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Written by: Michael Mullan

The use of high temperature short time heat treatment (HTST) of milk (72°C for 15 seconds) to destroy pathogenic bacteria, reduce the number of spoilage organisms and increase shelf life is well established (Juffs and Deeth, 2007).

The history of pasteurization (pasteurisation is also valid) is fascinating and is notable for its public health success and for the insights of many scientists and engineers. Prior to the introduction of pasteurization, consumption of raw cow milk was a major source of infection by bacteria causing tuberculosis. Pasteurization has eliminated heat-treated-milk as a source of infection. Regrettably raw milk and raw milk products remain a major source of new cases of bovine tuberculosis.

This article calculates the effect of HTST treatment on the number of log reductions of major milk pathogens and discusses the temperature milk should be pasteurized if Mycobacterium avium subsp. paratuberculosis (MAP) was designated as a human pathogen. The log reductions refer to log10 or decimal (10 fold) reductions in the concentration of viable bacteria. The article does not discuss the effects of heat on the functional properties or the nutritive quality of milk. An updated and reviewed version of this paper has been published (Mullan, 2019).

Learn more about heat treatment and survival of MAP

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Microbial testing is still important but it is critical to understand its limitations in assuring food safety.

Despite the global use of HACCP systems and a legal requirement for the use of HACCP in many jurisdictions' food poisoning remains an endemic problem and large numbers of people continue to be hospitalised, die and as a result companies either face substantial legal costs and / or in many cases are forced to cease trading.

While the use of HACCP systems significantly reduces the need for microbiological end point testing of foods, sampling schemes and microbial analysis have important roles in system validation and quality assurance. This article also provides access to three free On-Line calculators that enable the probability of detecting a pathogen in a food, the number of samples required to test to meet a food standard and how to calculate the prevalence of a pathogen when all the samples taken for testing return negative results.

This raises an issue concerning the adequacy of sampling schemes and microbial analysis in commercial food manufacture.

In September 2015 the US Centers for Disease Control and Prevention reported on a multistate outbreak of listeriosis allegedly caused by Mediterranean-type soft cheeses. Some 30 people were affected, twenty-eight people were hospitalized and three deaths were reported. However, listeria were not isolated from the cheeses produced by the manufacturer concerned.

Further information on the mathematics of microbial sampling

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Written by: Michael Mullan

Considerable effort has been devoted to modelling the growth of pathogenic and spoilage bacteria in food. This is referred to as predictive microbiology. Mathematical equations are used to describe the effect of environment, for example temperature, or in more complex models temperature, pH, available water (A_w) and other factors that affect microbial behaviour.

The advantages of modelling have been described in the article on "Modelling in Food Technology" including reducing the costs and time required in determining the safe shelf life of new products or in undertaking pathogen challenge testing. However, caution and scientific expertise are required e.g. the Food Safety Authority of Ireland (2012) has cautioned the food industry on the use of predictive models.

The purpose of this article and supporting material is to illustrate how published research in predictive microbiology can be used in practice. This is an area in which Food Science and Food Technology undergraduates sometimes find difficulty. Part of the difficulty may exist because the steps in the calculations involved are not usually presented.

This article describes a model for the growth of salmonella on cut tomatoes and a calculator where you can enter the initial numbers of salmonella, the incubation temperature and the incubation time to obtain a prediction of final numbers.

Modelling microbial growth

Because of the critical importance of temperature early work attempted to modify the Arrhenius Law to describe microbial growth but this was either unsuccessful or the relationships derived were generally too complex for routine use. In a classic paper, Australian workers (Ratkowsky et al., 1982) proposed a relatively simple, two–factor empirical equation (equation 1) to describe the influence of temperature on microbial growth up to the maximum growth temperature of an organism, T_max.  This is often called the square root model.

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Written by: Michael Mullan

Cakes are classified as intermediate moisture foods and may be subject to spoilage by moulds. Water activity (a_w), the water that is available, unbound or free, for chemical reactions and microbial growth is a major factor that can be utilised to limit or prevent microbial growth. Cakes generally have a_w values ranging from 0.65-0.9.

Mould spoilage on cakes tend to occur on the surface and work has been done to model the water vapour pressure above cakes with temperature to derive models for the mould free shelf life (MFSL) of these products. The water vapour pressure above a food is determined by several factors including temperature, the water content of the food, the solutes present and the water activity in the food.

All foods have their own equilibrium relative humidity (ERH). This is the humidity at a given temperature at which the food will neither lose nor absorb moisture to or from the atmosphere.

If the food is held below its ERH it will lose moisture and become drier; above this value, it will absorb moisture from the atmosphere.  The gain or loss of water can have a major effect on a food and can influence shelf life significantly. The EHR is determined by exposing the food to carefully controlled atmospheres containing defined water vapour pressures generated using for example standard solutions of salts.

EHR and water activity (a_w) are closely related. Water activity represents the ratio of the water vapour pressure of a food to the water vapour pressure of pure water under the same conditions.  Water activity is expressed as a fraction. If this is multiplied by 100 then ERH is obtained.  Most bacteria cannot grow below an a_w of 0.86 (86 % ERH).

Cauvain and Seiler (1992) found that the logarithm of the MFSL had a linear relationship with EHR over the range 74-90% at 21° and 27°C.  The equations derived (equations 1 and 2):

Equation 1. Log10 (MFSL, days at 27°C) =6.42 - (0.065 x ERH%)

Equation 2. Log10 (MFSL, days at 21°C) =7.91 - (0.081 x ERH%)

can be used to determine the shelf life of new cake products rapidly and inexpensively. These equations are available in expensive commercial software for determining the MFSL of cakes.

Determine the mould free shelf life of cakes.

Literature Cited

Cauvain, S.P. and Seiler, D.A.L. (1992). Equilibrium relative humidity and the shelf life of cakes. FMBRA Report No. 150, CCFRA, Chipping Campden, UK.

How to cite this article

Mullan, W.M.A. (2015). [On-line]. Available from: https://www.dairyscience.info/index.php/food-model.html . Accessed: 1 October, 2023.  

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Written by: Michael Mullan

Modelling the spoilage of pasteurized milk

Spoilage of pasteurized milk is almost always due to the growth of microorganisms. These are generally introduced after heat treatment and are referred to as post process contaminants (PPCs).

The shelf life of pasteurized milk is largely dependent on the number of PPCs and storage temperature (e.g. Muir, 1996). Muir (1996) has described a simple equation (equation 1) relating the number of number of PPCs and storage temperature to shelf life of pasteurised milk.

Equation 1. Shelf life (h)={0.00621*(T+273-(269.55-0.74))*(CFC¹⁵)-0.11 x ( CFC₁₅) x 2} ^-2.

Where T = storage temperature in °K; CFC₁₅, =log10 count after pre-incubation of pasteurized milk at 15°C for 24 hours enumeration on milk agar containing a selective supplement for pseudomonads called cetrimide-fucidincephaloridine (CFC).

Muir (1996) has explained that the equation can predict shelf life at storage temperatures between 6°C and 14°C to within 1 day for between 60 and 90% of samples. The accuracy of the equation has been reported to increase as the storage temperature of the pasteurized milk increases.

Go to Shelf Life of Pasteurized Milk Calculator .

How to cite this article

Mullan, W.M.A. (2015). [On-line]. Available from: https://www.dairyscience.info/index.php/food-model.html . Accessed: 1 October, 2023.  

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Commercial cheese correctly manufactured with pasteurised milk and lactic starter cultures has a well deserved reputation as a nutritious and safe product. However, under certain circumstances cheese may support the growth of food poisoning bacteria or serve as a ‘vehicle’ for their transmission.

Four pathogens are of particular significance, Listeria monocytogenes, Salmonella species, enteropathogenic Escherichia coli and Staphylococcus aureus.  Listeria monocytogenes, the causal agent of listeriosis, is arguably the most significant of this group.

L. monocytogenes is particularly significant since it can grow / survive for long periods in cheese and cause serious illness leading to death; the death rate arising from listeriosis can exceed 30%. It can also induce abortion in humans and its ability to cross the placenta, and access the brain makes it a particularly dangerous pathogen.

 This article provides an introduction to the binary and ordinal logistic regression models developed by Bolton and Frank (1999) for predicting the probability of L. monocytogenes growing in cheese after 42 days storage at 10°C.

Characteristics of Listeria monocytogenes

L. monocytogenes is a Gram-positive, non-sporing bacterium that can grow in high salt environments (up to 10 % sodium chloride), and over a wide pH (5.0-9.6) and temperature range (< 3° – 45°C); it can grow aerobically and microaerophilically ( Bajard et al., 1996; Pearson and Marth, 1990).

Read more about Listeria monocytogenes and cheese

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Written by: Michael Mullan

Commercially, cold-filled acidic pickles, sauces (e.g. salad cream, mayonnaise), and food dressings are preserved, and their microbiological safety and stability are assured, by the use of acetic acid, salt (NaCl), and sugar. This article provides an overview of a preservation model and access to the model to enable the effect of sauce components and pH to be investigated.

Comite´ des Industries des Mayonnaises et Sauces Condimentaires de la Communaute´ Économique Européenne (1992) (CIMSCEE) has provided guidance on a safety value, Σs, for a microbiologically safe product preserved using acetic acid and a stability value, Σ, above which microbial spoilage should not occur.

A safe product has been defined as one which is so formulated that when an inoculum of viable cells of Escherichia coli is  added to the product this is reduced by 3 log cycles in less than 72 h. Products exhibiting this level of antibacterial activity have a CIMSCEE safety value (Σs) of greater than 63. Σs is calculated using equation 1. A microbiologically stable product is one that will not support microbial growth at ambient temperature and has a Σ value of greater than 63. Σ is calculated using equation 2.

Equation 1. Σs =15.75 (1 - ɑ) (total acetic acid* %) + 3.08 (salt* %) + (hexose* %) + 0.5 (disaccharide* %) + 40 (4-pH). Note, values with an * must be calculated as water phase values.

Equation 2. Σ =15.75 (1 - ɑ) (total acetic acid* %) + 3.08 (salt* %) + (hexose* %) + 0.5 (disaccharide* %). Note, values with an * must be calculated as water phase values.

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Written by: Michael Mullan

Models in food technology, at the simplest level, are equations showing the relationship between two or more variables.  Dunn (1986) defined a mathematical model of a process as a 'system of equations whose solution, given specified input data, is representative of the response to a corresponding set of inputs'.

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