Integrative mathematical modelling for MAP design of fresh-produce: Theoretical analysis and experimental validation

Food Control 29 (2013) 444e450

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Integrative mathematical modelling for MAP design of fresh-produce: Theoretical analysis and experimental validation Maria J. Sousa-Gallagher*, Pramod V. Mahajan Department of Process and Chemical Engineering, School of Engineering, College of Science, Engineering and Food Science, University College Cork, Ireland

a r t i c l e i n f o

a b s t r a c t

Article history: Received 5 December 2011 Received in revised form 28 May 2012 Accepted 29 May 2012

Modified Atmosphere Packaging (MAP) of fresh produce is a dynamic system and relies on the modification of the atmosphere inside the package, achieved by the natural interplay between two processes, the respiration of the product and the transfer of gases through the packaging film, which leads to an atmosphere richer in CO2 and poorer in O2. The challenge is how to integrate the mathematical modelling depicting product respiration rate and package permeability to simplify the packaging design process. The aim of this paper is to show the application of integrative mathematical modelling for MAP design of fresh produce. Mathematical models on product respiration rate and package permeability have been compiled into a comprehensive database and by using engineering principles were integrated on a web-based software platform (Pack-in-MAPÒ) which can be used to design and simulate the packaging needs for fresh produce. The aim of this paper was to illustrate the use of Pack-in-MAPÒ software and additionally simulate and validate the MAP design for fresh whole strawberry. The experimental and predicted gas compositions during storage were closely matching thereby showing the ability of Pack-in-MAPÒ software to determine the ideal packaging solution and predict the gas composition inside the package during storage period. Further, it can also evaluate the impact of temperature variation, and variability of product/package on gas composition providing a system which allows selection of suitable packaging materials for fresh produce. The Pack-in-MAPÒ software can be used to test several solutions on a value-for-money basis in order to achieve results while minimising costs and avoiding costly trial-and-error approaches. Ó 2012 Elsevier Ltd. All rights reserved.

Keywords: Modified atmosphere packaging Integrative mathematical modelling Respiration Permeability Packaging Validation Strawberries

1. Introduction Integrative mathematical modelling of food processes is a highly interdisciplinary area of research involving process engineering, industrial practices and software programmers. Its ultimate aim is to combine information, tools, mathematical models to forecast impact of various factors on food quality/safety, and also simulate packaging design. It involves development of user friendly interface to integrate various parts of food models and processes. Using integrative modelling tools, physical reality can be replaced by its equivalent computer model, therefore, allowing testing “what-if” scenarios and insights of the systems. Mathematical modelling offers a systematic approach of the process and can assist as a tool for data analysis and screening tests. Today, modelling efforts are highly fragmented among food academia, food industry and software developers, as a result, little is available in terms of an integrated tool. A concerted effort is required to bring together the * Corresponding author. Tel.: þ353 21 4903594; fax: þ353 21 4270249. E-mail address: [email protected] (M.J. Sousa-Gallagher). 0956-7135/$ e see front matter Ó 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.foodcont.2012.05.072

three particular groups involved, have them communicate with each other to develop a road map for the most effective way to reach the goal (Datta & Halder, 2008). Modified atmosphere packaging (MAP) is a well known technique for preserving fruit and vegetables by extending their shelf life. It relies on the modification of the atmosphere inside the package, achieved by the natural interplay between two processes, the respiration of the product and the transfer of gases through the packaging film (Fig. 1), which leads to an atmosphere richer in CO2 and poorer in O2 (Mahajan, Oliveira, Sousa, Fonseca, & Cunha, 2006). In this system, atmosphere is generated naturally by product respiration rate. However, it is necessary to define conditions that will create the atmosphere best suited for the extended storage of a given produce while minimising the time required to achieve this atmosphere. The major challenge would be to find the most appropriate packaging material (or the number of perforations required) to match the respiration rate for each specific fresh product. As different products vary in their respiration behaviour, each package has to be optimised for a given set of environmental storage conditions.

M.J. Sousa-Gallagher, P.V. Mahajan / Food Control 29 (2013) 444e450

O2

CO2 Micro-perforated film

445

second group was to pack in the package optimally designed using Pack-in-MAPÒ software. 2.2. Selection of package

RO2

RCO2

Respiring product

Fig. 1. Gas exchange in a modified atmosphere packaging containing respiring fresh product.

There is already enough information available on various aspects of MAP (Fonseca, Oliveira, & Brecht, 2002; Hertog & Banks, 2001; Kader, 2010; Mahajan et al., 2006) which were compiled together to find packaging solutions for a particular fresh produce under a given set of processing and environmental conditions. By applying mathematical models, the development phase of MAP can be shortened. Such analysis could provide an initial screening of packaging options, point out their potential limitations, and allow focussing prototype testing in a smaller set of designs. Hertog and Banks (2001) said that experiments can be done behind the laptop checking all possible combinations that would otherwise take weeks to test in practise using “pack-and-pray approach”. However, significant work was needed to organise the information and integrate it into a user-friendly software tool (Mahajan, Oliveira, Montanez, & Frias, 2007; Mahajan & Sousa-Gallagher, 2011; Mahajan, Sousa-Gallagher, Yuan, Patel, & Oliveira, 2009). Using packaging of fresh produce as an example, integrative mathematical modelling would simplify the design process that would help in exploring several choices of film types, package size, and product quantity, creating combinations that will result in beneficial results, therefore, reducing number of experimental trials required to explore possible packaging options worthy of testing. This paper presents the integrative mathematical modelling tool the Pack-in-MAPÒ for designing MAP and illustrates its application by simulating and validating the results for fresh whole strawberries. An oral communication was presented at the proceedings of the Seventh International Conference on Predictive Modelling in Foods (Mahajan & Sousa-Gallagher, 2011).

A rigid tray (PET) of size 15.8  9  4 cm was used to pack 200 g of strawberries. Commercial packaging used by strawberry producers i.e. clamshell container (15.8  9  4 cm) with macroperforations on the rigid lid was used as the control package. The lid had two rectangular macro-perforations (4  1 cm) that enabled a transfer of gases much higher than the respiration rate of the amount of strawberries packaged, therefore gas composition was not modified inside the clamshell package. Strawberry is a high respiring product (Hertog, Boerriter, van den Boogaard, Tijskens, & van Schaik, 1999); therefore only a combination of polymeric film with micro-perforations could potentially provide adequate gas exchange for O2 and CO2. Lidding film (NatureFlex NVS, Innovia Films Ltd, Cumbria, U.K.) with breathable area of 142.2 cm2 was used for simulation and validation of the packaging (NVS). A needle was used to make perforations, as determined by Pack-in-MAPÒ software, on the lidding film in the optimal package. The O2 permeability of the NVS film was 18 cc/ m2 day atm at 23  C, 90% RH, permeability for CO2 was not available, therefore, a beta ratio ðPCO2 =PO2 Þ of 3.0 was assumed. Both sets of packages, i.e., commercial (control) and optimally designed (NVS) packages were stored at 10  C for 8 days. 2.3. Evaluation of package performance The change in gas composition (O2 and CO2) inside each package was monitored over time using a gas analyser (Dansensor, Checkmate 9900, Denmark). Quality parameters such as firmness, weight loss, visual fungal, overall appearance and aroma of strawberries packed in optimal and control packages were measured after 8 days of storage. Firmness was measured as the force required to compress the sample by 3 mm distance using 6 mm probe (Stable Microsystems, UK). Weight loss was expressed as percentage of initial weight of sample. For visual fungal, the quality of strawberries was visually assessed by counting the number of strawberries visibly affected by Botrytis, expressed as a percentage of the number of strawberries present (Hertog et al., 1999). Overall appearance and aroma was evaluated using 9-point numerical rating scale (1-poor, 9-excellent appearance and 1-no smell and 9-full typical aroma). 3. Integrative mathematical modelling for MAP design

2. Material and methods

3.1. Respiration rate of fresh produce

2.1. Selection of product

Fresh produce are living commodities which respire even after harvest i.e. they consume O2 and produce CO2. Due to the respiration process, an O2 and CO2 concentration gradient between the package headspace and the storage environment is generated. Thus, a gas flow is activated through the packaging material to the surrounding atmosphere. If this gas flow is controlled using suitable barrier properties of packaging material, equilibrium will be achieved. At this equilibrium, the rate of gas exchange between the product and the packaging material equals, therefore, subsequently the gas composition surrounding the product is maintained for the rest of the storage life. Extensive research has been done on the effect of temperature, O2, CO2 and storage time on respiration rate of fresh and fresh-cut fruits and vegetables (Fonseca, Oliveira, & Brecht, 2002). Mathematical models have been developed by several researchers (Fonseca, Oliveira, Frias, Brecht, & Chau, 2002; Iqbal, Rodrigues,

Pack-in-MAPÒ software database contains a wide range of fresh and fresh-cut fruits and vegetables. To illustrate the use of Pack-inMAPÒ software for MAP design, fresh strawberries were selected as a product for the validation. Strawberry fruit is a very perishable commodity, due to high respiration and it is highly susceptible to grey mould rot. Wszelaki and Mitcham (2003) reported that strawberries are highly suitable for packaging under modified atmospheres as research showed high CO2 concentration has a great potential for increasing shelf life and quality of strawberry fruit. To perform validation tests, strawberries (cv. Elsanta) were procured from a local whole supplier (Southern Fruit, Cork, Ireland). Strawberries were divided into two groups; one group was used to pack in commercially available clamshell package and the

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Mahajan, & Kerry, 2009; Lee, Haggar, Lee, & Yam, 1991; Peppelenbos & van’t Leven, 1996) considering different factors such as temperature, O2, CO2 in most of the models and storage time, in few models. The most commonly used expression to model the temperature dependence of respiration rate is the Arrhenius equation (Hertog et al., 1999; Rodriguez-Aguilera & Oliveira, 2009).

gas and water vapour between headspace of the package and surrounding atmosphere. Permeability in terms of O2 and CO2 is an important factor to be considered while designing MAP for fresh produce. It changes with temperature; hence, a mathematical model is required to predict the permeability change in the packaging material at a given temperature which is as a function of temperature (Exama et al., 1993).

RO2 ;CO2 ¼ Rref eðEa =R½ð1=TÞð1=Tref ÞÞ

PO2 ;CO2 ¼ Pref eðEa =R½ð1=TÞð1=Tref ÞÞ

(1)

where, RO2 ;CO2 is the respiration rate, T is the temperature, Rref is the respiration rate at reference temperature (Tref), Ea is the activation energy and R is the universal gas constant. Ea values range from 29.0 to 92.9 kJ/mol for common fruits and vegetables in air (Exama, Arul, Lencki, Lee, & Toupin, 1993). The most commonly used mathematical model to account for the influence of O2 and CO2 on respiration rate of fresh produce are based on MichaeliseMenten enzyme kinetics (Fonseca, Oliveira, & Brecht, 2002; Hertog et al., 1999; Iqbal et al., 2009; Mahajan & Goswami, 2001; Peppelenbos & van’t Leven, 1996). The equations used depend on the type of inhibition by CO2 as described in Eqns. (2)e(6) (Fonseca, Oliveira, & Brecht, 2002). Some of the models are extended with temperature dependence according to the Arrhenius equation resulting in a global model for respiration rate which takes into account the influence of both temperature and gas composition.

RO2 ¼

Vm $yO2 Km þ yO2

(8)

where, PO2 ;CO2 is permeability at temperature T, Pref is the permeability at reference temperature (Tref). Polymeric films commonly used in MAP have low values of permeability to O2, with values of the b ratio, PCO2 =PO2 , in the range of 2e10 (Paul & Clarke, 2002). This represents an important limitation of MAP for highly respiring products because a combination of low O2 permeability and high respiration rate easily leads to anaerobic conditions inside the package (Rodriguez-Aguilera & Oliveira, 2009). One of the alternatives to overcome these limitations is to use macro- or micro-perforations in the polymeric films. Perforations in a polymeric film represent a parallel route for gas transport. Mathematical modelling of mass transfer through perforated packaging have been reviewed by Rodriguez-Aguilera and Oliveira (2009). Apparent permeability, Eqn. (9), which is a function of the film permeability and of the number and size of holes (Fishman & Rodov Ben-Yehoshua, 1996) can be used for calculating the overall permeability of perforated film.

"

(2) PO2 ;CO2 ¼

PO2 ;CO2 þ

pR2H  DO2 $CO2 ðe þ RH Þ

#  NH

(9)

RO2 ¼

Vm $yO2
 Km 1 þ yCO2 =kc þ yO2

(3)

where, RH is the radius of the perforation and NH the number of perforations, D is diffusion coefficient of each gas in air.

RO2 ¼

V $y
m O2  Km þ 1 þ yCO2 =ku yO2

(4)

3.3. Optimum gas composition

RO2

Vm $yO2 
 ¼
Km þ yO2 1 þ yCO2 =kn

RO2 ¼

Vm $yO2
  Km : 1 þ yCO2 =kc þ yO2 $ 1 þ yCO2 =ku


(5)

(6)

where, Vm is maximum respiration rate, Km is MichaeliseMenten constant, k is inhibition constant for competitive (c), uncompetitive (u), non-competitive (n) type of inhibition, yO2 and yCO2 is the O2 and CO2 concentration, respectively. In some cases time also affects the respiration rate owing to product ageing or response to stress induced by product preparation (e.g. cutting), this effect has been modelled using Weibull frequency distribution (Fonseca, Oliveira, Frias, et al., 2002; Iqbal et al., 2005).

The optimum gas compositions required for maintaining product quality differs from product-to-product and has been extensively reported for fresh and fresh-cut fruits and vegetables (Saltveit, 2003). These include tabular or graphical form of O2 and CO2 range suitable for a given product. The range of gas composition that best extends product shelf life is often called the ‘window’ of recommended atmosphere. Optimum range of O2 and CO2 for strawberries are 5e10% and 15e20%, respectively (Kader, 1992). 3.4. Engineering packaging design

where, R0 and Req is the respiration rate at time zero and at equilibrium respectively, t is storage time, s is a time constant, and b is a shape constant.

To design MAP successfully, consolidated knowledge of product respiration rate, gas permeability (O2 and CO2) of packaging material, optimum atmosphere (O2 and CO2) for the given product, along with other parameters such as package geometry, product weight would be required. The simplest concept of packaging design is to use the packaging film as the regulator of O2 flow into the package and the flow of CO2 out as schematically represented in Fig. 1. Assuming that there is no gas stratification inside the package and that the total pressure is constant, the differential mass balance equations (Mahajan et al., 2006, 2007) that describe O2 and CO2 concentration changes in a package containing a respiring product are:

3.2. Permeability of packaging materials

Vf 

b R  Req ¼ eðt=sÞ R0  Req

(7)

Application of polymeric films are commonly used for MAP of fresh produce (Mangaraj, Goswami, & Mahajan, 2009). The film acts as a barrier between the environment and the product, controlling

Vf 


   d yO2 P ¼ O2  A  yout O2  yO2  RO2  M dt e
   d yCO2 PCO2 ¼  A  yout CO2  yCO2 þ RCO2  M dt e

(10)

(11)

M.J. Sousa-Gallagher, P.V. Mahajan / Food Control 29 (2013) 444e450

where Vf is the headspace (free volume) in the package, e is the thickness of polymeric film, and M is the weight of the product (M); the subscripts O2 and CO2 refer to oxygen and carbon dioxide, respectively and the superscript ‘out’ refers to external atmosphere. At steady-state the accumulation term in Eqns. (10) and (11) is zero, and these equations are reduced to: eq

out yeq O2 ¼ yO2 þ

eq

RO2  e  M

yCO2 ¼ yout CO2 

(12)

PO2  A Req CO2  e  M

(13)

PCO2  A

The models that describe the dependence of respiration rate on gas composition, temperature (and eventually time) and models that describe the dependence of the packaging material on temperature can be integrated to Eqns. (10)e(13). Thereby, it would be possible to calculate exactly the type of packaging material required, size and number of perforations that would result in the ideal packaging solution. A design protocol for the selection of packaging material using mass balance equations at steady state (Eqns. (12) and (13) was reported by Mahajan et al. (2006) and Mahajan et al. (2007). In a plot of CO2 versus O2 concentration, the points that correspond to equilibrium will lie along a straight line which crosses the point (0.21, 0, air composition) and has a slope equal to eRQ/b where RQ is respiration quotient, RCO2 =RO2 . Therefore, to ensure that a given packaging system may be able to yield the required gas composition, its permeability ratio has to be such that the resulting straight line crosses the window of recommended gas atmosphere for the selected product. A polymeric film with a high b results in an equilibrium atmosphere that is low in CO2 and in O2, while films with a low b (e.g., <2) tend to accumulate high levels of CO2 without regard to absolute permeation rates. Mahajan et al. (2006) further explained how to predict equilibrium gas composition and time required to achieve it. Finally, the mass balance Eqns. (10) and (11) were integrated with the mathematical models for respiration rate and for permeability, including micro- or macro-perforations, along with other parameters such as product weight, film area, film thickness, and package geometry.

447

3.5. Software application Considering the complexity of mathematical models and large number of parameters involved in MAP design, an integrative mathematical tool called Pack-in-MAPÒ software was developed (Mahajan et al., 2006; Mahajan, Oliveira, Montanez, & Frias, 2004, 2007). The user friendly software was developed in Matlab to solve mass balance Eqns. (10) and (11) considering mathematical models for respiration rate and film permeability. It was later further developed into a web-based (www.packinmap.com) software with added features e.g., user friendly interface, tailored packaging design (Mahajan et al., 2009) and packaging for mixed mixtures (Mahajan & Sousa-Gallagher, 2011). In Pack-in-MAPÒ software, the user selects the type of product (whole, fresh-cut, or mixed salad) and inputs the amount of product to be packed. It selects the optimum MAP conditions (O2, CO2, and temperature) with suitable package geometry and size. The software calculates the respiration rate for that product at the given storage conditions and it recommends the best possible films and number and size of micro-perforations, if required. Pack-inMAPÒ software then simulates how the package atmosphere (O2 and CO2) changes over storage time combining the models that predict the respiration rate as function of gas composition and temperature (and eventually time) and the models that predict the package gas permeability (OTR and CTR) as a function of temperature. It can also simulate at a given timeetemperature profile for the particular product, indicating the O2 and CO2 at equilibrium and the time required to reach it. The software also allows the user to evaluate the impact of variability of the product respiration rate or the package gas permeability on package gas atmosphere. 4. Results and discussion 4.1. Simulation of package atmosphere Pack-in-MAPÒ software was used to simulate the OTR, CTR for strawberry package, and considering the film selected indicate the number of perforation required for achieving the optimum gas composition. The predicted equilibrium gas composition for NVS film package with 200 g of strawberries at 10  C using different size and number of perforation is shown in Fig. 2. The equilibrium O2

25 O2, 0.25mm Φ

CO2, 0.25mm Φ

O2, 0.6mm Φ

CO2, 0.6mm Φ

Equilibrium gas composition, %

20

15

10

5

0 0

2

4

6

8

10

12

14

16

Number of holes Fig. 2. Predicted equilibrium gas composition (O2, solid line and CO2, dotted line) at different size (triangle, 0.25 mm F and circle, 0.6 mm F) and number of perforations for a NVS film package with 200 g of strawberries, at 10  C.

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21 100 g 140 g

18 Package O 2 and CO 2 , %

180 g 15 12 9 6 100 g 140 g

3

180 g 0 0

25

50

75

100

125

150

175

200

Time, h Fig. 3. Predicted gas composition (O2, continuous line and CO2, dotted line) during storage of strawberry in a NVS film package with 2 perforations of size 0.25 mm F, containing 100, 140 and 180 g of strawberries at 10  C.

increased and that of CO2 decreased with increasing number of perforations. At least one perforation of size 0.6 mm or two perforation of size 0.25 mm is required to avoid O2 going below the lower tolerance limit i.e. 5%. The predicted gas composition in a NVS film package with 2 perforations of 0.25 mm containing different amounts of strawberries is shown in Fig. 3. The gas dynamics in all combinations consisted of a decrease in O2 and increase in CO2 from initial gas concentration in the package to a steady state gas concentration in the package which was reached within 50 h of storage irrespective of weight of product. However, the levels of steady state were different, for 100 g of strawberries the CO2 level was below the desirable limit whereas for 140 and 180 g of strawberries both the O2 and CO2 levels were within the desirable limit. Other packaging design parameters which could be varied, e.g., could be a different product weight, different packaging material, and/or change size and number of perforations. There are multiple outcomes for a suitable modified atmosphere (MA) package for strawberries taking in consideration the target MA conditions as shown in Fig. 4. As an example, a package with either combination

of (number of perforation, size of perforation, weight of strawberry) 2, 0.25 mm, 200 g or 1, 0.6 mm, 200 g or 2, 0.25 mm, 180 g would be able achieve an equilibrium gas composition within the recommended range for strawberry. Therefore, a package with 2 perforations of size 0.25 mm diameter (0.098 mm2) containing 200 g of strawberries was selected for the validation stage as the optimal package. This package would yield an equilibrium atmosphere of 5% O2 and 18.3% CO2 within 2 days of storage. 4.2. Validation of simulated results Experiments were performed to validate the simulated results in the package optimally designed using Pack-in-MAPÒ software. The change of O2 and CO2 concentration with time inside the designed MAP package containing strawberries stored at 10  C is shown in Fig. 5. The changes in gas composition predicted using Pack-in-MAPÒ models are also shown for comparison. When using 2 perforations of 0.25 mm diameter, the equilibrium atmospheric composition was 4.8% O2 and 19.5% CO2 at 10  C, thus well in the recommended atmosphere (5e10% O2 and 15e20% CO2). These results are in agreement with Sanz, Perez, Olias, and Olias (2000)

25 25

20 Package gas composition, %

20

CO 2 , %

15

10

5

15

10

5

0 0

25

50

75

100

125

150

175

200

Time, hr

0 0

5

10

15

20

25

O 2, % Fig. 4. Recommended atmosphere for MA packaging of strawberry (dotted box). The symbols (circle, triangle, plus) represent the equilibrium O2 and CO2 at various combinations of perforation size, number and product weight, respectively.

Fig. 5. Experimental versus predicted gas composition as a function of time inside an optimal package (NVS film with 2 perforations, 0.25 mm diameter) designed using Pack-in-MAPÒ software. Predicted gas composition is shown with continuous line and experimental data on O2 and CO2 is shown with triangle and circle, respectively. Dashed lines represent predicted gas composition considering 10% variability in respiration rate and permeability of a perforated film.

M.J. Sousa-Gallagher, P.V. Mahajan / Food Control 29 (2013) 444e450

449

Visual fungal, %

Firmness, g

Appearance Control package Optimum package

Aroma

Weight loss, %

0

5

10

15

20

25

30

35

40

45

50

Quality indices Fig. 6. Changes in quality parameters of strawberry stored at 10 0.25 mm diameter).

C

for control package (clamshell with macro perforations) and optimum package (NVS film with 2 perforations,

who studied the effect of micro-perforations on package atmosphere for strawberries at 2  C for three days and then at 20  C for four days. Perforation degree affected final gas contents inside the packages, optimum number of perforations found were 2e4 holes of 1 mm diameter and 1 to 2 holes of 2 mm diameter for 500 g of strawberries. The predicted equilibrium gas composition was 5.0% O2 and 18.3% CO2. The mean relative percentage deviation modulus (MacLaughlin & O’Beirne, 1999) between experimental and predicted O2 and CO2 was 13.9 and 10.8%, respectively showing the ability of Pack-in-MAPÒ software to predict the gas composition inside the package during storage period. The equilibrium time was quite long, but one should note that after 2 days the gas composition inside the package was already in the recommended range for strawberry, and therefore a suitable MAP packaging design. Therefore, the use of Pack-in-MAPÒ software to determine the size and number of micro-perforations in packaging of fresh produce showed to be a feasible and low cost approach for optimum packaging design for fresh strawberries.

package were above the rejection limit for visual fungal decay and weight loss at the end of storage period in agreement with Hertog et al. (1999). Strawberries packed in micro-perforated package lost 6.4% weight whereas in control packages, the weight loss was 13.1% after 8 days of storage at 10  C (Fig. 6). The reason for the considerable weight loss in control package was due to macro perforations on lidding shell causing dehydration. Thus, it is possible to reduce the weight loss of strawberries and at the same time achieve optimal gas composition by using micro-perforated package as shown in this study. Although final water loss in micro-perforated package was above 6%, further work would be required to account for transpiration rate (rate of weight loss) as additional criteria for packaging design of fresh produce.

4.3. Quality parameters Strawberries in optimally designed package after 8 days at 10  C, showed better appearance, aroma, firmness with lowest fungal infection and weight loss, as compared with control package (Fig. 6). Strawberries in optimally designed package showed better overall appearance (Fig. 7) due to optimal package atmosphere (4.8% O2 and 19.5% CO2), whereas control packages, in which gas composition was not modified, the strawberries were beyond the rejection limit. These results showed that low O2 and high CO2 are particularly effective in minimising fungal decay and improving overall acceptance quality. Sanz, Perez, Olias, and Olias (1999) reported that strawberry fruits from micro-perforated packages which achieved gas composition close to the recommended gas composition showed a lesser degree of visual fungal of 2.8% as against 75% in control package, and those micro-perforated packages showed no fungal decay after five days with minimal weight loss. The reduction of decay in optimally designed package was due to atmosphere enriched with CO2 in agreement with Hertog et al. (1999). Sensory data obtained on aroma and overall appearance showed significant preference for the fruits stored in a micro-perforated package than the control package (Fig. 7). Strawberries packed in control

Fig. 7. Strawberries after 8 days of storage at 10  C in optimum package (NVS film with 2 perforations, and 0.25 mm diameter) and control package (clamshell with macro perforations).

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5. Conclusions Integration of product and package mathematical models in Pack-in-MAPÒ software enabled the users to choose suitable packaging solution for achieving MAP rapidly and within the optimal O2 and CO2 range. Validation showed a good agreement between the software predictions and experimental data on fresh strawberries at 10  C. Modified atmosphere package designed for strawberries reached optimum composition within 2 days, presenting an overall acceptance up to 8 days of storage at 10  C, showing its suitability in comparison with the commercially available packages. Pack-inMAPÒ can help the fresh produce industry to simulate “what-if” scenarios without any knowledge of mathematical models, package design and MAP itself. Potential users will benefit by testing several solutions of designed MAP on a value-for-money basis thus avoiding costly trial-and-error approaches. Acknowledgements The authors acknowledge financial support from FIRM (00/R&D/ UL55 and 08/R&D/UL661), administered by the Department of Agriculture, Fisheries & Food, and from Enterprise Ireland (PC/ 2008/0118 and CP/2009/0205). Thanks to Innovia Films Ltd, Cumbria, U.K. for supplying the NatureFlex NVS packaging film. References Datta, A. K., & Halder, A. (2008). Status of food process modelling and where do we go from here (synthesis of the outcome from brainstorming). Comprehensive Reviews in Food Science and Safety, 7, 117e120. Exama, A., Arul, J., Lencki, R. W., Lee, L. Z., & Toupin, C. (1993). Suitability of plastic films for modified atmosphere packaging of fruits and vegetables. Journal of Food Science, 58, 1365e1370. Fishman, S., & Rodov Ben-Yehoshua, V. (1996). Mathematical model for perforation effect of oxygen and water vapor dynamics in modified atmosphere packages. Journal of Food Science, 61(5), 956e961. Fonseca, S. C., Oliveira, F. A. O., & Brecht, J. K. (2002). Modelling respiration rate of fresh fruits and vegetables for modified atmosphere packages: a review. Journal of Food Engineering, 52, 99e119. Fonseca, S. C., Oliveira, F. A. O., Frias, J. M., Brecht, J. K., & Chau, J. K. (2002). Modelling respiration rate of shredded Galega kale for development of modified atmosphere packaging. Journal of Food Engineering, 54, 299e307. Hertog, M. L. A. T. M., & Banks, N. H. (2001). Improving modified atmosphere packaging through conceptual models. In L. M. M. Tijskens, M. L. A. T. M. Hertog, & B. M. Nicolai (Eds.), Food process modelling (pp. 289e308). USA: CRC Press. Hertog, M. L. A. T. M., Boerriter, H. A. M., van den Boogaard, G. J. P. M., Tijskens, L. M. M., & van Schaik, A. C. R. (1999). Predicting keeping quality of strawberries (cv. ‘Elsanta’) packed under modified atmospheres: an integrated model approach. Postharvest Biology and Technology, 15, 1e12. Iqbal, T., Oliveira, F. A. R., Mahajan, P. V., Kerry, J. P., Gil, L., Manso, M. C., et al. (2005). Modeling the influence of storage time on the respiration rate of shredded carrots at different temperatures under ambient atmosphere. Acta Horticulturae, 674, 105e111.

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