Fox, M.B.

Lieverloo, J.H.M.

Roode, M., de

Wells-Bennik, M.H.J.

Zwietering, M.H.

Wageningen Yield 

7th International Conference 
on Predictive Modelling of Food Quality and Safety
7ICPMF, September 12 — 15th, 2011, Dublin, Ireland
Radisson Blu Royal Hotel, Golden Lane, Dublin 8, Ireland
Conference Proceedings
www.icpmf.org/2011
E. Cummins, J.M. Frías and V.P. Valdramidis (Eds.), 
Predictive Modelling of Food Quality and Safety – Conference Proceedings, 
UCD, DIT, Teagasc, Dublin, Ireland
Multivariate regression model of thermal inactivation of 
Listeria monocytogenes in liquid food products 
J.H.M. van Lieverloo1, M. de Roode1, M. B. Fox1, M. H. Zwietering2, M. H.J. Wells-
Bennik1 
1 NIZO food research, Kerhemseweg 2, 6718 ZB Ede, The Netherlands (Hein.van.Lieverloo@nizo.nl; 
Matthew.deRoode@nizo.nl; Martijn.Fox@nizo.nl; Marjon.Wells-Bennik@nizo.nl)  
2 Wageningen University & Research centre, Bomenweg 2, 6703 HD Wageningen, The Netherlands 
(Marcel.Zwietering@wur.nl)  
Abstract 
A model was constructed from literature data for thermal inactivation of Listeria 
monocytogenes in liquid food products based on 735 sets of literature data. Significant 
variables were pH, sugar and fat content and the time and temperature of growth or storage 
before inactivation, as well as a heat shock. The model reduces the variability in the dataset 
due to these variables (known or controllable in practice), while keeping the variability of 
heat resistance of the 58 strains (unknown and not controllable in practice).  
 
Keywords: pasteurisation, food matrix, processing, Monte Carlo analysis 
Introduction 
The variability of the efficacy of thermal inactivation of L. monocytogenes (e.g. during 
pasteurisation) can be estimated by a model that is based on literature data. Differences in 
food composition, process conditions and other variables can influence thermal inactivation. 
When calculating inactivation of L. monocytogenes for a specific food and process using 
Monte Carlo simulations, there is likely an overestimation of the variability of the thermal 
inactivation efficacy. On the other hand, using inactivation data in a certain food based on a 
limited number of L. monocytogenes strains may lead to underestimation of the variability of 
strain resistance to heat. The objective of this research was to generate a multivariate 
regression model to predict (variability of) thermal inactivation from literature data while 
accounting for effects of food composition and processing conditions. As specific data on 
food composition is lacking in most literature on heat inactivation in solids (fish, sea food, 
meat, vegetables), the model was limited to fluids.  
Materials and Methods 
Inactivation data and some condition variables were present in a database constructed from 
literature as described by Van Asselt & Zwietering (2006). Data on more variables were 
collected from the original papers they cited and from the cited reviews of ICMSF (1996) and 
Doyle et al. (2001). The database was further supplemented with other, mostly more recent 
literature (Edelson-Mammel et al. (2005), Hassani et al. (2005a, 2005b, 2007), Huang (2004), 
Ignatova et al. (2007), Juneja & Eblen (1999), Maisnier-Patin et al. (1995), Van der Veen et 
al. (2007)). Missing data on pH and concentrations of fat, salt and sugars in growth media, 
dairy, juices and egg (parts) were estimated from other literature or the internet. Data sets (26) 
with antimicrobials (peroxide, lactoperoxidase, nisin and ethanol) were not included. In total, 
the 801 data sets from 53 papers included 58 L. monocytogenes strains or cocktails (7). 
Statistical analysis was performed using GenStat 13.2 (VSN International Ltd.). 
Concentrations of fat (0 – 83%), sodium chloride (0 – 20%) and sugars (0 – 58%) were 
10-logarithmically transformed to approach a normal distribution, as was the duration of the 
last temperature phase (0 – 336 h, culturing or storage, excluding heat shock). Zero values 
were transformed to -5 (% sodium chloride), and -4 (% fat and sugar). The highest, 
acceptable, colinearity found was between 10log(sodium chloride) and 10log (fat), with a 
correlation coefficient of 0.24 (-0.06 when zero values were excluded). The ‘all-subsets 
regression’ procedure was used to attain the basic linear model without interaction terms. 
202
Results and Discussion  
Preliminary multivariate modelling could not reduce unequal variance over the temperature 
range, the variance at 60 – 70 °C remained too high. High 10logD (D = time to 10-fold 
reduction) was linked to 5-20% sugar and/or sodium chloride added to liquid egg products. 
Low 10logD was linked to long cold storage in chicken gravy. As inclusion of 10log(sodium 
chloride), 10log(sugars) and 10log(duration of last temperature phase) in the model could not 
reduce this high variance at mid temperatures, chicken gravy data (40 data sets) were 
removed from the data set, as were liquid egg products with added sugar or sodium chloride 
(26 sets). This limited the concentration range of sodium chloride to a maximum of 8.8% 
(initially 20%), but stabilised the variance. Figure 1 shows the variability of all 10logD values, 
not corrected for food or process variables. The univariate model of 735 datasets (logD = 
9.07 – T / 6.74) had an R2 of 0.77 and a standard error of 0.409. 
 
-3
-2
-1
0
1
2
3
45 50 55 60 65 70 75 80 85
10
lo
g(
D
 in
 m
in
ut
es
)
Inactivation temperature (°C)
Media (n = 321)
Cabbage / fruit juice (n = 32)
Dairy (n = 260)
Liquid egg (n = 75)
Beef gravy (n = 47)
Chicken gravy (n = 40, excluded)
Egg + NaCl or sugar (n = 26, excluded)
 
 
Figure 1: Variability of inactivation times (D = time to 10-fold reduction) of Listeria 
monocytogenes per heating menstruum as a function of the heating temperature. Inactivation 
times are not corrected for effects of other variables. Total number of data sets is 801 and 66 
of these were excluded for further modelling (chicken gravy and liquid eggs with added sugar 
or sodium chloride). Fruit juices are apple, orange and white grape. Dairy includes milk, 
cream, butter and ice-cream. Liquid eggs are separated in whole, white and yolk. Media 
include deionised water, physiological saline, phosphate buffer, brain heart infusion, tryptose 
phosphate broth and trypticase soy broth (with or without yeast extract). 
 
To select variables for the basic multivariate model including processing conditions and 
menstruum composition, all possible combinations of variables were tested, including leaving 
out one or more variables. To limit the complexity of the initial model, individual menstrua 
(17 groups) were not included at first. The selected best model had an R2 of 88.3% and a 
standard error or 0.292 and is presented as model A in Table 1. Allowing for interaction 
between heating temperature and menstruum groups, i.e. allowing different slopes per 
menstruum group, did not change R2 or standard error, and consequently interaction terms 
were not included. 10log(sodiumchloride) was not significant (p = 0.055), had little effect on 
R2 (88.4%) and the standard error (0.292) and was not included in model A. 
203
Table 1: Coefficients (and standard error) of models of the effect of heat and other variables 
on 10log D (D = time in minutes for 10-fold inactivation). Significance levels are p < 0.001 
unless indicated otherwise: ** p < 0.01, * p < 0.05, # p < 0.1, & p > 0.1.  
Variable Model A  Model B 
Intercept 
Heating temperature (°C) 
pH 
10log(sugars % wt/vol) 
10log(fat % wt/vol) 
Last temperature phase (°C) a 
10log (last temp. phase (h)) a 
Heat shock difference (°C) b 
Heating method 2 c 
Heating method 3 c 
Heating method 4 c 
Liquid egg d 
Beef gravy d 
Cabbage / fruit juice d 
Media d 
Estimated standard error 
R2 
Number of data sets 
 
9.33 (0.189) 
-0.161 (0.0025), z = 6.21 
0.165 (0.011) 
0.081 (0.018) 
0.063 (0.014) 
0.0053 (0.009) 
-0.220 (0.028) 
0.0153 (0.018) 
-0.189 (0.047) 
-0.078 (0.037)* 
0.078 (0.049)& 
-0.142 (0.064)* 
0.516 (0.073) 
0.216 (0.077)** 
0.071 (0.051)& 
0.292 
88.3% 
735 
 9.01 (0.170) 
-0.157 (0.0023), z = 6,37 
0.167 (0.011) 
0.090 (0.017) 
0.060 (0.014) 
0.0060 (0.009) 
-0.249 (0.027) 
0.0138 (0.018) 
 
 
 
-0.074 (0.060)& 
0.414 (0.073) 
0.116 (0.071)& 
0.069 (0.050)& 
0.298 
87.8% 
735 
a  Duration and temperature of last temperature phase, either during culturing or storage, not heat shock.  
b Heat shock (54 sets) temperature difference with the last temperature phase (culturing or storage). 
c Heating method 1 = lab scale pasteuriser with flow (n = 93), 2 = low culture volume in large volume 
pre-heated menstruum (n = 211), 3 = low volume in submerged glass capillary tube or coil (n = 350), 
4 = large volume in glass vial in water bath (n=81). Reference method is heating method 1. 
d Reference menstruum is dairy 
 
 When all 17 individual menstrua were included in model A (instead of menstruum groups), 
milk, cream and some media were significantly different from other menstrua, R2 was 89.9% 
and standard error 0.271. Whereas there could be merits in considering all menstrua 
separately, doing so would result in considerable increase of model complexity and general 
applicability, which is undesirable. Allowing polynomial effects of variables and interaction 
between variables in model A, the model would improve slightly (R2 = 89.4, s.e. = 0.278),  
the polynome of 10log(sodium chloride) would be included, as would the product of 
10log(sodium chloride) and 10log(sugars). In this model, however, an increase of the 
10log(sodium chloride) terms would have a lowering effect on logD and this is contradictory 
to results in individual papers (Jorgensen et al. (1995), Juneja & Eblen (1999) and Edelson-
Mammel et al. 2005). Furthermore, these changes would result in a lower and more uncertain 
intercept, only a low increase of R2 and low decrease of the estimated standard error, as well 
as in increased complexity. Therefore, this change is suboptimal and model A is preferred. An 
even simpler model with a relatively high R2 and low standard error also excludes the effect 
of the heating method from model A, resulting in model B (Table 1). This model is overall 
preferred,  as the effect of heating method does not seem to follow logic; the best heating and 
cooling method (1: lab scale pasteuriser with flow) gives results that are not significantly 
different from the worst heating and cooling method (4: large volume in water bath). Model B 
is applied for inactivation of L. monocytogenes in raw milk (without pre-heating, i.e. no heat 
shock), described in Formula 1 (standard errors are given in Table 1). 
 
10logDraw milk  = 9.01 - 0.157 heating temperature (76 °C) + 0.167 pH (6.5 - 6.7)  
 + 0.090 10log(sugar (4.5 - 4.7%)) + 0.060 10log(fat (3.8 - 4.2%))  
 + 0.0060 temperature last storage phase (5-7 °C)   
 - 0.249 10log(time last storage phase (16 – 80 h)) ± 0.298    (1) 
204
Sanaa et al. (2004) estimated mean concentrations of L. monocytogenes in raw milk from two 
areas in France at 0.3 and 0.8 cells/l, with their mean being 0.55 cells/l. Assuming a 
distribution of the concentration of Poission(Gamma (1;0.55)) cells/l, the P99.9999 in raw 
milk is 13 cells/l (10 million iterations). With the univariate model of 735 data sets, 
uncorrected for the effect of food composition and processing conditions, there is a calculated 
probability of  5.10-5 of the presence of a surviving L. monocytogenes cell in a litre of milk 
pasteurised at 76 °C for 20 s (assuming equal variance at all temperatures). Using the 
preferred model B, and assuming uniform distributions of  variables with ranges described in 
Formula 1, the calculated probability is reduced to less than 1.10-7, due to the lower variability 
resulting from the inclusion of the effect of product and process variables.  
Conclusion 
A practical multivariate regression model from literature data can be used to predict heat 
inactivation of L. monocytogenes in fluids like dairy (milk, cream, butter), fruit and vegetable 
juices and liquid eggs without additives. The model includes variability of strain tolerance to 
heat and limits the variability for specific processing conditions and food composition. 
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Multivariate regression model of thermal inactivation of Listeria monocytogenes in liquid food products

de Roode, M.

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Multivariate regression model of thermal inactivation of Listeria monocytogenes in liquid food products

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