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'.

Claire Towler is employed as a marketing executive with Chr. Hansen in England, UK.

Chr. Hansen is a global biotechnology company that provides natural ingredients to the food, dairy, human health and nutrition, and animal health industries. The company is a leading supplier of cultures, probiotics, enzymes, colours and flavours which are applied in foods and beverages, pharmaceuticals, dietary supplements, and agricultural products.



Dr Michaell Mullan spreadsheet designerDuring the development of the Dairy Science and Food Technology ice cream mix calculator for calculating ice cream mix recipes seven packs of spreadsheets were developed and can be downloaded in return for a donation to support the continued development and maintenance of this website. Learn more about the conditions governing use of the spreadsheets prior to making a secure donation.

Because the spreadsheets have been configured to work with particular ingredients e.g. cream and skim milk powder; cream and whole milk powder they (without modification which you are free to do) will only work with the stated ingredients. So please download the correct spreadsheet pack. If in doubt send me an Email or read the additional user instructions.

There are no restrictions on users modifying or customising spreadsheets and some packs contain customised spreadsheets for the most commonly used ingredients e.g. cream, whole milk and skim milk powder. One of the simpler spreadsheets (Pack 2) has been converted to a web page to illustrate how this can be done. Batch sizes can be calculated and "costed", data inputs can easily be validated and alerts can be added e.g. if the MSNF is not optimal or within certain limits or if the fat: sugar ratio exceeds set limits.

To reduce costs some manufactures are using vegetable fat / milk fat blends. One of the spreadsheets in Pack 6 enables the quantities of milk fat and vegetable fat required to produce a mix to a desired dairy and vegetable fat ice cream recipe to be calculated. Alerts can also be added if the % vegetable fat exceed a set limit e.g. 40% w/w of the total fat or if the milk fat falls below 60% of the total fat.

Test out an On Line fully working spreadsheet for producing high protein ice cream mixes by going to .

DRAFT Article.

This article is available On Line to enable editing. Its draft status is scheduled to be removed by September, 2015. In the meantime comments are invited from scientists and technologists familiar with the subject area to help improve this article. I wish to acknowledge the generous comments and advice received from workers in this area. As a result of the feedback I will include more information about the principles behind modelling bacterial growth and the limitations of models.

Michael Mullan. 17th April, 2015

The purpose of this article is to explain how to derive a simple Ratkowsky square root model (Ratkowsky et al., 1982) that describes the growth of a fault causing bacterium on cooked meat over the temperature range 10° - 35 °C. 

An example of the growth curve of the fault causing bacterium on tomatoes at 35°C is shown in figure 1.

The curve shows the 4-typical growth phases, lag, logarithmic, stationary and decline.

growth-curve articles


The specific growth rate (k) is calculated for the  logarithmic phase using equation 1.

Equation 1. k=log10(Nt) - log 10 (N0)
                          T x 0.301


Nt = is the number of bacteria at the end of the observation period.
N0 = is the number when the observation period started.
T = is the time that has elapsed over the growth period in hours.

k= 9.146-6.669
        2 x 0.301

k= 4.115 generations h-1 at 37 °C.

Next we need to construct a series of curves at 10°, 20°, and 30 °C to find the specific growth rate at each temperature. We have got the growth curve at 35 °C already (Figure 1 above). The specific growth rates at each temperature are then tabulated using equation 1 against time (Table 1). Note I have not shown the growth curves at the other temperatures. 

  Table 1. The effect of temperature on the specific growth rates of a bacterial isolate on tomatoes
 Temperature, °C  Specific growth rate, h-1
 10  0.023
 20  0.16
 30  0.384
 35 0.518

 We can now use the Ratkowsky square root model (Ratkowsky et al., 1982) to derive the relationship between the growth rate constant, temperature and the initial number of microorganisms.

The equation has been described previously, √r= b (T-To), where r is the growth rate constant.  In particular we need to calculate b, the slope of the square root of specific growth rate versus temperature plot, and, To, the value at which the square root of growth rate intercepts the x axis.

The curve produced using linear regression (black line) and the actual data (blue line) using the data in table 1 is shown in figure 2.

 trend-line articles

Using Excel, the linear regression equation that describes the trend line (black line in figure, for the growth of the fault causing bacterium on cooked meat over the temperature range 10° to 35 °C is:

√r= 0.0228 (T-0.0693) where √r is the square root of the growth rate constant and T is the temperature in °C.

Use of Combase Tools

While the calculations described previously are not difficult it is possible to automate the derivation of growth rate equations using free tools from Combase.  DMFit is an Excel add-in to fit log counts vs. time data and extract parameters such as growth rate. It can be downloaded from Combase.

Model validation

Validation is an important element in model development. The literature cited below provides useful insights into model development and may prove useful during validation. The USDA Pathogen Modelling Program (PMP) and ComBase should be consulted for pathogen-models.


To be added.

Literature cited

Baranyi, J., Pin, C. and  Ross, T. (1999). Validating and comparing predictive models. Int. J. Food Microbiol. 48:159-166.

Baranyi, J.,  Ross, T., Roberts, T.A. and  McMeekin, T. (1996). The effects of overparameterisation on the performance of empirical models used in predictive microbiology. Food Microbiol. 13:83-91.

 Pin, C.,  Sutherland, J. P. and Baranyi, J. (1999). Validating predictive models of food spoilage organisms. J. Appl. Microbiol. 87:491-499.


To be added.

How to cite this article

Mullan, W.M.A. (2015). [On-line]. Available from: . Accessed: 8 July, 2020.  

An article on thermal process modelling has been added. 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.

 Effect of HTST treatment on the number of log reductions of major milk pathogens.

Phage release, the final stage in the phage-life cycle, has been extensively studied and is caused, at least in part, by the action of phage-induced hydrolytic or lytic enzymes.

Characteristics - Montebore is a characteristic conic-shaped cheese obtained by overlapping three cheeses of different diameters. The final product is named “Castellino (“Small castle”) and has a weight of about 0.5-1 kg. Ripening time ranges from 6 to 60 days. The crust is smooth, regular with a light pale-yellow colour. The dough is white or ivory-white with small and sparse holes. The texture is very soft and elastic in the fresh cheese, hard, solid, compact and friable in the ripening cheese. The odour is fine and delicate with milk and cream characteristics in fresh cheese but savoury, salty and intense in aged products.

Professor G ZeppaGiuseppe Zeppa is a researcher in the Food Technology Sector of Di.Va.P.R.A. (Department of Exploitation and Protection of theAgricultural and Forestry Resources) at the Agricultural Faculty of Turin University (Italy). He is a professor of Sensory Analysis and  Milk and Dairy Technology at Turin University.

Professor Zeppa has worked at Turin University since 1984.

 Research Interests and Current Research Projects

Professor Zeppa's research  is devoted to the study of chemical and sensory characteristics of foods. The main topics are the study of wine and cheese flavours, the study of relationships between technology and chemical/sensorial characteristics of foods, the use of gas-chromatography-mass spectrometry for food analysis, the food characterisation between the sensory analysis, the consumer science.

Commercially, cold-filled acidic pickles, sauces (e.g. salad cream, mayonnaise) and food dressings are preserved, and their microbiological safety 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.

The Comite´ des Industries des Mayonnaises et Sauces Condimentaires de la Communaute´ Économique Européenne (CIMSCEE) has provided guidance on a safety value, Σs, for a microbiologically safe product preserved using acetic acid (Anonymous, 1993). 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: Σs =15.75 (1 - ɑ) (total acetic acid %) + 3.08 (salt %) + (hexose %) + 0.5 (disaccharide %) + 40 (4-pH).


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