16.1 Introduction Conceptual models are descriptions of our understanding of a system that are used to shape the implementation of solutions to problems. 58 The quality and quantum of innovation that will occur in development of modified atmosphere packaging (MAP) strongly depends upon the insights gained from robust conceptual models of components of MAP. In this chapter, we outline a number of simple principles about modified atmosphere (MA) systems that we believe will assist industries that apply MA technology to move beyond the rather empirical ‘pack-and-pray’ approach that still predominates in commercial practice. This chapter will focus on the applications of MAP for the horticultural food industry, dealing with respiring plant produce, whole or minimally processed. However, most of the principles discussed will also hold for MAP of meat or processed food. MA is generally used as a technique to prolong the keeping quality 64 of fresh and minimally processed fruits and vegetables. 75 In the widest sense of the term, MA technology includes controlled atmosphere storage, ultra low oxygen storage, gas packaging, vacuum packaging, passive modified atmosphere packaging and active packaging. 30,38,39,71 Each of these techniques is based on the principle that manipulating or controlling the composition of the surrounding atmospheres affects the metabolism of the packaged product, such that the ability to retain quality of the product can be optimised. The different techniques come with different levels of control to realise and/or maintain the composition of the atmosphere around the product. While controlled atmosphere storage can rely on a whole arsenal of machinery for this purpose, active packages rely on simple scavengers and/or emitters of gases such as oxygen, 16 Improving MAP through conceptual models M.L.A.T.M. Hertog, Katholieke Universiteit Leuven, Belgium and N.H. Banks, Zespri Innovation Ltd, New Zealand carbon dioxide, water or ethylene either integrated in the packing material or added in separate sachets. Passive MA packaging, as an extreme, relies solely on the metabolic activity of the packaged product to modify and subsequently maintain the gas composition surrounding the product. Although much research has been done to define optimum MA conditions for a wide range of fresh food products, 37 the underlying mechanisms for the action of MA are still only superficially understood. The application of MA generally involves reducing oxygen levels (O 2 ) and elevating levels of carbon dioxide (CO 2 ) to reduce the respiratory metabolism. 38 Parallel to the effect on the respiratory metabolism, the energy produced to support other metabolic processes, and consequently these processes themselves, will be affected accordingly. 10 This still covers only part of the story of how MA can affect the metabolism of the packaged produce. The physiological effects of MA can be diverse and complex. 13 In MAP, the success of the package strongly depends on the interactions between the physiology of the packaged product and the physical aspects of the package; MAP is a conceptually demanding technology. Much of the work in the area of MAP has been, and still is, driven by practical needs of industry. 29 This has enabled commercial development based upon pragmatic solutions but has not always contributed substantially to advancing the conceptual basis upon which future innovation in MA technologies depends. As a result, there is a substantial potential for models to contribute to the field of MAP by making the complex and vast amount of, sometimes fragmental, expert knowledge available to packaging industries. In this chapter, we bring together existing concepts, models and sub-models on MAP to build an overall conceptual model of the complex system of MAP. Starting from this overall model, dedicated models can be extracted for specific tasks or situations. The benefits and drawbacks of the modelling approach are discussed, together with an identification of the future developments needed to create advantage to MAP commercial operations. 16.2 Conceptual models The ideal model integrating all critical aspects of MAP would inevitably have a multidisciplinary nature and a complexity that, at least in its mathematical form, is far beyond the scope of this chapter. Here we attempt to provide a sound conceptual model to assist understanding of the underlying mechanisms. Going in aggregation level from the macro (palletised packs) via the meso (individual packs) to the micro level (packaged product) the emphasis shifts from physics and engineering to include more and more biology; physiology and microbiology. In parallel to this shift, the level of complexity and uncertainty increases. 338 Novel food packaging techniques 16.2.1 Macro level The macro level is schematically presented in Fig. 16.1. Much research has been undertaken on heat and mass transfer, the effects of boundary layers and different flow patterns given different geometries, types of cooling and ventilation. 20,28 The same techniques have been applied to the storage of living and non-living food and non-food products all over the world. These techniques enable, in general, a good understanding of the storage environment of palletised or stacked packs, whether or not MA packs. Cooling is needed to remove heat from the packages and continuously to counteract the heat produced by the living product. Both forced airflow and turbulent convection are at this level major contributors to the transport of heat, water, gases and volatiles, to and from the packs. Fig. 16.1 A schematic outline at the macro level of MAP where forced airflow and turbulent convection are responsible for heat and mass transfer to and from the individual MA packs. Improving MAP through conceptual models 339 16.2.2 Meso level At the level of individual packs (Fig. 16.2) the emphasis moves towards natural convection and diffusion processes driven by concentration and thermal gradients. Heat produced by the product is conducted directly, or through the atmosphere in the package, to the packaging material and, eventually, is released to the air surrounding the pack. Water vapour, respiratory gases, ethylene and other volatiles are exchanged between the package atmosphere and the surrounding atmosphere by diffusion through (semi-) permeable packaging materials. Those packaging films can be either selective semi-permeable films or perforated films. In the case of perforated films especially, the diffusion rate of a gas can be influenced by a concurrent diffusion of a second gas. 57 A counter current generally hinders diffusion while a current in the same direction promotes diffusion of the first gas. Inside the package, the metabolic gases are either consumed (O 2 ) or produced (H 2 O, CO 2 , C 2 H 4 and other volatiles) by the product. Each of these gases may promote or inhibit certain parts of the product’s metabolism. In the end, the overall metabolism of the packaged product is responsible for maintaining the product’s properties. As long as the product properties relevant for the quality as perceived by the consumer stay above satisfactory levels the product remains acceptable. The steady state gas conditions realised inside an MA pack are the result of both the influx and the efflux through diffusion and the consumption and Fig. 16.2 A schematic outline at the meso level of MAP where heat and mass transfer from and to the packaged product are ruled by natural convection and diffusion processes. The packaging film acts like a selective semi-permeable barrier between the package and the surrounding atmosphere. Temperature has a marked effect on all processes going on at the meso level. 340 Novel food packaging techniques production by the product which are themselves strongly dependent on the composition of the package atmosphere. 35 For instance, water loss by the product is the main source for water accumulating in the pack atmosphere. The product elevates humidity levels within the pack to an extent that depends upon relative water vapour permeances of film and product. This elevated humidity inhibits further water loss to a progressively greater extent as relative humidity approaches saturation. This substantial benefit carries a risk of condensation that is exacer- bated by temperature fluctuations. Condensation creates favourable conditions for microbial growth that will eventually spoil the product and, as water condenses on the film, will also depress the overall permeance of the package. The time needed for a package to reach steady state is important as only from that moment on is the maximum benefit from MA being realised. In the extreme situation, the time to reach steady state could outlast the shelf-life of the packaged product. A typical example of how the atmospheric composition in an MA pack and gas exchange of the packaged product can change during time is illustrated in Fig. 16.3. The dynamics of reaching steady state depend upon the rates of gas exchange and diffusion and upon the dimensions of the package in relation to the amount of product contained. Packages with large void volumes take longer to reach steady state levels. Temperature has a major effect on the rates of all processes involved in establishing these steady state levels 4 and hence on the levels of the steady state gas conditions themselves. 16.2.3 Micro level Gas exchange The complexity of the biological system inherent in each fruit (Fig. 16.4) contributes significantly to the uncertainties in current knowledge on issues critical to the outcome of MA treatments. One of the central issues is the impact of MA upon the product’s gas exchange, its consumption of O 2 and production of CO 2 (Fig. 16.5). Total CO 2 production consists of two parts, one part coming from the oxidative respiration in parallel to the O 2 consumption and the other part originating from the fermentative metabolism. 51 At high O 2 levels, aerobic respiration prevails. In this situation, the respiration quotient (RQ; ratio of CO 2 production to O 2 consumption), influenced by the type of substrate being consumed, remains close to unity. At lower oxygen levels, fermentation can develop, generally causing a substantial increase in RQ. This is due to an increased fermentative CO 2 production relative to an O 2 consumption declining towards zero. Besides the effect of O 2 on respiration and fermentation, CO 2 is known to inhibit gas exchange in some produce as well. Although it would be convenient to consider gas exchange to be constant with time, there can be considerable ontogenetic drift in rates of gas exchange. 8 In so-called climacteric fruits especially, a respiration burst can be observed when the fruit starts to ripen. In addition, freshly harvested, mildly processed or handled fruit generally shows a temporary increased gas exchange rate. 10 Microbial infections can also stimulate gas exchange. 70 Improving MAP through conceptual models 341 Gas diffusion When one considers gas exchange as a function of O 2 and CO 2 levels, one is generally inclined to look at the atmospheric composition surrounding the product as the driving force. However, the actual place of action of gas exchange is inside the cells, in the mitochondria. Depending on the type of product, this means that an O 2 molecule has to diffuse through the boundary layer surrounding the product, through a wax layer, cracks, pores or stomata, through intercellular spaces, has to dissolve in water, and has to pass the cell membrane to get into the cell. 13 The CO 2 molecule produced by the gas exchange has to travel the same way in the opposite direction. The driving force for the diffusion comes from the partial pressure difference for O 2 and CO 2 between the fruit’s internal and external atmospheres generated by the gas exchange. The intracellular, in-situ, O 2 and CO 2 concentrations are much more relevant for Fig. 16.3 A typical example of the dynamics of MA. Due to the gas exchange, CO 2 starts to accumulate while the O 2 level starts to decrease (bottom). In response to the changing gas conditions, gas exchange rates are inhibited (top). Driven by the increasing concentration gradients between package and surrounding atmosphere, O 2 and CO 2 start to diffuse through the packaging film. Combined, this slows down the change in gas conditions. Eventually, gas exchange by the product and diffusion through the film reach steady state levels at which the consumption and production of O 2 and CO 2 equals the influx and efflux by diffusion. 342 Novel food packaging techniques the gas exchange than the fruit external gas conditions. Generally, it is assumed however, that the largest resistance in the diffusion pathway from the surroundings into the fruit exists at the skin of the fruit. 12,14 Therefore the largest gradient in concentration occurs at the skin while the concentration differences within a fruit are small. Even at identical external atmospheres, different species of fruit will have completely different internal gas compositions due to their different skin permeances. Fruit with a wax layer, like apples, have a much lower permeance than leafy vegetables like cabbages, which generally have a large amount of stomata present. 18 The skin permeance of different apple varieties will be strongly affected by thickness of their natural wax layers. Due to such a wax layer, the skin of tomato and bell pepper is relatively impermeable, forcing all Fig. 16.4 A schematic outline at the micro level of MAP where the product is considered to generate its own MA conditions due to the resistance of the skin. The internal gas conditions are responsible for affecting large parts of the metabolism either directly or via the gas exchange. This will influence quality related product properties determining the quality (Q) as perceived by the consumer. Depending on the MA conditions, microbes can interact with the product’s physiology influencing its final quality. Improving MAP through conceptual models 343 the gas exchange through the stem end of the fruit. 22 Consequently, some fruits become internally anaerobic in conditions where others are still aerobic. Water diffusion and water loss The diffusion of water vapour is limited by skin permeance in the same way as the diffusion of O 2 and CO 2 , the slight difference being that diffusion of O 2 and CO 2 takes place mainly through pores connected to intercellular spaces while water vapour is more easily released through the whole skin surface. 3,44 Water loss is driven by the partial pressure difference of water vapour between the fruit’s internal (close to saturation) and external atmospheres. Water loss is an important issue in relation to the overall mass loss, firmness loss and shrivelling or wilting of the product. Inside an MA pack, water loss can also be responsible for generating conditions favourable for microbial growth (high RH). Ethylene effects Being a plant hormone, ethylene takes a special place among the gases and volatiles produced by the product because of its potential impact on the product’s own metabolism. The pathways of biosynthesis and bio-action of ethylene are still subject to extensive study. 40 Most of the climacteric fruits show a peak of ethylene production at the onset of ripening. In most of these fruits, ripening can be triggered by exogenously supplied ethylene. This creates the situation that one ripening fruit in an MA pack will trigger the other fruit to ripen Fig. 16.5 A typical example of gas exchange as a function of O 2 partial pressures (P O 2 in kPa). (r O 2 ) is related to the oxidative part of CO 2 production (r CO 2 ) via the respiration quotient. Additionally, at low O 2 levels fermentative CO 2 production can take place resulting in increased CO 2 production as compared to the decreasing O 2 consumption. 344 Novel food packaging techniques simultaneously, due to the ethylene accumulating in the pack. MA can inhibit the normal development and ripening of products postponing climacteric ethylene production thus extending the keeping quality of the product. With kiwifruit, however, advanced softening of the fruit occurs before ethylene is produced. 6 Although the fruit is not yet producing any ethylene, the softening process is extremely susceptible to exogenously applied ethylene. Product quality The quality of the packaged product is based on some subjective consumer evaluation of a complex of quality attributes (like taste, texture, colour, appearance) which are based on specific product properties (like sugar content, volatile production, cell wall structure). 61 These product properties generally change over time as part of the normal metabolism of the product. Those developmental changes that are directly influenced by O 2 or CO 2 or driven by the energy supplied by respiration or fermentation will all be affected by applying MA conditions, potentially extending the keeping quality of the product. Some processes are more affected than others due to the way they depend on atmospheric conditions. To understand the mode of action of MAP for a specific product, a good understanding of how the relevant product properties depend on gas conditions and temperature is required. Spoilage and pathogenics MA conditions can also provide conditions favourable to the growth of microbes potentially limiting the keeping quality of the packaged product due to rot. This is especially the case for soft fruits or minimally processed fruit and vegetable salads when high humidity levels are combined with a tasty substrate. 7 Some microbes are known to be opportunistic, waiting for their chance to invade the tissue when ripe, damaged or cut. In this case, MA conditions inhibiting the ripening of fruit in combination with proper handling and disinfection can prevent some of the problems. Other microbes more actively invade the tissue, causing soft patches on the fruit. More insight is needed on how MA can inhibit not only the metabolism of the product but also that of the microbes present on the products. High CO 2 levels are generally believed to suppress the growth of microbes, although sometimes the CO 2 levels needed to suppress microbial growth exceed the tolerance levels of the vegetable produce packaged. 7,17 Variation Although the general concept of MAP is now almost complete, there is one thing left that affects all other issues outlined so far; the effect of variation. Variation can occur on different levels, like time and spatial variation in temperature control in storage, irregularities in the stacking of cartons influencing ideal flow patterns, irregularities in the thickness or perforation of films or differences between batches of film used. However, the most important non-verifiable factor is biological variation. Besides the more obvious differences between cultivars, distinct differences exist between produce from different harvests, years, soils or Improving MAP through conceptual models 345 locations. 42 Even within one batch, considerable variation between individual items can occur. 67 The amount of biological variation that can be expected generally depends on the organisation level looked at. Within packages, the product generally comes from one grower resulting in a relatively homogenous batch with limited fruit-to-fruit variation. Comparing different pallets involves product potentially originating from different growers and different harvest dates result in a much larger variation. When developing small consumer MA packages, variation in the rate of gas exchange is almost impossible to take into account. The larger the package, the more these differences tend to average out. However, in the case of fruit interactions, individual outliers can affect the other fruit in a pack, as with the spreading of rots, the onset of ripening through C 2 H 4 production or with off- flavour development. 16.3 Mathematical models Over the years, different elements of what has been discussed above have been subject to mathematical modelling. Other subjects are still to be explored. Models describing the physics of MAP are usually more fundamental than the ones describing the physiology of MAP. This is due to the increased complexity and the lack of knowledge of the underlying mechanisms. For this reason, empirical ‘models’ (arbitrary mathematical equations fitted to experimental data) still prevail in post-harvest physiology. This section gives an overview of the type of MAP-related models available in the literature with the emphasis on the physiological aspects of MAP. 16.3.1 Macro level With the strong development of computers, rapidly increasing computational power becomes available to food and packaging engineers. Associated with this, engineers can add new numerical tools to their standard toolkit such as Computational Fluid Dynamics, infinite elements and finite differences. In general, when modelling heat and mass transfer, conservation laws are applied to formulate energy and mass balances. 20 The space under study is subdivided in a number of defined elements. Each of them is represented by one point within the three-dimensional space and is assumed to exchange mass and heat with its neighbouring elements according the heat and mass balances defined. The accuracy of such a model strongly depends on the number and size of elements defined and the knowledge of system input parameters. To improve both accuracy and computational time, smaller elements can be defined in areas with steep gradients and larger elements in the more homogeneous areas. Theoretically, this approach is applicable at both the macro level to describe airflow in a cold room, at the meso level to describe diffusion within a pack, and at the micro level to describe gradients within the product. The main application is 346 Novel food packaging techniques however at the macro level and to a lesser extent at the meso level when large bulk packages are involved. 69 For small consumer-size packages the simplification of treating the pack atmosphere as one homogeneous unit is generally acceptable. At the micro level, there are too many system inputs still undefined to enable formulation of such a model, not to mention parameterising and validating it. 16.3.2 Meso level At the level of small consumer-size packages the physics simplifies to relatively easy diffusion equations based on Fick’s law describing gradient-driven fluxes from point A to B through a medium with a certain resistance. Gas permeates into (or out of) the package faster with increased film area, with thinner films and with larger concentration differences. 23 The permeance of a film typically depends on the material used. With the current range of polymers available, a wide range in permeability can be realised. Most films are selective barriers with different permeances from the different gases. 24 The standard industry test for determining permeance of a specific film is done at the single temperature of 23oC using dry air conditions. The conditions at which a film is exposed in MAP of fresh produce, ranges however from zero to 25oC and high humidity levels (>90%). Depending on the actual temperature, the permeance of the film changes accordingly. This temperature dependence is generally described using an Arrhenius equation. This is an exponential relationship originating from chemistry where it is used to describe the rate of chemical reactions as a function of temperature. The activation energy is the parameter quantifying temperature dependence. The higher the activation energy the faster permeance increases with increasing temperatures. An activation energy of zero means that the permeance does not change with temperature. The activation energy is characteristic for the film material used and is different for the different gases. The effect of humidity and condensation on the permeance of films is widely recognised and still subject to study. At high humidities, water can be absorbed by the film changing the permeance for other gases as well. Furthermore, due to temperature changes, water can condense on the film forming an extra barrier for diffusion. Both aspects are still to be modelled. When perforated films are considered, diffusion through the film can be separated into two processes, diffusion through the film polymer and diffusion through the pores. Perforations are generally much less selective as this involves just diffusion through air. In addition, the effect of temperature on diffusion through pores (air) is much less as compared to its effect on diffusion through the polymer. As diffusion through the pores accounts for most of the total diffusion through a perforated film, the activation energies for perforated films are close to zero. Due to the effect of boundary layers, diffusion through pores is not linearly related to pore area and film thickness and some corrections have to be made depending on pore size and pore density. Models, originally developed to describe stomatal resistance in leaves, have been applied for this. 26 Improving MAP through conceptual models 347 The effect of concurrent diffusions has been modelled using Stefan-Maxwell equations. 57 These equations take into account the effect of collisions between counter currents of different species of molecules on their final diffusion rates and can explain some of the observed diversions from Fick’s law of diffusion. The effect of pack volume on the dynamics of MAP is something that does not need to be modelled explicitly. As both diffusion and respiration are defined as a function of partial gas pressures, and as these partial pressures depend by definition on the number of molecules present per unit of volume, the volume is already incorporated implicitly. For instance, doubling the void volume of an MA pack means that twice the number of oxygen molecules are available. To reduce the oxygen concentration in the void volume to a certain level, twice the number of molecules have to be removed, which takes about twice as long. 16.3.3 Micro level Several attempts have been made to model gas exchange either by empirical models or greatly simplified fundamental or kinetic models using, for instance, a single Arrhenius equation. 48,73 A more fundamental approach was used by Chevillotte 19 who introduced Michaelis Menten kinetics to describe respiration on the cell level. Lee 41 introduced and extended this approach in the post- harvest field to describe the respiration of whole fruit. After him, several other authors successfully applied this Michaelis Menten approach to a wide range of products 27,56,62 and extended the original Michaelis Menten equation to include different types of CO 2 inhibitions 51 and to account for the effect of temperature. 15,34,65 Traditionally, the effect of temperature was described using the Q 10 system. More recently, the use of the Arrhenius equation has been favoured. The general applicability of the Michaelis Menten approach is probably due to the fact that it is simplified enough to enable parameterisation, and that it is detailed enough to account for the different phenomena observed. Driven by dissatisfaction with the Michaelis Menten approach, as it may not describe the respiration of fresh produce because actual respiration is composed of many steps of metabolic reactions, Makino et al. 46,47 felt the need to develop an even more simplified model. Based on Langmuir absorption theory, an O 2 consumption model was developed which, in the end, appears to be an exact copy of the Michaelis Menten approach, with parameters meaning the same, only labelled differently. Instead of developing an alternative for the Michaelis Menten approach, Makino unintentionally reinvented it and validated its assumptions via an analogous mechanistic approach. Although proven extremely applicable for practical use and indispensable for enhancing the understanding and interpretation of gas exchange data, the Michaelis Menten type of formulation is a considerable simplification of the biochemical reality. This stimulates ongoing research into generating models that are more detailed. 1 The developmental effect on gas exchange has not been modelled so far, except for some empirical corrections for an assumed drift of respiration during time. 10 348 Novel food packaging techniques Burton 13 added a whole new dimension to MA research by stimulating research on internal atmosphere compositions of products as a key concept in the responses of fruits and vegetables to MA. They emphasised the concept of the skin being a barrier between external and internal atmospheres. In the same way that film permeance alters gas conditions inside the package, the skin alters internal gas atmospheres. 2 Basically, the fruit can be considered as the smallest possible MA package. The mathematics behind modelling internal atmospheres is the same as is applied in modelling pack atmospheres. Assuming the largest resistance in the diffusion pathway exists at the skin of the fruit, diffusion from the pack atmosphere to the fruit internal atmosphere can be described with a simple diffusion equation using the permeance and area of the skin. The relation between fruit internal and external atmosphere conditions can be completely understood from the combined effect of skin permeance and gas exchange characteristics. However, the gas exchange model now has to be parameterised as a function of fruit internal gas conditions instead of pack atmosphere conditions. With regard to gas exchange, the combination of diffusion equations and Michaelis Menten type kinetics resulted in generally accepted and applicable models. As far as product specific issues are concerned, models are completely lacking or available only in a rudimentary form. However, to complete the overall MAP model we do need sub-models on how MAP is influencing the physiology of the packaged product beyond its gas exchange. How do the properties determining product quality depend on the gas conditions, either direct or via the changed gas exchange? The development of such models is severely hampered by the lack of physiological knowledge and complete sets of data for validation. Though empirical or statistical models can be useful to describe simple relationships found in a specific experiment, robust mechanistic models are needed to develop predictive models that can be applied under a wide range of conditions. A relatively simple problem like shrivelling of apples due to water loss can be easily understood from the diffusion of water from the fruit’s internal atmosphere into their external atmosphere. 45 The analysis of the results is hampered though, by the large biological variation in skin permeance. 43 However, due to its generic mechanistic approach, the model can easily be integrated within the larger MAP model for a wide range of products. The colour change of some products (tomatoes, 63 cucumber 60 ) has been successfully modelled. What remains to be investigated is how these colour changes are affected by the gas conditions. With the colour change of broccoli buds, MA conditions were shown to have an effect on the rate of colour change. 52 Whether this was directly related to the reduction in gas exchange was not tested. In the case of rot development in strawberries, Hertog et al. 32 assumed that the metabolic rate was the direct driving force for the process of ripening enabling microbes to develop rot. Reduction of spoilage under MA could be explained from this reduction of gas exchange. An extremely complex and relevant issue of how ripening of (climacteric) fruits is affected by gas conditions has not been unravelled, let alone been Improving MAP through conceptual models 349 modelled. However, based on some general concepts, Tijskens et al. 68 developed a simplified mechanistic model describing the softening of apples under MA including some of those climacteric developmental changes. Although this model is a strong simplification of the physiological reality, it shows the generic potential of well formulated mechanistic models. Understanding the mode of action of MAP for a specific product requires knowledge of how the relevant product properties depend on the gas conditions (composition and temperature). This is what makes MAP a laborious exercise as each product can have different quality-determining product properties responding in slightly different ways to the MA conditions applied. One way to get around this is by developing generic models describing phenomena like shrivelling, softening, sweetening, mealiness, flesh browning or skin colour change that can be validated independently for a wide range of products. Another option that has already proved itself successful is to stick to a more general level, describing keeping quality independent of the underlying product properties. This generic approach was originally developed by Tijskens and Polderdijk 64 to describe the effect of temperature on keeping quality for a wide range of commodities. This approach was extended to include the effect of MA, assuming all quality decay is driven by the metabolic rate. 31,52 Some further refinement would be needed to discriminate for instance between respiration- and fermentation-driven quality decay processes. 33 This approach can give an insight into how much MAP is able to extend keeping quality without the need to unravel the exact mechanism of how, for instance, firmness of apple is influenced by MA conditions on the biochemical level. Modelling in microbiology has always been important. Usually growth curves are described as a function of temperature, pH, water activity and in response to the presence of competing microbes at well-defined growth media. 72 The relevance of microbes for MAP increased with the increasing demand for convenience foods stimulating the markets for MA packaged cut and slightly processed fruit and vegetable mixes. Low numbers of microbes in foods may already result in hazardous situations. However, the currently available models in predictive microbiology are not set up to deal with these low numbers. 72 Instead of modelling actual numbers, the probability of presence should be taken into account. In addition, the composition of the natural growth medium in MA packages (being the fruit and vegetables) is not well defined and highly variable. To predict growth of microbes in MA packages, both the biological interaction between produce and microbes and the direct effect of changed atmospheric conditions on the growth rates of microbes should be taken into account. Research in this field is still developing 7 and given its complex nature, mechanistic models integrating the outlined microbial aspects will not be readily available. Although (biological) variation is hard to model, the effect of variation in a system can be easily demonstrated once a model of that system is available. Simply by running the model multiple times, taking randomly distributed values for one or more of the model parameters, the effect of variation becomes clear. Such a so- called Monte-Carlo approach can be applied to a MAP model by drawing 350 Novel food packaging techniques randomly distributed values for, for instance, film thickness or the product’s respiration rate. Based on the results a 95% confidence interval for the gas conditions inside an MA pack can be formulated (Fig. 16.6). Variation can induce certain risks, especially when package atmospheres are targeted close to what is feasible. When aimed for O 2 levels close to the fermentation threshold, 74 the risk is that some of the packages, depending on the variation in gas exchange rate, result in O 2 levels dropping below the fermentation threshold. 16 This results in packages with unacceptable fermented produce. Biological variation is generally much larger (±25% is not exceptional) than the physical sources of variation (generally less than ±10%) as the physical factors are generally easier to control. Biological variation also comes back in the initial quality of the packaged product resulting in different length of keeping quality or shelf-life. Some quality change models try to account for these sources of variation. 36,32,59,60 16.4 Dedicated MAP models Though it is possible to develop a model covering all facets of MAP at all levels, such a model would be impossible to operate. Before one is able to use such a model it needs to be fully parameterised. Generally, this information is not available in all situations. Moreover, it is not always relevant to go to such a level of completeness. Depending on the specific issues involved in a particular application, dedicated MAP models can be extracted from the overall conceptual model. Some elements need to be worked out in more detail while Fig. 16.6 For a given MA package the effect of 25% biological variation on gas exchange and 10% variation in packaged biomass were calculated. The average MA conditions developing during time (solid lines) and their 95% confidence intervals (dotted lines) were plotted based on 200 simulations. Improving MAP through conceptual models 351 others can be simplified or assumed to be constant, depending on the dedicated application. A retailer trying to deliver the best for the end users, is mainly interested in consumer size packs and how keeping quality develops during display in retail and after purchase at the consumer’s place (shelf-life). In this case, the emphasis would be on a product-specific keeping quality model linked to the change in pack atmosphere conditions. The surrounding conditions are taken as they are. A large exporting company sending off wrapped pallets with product would be interested in whether the MA conditions stay within some given target limits. The emphasis is now on how to control the conditions inside a container to maintain constant MA conditions and how to optimise package design and pallet stacking to promote homogeneous flows and heat exchange throughout the bulk load. When developing packages for minimally processed salads, the emphasis is on incorporating predictive models on microbial growth together with specific models on the product’s physiology. 16.5 Applying models to improve MAP The previous section mentioned some potential applications for MAP models. In this section, we explore some of this potential to enhance the practical imple- mentation of MAP and to lift it beyond the phase of ‘pack-and-pray’. 16.5.1 Dimensioning MAP There is more than one ‘right’ solution to the search for a suitable MA package for a specific product. Assuming the product is known, including its gas exchange characteristics and some optimum target MA conditions, and the external storage conditions are set but beyond control, there are still a number of degrees of freedom through which the MA package can be manipulated for better or for worse. To realise the target MA conditions the total permeance of the package has to be dimensioned in relation to the amount of product packaged. Besides choosing a different film material with a higher or lower permeability, film thickness and film area can be changed as well. A film that is too permeable to be used as a wrapping can give good results when used to seal the top of an impermeable tray because of the reduced diffusion area. A film that is suitable for a small consumer pack can be too impermeable to be used as a liner in a carton because of the increased amount of biomass per unit of available diffusion area. Trying to influence this ratio, by packing less produce in a package, results in an increased void volume. This increases the time needed for the product to bring the package gas levels to the target MA conditions. This is not favourable, as it takes longer before the product gets the maximum benefit of the optimum MA conditions. However, the buffering capacity of a relative large void volume can have its positive effects when the MA package has to survive short periods of 352 Novel food packaging techniques sub-optimal conditions. During a short warm period, a package with a small void volume could rapidly generate anaerobic conditions while a package with a large void volume could have been transferred to cooler conditions before becoming anaerobic. Dimensioning an MA package appears to be extremely complex due to the many different interactions involved. A MAP model can considerably enhance this search for a package with a fast enough dynamic phase, resulting in steady state values close to the target gas conditions and enough buffering capacity to be applicable in practice. 16.5.2 Developing new films In the case of a company wanting to bring a new MA pack on the market for a specific product with the package dimensions already set by other market requirements, one needs to search for the right film to complete the MA pack. Normally, film permeance is used as input in the MAP model. However, the model formulation can be turned around to calculate the required film permeance based on the product’s gas exchange characteristics, assuming some known optimum target MA conditions and given the external storage conditions. As the storage and transport conditions throughout a chain will not be constant, this exercise should be repeated over a range of temperatures or a number of different temperature scenarios. MA conditions that are optimal at one temperature do not need to be optimal at another temperature. For instance, the tolerance to low oxygen levels decreases with increasing temperature. 5,74 Once models are available to describe the effect of humidity and condensation on film permeance, they can be used to predict humidity levels inside the package and to predict how film permeability is affected by this. This will help to set detailed specifications for films with regard to this aspect. This will be especially usefully in the MAP of minimally processed produce, soft fruits and leafy vegetables, because of the high humidity levels occurring in these packages. 16.5.3 Optimising logistic chains Given the ultimate MA package for a certain product, its eventual success mainly depends on temperature control between the moment of packing and the moment of opening the package by the consumer. In a logistic chain where temperature is not controlled throughout, application of MAP is a waste of time, money and produce. Using a MAP model to simulate a package going through a logistic chain will give insight into the strong and weak parts of that chain. 35 It will make clear which parts of the chain are responsible for the largest quality losses of the packaged product and therefore need improvement. It enables the optimisation of a whole chain considering the related costs and benefits. To get the most out of such an exercise, a MAP model should be used that includes a keeping quality or quality change model. Assessing the benefits and Improving MAP through conceptual models 353 losses in terms of product quality gives much more insight than just the observation that the MA conditions dropped below or above their target levels. The question that should always be asked is how these deviations affect the quality and keeping quality. The product quality gives static information on the status of the product at a certain moment, for instance at the point of sale. Keeping quality provides dynamic information on how long a product can be stored, kept for sale, transported to distant markets or remains acceptable after sale to the consumer. 16.5.4 Sensitivity studies Generally, an MA package is developed based on some average product characteristics, assuming an average amount of product packaged, using the specifications of an average sample of film and assuming the MA pack will be handled and stored at certain average conditions. As the average MA pack does not exist, the question arises how the non-average package will behave at non- average conditions and how far the MA conditions will diverge from the ideal target levels. Sensitivity studies are ideal to test how sensitive a system of MAP is to changes in one or more parameters or conditions. Using a MAP model, sensitivity studies can be easily conducted by running the model multiple times, using a range of values for the different conditions under study. This will help identifying which aspects of MAP should be more strictly controlled because of their potential impact on the system as a whole. The results strongly depend on the MA pack under study. For instance, depending on the gas exchange rate the same change in packaged biomass will have different effects on the steady state MA conditions. So, it cannot be stated in general that MAP is insensitive to a change in biomass. Also, the gas conditions in an MA pack where film and produce have comparable temperature dependencies are insensitive to temperature. Using this same pack for packaging a produce with a different temperature dependency can result in gas conditions extremely sensitive to temperature. Even if the MA conditions in an MA pack are insensitive to temperature due to the balanced combination of film and product, this does not mean that the quality of the packaged product is insensitive to temperature. These are just two different ways of assessing MAP. If a good quality change model is lacking, the ‘optimum MA conditions’ are the only criteria to apply when judging MA packs. When a good quality change model is available, sensitivity studies can be performed on what is really important: product quality. 16.6 The risk and benefits of applying models Applying models to improve MAP has, like every technique, its pros and cons. Some of the advantages have already been mentioned implicitly in the previous sections describing the areas of application. By applying models, the 354 Novel food packaging techniques development phase of MAP can be shortened. Numerous experiments can be done behind the laptop checking all possible situations that would take weeks to test in practice. With a good conceptual model in mind and the mathematical equivalent available at the fingertips, developing MAP can be lifted beyond the phase of ‘pack-and-pray’. When developing a model, continued balancing should be going on between the completeness and relevance of the described phenomena and the level of detail and complexity of the model needed to realise this. For scientific purposes, the ultimate model would be a mechanistic one describing all relevant underlying processes. For practical purposes, one should start from such a detailed mechanistic approach and simplify as far as possible without affecting the explanatory power of the model for that specific dedicated application. In the practice of post-harvest physiology, that detailed mechanistic model is not available and the best one can do is to develop a hypothetical mechanism in agreement with the observed phenomena and in agreement with current general physiological and biochemical concepts. Such a mechanistic model can still be extremely valuable to develop concepts by verifying or falsifying hypotheses. Developing, for instance, a quality change model forces the expert to formulate a conceptual model and to realise where the gaps in his knowledge are. This is probably the most valuable and general advantage of developing mechanistic models as it enhances the understanding of a complex system and directs future research to fill the gaps. In spite of the advantages, one should stay aware of some potential traps. One of them being the risk of forgetting about real life, simply because not everything goes according to the model. The books can prescribe transport at 2oC but cannot prevent the driver turning off the cool unit when delivering early in the morning in an urban region not wanting to wake up its inhabitants. Kiwifruit could last another week according to the developed firmness model but in practice are already lost due to spoilage. This brings us to the fact that you cannot get anything out of a model you did not include to start with. When condensation is not included it is impossible to assess sudden temperature drops on their potential to induce condensation with all the consequences for the omnipresent microbes. If a quality change model leans heavily on one single limiting quality attribute, the user of the model should stay aware of specific situations turning another quality attribute into the limiting factor. At the same time it should be recognised that it is impossible to include everything in the model as it would be impossible to validate it completely. In conclusion, one should always be alert when applying models outside the range for which they were validated. In the case of empirical models especially, this can result in unrealistic predictions. A model can easily process unrealistic data without getting into a moral conflict. The user should always stay alert to recognise such anomalies. Improving MAP through conceptual models 355 16.7 Future trends Some of the trends needed to safeguard the future of MAP are very basic while others are on the level of refining existing knowledge. One of the most embarrassing gaps in current knowledge is a good database on permeance data of packaging films that includes their temperature dependency. The packaging film industry should develop a standard certificate for this that comes with each film they produce for MAP. To enable a fundamental approach to MAP the gas exchange of the different products should also be systematically characterised as a function of at least O 2 , CO 2 and temperature. This knowledge, essential for the success of MAP, is still very fragmented. To improve the models on MAP of minimally processed produce involving high humidity levels, a better understanding is needed of the effect of humidity and condensation on film permeances. A great deal of work has still to be done to integrate the expertise from microbiology within the field of MAP. Although models on gas exchange are becoming well established, models on how the physiology underlying quality is linked to the metabolism are not readily available. Their development is hampered by gaps in the knowledge of post-harvest physiology. However, to assess MA packages on the quality of their actual turnout, quality change models are needed. The ultimate goal would be to develop generic models that can be validated for a wide range of commodities. The last issue that needs to be covered in the near future is the characterisation of biological variation and its impact on product behaviour in general and on MAP in particular. Although this issue is important for the post- harvest industry as a whole, MAP would greatly benefit from a more fundamental approach. 16.8 Sources of further information and advice This chapter was first published as part of a book on food process modelling. 66 People interested in the applications of modelling and its potential in the food sector will find in this book a wide range of examples, providing a blend of conceptual and mathematical approaches, incorporating both developments of general principles and specific applications. Over the last 15 year several books on practical applications and technologies of MAP have been pub- lished. 9,49,50,21,11,25 These contain important sources of information for the industry covering a wide range of food products (fruit, vegetables, meat, fish, pre-cooked foods and bakery products), including regulations and guidelines. World-wide, research groups are trying to identify optimum storage conditions for particular products. 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