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chemical substance must follow a risk management decision. More restrictive rules are applied
for materials intended to be in contact with food, including an obligation of traceability of
processing and formulation of complex end products such as packaging materials (EC, 2004) and
risk assessment related to the desorption in food of impurities in starting substances,
decomposition and reaction products (proposal of "plastics" superdirective). To comply with
such strong requirements, both the European Health and Consumer Protection Directorate
General (EC, 2002) and the American Food and Drug Administration encourage the use of
mathematical modeling based on the physical description of mass transfer between the food
product and its packaging.

This chapter describes new methodologies of prediction of the contamination of food products by
packaging substances. The objective is to extend the range of applications for which deterministic
modeling can be applied and used robustly to demonstrate the compliance of a packaging or of
the use of a given substance, to audit a provider or to demonstrate that its product is safer than the
one of its competitor. The current limitations refer i) to our partial scientific knowledge about
transport properties (e.g. effect of chemical structure, morphology of the polymer), which control
the desorption of packaging substances, ii) to the non-disclosure agreements in the formulation
and process of materials and finally iii) to other sources of uncertainties including: reaction
products generated during processing, fluctuations in storage temperature, food variability,
misuse of the packaging material (e.g. reuse, inadequate microwave heating, contact with organic
solvents...). The proposed methodologies illustrate how to take into account such sources of
uncertainty and to quantify their effects on the prediction of the contamination of food products.
Until more experience is gained, it would be premature to give here prescriptive guidance. We
identify here the approaches that appear promising for the needs of the chemical, packaging and
food industry.
The next section reviews the transport models used to predict the contamination from monolayer
and multilayer materials. Dimensionless formulations are detailed to identify, which situations
are self-similar and generate similar effects to different sources of uncertainty. Section 4
introduced the concept of tiered approaches to refine progressively the characterization of
uncertainty and risks. These screening approaches are based on the description of desorption
kinetics via a serial association of mass transport resistances, whose complexity is iteratively
increased according to the available knowledge. It is shown that this approach is particularly
efficient for complex multilayer structures, where the large number of unknown inputs prevents a
direct simulation of the complete problem. Section 5 details more sophistically approaches,
which were recently proposed by us, to assess probabilistically the contamination of food
products. This high-level approach leads to solve simultaneously the transport equations for a
large number of combined conditions. An efficient implementation is proposed here and detailed
for the assessment of the combined effects of uncertainties on transport properties (diffusion
coefficient, mass transport coefficient at the food-packaging interface, partition coefficient). This
approach requires an additional modeling step to quantify the relative likelihood or frequencies of
different values within a credible range of each input parameter. This contribution is also
discussed. The concluding section resituates the uncertainty and risk assessments in its practical
industrial context. Finally, the current research needs are identified.