background image
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barrier effect due to layers 1 and 2 (diffusion and solubility), overestimation of a reservoir effect
due to layers 2 and 3.

The highest value of k
j
(with k
0
=1) was retained in all approximations to account for the
partitioning between P and F. Besides, it emphasized that the initial configuration is out of the
equilibrium (i.e. the partial pressure are not equal at the interfaces between layers). This is
generally the case immediately after the assembling of different materials. If the material is
expected closer to the equilibrium prior to the contact with food due to a process at high
temperature or to a long storage of the material mass transport must be simulated successively
without contact (impervious BC) and with a contact with food.

The results are plotted in Figure 9 by assuming that the contaminations from each layer are
independent and by cumulating all overestimations. The individual contribution of each layer to
the overall
*
v was calculated by the ratio:
F
F
Fo
eq
C
C
. The overall
*
v was computed by the
average of all
*
v calculated individually for each layer. The weights were chosen equal but the
final result can be weighted according to the initial amount within each layer. This last result is
finally compared with the result obtained by simulating the mass transport in the complete
trilayer structure (Figure 9d, 9h and 9l). The overestimated profiles exhibit always a higher slope
at the F-P interface than the reference profiles so that the migration rates are always
overestimated. It is worth to notice that the proposed approximations do not exaggerate
overestimations and remained still consistent with both the true profiles and the true kinetics.
5 Probabilistic estimation of the contamination

Worst case analyzes assume generally a combination of several pessimistic of scenarios (see
Figure 4) without weighting each overestimation according to their frequency of occurring. As a
result, the calculations are performed with a significant safety margin without always controlling
reliably the value of the safety margin. The objective of probabilistic modeling is to make
possible the calculation of the contamination with a controlled risk that the real contamination
exceeds the estimated one. As a result, an overestimate of the real contamination means an
estimate, which may be exceeded with a risk lower than 50%. On the opposite, an underestimate
will present a risk higher than 50%. In this approach, the effects of both sources of uncertainty
and variability and their interactions can be inferred.
An efficient adaptation of pseudo-Monte Carlo techniques has been proposed by Vitrac and
Hayert (2005) for monolayer materials. A web-based application, so-called M
IGRARISK
, has been
developed and is available on our server (Vitrac, 2006). It has been applied to assess the
contamination of 12 packaged food products on the market by ubiquitous contaminants from
packaging materials (Vitrac et al., 2006) and to assess the exposure of consumer to styrene from
yogurt pots according to household practices (Vitrac and Leblanc, 2006).

This section presents first the general principles, which are used to predict the distribution of the
contamination of food products by substances originating from monolayer materials according to
the distributions of all input parameters detailed in section 3.2 : initial concentration in P, contact
time, transport properties. The distribution of each parameter represents indifferently the effects