Aaron L. Brody

Food products conceived and developed by food marketers, scientists, and technologists only rarely can remain identical from laboratory bench or production line through to the target consumers. Only an infrequent few food products survive the distribution process to maintain or display improved quality. That period during which the product retains its desired properties usually has been designated as shelf life, and the proper measure of this somewhat unscientific and certainly imprecise term is by the target consumer.

Perhaps because of the paucity of quantitative data on the complex, interacting, stress-induced changes, some purists denigrate the notion of measurement and prediction of “shelf life.” Commercial interests often dictate a time and demand that the technology fit the market desires— hence, the not-infrequent arbitrary “one-year” time frame for many “shelf-stable” foods.

Recent research and publications from organizations driven by distribution need have demonstrated that, however multifaceted is shelf life quantification, it is capable of being modeled within closer parameters than ever before envisioned.

Heard and read too often are assertions that shelf life (1) is not a necessary element of food product development; (2) may be determined by placing a package on one’s desk and observing it for a week or so; (3) is so ingrained into food science and technology curricula that a separate course on shelf life is superfluous; (4) is a packaging problem and so not part of classical food science and technology; and (4) is impossible to handle, so why bother?

The role of food product shelf life in the structure of our discipline is a topic that should be discussed in depth on these pages and during the Institute of Food Technologists’ Annual Meeting and other assemblies. Meanwhile, this article will tread into the treacherous territories of predictive mod modeling of shelf life, as offered recently by several professional colleagues.

Factors Affecting Shelf Life
Shelf life depends on a multiplicity of variables and their changes, including the product, the environmental conditions, and the packaging. Depending on the product and its intended application, shelf life may be dictated by microbiology, enzymology, biochemistry, and/or physical effects. Microbiological changes may be innocuous, spoilage, pathogenic, or some combination. Enzymatic and biochemical are often facets of the same reactions that may be affected by internal reactions alone, external forces alone, or some combination. Review of the published literature reveals a surprising shortage of information on enzymatic action as a driver for the truncation of shelf life. Biochemical shelf life reports appear to emphasize lipid or vitamin C oxidation—important, but hardly lone, chemical changes in food products. Too often, biochemical reactions that adversely affect appearance, flavor, and/or mouthfeel can precede the feared microbiological growth patterns. And physical changes such as moisture gain or loss or carbon dioxide loss are too frequently overlooked—or cited as the primary concern—in shelf life discussions. All of these attributes define quality as perceived and defined by consumers, and also reflect nutritional value.

Product changes subsequent to leaving the laboratory bench have been enumerated— although hardly comprehensively— in several publications.

Among the influencing variables that accelerate or retard shelf life are temperature, pH, water content, water activity, relative humidity, radiation, gas concentration, redox potential, the presence of metal ions, and pressure.

With regard to product deterioration, shelf life may be measured and predicted by selecting a single variable whose change is perceived first by the target consumers to signal the loss of quality that sparks some conscious change in behavior. Usually, but not always, one change begins the consumer response—even if some other variable is measurable by instrumental analysis or by other “objective” protocol.

Shelf life measurement and prediction are based on two simultaneous events: the product itself deteriorating and the positive or negative contribution of the package structure.

The end of product or packaged product shelf life is not reached precipitously on one day after time. Quality attributes that define shelf life gradually deteriorate over time, with the “end” falling into a range that is different for different consumers and attributes. As discussed in Brody and Lord (2000), Man and Jones (2000), and Robertson (1993), the rate of deterioration is generally described by the equation:
–dc/dt = f(I, E)
where c = index of deterioration, t = time, where n = order of reaction, dA/dt = rate of reaction, and k = rate constant. I = intrinsic variables, and E = extrinsic variables; or, more specifically, as:
dA/dt = kAn
where n = order of reaction, dA/dt = rate of reaction, and k = rate constant.

In zero-order reactions, such as nonenzymatic browning, which follow a linear rate independent of the concentration of reactants,
Ae = Ao – kts
where Ae = the value of attribute A at the end of shelf life and ts = shelf-life time.

In first-order reactions, such as microbiological growth, which follow a nonlinear rate dependent on reactant concentration,
Ae = Ao e–kt
Most food deteriorations are zero- or first-order reactions, but some are second order.

Although a large number of environmental variables influence the rate of product deterioration, probably the most important is temperature, whose effect is best described by the Arrhenius relationship:
k = koe–E/RT
where k = the rate constant for the deteriorative reaction; ko = the rate constant, independent of temperature; E = the activation energy; R = the gas constant; and T = the absolute temperature. Essentially, the rate of food product deterioration as a function of temperature generally increases exponentially with linear increase in temperature.

Predictive Modeling
Measurements and predictions of shelf life of the product independent of the package structure are made first and then integrated with the measurements and predictions made of the effect of the package. Among the more relevant package properties are water vapor transfer, gas transfer, odor transfer, flavor scalping, and other product/package interactions.

To perform predictive modeling, the food model must be integrated with the package model. The package model must fit the food model; e.g., the package should be analyzed for its ability to function as a barrier against those variables that have been identified as critical for the food shelf life. Distribution parameters should be quantified to determine their variability within the distribution environment.

As a first assumption, assume that the main characteristics are the package barrier properties, such as water vapor, oxygen, or carbon dioxide barrier, and that the package material is unaffected by packaging operations and distribution; i.e., use data for the pristine package material, however prone to error it may be as a result of closures, creasing, fracturing, etc.

In the predictive model, assume that the internal package environment changes as a permeant, such as water vapor, carbon dioxide, or oxygen, enters or exits the package. Also, assume that the permeant moves from a region of low concentration to one of higher concentration. Standardize the permeation rate for the area, gauge, and permeation properties of the package material/ structure and the environmental conditions—in particular, temperature and partial pressure. Permeation is a function of dissolution into and diffusion across the package material due to partial pressure P. The model is thus based on mass transfer, with the effect on the product being the net gain or loss of the permeant with the product, e.g., loss of carbon dioxide in a carbonated beverage or loss of oxygen attributable to reaction with a food component. 

The predictive model for the package takes the general form:
dW/dt = (k/l)AdP
where dW = the change in the weight of the critical food component; k = the permeation coefficient of the package material; l = the package material gauge; A = the surface area of the package; and dP = the difference in partial pressure of the permeant inside and outside of the package structure. Partial pressure requires knowledge of the permeant: for oxygen external to the package, it is 0.209; for carbon dioxide outside the package, 0.0003; for water vapor on the exterior, six times the relative humidity of the distribution environment; etc.

The elementary predictive model is for a monolayer material structure of uniform gauge. When the thickness changes, differential equations for thickness are incorporated into the model. When two or more materials are present, as in a lamination, a coextrusion, or a coated bottle, the net permeation is described by the sum of the reciprocals of the individual permeations:
1/P = 1/P1 + 1/P2 + ... + 1/Pn
plus the reciprocal of the permeation across the boundary of the different materials.

Probably the best of the recently developed predictive models is the M-Rule Container Performance Model for Beverages, from, in a serendipitous play on words, Mark Rule of Container Science, Inc., Atlanta, Ga. (www.containerscience.com). Much of this model is targeted at the loss of carbon dioxide from plastic bottles of carbonated beverages, but oxygen ingress, water loss, and vitamin C oxidative degradation are also included.

M-Rule features include the incorporation of plastic-material variables such as resin properties, package geometry (shape, surface area, gauge, etc.), and closure characteristics, since gas transmission through the closure material (usually polypropylene) is usually very different from gas transmission across the bottle material (usually polyester).

Models are generated of the bottle and its carbon dioxide, oxygen, water vapor, and nitrogen transmissions; the beverage and the rate of loss/gain of those components with temperature, stress, and partial pressure; and the beverage’s “end point,” i.e., when the target consumer declares the product to be unacceptable. The model then generates data quantifying the change in these components over time under most conditions of bottle structure, beverage contents, environmental temperature, and, consequently, shelf life. Notably, the model allows the user to evaluate many different package parameters, including plastic blends, multilayers, and some of the new plasma coatings.

The M-Rule for vitamin C loss assumes a reaction of the oxygen within the bottle with vitamin C at a defined rate, coupled with transmission of oxygen from the exterior into the interior of the package. Again the “end point” of shelf life is a measure decided by consumers, as measured in actual consumer acceptance testing, supported by analytical chemical measurements. Similarly, the M-Rule for moisture loss or gain uses the same principles to predict reaction of the water vapor with the contained product and the water vapor permeation across the package material structure.

An important distinction of the M-Rule over previous models is that it inherently calculates the solubilities and diffusion of all four permeants simultaneously, and therefore captures the impact of each permeant on the diffusion of the others. Previous empirical models have always treated these permeants independently; the M-Rule model shows that this assumption can be overly simplistic. For example, the presence of carbon dioxide can double or triple the rate of oxygen ingress (beer packagers, take note).

Assumptions required for application of the M-Rule might appear to be arbitrary, but in practice are generally quite rational. Final measures of the shelf-life end point are not mathematically driven by chemical kinetics but rather by target consumer parameters: carbon dioxide loss, water gain in dry foods, oxidation of key flavor constituents, etc. Data on almost all of these variables and their effect on product quality are identifiable and measurable. In prior incarnations, shelf-life modeling and prediction have been limited by a serious paucity of key variables, such as using only water vapor gain as a measure with no consumer acceptability input. The ability of the computer model to incorporate all of the known relevant variables permits the food scientist, in concert with the packaging technologist, to accurately and precisely predict the results of a package material and/or structural design change on the shelf life of most product contents.

Before leaping into predictive modeling as the definitive answer to all shelf-life issues, not all reactions are responsive to the model: many complex food deteriorations are still being studied to determine their interactions with the environment and the package properties. Furthermore, and most important, no rational food packaging technologist would employ computer predictive modeling at the outset without actual testing as the basis or the confirmatory input. And because of the time required to gain real-time data, accelerated testing, such as at elevated temperature and/or relative humidity, is suggested. For many reactions, such as carbon dioxide loss through plastic bottles, relatively straightforward accelerated testing is accurate. For many food products that undergo phase changes at elevated temperatures, accelerated testing is not possible— yet.

Data being generated today and in the future will expand the range of products and packages whose shelf life may be predicted with confidence. With each demonstration of the usefulness of these models, food scientists and technologists are accepting the key fact that shelf life is a critical variable that must be incorporated into their research findings.

Contributing Editor
President and CEO, Packaging/Brody, Inc.
Duluth, Ga.


Brody, A.L. and Lord, J. 2000. “Developing New Food Products for a Changing Marketplace.” CRC Press, Boca Raton, Fla.

Man, D. and Jones, A. 2000. “Shelf Life Evaluation of Foods.” Aspen, Gaithersburg, Md.

Robertson, G. 1993. “Food Packaging.” Marcel Dekker, New York.