Model  Microbial spoilage models with userdefined parameter values: Squareroottype model 
Reference  Dalgaard,
P., Cowan, B.J., Heilmann, J. and S. Silberg 2003. The Food Spoilage
and Safety Predictor (FSSP). In: Predictive
Modelling in Foods  4th
International Conference Proceedings. Van Impe, J.F.M., Geeraerd, A.H.,
Leguérinel, I., Mafart, P. (eds.) 1519 June
2003, Quimper, France. pp 256258.
Ross, T. and P. Dalgaard 2004. Secondary models.
In: McKeller, R.C., Lu, X. (Eds.), Modeling Microbial Responses in Foods. CRC
Press, Boca Raton, USA, p 76. 
Primary growth model  Logtransformed 3parameter Logistic model 
Secondary growth model  Squareroottype model 
Environmental parameters in model  Temperature, % CO_{2} (equilibrium concentration), water activity (a_{w}) and pH 
Product validation studies  Not studied  depends on microorganisms and selected model parameter values (See other MS models in FSSP) 
Range of applicability  Not studied 
This FSSP model with userdefined parameter values can compare growth and shelflife for: i) two microorganisms with known and different cardinal parameter values when growing under a given set of storage conditions and product characteristics. ii) a single microorganisms with known cardinal parameter values when growing under different storage conditions and/or different product characteristics (temperature, equilibrium CO_{2} concentration in MAP, water activity and pH) In both cases, growth under constant or fluctuating temperature conditions can be compared. The secondary squareroottype growth model used by FSSP is shown in Eqn. 1. The model includes a constant (b) and the cardinal parameters T_{min} (theoretical minimum growth temperature), %CO_{2 max }(theoretical maximum concentration of CO_{2 }that allow growth), a_{w min} (theoretical minimum water activity that allow growth) and pH_{min} (theoretical minimum pH value that allow growth). 
Secondary growth model: 
Eqn. 1 
This MS model with userdefined parameter values can e.g. compare growth of two microorganisms with different T_{min}values. As shown in the FSSP output window below a T_{min}value of 10°C results in much faster predicted growth than a T_{min}value of 5°C with identical product characteristics and storage conditions. 
The MS model with userdefined parameter values can be applied for all bacteria where an estimate of the constant b and the cardinal parameter T_{min} can be obtained. Estimates of the other cardinal parameter values are not needed but clearly allow for a more flexible use of the model when available. To illustrate how the model can be applied Photobacterium phosphoreum will be used as an example. For this food spoilage bacterium the following model parameter values can be obtained from the literature: b = 0.032, T_{min} = 8.8°C, %CO_{2 max }= 368, a_{w min} = ~0.95 and pH_{min} = ~4.3 (Dalgaard et al. 1997; Dalgaard 2002). As shown in the left FSSP dialog box below Eqn. 1 used together with these parameter values predicts a shelflife of 8.2 days for 0°C, 0% CO_{2, }a_{w} of 0.997 and pH of 6.6. The dialog box also shows that an equilibrium CO_{2 }concentration of 50% extends shelflife to 11 days. The right FSSP dialog box below shows that lowering of pH from 6.6 to 6.0 or reducing a_{w} from 0.997 to 0.985 have the same predicted shelflife extending effect as an equilibrium concentration of 50% CO_{2.} In addition, FSSP showed that lowering of a_{w} from 0.997 to 0.990 together with a reduction of pH from 6.6 to 6.3 e.g. has the same effect as a reduction of pH from 6.6 to 6.0. In this way FSSP can be used to identify combinations of preserving parameters that results in an equivalent shelflife extending effect. 



To predict shelflife, FSSP rely on eqn. 2 below and users must enter a realistic minimal spoilage levels (MSL) for each microorganisms studied. Eqn. 2 is appropriate for prediction of remaining shelflife but when remaining shelflife values become negative, i.e. the product is spoiled and the concentration of microorganisms has reached their maximum values, then eqn. 2 is no longer valid. Therefore negative remaining shelflife data are not shown in the FSSP output window by the microbial spoilage models with userdefined parameter values.

Eqn. 2 