doody (1984)
showed a dependence of the diffusion coefficient with the residual monomer concentration.
Similarly, the effect of mineral oil as possible plasticizer of styrene container (Jickells et al.
1994, International Life Sciences Institute 2002), which may modify diffusion coefficients by
a factor ranged between 5 and 25 (Licky et al. 1995) can be analyzed and introduced in the
exposure assessment as initial uncertainty in D values.
3.5 Correlations between contact times, purchase practices and individual exposure
Possible correlations at household scale between model quantities are analyzed this sub-
section. General recommendations for the development of either robust or simplified
strategies are finally discussed by comparing results derived from the full approach at
household scale and from rough approximations.
Previous results suggested that highly exposed consumers would not only be related to high
consumers but also to particular purchase and storage practices. Since it is expected that
highly consumers are more likely to minimize their storage time and their stock volume, this
part analyzes conditions that modify significantly the 95th percentile exposure value calculated
at household scale. Once again, it is emphasized that this study does not seek absolute
reference values of consumer exposure to styrene but assesses the effects of combined sources
of uncertainty or variation in household behaviors on exposure estimates derived from a full
probabilistic approach and a set on initial inputs (see table 1).
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3.5.1 Correlations between consumption rates and contact times
Since contact times are expected to be related to consumption rates, figure 6 plots on a log
scale the apparent correlation between contact times and averaged individual consumption
rates for both scenarios H1 (figures 6a and 6c) and H2 (figures 6b and 6d). The individual
consumption is expressed in number of packaging units (pots of 125 g). All scattered data are
averaged over all yogurt pots consumed during one year by each household. The surface of
each symbol is proportional to the 95th percentile of the cumulated individual styrene
exposure. In addition, since the concentration in styrene and subsequently exposure are
expected to vary significantly with the assumed resistance to mass transfer at the interface,
both results inferred from the extreme boundary condition 1Bi = (figures 6a and 6b) and the
likely boundary condition 100Bi = (figures 6c and 6d) are also depicted.
Similar conclusions are derived from both contact time scenarios. As expected, contact times,
ranged between 8 and 22 days, are maximum when consumption rates are minimum. Below
0.1 pot⋅day-1⋅pers-1, contact times are not correlated with consumption rates. For average
consumption rates ranged between 0.1 and 2 pot⋅day-1⋅pers-1, an increase in consumption rate
is related to a significant reduction in contact times. For a same consumption rate, the
variability between households is however very significant; it is ranged between 1 and 12 days
under scenario H1 (figures 6a and 6c) for a typical individual consumption rate of 1 pot (1
yogurt) per day. For a same consumption pattern, these heterogeneities in contact times
suggest significant related variations in styrene exposure.
Both possible combined effects of consumption and storage practices on the individual
exposure to styrene originating from yogurt pots are illustrated by the orientation of symbols
with similar size ((i.e. Related to similar exposure values). High exposure values are in
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particular related either to high consumption rates or to long contact times. It is noticeable that
the spreading of exposure values is similar when consumption rate is the only variable
parameter (i.e. when the contact time is fixed) and when contact time is the only free
parameter (i.e. when the consumption rate is fixed). In other words, individual exposure
cannot be realistically estimated by accumulating an amount of styrene that would correspond
to a particular contact time and consequently that would not vary between households. This
conclusion is particularly illustrated in figure 5, where scenario H3 generates distributions of
95th exposure values that are highly dissimilar in shape. A same bias will occur if exposure to
styrene is only based on the measured concentrations in styrene of yogurts that are sampled on
the market or that are subjected to non realistic storage conditions.
In details, the 4 tested conditions lead to very different scales for the estimated 95th percentile
exposure values. The lowest range of exposure values, 10-2 and 2 µg⋅day-1⋅pers-1, is derived for
scenario H1 associated with boundary condition 1Bi = (figure 6a). The highest range, 0.7 and
75 µg⋅day-1⋅pers-1, is obtained for scenario H2 associated with 100Bi = (figure 6d). Based on
scenario H1, the likely situation corresponds to an average consumption rate of 0.25 pot⋅day-1⋅
pers-1 and a contact time of 5 days. This situation corresponds to exposure ranges of 0.4-1 µg⋅
day-1⋅pers-1 and 10-40 µg⋅day-1⋅pers-1 respectively to boundary conditions 1Bi = (figure 4a) and
100Bi = (figure 4c). Scenario H2 related to a likely contact time of 12 days leads to intervals
of 1.5-2.5 µg⋅day-1⋅pers-1 and 20-40 µg⋅day-1⋅pers-1 respectively to boundary conditions 1Bi =
(figure 4a) and 100Bi = (figure 4c).
3.5.2 Identification of household practices that possibly increases the exposure to styrene for a
same consumption rate
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As previously detailed, exposure to styrene increases globally with consumption rate. For a
same consumption pattern, household practices, which may affect contact times, can also
worsen exposure. Two parameters influencing contact times are investigated independently:
the averaged volume of purchases (figure 7) and the delay between purchases (figure 8). For
each figure, the scatter of 95th exposure values is plotted versus each explicative value for both
scenarios H1 and H2 and both boundary conditions 1Bi = and 100Bi = . The surface are of
each symbol is proportional to the average consumption rate. A significant correlation with
the explicative variable is identified by an orientation of the scatter.
The exposure increases significantly with the average volume of purchases (figure 7). Since
symbols with a similar size (i.e. related to a similar consumption pattern) are also oriented
along the scatter, it is hinted that this effect is partially independent on consumption rate. High
exposures are thus a consequence of both high consumption rates and high purchase volumes.
Figure 8 generates more complex results. The delay between purchases is globally poorly
correlated to exposure. According to the global orientation of the scatter, the exposure seems
decreasing when the delay between purchases increases. This global effect is accompanied
with a reduction in symbol size, which corresponds a simultaneous reduction of the
consumption rate when the delay between purchases increases. In details, an apposite trend is
discernible for high consumption rates showing by contrast an increase in exposure when the
delay between purchases is increasing. For a same high consumption rate ranged between 2
and 10 pots⋅day-1⋅pers-1 , a variation in the delay between consecutive purchases from 2 day to
20 days increases the individual exposure by a factor ranged between 3 and 7. High
consumption rates and doing infrequent purchases are both worsening factors. The effect of
consumption rates appears at median consumption rates but is indiscernible for very low
consumption rates.
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For a same consumption pattern, figures 7 and 8 demonstrate that the average delay between
purchases and the volume of purchases may modify household exposure in all considered
scenarios and conditions. At low consumption rates, the effect of the volume of purchases
dominates while the average delay between purchases is one of the main dominating factor at
high consumption rates. The last effect is expected to be higher if storage is prolonged beyond
28 days.
3.6 Comparison of realistic exposure estimates with simplified quantifications
The simplification of the current approach may be of high concern for domains that require
clear conclusions without reflecting accurately the reality, for instance: risk assessment
regarding a specific application or usage based on worst case scenarios, guidance for further
detailed sanitary survey based on a classification of packaged products. These domains require
conservative conclusions that ensure enough safety margins for the consumer, that is to say:
that introduce overestimations above the previously identified aggregated range of uncertainty
and variability. The addressed questions are therefore what could be the amplitude of the
required safety range/margin ? what could be the appropriated simplifications ?
Within the general framework of the proposed methodology, figures 9 and 10 analyze the
effects of two exposure approximations on exposure estimates: time aspect of migration are
first neglected and all yogurts are consumed at the sale-by-date (figure 9); secondly, the
external resistance to mass transfer is additionally neglected (figure 10). These effects are
analyzed as correlation plots, where realistic estimates calculated for all combinations of
( ) ( )1 2H ,H 1, 100,Bi Bi Bi´ = = ® ¥ are plotted on a log-log scale against corresponding
approximated ones, respectively ( ) ( )1 2H ,H 1, 100Bi Bi´ = = (figure 9) and ( ) ( )1 2H ,H Bi´ ® ¥
(figure 10). Since all tested approximations overestimate the expected exposure, all
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approximated results are below the straight line. The distance to the line y x= depicts the
corresponding bias or the equivalent safety margin when “worst case” scenarios or conditions
are applied. To illustrate how the bias may fluctuate between consumption patterns, the
surface area of each symbol is proportional to the average consumption rate. Two percentile
values of exposure are plotted : 50 and 95th. It is underlined that the 95th percentile value takes
into account the uncertainty in the real contamination value of yogurts.
At first sight of figure 9, the scatter of 50 and 95th percentile values are spread in a direction
almost parallel to the straight line y x= . The scattering along y rises when the expected
exposure increases, but is noticeable that the ratio between the overestimate and the maximum
corresponding expected value (predicted with realistic and/or detailed assumptions) remains
almost constant when the exposure increases. In other words, assuming that all yogurts are
consumed at the sale-by-date provide a safety ratio regarding the most exposed person, noted
Sr . Sr is independent of the assumed true exposure and varies between 1.4 and 2 depending on
the considered boundary condition and the considered percentile value. Since the additional
storage time due to handling and retailing is disregarded in both scenarios H1 and H2, Sr
ranges may be comparable to the uncertainty in contact times before household storage.
Deviations with similar magnitudes are observed between exposure values estimated either
according to scenarios H1 or H2, or according to 50th and 95th percentiles.
In details, for a same exposure overestimate, Sr is significantly lower than the ratio between
the lowest and the highest expected values. The latter ratio is noted Vr and it is related to the
effect of the variability of behavior between households. From this interpretation, scenario H3
overestimates slightly the expected exposure of the least exposed consumer by a factor up to
one decade and defined by S Vr r× . The overestimation is particularly higher when the exposure
or the consumption rate is high. This trend observed for very different boundary conditions,
1Bi = and 100Bi = , confirms that scenario H3 is only realistic for low consumers while it
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deviates significantly from the likely averaged exposure for regularly consumed products. In
particular, it is shown that an analysis not performed at household scale, as scenario H3, does
not take into account that households with high consumption rate are less exposed due to
quicker turnovers of their stock. This effect is identified in figure 9 by vertical gradients in
symbol sizes.
The sensitivity to contact time scenarios is characterized by S Vr r× values lower than 10
verifying the following inequality S Vr r< . By contrast, the sensitivity to boundary conditions,
as recapitulated in figure 10, is characterized by higher total deviations S Vr r× (up to 30 for
1Bi = , figures 10a and 10b) and a different inequality: S Vr r³ . As a result, the Bi value must
be chosen with care if realistic exposure estimates are required. When only exposure
overestimates are required, the appropriated simplifications depend mainly on the food
texture.
For solid food (figures 10a and 10b), the value Bi ® ¥ provides a sufficient margin ( S Vr r>>
) so that the variability between households (contact times) and other sources of uncertainty
(initial concentration, diffusion coefficient) may be disregarded.
For liquid or semi-liquid food (figures 10c and 10d), the condition Bi ® ¥ generates safety
margins, Sr , about 2, which are of similar magnitude as the inter-household variability Vr and
the uncertainty in contamination values (defined by the ratio between the 50th and 95th
individual exposure values). Since the condition Bi ® ¥ does not overestimate dramatically
the migration level (figure 2), the choice of Bi ® ¥ seems an appropriate alternative for food
materials with low viscosities when no pertinent information is available on realistic Bi
values. Neglecting the sources of uncertainty (initial concentration and diffusion coefficients)
would underestimate the 95th expected exposure by a factor 2 which cannot be envisioned
without a significant source of overestimation in addition to the safety margin provided by the
assumption Bi ® ¥ . For example, neglecting the variability between households by assuming
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a similar contact times for all yogurts would additionally overestimate the expected exposure
by a factor 3 to 5 on average (figure 9).
In solid food materials that include a liquid phase, as a supernatant or an exudate, the choice
of high Bi values may also be of interest when the risk assessment includes the consumption
of the liquid surrounding the solid food.
As a rule of thumb, the choice of additional overestimations combined with the approximation
Bi ® ¥ is not encouraged, since all sources of uncertainty (in both 0c and D values, Bi
guess, reconstructed contact-times) and the expected variability in storage practices have
similar effects on exposure for a same averaged consumption rate. The particular combination
of approximations total contact time equal to the sale-by-date and no external resistance to
mass transfer would reflect no reality. Indeed, this extreme exposure would correspond to
unlikely associations of practices by consumers that aim at promoting mass transfer between
food and its packaging material such as storage at high temperature (or long term storage)
associated with a mechanical modification of food texture (e.g. mixing). Such estimates do
not fulfill with consistency requirements for risk assessment but can be of high concern for
risk managers to demonstrate that, for a given consumption rate (e.g. 1 kg), a great security
margin exists between the maximum physically realistic accumulated exposure and the dose
that is potentially considered dangerous by toxicologists. Thus, from the cumulative densities
functions plotted in figures 4e and 4i, assuming scenario H3 and Bi ® ¥ , when the reality
would match with scenario H2 and 100Bi = , leads to overestimate the gathered exposure by a
factor up to 8.
4. Conclusions
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This work describes a multiscale approach to assess the exposure of consumers to substances
originating from the plastic layer in contact with food. Since at the most granular scale, it is
based on the prediction at the scale of all packaged food product units that are consumed by a
given household or individual during a long period (e.g. 1 year), the approach can be used to
investigate the cumulative intake of particular substances originating from packaging
materials according a given consumption pattern, household composition, household practices
(e.g. frequency of purchases, storage conditions, reuse conditions…). Mechanistic models of
the migration based on consistent physicochemical properties are particularly efficient in
refined exposure assessment procedures as they can predict the possible contamination of food
in realistic conditions of migration by accounting for the true geometry of packaging and food
materials, the conditions of storage (duration, temperature…), the texture of food, the initial
concentration in packaging material... The uncertainty in model parameters is propagated
through a stochastic resolution of transport equations as described in Vitrac and Hayert (2005)
or by performing a sensitivity analysis including interactions that relies on likely intervals of
each parameter. In both situations, efficient algorithms (based on Monte Carlo or pseudo
Monte Carlo sampling, interval algebra) are available in the literature.
This paper examines the application of a “full probabilistic” approach of both contamination
and consumption to assess the exposure to styrene originating from yogurt pots at household
scale. Since a large panel of households (5,473) is considered, the exposure of a given
population is also derived. From the methodological point of view, styrene is particularly
interesting as its main source in both the diet and food contact application is particularly well
identified and makes it possible to a perform a detailed sensitivity analysis of the whole
methodology. Main input data are volume and frequency of purchases extracted from
marketing databases. The main unknown at the scale of each packaging unit is reconstructed
from two likely storage handling scenarios, H1 and H2, already applied in Vitrac et al. (2005).
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The individual cumulative exposure to styrene is estimated at household scale by
accumulating the amount of styrene that is expected to migrate in all yogurts purchased by a
given household. The concentration in each yogurt is calculated by accounting for the
expected variability in the initial concentration in packaging materials and for the uncertainty
in the diffusion coefficient of styrene monomer in polystyrene. The main source of uncertainty
is related to boundary conditions between food and packaging materials, the non linear effect
of Bi on exposure estimates is analyzed via typical values: { }1,100,Bi = ¥ .
Both scenarios of reconstruction of contact times H1 and H2 show that individual exposure
does not vary independently with the averaged consumption rate and contact time. High
consumers consume products that are up to 5 times less contaminated than those consumed by
low consumers. In a same manner, for a same consumption rate, the individual exposure may
vary by a factor up to 3 according to household practices. This effect is significant since it
higher than the initial uncertainty in input parameters (initial concentration in the packaging
material, diffusion coefficient at conditions of storage). The volume of purchase and the
average delay between purchases are the main explicative parameters of the discrepancy
between similar consumers.
The median individual exposure value (respectively the 95th percentile value) derived from the
gathered distribution varies between 0.3 (0.72) µg⋅day-1⋅pers-1 and 35 (120) µg⋅day-1⋅pers-1
between extreme tested conditions ( )1H 1Bi´ = and ( )3H Bi´ ® ¥ . The likely condition
( )2H 100Bi´ = leads to 12 (35) µg⋅day-1⋅pers-1. Since yogurt pots represent one the main
source of styrene through the diet (Palmer, 1996), it is found that the calculated likely values
have magnitudes consistent with previously published value of diet exposure to styrene. For
consumers combining both high consumption pattern and high storage time, this work shows
however that exposure to styrene originating from consumption of yogurts could be as high as
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exposure through inhalation. For a regularly consumed products as yogurts, changing the
scenario H2 to H1 yields similar conclusions 8 (21) µg⋅day-1⋅pers-1. On the contrary, the
scenario H3, which assumes that all yogurts are consumed at the sale-by-date give significantly
overestimated values 25 (80) µg⋅day-1⋅pers-1 for a same likely 100Bi = value. For a same
consumption rate, the scenario H3 overestimates coarsely the variability between households.
Thus, for a median consumption rate (respectively 95th percentile of highest consumers), the
95th percentile of individual exposure is expected to be ranged respectively between 9 and 25
(32 and 65) µg⋅day-1⋅pers-1 and under the likely condition ( )2H 100Bi´ = .
As a result, conventional probabilistic approaches of exposure, based on accumulated and
assumed uncorrelated distributions of food contamination and consumption, provide only
overestimates of individual exposure. Indeed, when contamination values are controlled by
time dependent processes, the bias related to the overestimation of food contamination may
arises from both an overestimation of the “true” contact time but also from the increasing
uncertainty on the migration kinetic when time is running. Coarse risk assessments, which do
not include household practices, may therefore conclude that the risk is only related to
consumption factors without identifying potential risky practices or misuses of packaging.
By contrast, risk managers may promote rough overestimates. This work provides first ranges
of uncertainty associated to conventional approximations used to simulate the migration from
contact materials into food starting from migration testing in simulants or numerical
simulations. In descending order, neglecting the external resistance to mass transfer between
food and its packaging overestimate the “true” exposure by a factor ranged between 2 and 30.
Assuming a pessimistic contact time based on the sale-by-date and not on the “true” or likely
distribution of contact time increase the individual exposure by a factor ranged between 1.5
and 3. Uncertainty related to the initial concentration in food packaging material and
conditions of storage adds a factor between 1.2 and 2.
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890
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5. Prospects
The proposed probabilistic approach based on modular approaches may provide a suitable
basis for the reevaluation of reduction factors, or for the risk assessment and management
associated to the use of complex materials (e.g. multi-layers materials, active/intelligent
materials) or particular conditions of use (e.g. reuse, cooking purposes) or recycling. Indeed,
the strategy that would assume very conservative assumptions, such as “package in the same
material for lifetime”, “same additives”, “100 % migration”, “100 % market share”, is not
appropriate as it dramatically increase the adverse to risk related to the rejection of a safe
application and could lead to erroneous conclusions for miss-used approximations. Complex
packaging applications need sophistications in the predictive migration models and additional
physicochemical properties such as activation energy and partition coefficients.
The extension of the current approach to screening strategies for a wide range of migrants
requires a significant effort in collection of non-aggregated information on packaging usage
(type, geometry, food application, typical formulation of the packaging material) at EU scale.
A cost effective strategy relies on the use of purchase data alone as those available through
marketing companies. The available information is however disparate in quality (tested
population, product type, time frame…) and incomplete regarding the dependent migration
problem. Algorithms of reconstruction of missing information (contact time, identified
consumers within the tested household…) based on likelihood maximums require to be
validated or completed on purpose with dedicated household surveys.
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List of figures
Figure 1. Risk scheme detailed at household scale. A and B are two arbitrary households that
do not exchange food products. Yogurt pots are darkened respectively their expected
contamination value in styrene.
Figure 2. Dimensionless migration kinetics ( *v ) for a) 1Bi = , b) 100Bi = , c) Bi ®¥
assuming 1K = and 210L -= . The developed stochastic approach is illustrated for the
condition { }0.1, 0.5,1Fo = and 0.15Ds = .
Figure 3. Comparison of contact times estimated according to scenarios H1 and H2. Each
symbol represents averaged results for all yogurt pots consumed by a given household during
one year. The averaged household consumption is proportional to the surface of each symbol.
The straight line y=x is plotted in continuous line.
Figure 4. Distributions of individual exposure to styrene for 3 typical consumption patterns
(5th, 50th and 95th percentiles) according to scenarios a,d,g) H1, b,e,h) H2, c,f,i) H3 and boundary
conditions: a,b,c) 1Bi = , d,e,f) 100Bi = , g,h,i) Bi ®¥ . Each consumption pattern is based on
20 households with similar individual consumption rate.
The corresponding distribution weighted over all households is depicted in dashed line.
Figure 5. Distributions of 50th and 95th percentiles of individual exposure to styrene based on
scenarios a,d,g) H1, b,e,h) H2, c,f,i) H3 and boundary conditions: a,b,c) 1Bi = , d,e,f) 100Bi = ,
g,h,i) Bi ®¥ . The distributions are based on 5473 households.
List of Tables & Figures – Paper 04-JG-FAC_090 version 2 1/4
5
10
15
20
25
Figure 6. Effect of individual consumption rates on contact times reconstructed based on
scenarios a,c) H1 and b,d) H2. Each symbol represents averaged results for all yogurt pots
consumed by a given household during one year. The surface of each symbol is proportional
to the 95th percentile of the individual exposure to styrene. Two boundary conditions are
considered: a,b) 1Bi = and c,d) 100Bi = .
Figure 7. Effect of individual consumption rate and volume of purchase on exposure to
styrene based on scenarios a,c) H1 and b,d) H2 and boundary conditions: a,c) 1Bi = and b,d)
100Bi = . Each symbol represents averaged results for all yogurt pots consumed by a given
household during one year. The surface of each symbol is proportional to the averaged volume
of purchase of each household.
Figure 8. Effect of individual consumption rate and delay between purchases on exposure to
styrene based on scenarios a,c) H1 and b,d) H2 and boundary conditions: a,c) 1Bi = and b,d)
100Bi = . Each symbol represents averaged results for all yogurt pots consumed by a given
household during one year. The surface of each symbol is proportional to the averaged delay
between purchases of each household.
Figure 9. Comparison of individual exposure to styrene (50 and 95th percentile) based on
scenarios a,c) H1 and b,d) H2 and boundary conditions: a,c) 1Bi = and b,d) 100Bi = with
values derived from the worst case scenario H3. The straight line y=x is plotted in continuous
line. The 50th percentile values are plotted with black filled symbols and 95th percentile values
with open symbols.
Figure 10. Comparison of individual exposure to styrene (50 and 95th percentile) based on
scenarios a,c) H1 and b,d) H2 and boundary conditions: a,c) 1Bi = and b,d) 100Bi = with
List of Tables & Figures – Paper 04-JG-FAC_090 version 2 2/4
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35
40
45
50
values derived from the worst boundary condition Bi ®¥ . The straight line y=x is plotted in
continuous line. The 50th percentile values are plotted with black filled symbols and 95th
percentile values with open symbols.
List of Tables & Figures – Paper 04-JG-FAC_090 version 2 3/4
List of tables
Table 1. Geometrical, physical and technological parameters used to assess the consumer
exposure to styrene from yogurt pots.
Table 2. 50th and 95th percentile values of individual exposure derived from distributions
calculated for “gathered” households and typical consumption patterns as depicted in figure 4.
Consumption patterns 1, 2 and 3 consist respectively in low (5th percentile), medium (50th
percentile) and high (95th percentile) consumers including 20 households each. Minimum and
maximum values are given for all considered consumption patterns.
Table 3. Likely values of the distributions of 50th and 95th percentiles of exposure calculated at
household scale and depicted in figure 5.
List of Tables & Figures – Paper 04-JG-FAC_090 version 2 4/4
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Table 1
quantity meaning value unitsl thickness 10-4 mL dilution factor 1/110 –K partition coefficient 1 –D likely diffusion coefficient 10-16 m2⋅s-1
Ds distribution shape related factor 0.2 –Bi mass Biot number { }1,100,¥ –
0clikely initial concentration in the
packaging material 500 mg⋅kg-1
0cs distribution shape related factor 0.15 –0M mass of yoghurt 0.125 kg
Table 2
conditionH1 H2 H3
50th
percentile95th
percentile50th
percentile95th
percentile50th
percentile95th
percentile
1Bi =
gatheredpattern 1pattern 2pattern 3
0.300.01–0.070.15–0.40.50–1.3
0.720.02–0.090.19–0.510.63–1.6
0.500.03–0.090.32–0.820.88–2.1
1.40.04–0.110.41–1.01.1–2.7
1.10.07–0.170.93–1.23.8–4.0
3.60.10–0.231.2–1.54.8–5.1
100Bi =
gatheredpattern 1pattern 2pattern 3
80.37–1.84.8–10 16–35
210.53–2.4
6–1320–44
120.81–2.38.6–1926–51
351.1–2.911–2432–63
251.8–3.922–2582–85
802.5–5.128–31
102–106
Bi ®¥
gatheredpattern 1pattern 2pattern 3
160.87–3.611–2038–67
431.2–4.614–2547–84
231.7–4.217–3154–88
652.3–5.321–39
67–110
353.3–6.436–39
129–134
1204.4–8.346–48
162–167results are expressed in µg⋅day-1⋅pers-1
Table 3
conditionH1 H2 H3
50th
percentile95th
percentile50th
percentile95th
percentile50th
percentile95th
percentile1Bi = 0.3 0.4 0.7 0.85 1.5 1.9100Bi = 10 12 16 20 28 40
Bi ®¥ 19 25 28 38 41 64results are expressed in µg⋅day-1⋅pers-1
Figure 1
Figure 2
Figure 3
Figure 4
Figure 5
Figure 6
Figure 7
Figure 8
Figure 9
Figure 10