Model-based design of smart active packaging systems with antimicrobial activity

Model-based design of smart active packaging systems with antimicrobial activity Carlos Vilasa, Miguel Mauricio-Iglesiasb, M´ıriam R. Garc´ıaa,∗ a(Bio)Process Engineering Group, IIM-CSIC, r/ Eduardo Cabello, 6, 36208, Vigo (Spain) bDepartment of Chemical Engineering, School of Engineering, Universidade de Santiago de Compostela, r/ Lope G´omez de Marzoa, E-15782 Santiago de Compostela (Spain) Abstract Smart active packaging is an innovative packaging system that combines the benefits of measuring, estimating or predicting different aspects of food quality or safety with the release of an active substance that extends product shelf life. Nevertheless, in its typical configuration, the active packaging and the smart packaging are not connected, and the information provided is not exploited to design the release of the active substance. In this work, we demonstrate how smart active packaging systems using predictive mathematical models allow the automatic optimisation of food packaging design and the prediction of the expected shelf life along the food chain. On the one hand, the system calculates the best design of the active packaging and the concentration of the active substance in the different layers that maximise food quality and safety. On the other hand, the model allows to calculate and update shelf life values along the food chain under unexpected changes in the storage conditions. Shelf life estimations and prediction will help distributors and sellers to adjust the product market prices. For example, prices can be lowered to avoid food losses when the product is close to its use-by date. Hake (Merluccius merluccius) represents an example of a highly relevant and perishable food that can be conserved using natural antimicrobials. Therefore, the case study selected to illustrate the proposed methodology consists of the ∗Corresponding author Email address: [email protected] (M´ıriam R. Garc´ıa) Preprint submitted to Food Packaging and Shelf Life December 9, 2019 smart active packaging of hake using carvacrol as the active substance (antimicrobial). Besides, different polymers are considered as possible active packaging materials. The Matlab™codes required to perform the simulations of the models described in this work as well as the optimisations for packaging design are available at https://doi.org/10.5281/zenodo.3244153. Keywords: Smart active packaging, Model-based optimal design, Predictive Microbiology, Shelf life, Antimicrobial activity, Fish freshness 1. Introduction Smart active packaging is an innovative packaging system that combines the benefits of measuring, estimating or predicting different aspects of food quality or safety (Yam et al., 2005; Garc´ıa et al., 2017) with the release of an active substance that extends product shelf life (Wyrwa & Barska, 2017).5 This innovative packaging system responds to current consumer’s preferences for minimum processing foods of high quality, while allowing distributors and sellers to avoid food wastage by adjusting market prices based on reliable information about product shelf life (Zhang et al., 2015; Garc´ıa et al., 2015). The smart active packaging is a crucial element for an emerging food industry 4.0 with10 adaptive production and intelligent tracking systems. The combination of smart and active packaging solutions originates from the need to develop a general approach that permits to predict food product shelf life and to exploit this information to design the release of the active substance. Nevertheless, and despite a large number of works demonstrating the15 benefits of innovative packaging systems, this general approach is still missing (Guillard et al., 2018). The main problem is that, although smart packaging alone is able to provide information on current food state, using either direct or indirect measurements (Pacquit et al., 2007; Giannoglou et al., 2014), it does not provide estimations or the influence of factors such us package design or20 storage conditions on expected product shelf life. Shelf life predictions require the harmonisation of two different types of dy- 2 namic quantitative models in smart active packaging: (1) one model describing the release of the active substance and (2) another model describing shelf life in terms of food safety and quality. Shelf life predictions are critical to optimally25 design aspects such as the selection of the multilayer packaging material, the robustness of the chosen design to variable storage conditions or the initial concentration of the active agent. Recently developed predictive tools for enhanced packaging have focused on the simulation of modified atmosphere packaging (Chaix et al., 2015; Antunes-Rohling et al., 2019). The development of a whole30 framework to assist in packaging and product design is required to boost the use and confidence of the food industry in these novel solutions, and in particular, in active packaging. There is an established and reliable theory for mathematically describing the release of the active agent in active packaging. Such release from a polymeric35 packaging material is, in general, governed by three parameters: the diffusivity in the packaging (Di), the partition coefficient (Kpf ) describing the affinity for the active agent between the food product and the packaging, and the mass transfer coefficient (kL) or the diffusivity in the food product, for liquid-like or solid foodstuff respectively (Martinez-Lopez et al., 2015). In most cases,40 diffusion in the packaging and partition between compartments are the limiting steps and therefore the most crucial parameters needed for simulation, although additional information is required when deviations from Fickian diffusion are relevant as in the case of polymer swelling (Mauricio-Iglesias et al., 2009). As a conclusion, the biggest challenge in simulating the active agent release is the45 availability of the relevant parameters (Diand Kpf ) given that the mathematical description and solution are well-established. More challenging is the modelling of food shelf life: a complex and dynamic concept that combines different food safety and quality aspects, including subjective or cultural organoleptic preferences. Shelf life is a dynamic estimation of50 the time span where the product is in good conditions for consumption and depends on multiple factors such as storage temperature (Jedermann et al., 2014). In general terms, shelf life is defined to guarantee food safety (“use-by” date), 3 or to ensure both safety and quality food standards (“best-before” date). Good predictive shelf life models are product specific and are especially55 advantageous for highly perishable foods such as fresh shellfish and fish meat (Cerisuelo et al., 2013). Among them, the value of hake (Merluccius merluccius) landed in the EU is the highest, accounting for 470 million e(roughly 7% of the total) in 2015 EUMOFA (2017). Carvacrol, the principal antimicrobial agent in oregano essential oil, has been reported as one of the most active natural60 antimicrobial compounds inducing permeability alteration in cell membranes resulting in cell death (Ben Arfa et al., 2006). As a result, it has been used as a standard option to extend fish shelf life, including hake (Otero-Tu´arez et al., 2019). A critical safety index both in fresh and cooked seafood products is the65 growth of Listeria monocytogenes. One of the first documented outbreaks with death casualties linking L. monocytogenes with the consumption of shellfish and raw fish dates from 1980 (Dillon & Patel, 1992). L. monocytogenes may survive cooking and growth at refrigeration temperatures and affects widely consumed products such as cold-smoked salmon, frozen canned cooked crab meat and70 surimi products among others (Benabbou et al., 2018; Dillon & Patel, 1992). Fish quality, usually associated with freshness, does not only relate to safety. It is a complex attribute that depends on both microbial and biochemical changes as well as cultural and personal preferences. Spoilage microorganisms commonly degrading quality in fish muscles at low temperature are (psy-75 chrotrophic) Pseudomonas and Shewanella (Gram & Dalgaard, 2002). Biochemical changes may be detected using different measurements such as the total volatile base-nitrogen generated (TVB-N) or thrimethylamine (TMA). Conventional detection of early changes in quality attributed is determined using the KI-value for fresh and frozen fish (Saito et al., 1959; Karube et al., 1984; Hong80 et al., 2017; Li et al., 2019). This index relates the concentration of Inosine monophosphate (IMP), Inosine (Ino) and Hypoxanthine (Hx) in fish muscle. IMP is related to the umami taste of fish whereas its degradation and the formation of Hx is connected to unpleasant bitterness. Recently, Vilas et al. 4 (2018) showed that spoilage bacteria accelerate the degradation of IMP into Ino85 and Hx. The authors derived a mathematical model describing the degradation of IMP, including the effect of spoilage bacteria (Pseudomonas spp. and Shewanella spp.) as well as leaching of nucleotides. Under active packaging, the antimicrobial agent limits spoilage bacterial growth, thus delaying quality degradation.90 In this work, we present a procedure for the integral design of smart active packaging systems by using mathematical models to: (1) optimally design the packaging/food system for a given objective and (2) assess and predict shelf life taking into account changes on the food chain conditions. To the authors knowledge, this work is the first one providing a mathematical model that de-95 scribes the evolution of quality and safety indicators in a system comprising both active packaging and food product. The contribution also provides modelbased tools and formulations for systematic design, food chain assessment, and shelf-life estimations. We demonstrate our approach by designing a smart active packaging of hake fillets, with increased shelf life thanks to the steady release100 of the antimicrobial carvacrol. In this regard, we consider different polymers as active packaging materials and select the optimal configuration of the multilayer packaging material, including the thickness of each layer. We also provide the optimal concentration of carvacrol in each layer. Robustness of the chosen design is tested by considering variable storage conditions, including tempera-105 ture abuses and changes of the time span between packaging manufacturing and food-packaging contact. 2. Materials and Methods 2.1. Smart active packaging description The active packaging/food product selected in this work represents a packed110 foodstuff that is modelled as a multi-compartment system composed by several film layers wrapping the food product as described in Figure 1. At t= 0, the active compound, carvacrol, is only present in the packaging, and it is transferred 5 to lower concentration regions both in the food and in the different layers of packaging. Likewise, at t= 0, a certain initial microbial load is assumed in the115 surface of the fish fillet. The evolution of the microbial load depends on the temperature and on the concentration of carvacrol in the fillet surface. Seeking a trade-off between model fidelity and simplicity of use, the following assumptions were considered in model derivation: •Transfer rate of carvacrol is well described by 1-D transfer in the thickness120 dimension as the packaging thickness is much smaller than its length or width. •No carvacrol is transferred to the outer environment due to carvacrol’s low volatility, although flux conditions can be used to simulate more volatile active compounds.125 •Inner packaging layer is in good contact with the food product and resistance to transfer is low, which is a suitable approximation for solid/solid interfaces. Note, in any case, that the model formulation allows situations such as imperfect contact which can be modelled as an increased mass transfer resistance (Roca et al., 2008).130 •Temperature is homogeneous in both the packaging and the fillet surface and it is equal to environmental temperature at all times. Note that heat transfer is considerably faster than mass transfer both in packaging and food (Lewis number >> 1). •Bacteria are initially located on the fillet surface, which might have been135 contaminated during the cutting process (Proctor & Nickerson, 1935). Also, bacterial migration to the food matrix interior is much slower than carvacrol diffusion. In consequence, quality and safety issues are more relevant on the surface. Therefore, modelling bacterial and carvacrol distribution inside the food matrix is not required.140 It should be noted that some parts of the presented model, namely bacterial growth and nucleotide degradation, have been validated in previous works 6 (Garc´ıa et al., 2015; Vilas et al., 2018). The diffusion of carvacrol in polymers is expected to be well described by Fickian kinetics. On the other hand, the effect of carvacrol on the bacteria would require a case-by-case experimental145 validation before implementation into a specific industrial application. Layer 1 Layer 2 Foodstuff Carvacrol concentration (a.u.) Figure 1: Diagram of the packaging/food system illustrating a bilayer packaging material and the food product with varying carvacrol concentration (red line) in the direction of the packaging thickness. Quasi-homogeneous carvacrol concentration is expected in the foodstuff as mass transfer limitation takes place in the packaging compartment(s). 2.1.1. Prediction of active substance release Mass transfer across polymeric food packaging takes place mainly by diffusion. Therefore, we use Fick’s law, with diffusivity term independent of solute concentration (Mauricio-Iglesias et al., 2009), in combination with a mass bal-150 ance to describe the evolution and distribution of carvacrol in the packaging: ∂Ci ∂t =Di ∂2Ci ∂x2; with i= 1,2, ..., n;t > 0; and xi−1< x < xi(1) where Ci(t, x) (kg/m3) and Di(T) (m2/s) are, respectively, the concentration of carvacrol and its diffusivity in layer i.xis the distance to the environment. Layer iis defined between spatial coordinates xi−1and xi, where x0= 0 and155 xn=H. In order to solve Eq (1) initial and boundary conditions must be 7 defined. Initial carvacrol concentration in each of the layers is defined as: C1(t0, x) = C1,0(x); 0 ≤x≤x1 C2(t0, x) = C2,0(x); x1≤x≤x2 . . . 160 Cn(t0, x) = Cn,0(x); x2≤x≤H The active packaging has three types of boundaries: the outer environment, interface between films and the food matrix. As mentioned above, no flux of carvacrol is considered between the active packaging and outer environment. Mathematically, this is formulated as: ∂C1 ∂x x=0 = 0.(2) Contact between films in multilayer is considered as perfect and, at the interface,165 the equilibrium condition holds. Hence, between layers iand i+ 1, boundary condition is written as: Ci|x− i=Ci+1|x+ i Ki,i+1 (3) with Ki,i+1 being the partition coefficient. Flux of carvacrol between the active packaging and the food matrix is described by: Dn ∂Cn ∂x x=H =kL(Kpf Cf−Cn|x=H).(4) where Kpf is the partition coefficient between the packaging and the product,170 and kL(m/s) is the mass transfer coefficient in the packaging/food interface. The concentration of carvacrol in the fillet surface (Cf) is determined by a mass balance: dCf dt =−kLa(Kpf Cf−Cn|x=H),(5) where ais the specific exchange area defined as: a=A VL =exchange area liquid volume . Initial conditions for Eq (5) are of the form:175 Cf(t0) = C0 8 Diffusivity changes with temperature are modelled by an Arrhenius-like dependence: Di(T) = Di(Tref ) exp −EA,i R1 T−1 Tref  (6) where EAis the activation energy, Ris the ideal gas constant and Tis the temperature. Model parameters are summarised in Table 1. Some of the parameters in the table were obtained by combining the values provided in several180 references. The reader is referred to Appendix A for details on such derivation. Table 1: Mass transfer parameters for carvacrol in the different layers: polypropylene (PP); low-density polyethylene (LDPE); high-density polyethylene (HDPE). Parameter Value Units References Tref 293 K - DP P (Tref ) 1.77 ×10−15 m2s−1(Cerisuelo et al., 2012; Krepker et al., 2018) DLDP E (Tref ) 8.10 ×10−14 m2s−1(Rupika, 2010) DHDP E(Tref ) 1.8×10−17 m2s−1(Peltzer et al., 2009) EA,P P 1.27 ×105J mol−1(Cerisuelo et al., 2012; Krepker et al., 2018) EA,LDP E 1.01 ×105J mol−1(Rupika, 2010) EA,HDP E 2.14 ×105J mol−1(Peltzer et al., 2009) Kpf 124 m3food m3P P (Cerisuelo et al., 2012, 2013) kL5.0×10−3m s−1(Martinez-Lopez et al., 2015) a60 m−1(EU Commission, 2004) R8.314 J mol−1K−1- Regarding partition coefficients in boundary condition (3), it is likely that carvacrol partitions in a similar way between LDPE, HDPE and PP, given that these polymers are chemically similar. Therefore, in multilayer configurations we consider K1,2=K2,3= 1, although other values could be easily implemented.185 9 Table 4: Scheme of the different configurations of the active packaging layers considered in this work. For multilayer configurations (2 or 3 layers), the layer at the left is in contact with the environment whereas the layer at the right is in contact with the food. For instance, the three layer configuration PP-HDPE-LDPE indicates that PP is in contact with the environment, LDPE is in contact with the food and HDPE is between the other two. Number of layers Configurations 1 PP LDPE HDPE 2 PP-LDPE HDPE-LDPE PP-HDPE 3 PP-HDPE-LDPE LDPE-PP-LDPE LDPE-HDPE-LDPE HDPE-PP-LDPE HDPE-PP-HDPE (initial carvacrol concentration in each layer and film thickness) decision variables. The presence of integer variables makes the optimisation problem much305 more challenging to solve. However, in this problem, the number of possible layer combinations is low enough (eleven according to Table 4) to consider all of them individually. In this way, we can remove the discrete variables from the optimisation problem. In other words, the number of layers and their configuration will not be explicitly considered in the optimisation problem as decision310 variables. 16 Decision variables in the optimisation problem are, therefore, reduced to the thickness of the films and the initial concentration of carvacrol in each of them. The optimisation problem is solved numerically using a hybrid (global/local) strategy. The global optimisation approximates the neighbourhood of the global315 optimum whereas the local optimisation rapidly converges to the maximum of this global optimum. We have selected, for the global optimisation, the method of Differential Evolution (DE) (Storn & Price, 1997) because of its good convergence properties. On the other hand, the Matlab algorithm fmincon, in particular, the interior point method (Byrd et al., 2000), has been chosen320 for the local search. Regarding time integration, we have used the Matlab function ode15s, with the default numerical differentiation formulas, because of its capacity to solve stiff systems. 3. Results The objective is to design the package system to maximise use-by date (Case325 1); best-before date (Case 2); and to assess the changes in food shelf life due to variations on the transport/storage temperature profile and on the time span between package manufacturing and packaging contact with the food (Case 3). Estimations of use-by date rely solely on safety criteria whereas best-before date labelling is a more restrictive date relying on both safety and quality standards.330 As mentioned above, Listeria monocytogenes concentration and KI-value are selected as safety and quality indicators, respectively. The Matlab™codes used in the different case studies are available at https://doi.org/10.5281/ zenodo.3244153. 3.1. Case 1: Active packaging design to extend use-by date335 The objective is to select the active packaging film materials, their thicknesses (Liwith i= 1,2,3) as well as the initial concentration of carvacrol in each of them (Ci,0) to maximise the use-by date (tf). Mathematically this 17 expressed as: maximise tf,Li,Ci,0 Use-by date (tf) subject to Safety constraints, Design constraints. We consider, in this case study, ideal transport and storage conditions with constant room temperature T(t) = 3 ◦C. However, the methodology allows considering other cases such as time-varying profiles (see section 3.3). The use-by date is based on safety requirements. For fresh fish products safety is defined as the amount of time required to reach 100 CFU/g of Listeria340 monocytogenes. This constraint is based on EFSA recommendations (Commission of the European Communities, 2005). On the other hand, carvacrol has an effect on the organoleptic properties of food and, at large concentrations, it causes safety problems. As a result, there is a limit on carvacrol concentration allowed in the food matrix. Based on maximum concentrations reported in food345 and beverages (Burdock, 2010), we fix a limit of 0.03 kg/m3= 30ppm. This limiting carvacrol concentration avoids excessive oregano-like flavour and it is significantly lower than the reported toxicity levels of carvacrol in the literature (Suntres et al., 2015). Therefore, the optimisation is subject to the following constraints:350 •Listeria concentration at final time -Equation (12)-: Lm(tf)≤100 CFU/g. •Concentration of carvacrol in the food at all times -Equation (5)-: Cf(t)≤ 0.03 kg/m3. In practice, taking into account reasonable costs for food packages, bounds must be considered for film thickness. After stretching, the minimum layer355 thickness lies around 10-12 µm considering that PE and PP can be processed without tie layers given their compatibility (Butler & Morris, 2010). Additionally, fish primary packaging has a gauge between 40-90 µm with a growing tendency to thinner packaging. Although up to seven or even nine layers are possible in multilayers, two or three layers are still the most commonly used.360 18 Finally, maximum carvacrol initial concentration in each layer must be taken into account. Hence, we consider the following bounds on the decision variables: •Thickness of each individual layer: 12 ×10−6µm≤Li≤70 ×10−6µm. •Total thickness of the active packaging: 35×10−6µm≤L≤70×10−6µm. •Initial concentration of carvacrol in each layer (Cerisuelo et al., 2013):365 Ci,0≤80 kg/m3. Optimisation results are summarised in Table 5. Each row corresponds to one of the considered designs, being the first row the case without carvacrol (no active packaging). We observe that the use-by date is either (1) similar to the case without370 carvacrol, i.e. tfclose to 13.5 d, or (2) extended to values close to 15.8 d. The reported value for HDPE carvacrol diffusivity is very low, so its release into the food compartment is much slower than in the other two cases (PP, LDPE). As a consequence, when HDPE is the layer in contact with the food, release of carvacrol is considerably slow. Therefore L. monocytogenes concentration375 reaches the safety constraint before any inhibitory effect can be appreciated. The best designs use LDPE for the layer in contact with the food. LDPE has the largest carvacrol diffusivity which is equivalent to quickly transferring the carvacrol to the food product and inhibiting the growth of pathogens. Such strategy is limited by the maximum amount of carvacrol allowable in the food380 product (0.03 kg m−3). A slight improvement can be achieved by using bi- or trilayers where LDPE is in contact with the food product. Again, LDPE inhibits the growth of pathogens right after the contact and the other layers act as reservoir steadily releasing carvacrol. Note also that the length of LDPE in contact with the food corresponds with the minimum allowed (35 µm for385 monolayer and 12 µm for multilayer). Figure 2 shows the evolution of Listeria monocytogenes and carvacrol concentration in the food. Blue lines correspond to the best configuration of the active packaging (LDPE-PP-LDPE). Black lines represent the simulation results 19 Table 5: Optimal designs of active packaging to extend the use-by date (tf) First row corresponds with the control case (without carvacrol). Ci,0represents initial concentration of carvacrol in layer i.Licorresponds with the size of layer i. Units are: [d] for time, [kg/m3] for concentration, and [µm] for layer sizes. Layer Use-by date 1st layer 2nd layer 3rd layer configuration tfC1,0L1C2,0L2C3,0L3 - 13.43 - - - - - - PP 14.94 49.2 70.0 - - - - LDPE 15.69 18.2 35.0 - - - - HDPE 13.51 80.0 70.0 - - - - PP-LDPE 15.78 3.4 39.1 47.7 12.0 - - PP-HDPE 13.51 66.9 56.7 80.0 13.3 - - HDPE-LDPE 15.78 3.6 39.1 47.2 12.0 - - PP-HDPE-LDPE 15.78 57.0 13.3 3.6 42.2 48.7 12.0 LDPE-PP-LDPE 15.78 3.9 29.8 3.0 16.0 48.8 12.0 LDPE-HDPE-LDPE 15.78 57.0 13.3 3.6 42.2 48.7 12.0 HDPE-PP-LDPE 15.78 15.6 20.6 2.5 13.7 48.5 12.1 HDPE-PP-HDPE 13.51 78.9 33.0 17.0 23.8 80.0 13.3 obtained when no active packaging is used (control case). Dashed horizontal390 lines indicate admissible limits for the variable. The best design extends the use-by date by 18 % when compared with the control case. The improvement relates to the rapid release of carvacrol without exceeding the limit of 0.03 kg/m3. 20 0 0.01 0.02 0.03 0 2 4 6 8 10 12 14 16 (a) 1.6 1.7 1.8 1.9 2 0 2 4 6 8 10 12 14 16 (b) Carvacrol [kg/m3] Time [d] Without A.P. With A.P. Listeria [log CFUg−1] Time [d] Without A.P. With A.P. Figure 2: Time evolution of (a) carvacrol concentration in food; (b) Listeria monocytogenes. The figure corresponds with the LDPE-PP-LDPE configuration and room temperature is kept constant at 3 ◦C. Black line corresponds with the case where no active packaging is used. Dashed lines indicate bounds on the variables. 3.2. Case 2: Active packaging design to extend best-before date395 The objective is similar to the previous case but maximising best-before date instead of use-by date, and therefore, requiring standards for both food safety and quality. Mathematically, the problem is stated as: maximise tf,Li,Ci,0 Best-before date (tf) subject to Quality constraints, Safety constraints, Design constraints. As in the previous case, constant profile in room temperature is assumed T(t) = 3◦C. Safety and design constraints correspond with the ones selected in case 1 (Section 3.1), but the optimisation is now also subject to quality constraints. In this regard, and for fish products, KIvalues below 50% are considered mod-400 erately fresh whereas values above 70% indicate that fish is not fresh (Saito et al., 1959; Oca˜no-Higuera et al., 2011). Therefore, the following constraints are considered for the solution of the optimisation problem: •Listeria concentration at final time -Equation (12)-: Lm(tf)≤100 CFU/g. 21 •Concentration of carvacrol in the food at all times -Equation (5)-: Cf(t)≤405 0.03 kg/m3. •KI-value at final time: KI(tf)≤50 %. Table 6 summarises the results of the optimisations for different designs. First row corresponds to the case without active packaging (control case). Best- Table 6: Optimal designs of active packaging to extend best-before date (tf) while guaranteeing food safety and quality. First row corresponds with the control case (without carvacrol). Cx,0represents initial concentration of carvacrol in layer x.Lx corresponds with the size of layer x. Units are: [d] for time, [kg/m3] for concentration, and [µm] for layer sizes. Layer Best-before date 1st layer 2nd layer 3rd layer configuration tfC1,0L1C2,0L2C3,0L3 - 7.40 - - - - - - PP 8.58 63.9 70.0 - - - - LDPE 9.11 18.2 35.0 - - - - HDPE 7.44 80.0 70.0 - - - - PP-LDPE 9.20 3.0 56.6 48.6 12.0 - - PP-HDPE 7.44 67.0 19.8 80.0 50.2 - - HDPE-LDPE 9.20 3.6 37.0 47.2 12.0 - - PP-HDPE-LDPE 9.20 0.0 31.5 3.6 16.5 48.8 12.0 LDPE-PP-LDPE 9.20 11.7 23.8 2.9 24.4 49.4 12.0 LDPE-HDPE-LDPE 9.20 69.3 15.9 3.6 32.1 48.7 12.0 HDPE-PP-LDPE 9.20 28.5 30.4 2.5 17.7 49.5 12.0 HDPE-PP-HDPE 7.44 77.7 14.4 79.9 42.3 80.0 13.3 22 before date is reduced by several days as compared with the case where only410 safety constraints were considered (case 1). The reason is that the constraint on the KI-value is the more restrictive than the safety constraint. For the best designs, active packaging with multi-layer increases the bestbefore date in around a 24 %. Again, results show two main patterns: (1) those with a best-before date close to 7.4 d that correspond to the cases where HDPE415 is in contact with the food, and (2) those with a best-before date close to 9.2 d, where the layer in contact with the food is made of LDPE. Figure 3 represents the evolution of carvacrol, Listeria monocytogenes and KI-value for case study 2. Blue lines correspond to the best active packaging configuration (LDPE-PP-LDPE). Results when no active packaging is consid-420 ered are also represented (black line). As in the previous case, the best results 0 0.01 0.02 0.03 0123456789 (a) 1.6 1.7 1.8 1.9 2 0123456789 (b) 0 10 20 30 40 50 0 1 2 3 4 5 6 7 8 9 (c) Carvacrol [kg/m3] Time [d] Without A.P. With A.P. Listeria [log CFUg−1] Time [d] Without A.P. With A.P. KI-value [%] Time [d] Without A.P. With A.P. Figure 3: Time evolution of (a) carvacrol concentration in food; (b) Listeria monocytogenes; and (c) KI-value for the second case study. The figure corresponds with the LDPE-PP-LDPE configuration and room temperature is kept constant at 3 ◦C. Black line corresponds with the case where no active packaging is used. Dashed lines indicate bounds on the variables. are obtained with the configurations where carvacrol diffuses rapidly to reach the selected constraint of Cf(t) = 0.03 kg/m3. 3.3. Case 3: Effect on shelf life of transport/storage temperature profiles and packaging storage after manufacturing425 As discussed in Jedermann et al. (2014), shelf life is a dynamic value related to the actual quality and environmental conditions history that goes beyond any static use-by and best-before date. In this section, we will study the effect, on the KI-value, of changes in (i) the transport/storage temperature; and (ii) the 23 storage time of the package after its manufacturing and before being in contact430 with the food matrix. For the first case, we implement different time-temperature profiles simulating different abusive temperatures during transport/storage (see Figure 4(a)). We have chosen 50 randomly generated profiles in order to cover a wide range of possibilities. Transport and storage temperature is assumed to be 3 ◦C. How-435 ever, at a given time a perturbation is introduced in the storage temperature to simulate the effect of a malfunction on the temperature control devices. Perturbations have a maximum value of 30 ◦C, and their duration vary between 1 and 8 h. The specific value of the perturbation, the moment at which the perturbation occurs and its duration are randomly chosen as shown in Figure 4(a). Figures 0 5 10 15 20 25 30 0 2 4 6 8 10 (a) 0 10 20 30 40 50 0 2 4 6 8 10 (b) Max. t = 9.10 d Mean t = 8.51 d Min. t = 6.06 d One layer (LDPE) 0 10 20 30 40 50 0 2 4 6 8 10 (c) Max. t = 9.19 d Mean t = 8.56 d Min. t = 6.07 d Two layers (PP-LDPE) 0 10 20 30 40 50 0 2 4 6 8 10 (d) Max. t = 9.19 d Mean t = 8.57 d Min. t = 6.08 d Three layers (LDPE-PP-LDPE) 0 10 20 30 40 50 0 2 4 6 8 10 (e) Max. t = 7.28 d Mean t = 6.78 d Min. t = 5.25 d No active packaging Temperature [◦C] Time [d] KI-value [%] Time [d] KI-value [%] Time [d] KI-value [%] Time [d] KI-value [%] Time [d] Figure 4: (a) Time-temperature storage profiles used in case study 3. (b)-(e) Evolution of the KI-value in the food using the time-temperature storage profiles of Figure 4(a). Figures (b)-(d) correspond, respectively, to one layer, two layers and three layers cases. Figure (e) presents the results obtained when no active packaging is considered. Colours used in KI evolution figures correspond to the colours used in the time-temperature profiles. Horizontal dashed line indicate bound on the variable. Maximum, mean and minimum values of the best-before date for each of the cases are also indicated. 440 4(b)-(d) show the effect of these time-temperature profiles on the KI-value for the best monolayer, bilayer and trilayer configurations, respectively. The three configurations resulted in almost equivalent KI-values, as expected from the results obtained in the previous section. Shelf life (time for the Ki-value to reach 24 50 %) vary between 6.2 d and 9.2 d. Finally, Figure 4(e) corresponds to the445 case without active packaging. Considering active packaging increases shelf life, in mean value, around 20%. Temperature profiles of Figure 4(a) have also an impact on the maximum carvacrol concentration on the fish fillet surface. In most of the cases, such concentration remains below the maximum allowed (0.03 kg m−3). However, when450 considering three layers, some of those profiles result in maximum carvacrol concentrations of around 0.031 kg m−3, i.e. above the constraint. The smart active packaging approach allows evaluating safety and quality criteria under unexpected storage perturbations. In multilayer configurations, carvacrol concentration varies within the differ-455 ent layers even if the packaging is not in contact with the food. In other words, after packaging manufacturing and before packaging use, carvacrol concentration will change within the layers. The procedure proposed in this work allows us to take these changes into account. The aim of the second test is to evaluate the effect, on the KIvalue, of the time span between packaging manufacturing460 and packaging use. To that purpose we perform two simulations. The first simulation is carried out to obtain the carvacrol distribution in the layers just before the package is used to wrap the food. In the second simulation, we use such distribution as initial conditions for the package/food model. Before the package is used, the model describing the evolution of carvacrol465 within the layers is formed by equations (1)-(3) and ∂Cn ∂x x=H = 0, indicating that no flux of carvacrol is considered between the right boundary and the outer environment. Using this model we obtain the concentration of carvacrol in the package at different times (t= 0,3,6,12,18,24,30), see Figures 5(a) and 5(c) for two layer (PP-PDE) and three layer (LDPE-PP-LDPE)470 configurations, respectively. As mentioned above, the results of such simulations are used as initial conditions for the model that considers both package and food, i.e. Eqs. (1)- (19), 25 Cerisuelo, J. P., Muriel-galet, V., Berm´udez, J. M., Aucejo, S., Catal´a, R., Gavara, R., & Hern´andez-Mu˜noz, P. (2012). 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(2005). Intelligent Packaging: Concepts and Applications. Journal of Food Science,70, R1–R10. 36 Zengin, H., & Baysal, A. H. (2015). Antioxidant and Antimicrobial Activities765 of Thyme and Clove Essential Oils and Application in Minced Beef. Journal of Food Processing and Preservation,39, 1261–1271. Zhang, H., Hortal, M., Dobon, A., Bermudez, J. M., & Lara-Lledo, M. (2015). The Effect of Active Packaging on Minimizing Food Losses: Life Cycle Assessment (LCA) of Essential Oil Component-enabled Packaging for Fresh Beef.770 Packaging Technology and Science,28, 761–774. Appendix A. Derivation of Diffusion equation parameters Parameter values indicated in Table 1 were obtained by combining the values presented in different scientific contributions. In this regard, for polypropylene (PP) layer, diffusivities at two different temperatures (T= 296.15 K, T=775 373.15 K) are presented in Cerisuelo et al. (2012) and Krepker et al. (2018), respectively: DP P (296.15 K) = 3.00 ×10−15,DP P (373.15K) = 9.42 ×10−13 m2s−1. Using Eq. (6), we obtain DP P (296.15) = 3.00 ×10−15 =DP P (Tref ) exp −EA,P P R1 296.15 −1 Tref  DP P (373.15) = 9.42 ×10−13 =DP P (Tref ) exp −EA,P P R1 373.15 −1 Tref  which, by dividing both equations, can be expressed as:780 3.00 ×10−15 9.42 ×10−13 = exp −EA,P P R1 296.15 −1 373.15 Taking into account that R= 8.314 J mol−1K−1, we obtain EA,P P = 1.27 ×105 J mol−1. On the other hand, reference temperature in Table 1 is Tref = 293.15 K so that: 3.00 ×10−15 =DP P (293.15) exp −1.27 ×105 8.134 1 296.15 −1 293.15 therefore, DP P (Tref ) = DP P (293.15) = 1.77 ×10−15 m2s−1.785 37 For high-density polyethylene (HDPE) layer we used the values in Peltzer et al. (2009), i.e. DHDP E(298.15K) = 8.13 ×10−17 m2s−1; and DP P (313.15K) = 5.01 ×10−15 m2s−1. Following the same procedure as in the case of PP layer, we firstly obtained the activation energy value, EA,HDP E = 2.14 ×105J mol−1 and secondly we used such value to obtain the diffusivity at the reference tem-790 perature, i.e. DHDP E (Tref ) = DHDP E (293.15) = 1.80 ×10−17 m2s−1. Finally, Rupika (2010) presented the values of carvacrol diffusivity in lowdensity polyethylene (LDPE) at three different temperatures: DLDP E (293.15K) = 8.10 ×10−14;DLDP E (288.15K) = 3.80 ×10−14; and DLDP E (283.15K) = 1.90 ×10−14 m2s−1. In order to obtain the activation energy, logarithms are applied to the795 diffusivity equation so that: log (DLDP E (T)) = log (DLDP E (Tref )) −EA,LDP E R1 T−1 Tref  This corresponds to a line equation with slope −EA,LDP E R. Activation energy can be, therefore, computed using linear regression: EA,LDP E = 1.01 ×105 J mol−1. 38