Mejlholm, O. and P. Dalgaard (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.

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 seafood 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). SSSP uses a relative lag time of 4.5 for L. monocytogenes. See the SSSP dialog box and output window below (Fig. 1).

SSSP can predict growth of L. monocytogenes for both constant and changing storage temperatures. Simple temperature profiles can by 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, SSSP 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). SSSP 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 5°C (red curve) compared to growth of L. monocytogenes predicted for a temperature profile including storage at 5°C as well as 48 hours at 10°C and 48 hours at 15°C (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.

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  (µ_max, h^-1) at a reference temperature of 25°C (µ_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 (LAC_U), diactate (DAC_U), acetic acid (AAC_U), benzoic acid (BAC_U), citric acid (CAC_U) and sorbic acid (SAC_U)) all have a value between 0 and 1. SSSP predicts the growth boundary of L. monocytogenes as the combination of environmental conditions resulting in µ_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 (LAC_U) and undissociated diacetate (DAC_U) 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). SSSP 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 seafood and meat 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 seen 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 are in practice very difficult to avoid) do not result in conditions that allow L. monocytogenes to grow.

Evaluation and validation of the Listeria monocytogenes growth and growth boundary model: 

The model included in SSSP has been extensively validated by comparison of observed growth rates and growth/no-growth responses in inoculated challenge tests with seafood and meat products (Mejlholm et al. 2009). The model performed very well as shown below. The fail-safe predictions corresponds to product where growth was predicted but not observed and the fail-dangerous predictions corresponds to products where growth was observed but predicted to occur.