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Model Listeria monocytogenes growth and growth boundary models
References Mejlholm, O. and Dalgaard, P. (2007a). Modeling and predicting the growth boundary of Listeria monocytogenes in lightly preserved seafood. J. Food Prot. 70, (1) 70-84.

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 (10), 2132-2143.

Mejlholm, O., Dalgaard, P. (2015). Modelling the simultaneous growth of Listeria monocytogenes and lactic acid bacteria in seafood and mayonnaise-based seafood salads. Food Microbiol. http://dx.doi.org/10.1016/j.fm.2014.07.005

Mejlholm, O., Bkns, N., Dalgaard, P. (2014). Development and evaluation of a stochastic model for potential growth of Listeria monocytogenes in naturally contaminated lightly preserved seafood. Food Microbiol. http://dx.doi.org/10.1016/j.fm.2014.06.006

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)
Product validation studies The model has been extensively validated using data from ready-to-eat food products (Mejlholm & Dalgaard 2007a,b; Mejlholm & Dalgaard, 2009, 2015; Mejlholm et al. 2010, 2014).
Range of applicability Temperature (2-25C), atmosphere (0-100 % CO2), water phase salt (0.7-9.0 %), pH (5.6-7.7), smoke components/phenol (0-20 ppm), nitrite (0-150 ppm in product), acetic acid (0-11000 ppm in water phase), benzoic acid (0-1800 ppm in water phase), citric acid (0-6500 ppm in water phase), diacetate (0-3800 ppm in water phase), lactic acid (0-60000 ppm in water phase) and sorbic acid (0-1300 in water phase).

With mayonaised-based seafood salads the models range of applicability is limited to pH values of 6.0 and above.

This model includes the effect of 12 environmental parameters (See range of aapplicability above) on growth and on the growth boundary of L. monocytogenes. Information on the lag time of L. monocytogenes in naturally contaminated lightly preserved food is still limited. Therefore, the growth model for L. monocytogenes can be used without lag time (fail safe predictions) or with lag time (more realistic predictions for naturally contaminated products). FSSP uses a relative lag time of 4.5 for L. monocytogenes. See the FSSP dialog box and output window below (Fig. 1).

FSSP can predict growth of L. monocytogenes for both constant and changing storage temperatures. Simple temperature profiles can be typed in as 'Series of constant temperatures' whereas actual product temperature profiles most often are entered as 'Temperature profiles from data loggers' (See Fig. 2).

 

 

Fig. 1. Predicted growth of L. monocytogenes. Product 1 is added benzoic acid and sorbic acid whereas product 2 is added acetic acid and lactic acid. Importantly, FSSP can be used to evaluate if one set of food preservatives (like benzoic and sorbic acid) can be replaced with another set of preservatives (like acetic and lactic acid). FSSP predicts the time needed for the concentrations of L. monocytogenes to increase 100-fold under the selected product characteristics and storage conditions. The concentrations of L. monocytogenes shown in the bar at the bottom of the output window was obtained by using the mouse to click on the graph at a specific point in time.       

 

 

Fig. 2. Predicted growth of L. monocytogenes at a constant storage temperature at 5C (red curve) compared to growth of L. monocytogenes predicted for a temperature profile including storage at 5C as well as 48 hours at 10C and 48 hours at 15C (blue curve).

 

Primary model for growth of Listeria monocytogenes
The Logistic model with delay as shown in Egn. 1 is used to predict changes on concentrations of Listeria monoocytogenes during storage at constant or at changing storage temperatures.

                   

Eqn. 1. Logistic model with delay (tlag).
 
Secondary growth and growth boundary model:
Eqn. 2 below shows the secondary growth model for L. monocytogenes. This simplified cardinal parameter model describes how the maximum specific growth rate  (max, h-1) at a reference temperature of 25C (max-ref  = 0.419 1/h) is reduced when conditions become less favourable for growth. The term for each of the environmental parameters (temperature, water activity/water phase salt, pH, phenol (smoke components), CO2 (atmosphere), nitrite and undissociated lactic acid (LACU), diactate (DACU), acetic acid (AACU), benzoic acid (BACU), citric acid (CACU) and sorbic acid (SACU)) all have a value between 0 and 1. FSSP predicts the growth boundary of L. monocytogenes as the combination of environmental conditions resulting in 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 (Eqn. 2. With temperature (T), undissociated lactic acid (LACU) and undissociated diacetate (DACU) as examples). Eqn. 3, 4 and 5 show how the value of the interaction term (ξ) is calculated. Importantly, the parameter ψ (psi) from eqn. 5 provides a measure of the distance between a given set of environmental conditions and the growth boundary (Le Marc et al. 2002; Mejlholm & Dalgaard, 2009). FSSP is able to predict boundary conditions corresponding to different ψ-values between 0.5 and 2.5. This is important as it allows identification of combinations of product characteristics and storage conditions that prevent growth of L. monocytogenes and at the same time is located in a safe distance from the growth boundary. We recommend using a ψ-value of 2.0 when product characteristics to prevent growth of L. monocytogenes in food products are identified. The effect of using a ψ-value of 1.0 (corresponding to the growth boundary) and a ψ-value of 2.0 is shown below by comparison of Fig 3 and Fig. 4. The higher concentrations organic acids needed to reach a ψ-value of 2.0 provide a safety margin so that small variations in product characteristics (that in practice are very difficult to avoid) do not result in conditions that allow L. monocytogenes to grow.

 

Eqn. 2. Secondary growth and growth boundary models for L. monocytogenes.

 

 

                   

 

        

Fig. 3.  Predicted growth boundary (ψ-value = 1.0) of L. monoocytogens at different pH and for different concentrations of sorbic acid and banzoic acid.
 

        

Fig. 4. Predicted boundary conditions (ψ-value = 2.0) that prevent growth of L. monoocytogens and at the same time are located in a save distance from the growth boundary.

 

Evaluation and validation of the Listeria monocytogenes growth and growth boundary model: 
The model included in FSSP has been extensively validated by comparison of observed growth rates and growth/no-growth responses in inoculated challenge tests with food products (Mejlholm et al. 2010). The model performed very well as shown below. The fail-safe predictions corresponded to product where growth was predicted but not observed and the fail-dangerous predictions corresponds to products where growth was observed but not predicted to occur.

Importantly, this model has ben shown to accuratelt predict L. monoocytogens growth in naturally contaminated cold-smoked salmon and naturally contaminated cold-smoked Greenland halibut (Mejlholm et al. 2014). With mayonaised-based seafood salads the models renge of applicability is limited to pH of 6.0 and above (Mejlholm and Dalgaard, 2015).

Model Data used for evaluation and validation of the model Indices of performance
L. monocytogenes growth rate model (Mejlholm & Dalgaard, 2009)

640 growth curves for L. monocytogenes in inoculated challenge tests with meat, seafood, poultry and dairy products (Mejlholm et al. 2009).

Bias factor            = 1.0

Accuracy factor    = 1.5

L. monocytogenes growth boundary model (Mejlholm & Dalgaard, 2009)

1014 growth and no-growth responses for L. monocytogens in inoculated challenge tests with various foods (Mejlholm et al. 2009).

Correct prediction (%): 89

Fail-safe (%): 6

Fail-dangerous (%): 5