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Claire Towler is employed as a marketing executive with Chr. Hansen in England, UK.
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 https://www.dairyscience.info/protein/protein.htm .
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.
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.
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|
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.
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.
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.
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: https://www.dairyscience.info/index.php/cheese-starters/209-articles.html?start=90 . Accessed: 11 December, 2019.
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.
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.
Giuseppe 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