Lm-intro

Model	FSSP generic growth model
References	Dalgaard, P. (2009). Modelling of microbial growth. Bulletin of the International Dairy Federation, 433 45-57. Mejlholm, O. and Dalgaard. P. (2009). Development and validation of an extensive growth and growth boundary model for Listeria monocytogenes in lightly preserved and ready-to-eat shrimp. J. Food Prot. 70, 2132-2143. Mejlholm, O, Dalgaard, P. (2013). Development and validation of an extensive growth and growth boundary model for psychrotolerant Lactobacillus spp. in seafood and meat products. Int. J. Food Microbiol. 167, 244-260. Řstergaard, N.B., Eklöw, A., Dalgaard, P. (2014). Modelling the effect of lactic acid bacteria from starter- and aroma culture on growth of Listeria monocytogenes in cottage cheese. Int. J. Food Microbiol. 188, 15-25.
Primary growth model	Logistic model with delay
Secondary growth model	Simplified cardinal parameter type model
Environmental parameters in model	Temperature, atmosphere (CO2), water phase salt/aw, pH, smoke components/phenol, nitrite and organic acids in water phase of product (acetic acids, benzoic acid, citric acid, diacetate, lactic acid and sorbic acid)

This generic model is a highly flexible tool to predict growth of various microorganisms in different foods. The FSSP generic growth model allows users to define values of 12 environmental parameters (See the FSSP dialog box and eqn 1 below). In addition users can specify a reference maximum specific growth rate (ľref, 1/h) for each model and a relative lag time (RLT value. In ths way the FSSP generic growth model can predict responses of most microorganism/food combinnations and this flexible tool has many applications. The FSSP generic growth model can for example be used to:

Expand and/or modify available models:
- By adjusting ľref and/or adding new cardinal parameter values to an available model FSSP can be used for new food products including products where new antimicrobial ingredient have been added.

Evaluate growth responses for a wide range of environmental parameters:
- FSSP can be used for wide ranges of many environmental parameters and the effect of dynamic temperature, pH and lactic acid conditions can be predicted.

Evaluate model uncertaintly under a wide range of constant and dynamic conditions:
- By using a model with different relative lag time (RLT) values FSSP can evaluate the effect lag time uncertainty of growth responses. Furthermore, by adjusting cardinal parameter values of an available model FSSP can evaluate growth responses of resistant isolates of specific microorganisms.

Disseminate new models:
- FSSP can save, export and import models with new or adjusted cardinal parameter values. This allow users of FSSP to conveniently disseminate the models they developo using this tool.

How to use the FSSP generic model tool:

To start using the FSSP generic model tool you must first 'Add model' or 'Import model' and then Select growth model (sse FSSP dialog box below).

Fig1

Fig. 1. FSSP dialog box for the Generic growth model.

When pressing the 'Add model' bottom the dialog box below appears and allow users to (i) modify the indicated default paramter values and (ii) name and save the new model. Saved models can be Exported to an XML-file. This file can be send to other users of FSSP and they can easily Import, Select and used this model. When a model is selected in FSSP it can be modified by pressing the 'Edit model' bottom and then changes can be saved under the same or under a new model name. FSSP Generic growth models are highly flexible but if a model is used for a fresh food product without salt, without smoke, without nitrite and/or without added organic acids then these model terms can easily be inactivated by applying the relevant boxes in the 'Not in use' column (See dialog box belowe).

Fig2

Fig. 2. 'Add model' dialog box used to enter new parameter values and to save a new model.

Like for other models in FSSP the Generic growth model can provide predictions at constant and dynamic temperature store conditions. Figure 1 shows an example where growth is predicted at a constant temperature of 8.0°C. Figure 1 also showns how Generic growth models can be used with relative lag time (RLT) values selected by the user.

In addition to dynamic storage temperaures FSSP can predict the effect of changing pH and changing lactic acid concentrations on growth resonses. Figure 3 and Figure 4 below show how pH and lactic acid profile data are imported by using the FSSP raw data importer. Fugure 5 below shows how the predicted growth (red curve) is dampend when pH (purple curve) decreases below ca. 5.5 and the concentration of lactic acid (green curve) increases to more then ca. 2000 ppm.

Fig. 3. Import of temperature, pH and lactic acid profiles by usinf the FSSP raw data importer.

Fig. 4. The FSSP raw data importer allow data to be transfered too FSSP from spreadsheets by copy and paste.

Fig. 4. FSSP Generic growth model output window showing how growth is dammpend when pH decreases and the lactiac concentration oncreases.

Primary model for growth
The FSSP Generic growth model uses the Logistic model with delay as primary growtg model (Egn. 1). The delay or lag time (t_lag) in Eqn. 1 is related to the maximum specific growth rate (ľmax, 1/h), and thereby to the secondary growth model, by the relative lag time (RLT): t_lag = (RLT x Ln(2))/ľmax).

Eqn1

Eqn. 1. Logistic model with delay.

Secondary growth and growth boundary model:
Eqn. 2 below shows the secondary growth model used by the FSSP Generic growth model. This simplified cardinal parameter model describes how the maximum specific growth rate (ľ_max, h^-1) at a reference temperature (ľ_ref , specified by the user) is reduced when conditions become less favourable for growth. The term for each of the environmental parameters (temperature, pH, water activity/water phase salt, phenol (smoke components), CO₂ (atmosphere), nitrite and undissociated organic acids (acetic acid (AAC_U), benzoic acid (BAC_U), citric acid (CAC_U), diactate (DAC_U), lactic acid (LAC_U) and sorbic acid (SAC_U)) all have a value between 0 and 1. FSSP predicts the growth boundary as the combination of environmental conditions resulting in ľ_max = 0 and a specific term (ξ) is included in the cardinal parameter models to take into account the effect of interaction between all the different environmental parameters. Like other terms in the secondary model 'ξ' has a value between 0 and 1 (See other FSSP model for details on this aspect). Figure 5 below shows how MIC values for undissociated organic acids and model terms for each organic acid is indicated with appropriate values of n1 and n2 in the FSSP dialog box.

Eqn2

Eqn. 2. Secondary growth and growth boundary model used by the FSSP Generic growth model tool.

Fig6

Fig. 5. FSSP dialog box showing how MIC values for undissociated organic acids and model terms for each organis acid is indicatd with appropriate values of n1 and n2..