1. Introduction


The term migration refers to the mass transfer of chemicals from packaging and other food contact articles (FCAs) to food (Shepherd 1982; Castle 2007; Piringer 2007; De Meulenaer 2009; JRC 2015; see FPF background article on Migration). Chemical migration can impact 1) food safety, if harmful substances migrate into food at relevant concentrations, and 2) food quality, if the migrating substances impair the food’s properties (e.g., color, odor, taste) (Lum Wan et al. 1995; Castle 2007). For these reasons, migration is regulated in most countries (Lum Wan et al. 1995; Arvanitoyannis & Bosnea 2004; Vitrac and Goujon 2014) and is addressed in specific regulations covering food contact materials (FCMs) and FCAs (see FPF background article on Regulation on food packaging). From a public health point of view, migration from FCAs contributes to the general population’s overall exposure to chemicals (FPF reported).

Chemical risk assessments are carried out in order to ensure consumers’ safety (see FPF background article on Chemical risk assessment). To quantify the risk of an adverse health effect due to chemical exposure, information on both chemical hazard (i.e., toxicity) and exposure level need to be available. In the case of food contact chemicals (FCCs), exposure is related to the level of a chemical in food; therefore, in most cases, it is directly linked to migration from FCAs. Hence, migration modeling is an important tool for estimating consumer exposure to chemicals from FCAs (Franz 2005) and is often the only exposure-related information for risk assessment. However, migration modeling has mainly evolved as a tool for regulatory compliance testing aimed at overestimating real migration (see section on Plastic). Notably, migration modeling can only be used if the migrating chemical and its initial concentration in the packaging are known. This is not always the case, as many unknown and unidentified compounds migrate from FCAs into foods (see FPF background article on Non-intentionally added substances (NIAS) and FPF peer-reviewed paper on Scientific challenges in the risk assessment of food contact materials).

The following factors control the migration of chemicals from FCMs into food (Castle 2007; De Meulenaer 2009; Vitrac and Goujon 2014; see FPF background article on Migration and FPF fact sheet on Food packaging and human health):

  • Temperature of contact (chemical migration increases at higher temperatures)
  • Contact time (migration levels increase with time)
  • Surface-to-volume-ratio (small packaging sizes have high ratios leading to higher migration levels)
  • Type of food (e.g., aqueous, acidic, alcoholic, fatty, dry; many chemicals preferably migrate into fatty or acidic foods)
  • Type of FCM (e.g., plastics, paper and board, glass, metal, ceramics, printing inks, wax, wood)
  • Composition of the FCM (e.g., initial concentration of migrating substance in the FCM)
  • Type of contact (e.g., direct or indirect, solid or liquid food, presence of functional barriers retarding, limiting or preventing migration)
  • Physico-chemical properties of the migrating substance (e.g., volatility/vapor pressure, water solubility, octanol solubility, polarity)
  • Mobility of chemicals in FCM (e.g., impermeable, permeable, porous materials; see Type of FCM)
  • Kinetics and thermodynamics of the migration process (i.e., how fast and to what extent will a substance transfer from the FCM into food)

Chemical fate modeling

Generally, “chemical structures cause the molecular interactions that govern the various transfer and reaction processes” a substance undergoes within an environment (Schwarzenbach et al. 2003). Based on their structure, chemicals have intrinsic properties like vapor pressure, water solubility, octanol solubility that determine their behavior to partition into different phases/media (e.g., FCA and food). For a more detailed description of the interrelationship between chemical structure and environmental behavior, see, for example, the book Environmental Organic Chemistry by Schwarzenbach et al. (2003).

Migration modeling

There are different approaches to mathematically modeling the migration of chemicals from FCAs into food (Lum Wan et al. 1995; Chatwin 1996; Poças et al. 2008; Biryol et al. 2017):

Deterministic or mechanistic models mathematically describe the physico-chemical mechanisms underlying the phenomenon of migration. Various scientific studies have shown that the migration of chemicals from FCMs into food follows predictable physical, and mathematically characterizable, processes. Therefore, the majority of the scientific literature on migration modeling is dedicated to the deterministic approach. In many cases, migration is governed by a mass transfer process called diffusion that can be described by (Lum Wan et al. 1995; Chatwin 1996; Brandsch et al. 2002; Franz 2005; Vergnaud and Rosca 2006; Piringer 2007; Poças et al. 2008; De Meulenaer 2009; PlasticsEurope 2013; Vitrac and Goujon 2014; JRC 2015). Data for two fundamental constants is needed to reasonably predict migration/diffusion: 1) The partition coefficient of the migrating substance between the FCM and the foodstuff, and 2) the diffusion coefficient of the substance in the FCM (Brandsch et al. 2002). The first constant expresses the migrating substance’s (relative) preference to reside in the FCM or the foodstuff (i.e., how much of the migrant will partition into food), and the latter provides information about the substance’s mobility within the FCM (i.e., how fast the migrant moves in the FCM) (Franz 2005). When both constants are available (either experimentally determined or modeled/estimated), the migration rate can be calculated according to Fick’s second law of diffusion (Brandsch et al. 2002; Crank 1975). The model variables assume single and constant values, resulting in a single value of migration as model output.

Empirical models are based on mathematical equations that produce a good fit with experimental observations on migration. Such models are purely mathematical and are not concerned with the physical meaning of the model constants or the underlying mechanisms of migration. The Weibull model, based on the function, is an example of an empirical model to describe migration from certain FCMs (Poças et al. 2008; see section on Paper and board).

Stochastic models use mathematical functions of probability distributions. They predict the probability that a certain level of migration will occur or what migration levels are most likely to occur. The is an example of a probability distribution function that can be used in stochastic models (Poças et al. 2008).

Probabilistic models take into account the variability and uncertainty in the model variables as well as the probability of their occurrence. This also comprises mixed effect models where deterministic models are complemented with variability in the model parameters. As a consequence, the model constants and the model output are represented by a distribution of values rather than a single value. Probabilistic models use methods that propagate information about variability and uncertainty through the model. The , based on simulated random sampling, is an example of a numerical simulation method that is commonly used in probabilistic models. is another example of a numerical simulation method (Poças et al. 2008).

Alternative approaches include molecular modeling, or molecular thermodynamics, as presented by the works of Nguyen et al. (2016) and Li et al. (2017).

2. Modeling approaches for different packaging materials


Most of the scientific studies on migration modeling focus on plastic packaging and use a deterministic approach based on Fick’s law of diffusion (see Introduction). Migration modeling can complement or, in part, substitute actual laboratory migration experiments that are often expensive and time-consuming. Therefore, it has become a popular tool for researchers, industry, and regulators to predict migration. In the EU and the U.S., there are accepted deterministic migration models that can be used to assess compliance of plastic FCMs with regulatory specific migration limits (SMLs) (Lum Wan et al. 1995; Brandsch et al. 2002; Begley et al. 2005; Franz 2005; Vergnaud and Rosca 2006; Piringer 2007; Poças et al. 2008; De Meulenaer 2009; PlasticsEurope 2013; Vitrac and Goujon 2014; JRC 2015; Fang and Vitrac 2017). These models make simplifications and assumptions to calculate ‘worst-case’ or overestimated migration (i.e., the whole amount of a given chemical in a plastic FCM will migrate into the food). The main assumptions include: 1) The migrant is initially homogenously distributed in the FCM (concentration has to be known), 2) the initial concentration of the migrant in the food is zero, 3) there is no boundary resistance for the transfer between the FCM and the food, 4) the migrant is homogenously distributed in the food after transfer, 5) the total amount of the migrant in the FCM and the food remains constant (no reaction, no loss), and 6) the migrant is very soluble in food (partition coefficient between FCM and food equals 1). If the overestimated migration does not exceed the SML, it can be considered that safety is assured and no model refinements or actual migration experiments are required.

In recent years, efforts have been made to modify the common ‘worst-case’ deterministic models to better reflect more realistic migration scenarios. These approaches include probabilistic and stochastic modeling that take into account variability and uncertainty in the mass transfer parameters (see Introduction). Migration/Diffusion modeling could thus be increasingly used for risk assessment, designing packaging with low migration risk, or synthesizing plastic additives with low diffusivity (Vitrac and Hayert 2005; Nguyen et al. 2013; Vitrac and Goujon 2014; Brandsch 2017; Fang and Vitrac 2017; Gavriil et al. 2017; Gavriil et al. 2018).

Other approaches use migration modeling to predict consumer exposures to chemical migrants from FCMs for large numbers of chemicals (Vitrac and Leblanc 2007; Biryol et al. 2017; Ernstoff et al. 2017). Mechanistic or empirical migration models can be combined with food consumption data to estimate dietary exposure to FCCs. Such high-throughput (HT) methods can serve as screening-level tools for prioritizing chemicals for further scrutiny and can be compatible with other screening and prioritization tools such as Life Cycle Assessment (LCA) and High-Throughput Risk-based Screening (HTRS). They are, however, associated with an increased level of scientific uncertainty.

Paper and board

Much less effort has been made to understand the factors influencing migration of chemicals from paper and board FCMs, as well as to develop mathematical modeling thereof. This is due to the inhomogeneity of these materials which makes modeling difficult (Aurela and Ketoja 2002). However, in recent years, several scientific studies have emerged taking on this topic (Poças et al. 2010; Zülch and Piringer 2010; Barnkob and Petersen 2013; Hauder et al. 2013; Huang et al. 2013; Cai et al. 2017; Nguyen et al. 2017). The applicability of the mechanistic diffusion model for paper and board is limited because it cannot adequately describe the mass transfer processes occurring in these heterogenous, porous, fiber-based materials (Poças et al. 2010). Nevertheless, successful attempts have been made to adapt the classical diffusion model so as to fit observed migration from certain paper and board FCMs into food (Castle 2004; Zülch and Piringer 2010; Barnkob and Petersen 2013; Hauder et al. 2013; Huang et al. 2013).

The empirical Weibull model (see Introduction) has been reported to well describe the shape of experimentally determined migration curves for chemicals in paper and board FCMs (Poças et al. 2010; Cai et al. 2017). Because of its simplicity and flexibility, the model is able to describe “several mass transfer processes within [the] food engineering area and in food packaging systems, in cases where diffusion theories could not fully explain the mass transfer process” (Poças et al. 2010).

Other materials

Even less scientific literature is available on migration modeling approaches for other FCMs such as ceramics or printing inks. Regarding the former, the mechanistic diffusion model has been applied to predict migration of toxic metals into acidic food (Dong et al. 2015). The diffusion model has been found to well describe or slightly overestimate migration from ceramics at room temperature. Regarding the latter, the diffusion model has also been applied and adapted (Gao et al. 2014; Aparicio and Elizalde 2015; Wang et al. 2015). Good agreement between diffusion model predictions and experimental data was found for substances migrating from printing inks on paper and board packaging into food.

Migration modeling software

There is user-friendly migration modeling software that has been reported in the scientific literature, for example MIGRATEST Lite 2000/2001 by Fabes GmbH, Germany (Brandsch et al. 2002; Poças et al. 2008; De Meulenaer 2009; Barnkob and Petersen 2013), the AKTS-SML Software by The Advanced Kinetics Technology Solution AG, Switzerland, and the Swiss Federal Office of Public Health (SFOPH) (Poças et al. 2008; Franz et al. 2016; Brandsch 2017; Gehring and Welle 2017), SMEWISE (Simulation of Migration Experiments with Swelling Effect), MULTITEMP, MULTIWISE, the Safe Food Packaging Portal, and SFPP3 by the French National Institute for Agricultural Research (INRA) (Poças et al. 2008; De Meulenaer 2009; Fang and Vitrac 2017), and FMECAengine (Failure Mode Effects and Criticality Analysis) (Nguyen et al. 2013; Vitrac and Goujon 2014; Fang and Vitrac 2017). Another tool for probabilistic modeling of consumer exposure to FCCs from primary packaging is the Flavours, Additives, and food Contact materials Exposure Task (FACET) model (Oldring et al. 2014; Seiler et al. 2014; Maia et al. 2016; see FPF background article on FACET).

3. Discussion and conclusions

Mathematical modeling can be a useful tool to predict migration of chemicals from FCMs into food. It can, to some extent, replace laboratory migration experiments and thus save time and money. However, migration models should only be used by trained experts with in-depth knowledge about chemical migration in order to make reliable predictions and correctly interpret the results (Piringer 2007; De Meulenaer 2009). Also, migration modeling applies assumptions and simplifications about the migration process, the FCM, and the chemical migrant, and may thus overestimate or underestimate actual migration. Further, the migrating chemical and its initial concentration in the packaging have to be known in order to model its transfer from the FCM to the food. Therefore, these tools are not suitable for assessing the migration of unknown NIAS. Also, since initial concentrations are often not available to packaging end-users, mainly the chemical industry and plastic converters can make use of migration modeling. So far, migration modeling has mainly been focused on plastic FCMs. ‘Worst-case’ migration modeling (i.e., the entire amount of a given chemical will migrate from the FCM into food) can be used to prove compliance with regulatory SMLs. However, it does not reflect realistic migration scenarios and the assumption of ‘worst-case’ conditions does not always lead to an overestimation of actual migration (Ernstoff et al. 2017; Gavriil et al. 2017; Gavriil et al. 2018). Probabilistic models are more elaborate, provide more accurate migration estimates, and can thus be used in risk assessment and for safe packaging design (Vitrac and Hayert 2005; Nguyen et al. 2013; Brandsch 2017; Fang and Vitrac 2017). Both ‘worst-case’ and probabilistic diffusion modeling can only be applied to one chemical at a time. High-throughput models offer a tool to screen many chemicals at once, calculate exposure estimates, and prioritize chemicals for further study. However, due to the many uncertainties associated with these methods, they are not appropriate for the assessment of single chemicals (Biryol et al. 2017; Ernstoff et al. 2017). More work needs to be done on paper and board and other materials to establish recognized migration models. Thus far, most studies on modeling migration from non-plastic materials have applied and adapted the deterministic diffusion model that has been developed for plastics. Another model, namely the empirical Weibull model, has been shown to provide promising results for the prediction of chemical migration from paper and board FCMs. However, empirical models do not elucidate the underlying migration mechanisms.

Another specific area where the applicability of diffusion-based migration modeling is limited is nanomaterials (FPF reported). Diffusion modeling only predicts migration for small nanoparticles (up to a few nm) which is not in line with experimental studies that have also observed migration of much larger nanoparticles from FCMs (Jokar et al. 2017; Stoermer et al. 2017). Desorption, dissolution, and polymer degradation are likely more important migration mechanisms for nanoparticles than diffusion. Therefore, new mathematical models that consider these mechanisms need to be developed (Jokar et al. 2017).

4. References and further reading

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Barnkob, L.L., and Petersen, J.H. (2013). “Effect of relative humidity on the migration of benzophenone from paperboard into the food simulant Tenax® and modelling hereof.” Food Additives & Contaminants: Part A 30(2):395-402.

Begley, T., et al. (2005). “Evaluation of migration models that might be used in support of regulations for food-contact plastics.” Food Additives & Contaminants 22(1):73-90.

Biryol, D., et al. (2017). “High-throughput dietary exposure predictions for chemical migrants from food contact substances for use in chemical prioritization.” Environment International 108:185–194.

Bodai, Z., et al. (2016). “Solubility determination as an alternative to migration measurements.” Food Additives & Contaminants: Part A 33(3):574-581.

Bradley, E.L., et al. (2014). “Model studies of migration from paper and board into fruit and vegetables and into TenaxTM as a food simulant.” Food Additives & Contaminants: Part A 31(7):1301-1309.

Brandsch, J., et al. (2002). “Migration modelling as a tool for quality assurance of food packaging.” Food Additives & Contaminants 19(S1):29-41.

Brandsch, R. (2017). “Probabilistic migration modelling focused on functional barrier efficiency and low migration concepts in support of risk assessment.” Food Additives & Contaminants: Part A 34(10):1743-1766.

Cai, H., et al. (2017). “Migration kinetics of four photoinitiators from paper food packaging to solid food simulants.” Food Additives & Contaminants: Part A 34(9):1632-1642.

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