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Food Research International

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Quantitative microbiological risk assessment in food industry: Theory andpractical application

Jeanne-Marie Membré⁎, Géraldine BouéSECALIM, INRA, Oniris, Université Bretagne Loire, 44307 Nantes, France

A R T I C L E I N F O

Keywords:QMRAPredictive microbiologyProbabilistic techniquesMicrobial inactivationMicrobial growth

A B S T R A C T

The objective of this article is to bring scientific background as well as practical hints and tips to guide riskassessors and modelers who want to develop a quantitative Microbiological Risk Assessment (MRA) in an in-dustrial context. MRA aims at determining the public health risk associated with biological hazards in a food. Itsimplementation in industry enables to compare the efficiency of different risk reduction measures, and moreprecisely different operational settings, by predicting their effect on the final model output.

The first stage in MRA is to clearly define the purpose and scope with stakeholders, risk assessors andmodelers. Then, a probabilistic model is developed; this includes schematically three important phases. Firstly,the model structure has to be defined, i.e. the connections between different operational processing steps. Animportant step in food industry is the thermal processing leading to microbial inactivation. Growth of heat-treated surviving microorganisms and/or post-process contamination during storage phase is also important totake into account. Secondly, mathematical equations are determined to estimate the change of microbial loadafter each processing step. This phase includes the construction of model inputs by collecting data or elicitingexperts. Finally, the model outputs are obtained by simulation procedures, they have to be interpreted andcommunicated to targeted stakeholders. In this latter phase, tools such as what-if scenarios provide an essentialadded value.

These different MRA phases are illustrated through two examples covering important issues in industry. Thefirst one covers process optimization in a food safety context, the second one covers shelf-life determination in afood quality context. Although both contexts required the same methodology, they do not have the same end-point: up to the human health in the foie gras case-study illustrating here a safety application, up to the foodportion in the brioche case-study illustrating here a quality application.

1. Quantitative microbiological risk assessment in food industry

Microbiological Risk Assessment (MRA) is a structured process fordetermining and characterizing the risk associated with biological ha-zard in a food (Codex Alimentarius Commission, 1999). In an industrialcontext, the term “risk” could be used to a broader sense, covering foodsafety issues, but also food quality issues (as the quality could be alteredby microbial spoilage). Covering spoilage beside safety is acknowledgedby the food authority, at least in Europe: the Food Law (EuropeanCommission, 2002) specifies that “Food shall not be placed on themarket if it is unsafe”, this includes food “injurious to health” as well as“unfit for human consumption”. In other words, a food product can beconsidered as unacceptable for human consumption due to pathogenbacteria, which is a food safety issue, or due to spoilage bacteria, whichis a food quality issue.

In a food processing context, both food safety and food quality

issues can be raised, the four steps of MRA (Codex AlimentariusCommission, 1999) are then adapted as follows:

i). Hazard identification consists of the identification of the micro-biological agent present in a particular food capable of causingadverse health effect (for pathogen bacteria) or an inedible product(for spoilage bacteria);

ii). Hazard characterization is the evaluation of the nature of the ad-verse health effect associated with a pathogen bacteria (type ofillness) or the effects associated with a spoilage bacteria (type ofproduct quality default);

iii). Exposure assessment consists of estimating the likely intake of apathogenic bacteria or the likely level of a spoilage bacteria in thefood, it considers changes from raw materials up to consumption;

iv). Risk characterization is based on hazard identification, hazardcharacterization and exposure assessment. It consists in estimating

https://doi.org/10.1016/j.foodres.2017.11.025Received 29 August 2017; Received in revised form 3 November 2017; Accepted 19 November 2017

⁎ Corresponding author at: UMR1014 SECALIM, INRA, Oniris, Route de Gachet, CS 40706, 44307 Nantes, France.E-mail address: [email protected] (J.-M. Membré).

Food Research International xxx (xxxx) xxx–xxx

0963-9969/ © 2017 Elsevier Ltd. All rights reserved.

Please cite this article as: Membré, J.-M., Food Research International (2017), https://doi.org/10.1016/j.foodres.2017.11.025

for pathogen bacteria the probability of occurrence and severity ofknown or potential adverse health effects in a given population; forspoilage bacteria it consists in estimating the probability of foodquality changes.

The World Health Organization and the Food and AgricultureOrganization, particularly through the Codex Alimentarius Commission(CAC) have encouraged the research community (academy, regulatoryagencies) to perform MRA. In 1999, they published a guideline to fa-cilitate the use of MRA (Codex Alimentarius Commission, 1999) and in2002, they set down the basis of risk-based food safety management(FAO/WHO, 2002). Risk-based food safety management is based on theprevention of food safety events linked to specified hazards rather thanend-product controls which was not efficient to protect consumers(highlighted by different foodborne crisis up to years 1990s). Thismodern food safety management has huge consequences at the opera-tional level as it involves in industry to put in place a strategy enablingsetting a certain level of stringency at each processing step in order toensure the desired level of consumer protection (Koutsoumanis &Aspridou, 2016). Within primary and secondary manufactures but alsoin food distribution supply-chain, the risk-based food safety manage-ment concept has to be translated into practical guidelines for opera-tional use. The key terms and their practical translations in food in-dustry are provided in Table 1.

Translating risk-based food safety management concepts into prac-tical settings is not always straightforward. Indeed, establishing how afood process, a food formulation and/or a shelf-life determination havean effect on the level of contamination at the moment of food con-sumption could involve rather complex mathematical developments.The microbial propagation during food transformation/distributionwithin the “farm-to-fork-to-human health” continuum has to be quan-tified accurately. Related to safety issues, there are many studies de-scribing the impact of process manufacture steps on level of pathogen

on food in consumer portions or at a step earlier such as at manufacturerelease (Malakar, Barker, & Peck, 2011; Membré et al., 2015; Nauta,2001; Nauta, Van Der Fels-Klerx, & Havelaar, 2005). In the spoilagearea, there are as well quantitative studies focused on the effect ofprocessing steps on levels of bacteria (Rigaux, André, Albert, & Carlin,2014; Zimmermann, Schaffner, & Aragão, 2013), including severalapplications such as ground meat (Koutsoumanis, 2009; Koutsoumanis,Stamatiou, Skandamis, & Nychas, 2006), cooked cured meat products(Mataragas, Drosinos, Vaidanis, & Metaxopoulos, 2006), sliced cookedham (Kreyenschmidt et al., 2010), raw poultry (Dominguez &Schaffner, 2007), canned bean green (Rigaux et al., 2014), yogurt(Gougouli, Kalantzi, Beletsiotis, & Koutsoumanis, 2011), bakery pro-ducts (Guynot, Marin, Sanchis, & Ramos, 2005; Huchet et al., 2013;Rosso & Robinson, 2001), green table olives (Panagou, Skandamis, &Nychas, 2003), etc.

In this context where MRA is becoming an essential tool in foodsafety and quality management, the objective of this article is to bringscientific background as well as practical hints and tips to guide riskassessors and modelers who want to develop a quantitative MRA in anindustrial context. Examples of quantitative techniques run on foie grason one hand and brioche on the other hand are detailed for practicalillustration, they cover here safety and quality issues, respectively.

2. Practical considerations when conducting a QMRA

Conducting a QMRA, involves several steps summarized in Fig. 1and explained below.

2.1. Define the purpose and scope of QMRA,

The first thing to do before building a QMRA model is to state ex-plicitly the question to be answered and to frame the scope by outlyingthe objective of the assessment and the goals that need to be met to

Table 1Risk-based food safety management terminology and practical translations in food industry.

Risk-based food safety management terminology, adapted from(FAO/WHO, 2002)

Translation of risk-based food safety management concepts in food industry

Who set this indicator? Example

ALOP, Appropriate Level of ProtectionStatement of the degree of public health protection that is to be

achieved by the food safety systems implemented within acountry (World Trade Organization, 1995).

Note: The current hypothesis is that the present number ofillnesses per million inhabitants is deemed acceptable and couldbe then assimilated to an ALOP (EFSA, 2007; Gkogka, Reij, Gorris,& Zwietering, 2013).

Food Safety AuthorityAn ALOP cannot be directly translated by the industry into apractical measure. Instead, a measurable target for producers,manufacturers and control authorities is required; this is the basisof the Food Safety Objective (FSO) concept.

0.2 cases of Listeriosis per 100,000people per year

FSO, Food Safety ObjectiveAn FSO corresponds to the maximum frequency and/or

concentration of a hazard in a food at the time of consumptionthat provides or contributes to the ALOP.

There is a quantitative link between FSO and ALOP but thereare not yet a lot of guidelines to derive an FSO from an ALOP.

Food Safety AuthorityTo be operational, FSO and PO must be translated into criteria thatcan be controlled and measured in the food supply chain.

FSO as< 100 cfu/g of Listeria atthe point of consumption

PO, Performance ObjectiveA PO corresponds to a maximum frequency and/or

concentration of a hazard in a food at a specified step in the foodchain before the time of consumption that provides or contributesto an FSO or ALOP, as applicable.

Food Safety Authority and / or the food business operators PO as< 10 cfu/g of Listeria at themanufacture release

PC, Performance Criteria (PC)The PC is the effect required of one or more control measure(s)

working in concert to meet a PO.

Food business operators PC> 4 log reduction during foodprocessing, obtained by thermaltreatment

PrC, Process Criteria and PdC, Product CriteriaPrC and PdC are control measures, implemented at the

operational level, associated with the process and theformulation, respectively.

Food business operators PrC: Heat-treatment time> 1 minat 70 °C (or equivalent)PdC: pH of the product duringthermal treatment step< 5

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answer satisfactory to the question raised.When thinking “risk” in terms of “public health risk” or “spoilage

risk”, a specific population is targeted according to what risk estimationshould be provided. In microbiology, the population of interest isusually the population consuming the product (e.g. infants, adults,whole population, …). The population has to be identified right fromthe beginning to define inputs accordingly. For instance, if the popu-lation of interest is France, it will be necessary to look at relevantFrench surveys to gauge food consumer habits and preferences.

2.2. Agreement on vocabulary within the QMRA working group

The vocabulary has to be understood by everyone involved in therisk assessment and the decision-making process. Input and output unitsmust be carefully defined to avoid misunderstanding, for instance“Absence of ….” means no bacteria in a portion (from a safety per-spective) while food microbiologists often use the logarithm transfor-mation and report the contamination level per g (or ml). Moreover,when performing a Monte Carlo simulation, it is crucial to agree onwhat a simulation means, what an iteration means (e.g. the wholebatches run for a given process line, for a given formulation andpackaging).

2.3. Building the model: structure, equations, inputs

The model structure explains how the response (i.e. the main modeloutput) is connected to the inputs, often with a scheme. Also, a modelhas to be documented, with in particular the assumptions underneaththe model development which have to be clearly stated and justified.The choice of equations and the source of data to inform the inputs haveto be provided. To have more information on model structure anddocumentation, see the literature (Barlow et al., 2015; Basset, Nauta,Lindqvist, & Zwietering, 2012; Bean et al., 2012; Brown & Stringer,2002; FAO/WHO, 2006; Haas, Rose, & Gerba, 2014; Vose, 2008).

Once the structure is established and agreed among risk assessorsand modelers, the model equations could be considered. In QMRA,there are schematically four categories of equations:

– Probability functions describing a large set of phenomena such aspartitioning, model error, prevalence uncertainty, etc.

– Equations related to mass and heat transfer models describing es-sentially recontamination and physical gradient phenomena (e.g.profiles of temperature in a big product tank or in a single productunit pack).

– Equations related to predictive microbiology describing for instanceinactivation and growth steps. Predictive microbiological modelsare used in MRA to estimate the level of microorganisms in food atthe time of consumption (McMeekin, Olley, Ratkowsky, & Ross,2002). More generally, it aims at predicting the level of

microorganism at a given time, at a specific step under the farm-to-fork continuum, e.g. level after heat treatment, after storage, etc.(Pérez-Rodríguez & Valero, 2013).

– Dose-response models describing the probability of an adverse effect(safety or spoilage), as a function of an exposure to microorganisms.

2.3.1. Model equationsMain equations used in QMRA are provided below, but more details

can be found in books (McKellar & Lu, 2004; Membré & Valdramidis,2016; Pérez-Rodríguez & Valero, 2013; Valdramidis, Cummin, & vanImpe, 2017). In addition specific information on probability functionsapplied to risk assessment could be found in Vose (2008), on mass andheat transfer models related to thermal treatment of food products inValdramidis and Van Impe (2012). Predictive models are also im-plemented in software tools, listed recently by Koutsoumanis, Lianou,and Gougouli (2016) or Tenenhaus-Aziza and Ellouze (2015). Likewise,some QMRA tools are now publicly available, for instance, iRISK onlinesystem (https://irisk.foodrisk.org/Default.aspx) enables to perform aQMRA with a pre-defined structure (Chen et al., 2013).

2.3.1.1. Heat treatment inactivation. When a heat treatment step isinvolved, conventionally, the resulting microbial inactivation isdescribed using a first-order kinetic model:

= × −N N 10 t D0

/HT (1)

where:

– N is the number of bacteria after heat treatment (cfu per batch, perproduct unit…),

– N0 is the number of bacteria before heat treatment (same unit as N,e.g. cfu per product unit),

– tHT is the heat-treatment time (min),– D is the decimal reduction time (min). D can be described by asecondary model which takes into account the heat-treatment tem-perature and sometimes product characteristics (Bean et al., 2012;Valdramidis et al., 2017).

When N0 = 1, i.e. when there is only one bacterium in the foodproduct unit in Eq. (1), N corresponds actually to the probability thatone bacterium survives the heat treatment (Nauta, 2001), written as inEq. (2):

= −P 10one bacterium to survivet D/HT (2)

Note that in Eq. (2), the ratio “tHT/D” corresponds to the log re-duction, and then to a performance criterion, PC.

The number of bacteria after heat treatment is not derived directlyfrom Eq. (1) as it follows a Binomial process:

N N P~Binomial( , )one bacterium to survive0 (3)

Fig. 1. Key steps in QMRA model development.


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Eq. (3) could be simplified into N~Poisson(N0 × Pone bacterium to

survive) if N0 is large and Pone bacterium to survive is small.Calculating the number of bacteria after heat treatment, N, using the

conventional method (Eq. (1)) is a deterministic estimation of thenumber of bacteria (e.g. only one result is expected) whereas usingprobabilistic method (Eq. (3)) provides a distribution of all potentialresults (e.g. different levels of bacteria can be obtained with associatedprobabilities of occurrence). The use of either conventional or prob-abilistic approach does not have any impact on the prevalence (i.e.number of packs contaminated after the heat treatment) when log N0 ismuch larger than tHT/D (equivalent to a Performance Criteria PC),however when log N0 and tHT/D are at the same order of magnitude,that makes a difference. For instance, with an initial level of con-tamination and a heat treatment of 4 logs cfu/pack, we estimate withthe conventional calculation 100% of packs contaminated whereas only63% of packs are probably contaminated (Fig. 2).

Note that the inactivation step has been illustrated here with athermal process, but it can be modelled in the same way with anotherprocess, as done by Lerasle et al. (2014) with high hydrostatic pressure.

2.3.1.2. Bacterial growth during storage. Periods of storage atmanufacture (for example between two operational steps), at retailer'sand at consumer's, could enable the growth of microorganisms.However, before growth, bacteria need a period of time of adaptationto environmental conditions, namely the lag phase, tlag. This periodcould be relatively long if bacteria have been injured by differentprocess steps like a heat treatment as bacteria cells will need to berepaired before being able to grow. To estimate the number of bacteriaafter the storage, primary and secondary models are used (McKellar &Lu, 2004; Pérez-Rodríguez & Valero, 2013). Primary models describethe number of bacteria over the time. Secondary models describe theeffect of formulation and/or process on growth rate and lag phase.

In QMRA when considering a public health risk, the maximumnumber of cells reached at the plateau is not of interest (PO, FSO are

generally much lower than 107, 108 cfu/g), a simple primary growthmodel is commonly used (Nauta, Litman, Barker, & Carlin, 2003), Eq.(4).

= ⎧⎨⎩

≤× × − <

NN if t tN t t if t texp(µ ( ))t

init st lag

init st lag lag stst

(4)

where

– Ntst is the number of cells per portion at time t (cfu/product unit,cfu/portion),

– Ninit is the number of cells per portion at time 0, for instance justafter heat treatment (cfu/pack), in that case Ninit equals N of Eq. (3),

– tst is the storage time (h),– tlag is the duration of the lag phase (h),– μ is the specific growth rate (h−1).

2.3.2. Determine model inputsMathematical models require data called inputs to estimate outputs.

It is important to emphasize that when developing a model used by anoperator in an industry, there are two kinds of inputs: variables andsettings.

– Inputs defined as “settings” are directly linked to management op-tions, such as formulation or process settings (called also, within therisk-based food safety management, Product and Process criteria).Their value can be changed to reduce the risk. For instance, the timeof the thermal treatment is a process setting, the pH of the foodproduct is a formulation setting. In a model, the operator can setthem to a single value (for instance to an average value in a baselinescenario representative of a generic factory line), to compare whatthe model output is when the setting is fixed to another value, in awhat-if scenario analysis;

– Inputs called “variables” cannot be associated with any management

Process step: Inactivation

Estimation of the number of packs contaminated after the heat-treatment step with associated levels of contamination

Initial level of contamination

Distribution of levels of contamination after heat-treatment (cfu/pack) Levels of contamination in packs

N0 = 1 million bacteria

(6 logs) Percentiles

Mean 5th 50th 95th

100 84 100 117

N0 = 10 000 bacteria

(4 logs)

Percentiles

Mean 5th 50th 95th

0.99 0 1 3

Fig. 2. Illustration on the prevalence (number of packs contaminated) of the heat-treatment step. Calculations based on Eqs. (2) and (3). Note that calculation based on Eq. (1) will lead toprevalence of 100% in both cases.


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options. For instance, the mass density of a food raw material is avariable required in the model to make conversion between bac-terial concentration per g to per liter, which cannot be used tocontrol and/or reduce the risk. Variable inputs can be either definedwith a deterministic value or a range of different values with theirassociated probability of occurrence, corresponding to variabilityand/or uncertainty. Variability refers to real and identifiable dif-ferences between individuals within a population addressed by riskassessment, it is inherent to any biological process (Haas et al.,2014; Thompson, 2002) and does not disappear with more datacollection. For example, the variability of G. stearothermophilusstrains heat resistance (D-value) corresponds to real differencesbetween strains. In contrast, the uncertainty captures the lack ofknowledge (lack of data, lack of certainty of subject-matter expertsof the domain), for example, the lack of data/knowledge to buildprecisely the distribution of G. stearothermophilus D-values. In themodel developed for canned green bean (Rigaux et al., 2014), thelogarithm of D-values was described by a Normal distribution(Normal(μ, sd)) to reflect the strain variability; next, μ was describedby a Normal distribution and sd by a lognormal distribution to takethe uncertainty dimension into account. The current trend inquantitative MRA is to distinguish between variability and un-certainty by running second order Monte Carlo simulations(Cummins, 2016).

The process of informing the model inputs takes time and is quitecomplex. Basically, it depends on data and knowledge available be-forehand. Data can be provided through various sources: scientificpublications, reports, books, databases (e.g. ComBase), and experi-ments. Knowledge comes from experts who have acquired scientificevidence and knowledge (“rules of thumb”) about mechanism andprocesses useful to define inputs (Membré & Boué, 2017). As an ex-ample of translating expert elicitation information into a probabilitydistribution is presented here with the level of contamination of a rawmaterial. Let's assume that experts provided the level of contaminationsuch as 2 log as minimum, 3 log as likely value and 6 log as maximum.Next, the degree of certainty with which experts had provided eachvalue was elicited. They provided interval bounds around theminimum, likely value and maximum parameters. For the minimum of2 log, the uncertainty interval bounds were 1.5 and 2.5, translated witha Uniform distribution, U(1.5,2.5). For the likely value of 3, the un-certainty interval bounds were 2.8 and 3.2, translated with a Uniformdistribution, U(2.8,3.2). For the maximum of 6, the uncertainty intervalbounds were 5 and 7, translated with a Uniform distribution, U(5,7).Overall, the raw material contamination varied from 1.5 to 7.0 (Fig. 3).The mean contamination value was estimated to 3.3 (varying from 3.2

to 3.6 due to uncertainty). In this example, uncertainty is much lowerthan variability: ca 1 log versus 4 log.

2.4. Interpretation of a probabilistic QMRA model output, what-if scenarios

The first output obtained when performing a QMRA model calcu-lating the propagation of microorganisms, from farm to fork, is aquantity or a concentration of microorganisms in a food product and/orin a consumer's portion. Strictly speaking, a farm-to-fork model is thenan exposure assessment model.

However, if the QMRA model is designed to calculate the prob-ability of illness in a population, the main output will be this probabilityand then the number of human cases (i.e. number of people ill). In thiscase, the model is going up to the effect in humans and considersbacteria propagation all along the food chain. Thus we can suggest toextend the concept of the “farm-to-fork” up to human health and callthis assessment a “farm-to fork-to-human health” assessment.

In both types of assessment, the output is not provided as a singlevalue, but as a range of values with their probability of occurrence. Aprobability distribution (density or cumulative) has then to be inter-preted. That is not always straightforward for food safety scientists andfood microbiologists working in R&D department of industry.Nevertheless, graphics and summary table of results can help to inter-pret and communicate results.

What-if scenarios are visual tools particularly useful. They couldtake several formats. For instance, model outputs (e.g. number of casesper year in a population) could be reported for a series of possiblesettings, i.e. a series of Process criteria on which the operators have acontrol. In the next section, an example of thermal process optimizationof a food product is given. Another possible format is a 2D-plot de-picting an iso-risk curve. In that case, what-if scenarios are run for alarge number of combinations of levels of settings, and then, combi-nations providing the same risk are connected by a line in the plot. Aniso-risk curve is presented in the next section, using shelf-life determi-nation as example.

3. Case studies: food process optimization and shelf-lifedetermination

Two industrial cases have been selected to illustrate furthermore thebenefit of applying QMRA tools in an industrial context. The first ex-ample deals with process optimization of foie gras product, it is relatedto food safety issue. The second example deals with shelf-life determi-nation of bakery product, it is related to food quality issue.

3.1. Optimizing food process while ensuring food safety

Foie gras is a popular and well-known delicacy in French cuisine, bylaw, it belongs to the protected cultural and gastronomical heritage ofFrance. Canned foie gras product (fatty duck liver) is a low-acid, am-bient-stable canned products. The main microbial hazard associatedwith this category of products is proteolytic Clostridium botulinum whichis a mesophilic anaerobic spore forming bacterium (Frazier, 1967;Stumbo, 1973).

The heat-treatment process could be characterized by the F0 value,the equivalent time of heating at 121.1 °C (Eq. (5)).

∫= −F dt10t T z

0 0( 121.1)/

(5)

where

– T is the heating temperature,– z is the increase of temperature required to reduce the decimal re-duction time, D, to 10-fold reduction (°C), z equals 10 °C.

In the risk-based food safety management terminology, F0 value

0.0

0.2

0.4

0.6

0.8

1.0

1 2 3 4 5 6 7

no

it

ub

ir

ts

id

y

ti

li

ba

bo

rp

ev

it

al

ul

uC

Microbial concentration (log cfu/g)

Fig. 3. Cumulated probability distributions of raw material contamination with bothvariability and uncertainty dimensions separated. The present figure enables to visualizethe effect of variability and uncertainty on the output. The microbial concentration variesfrom 1.5 log cfu/g and 6.5 log cfu/g in the variability dimension (the black line). Theuncertainty is materialized by the grey lines. For example, the 80th percentile is uncertain,it is around 4 log cfu/g but varies between 3.5 and 4.3, it is summarized by an uncertaintyinterval: 80th percentile = 4 [3.5; 4.3] log cfu/g.


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corresponds to a Process criterion, it is a setting as the operator canchange it.

The thermal treatment of the foie gras product is here taken as acase-study to illustrate how QMRA could help in optimizing a foodprocess. In practice, this is done by running a what-if scenario once theQMRA model is built. Definitively, since C. botulinum is a severe mi-crobial hazard, it makes sense to perform a farm-to-fork-to-humanhealth assessment, i.e. choosing the number of cases per year as modeloutputs to make the optimization rather than the level of bacteria at thetime of consumption.

The QMRA model used here for the illustration was developed byMembré et al. (2015). It included the level and frequency of C. botu-linum in raw foie gras, the effect of heat treatment, the effect of nitriteadded in the product, the proportion of people eating foie gras, theirserving size and frequency of consumption, and finally, the probabilityof illness knowing the dose ingested. The worst-case assumption con-sidered was that 1 cell was sufficient to make a person ill.

Concerning the heat-treatment effect, it was divided into two ef-fects: probability of inactivating the spores and probability of inhibitingthe recovery of surviving heat-damaged spores.

The probability of inactivating the spores, PHT, was derived from Eq.(2) using D-values of C. botulinum in “oil and cream products” (Diao,André, & Membré, 2014). The probability of inhibiting the recoverycame from experimental studies as explained in Membré et al. (2015). Itwas determined for various F0 values and various nitrite concentrations.

Finally, for a given value of F0, there were an estimation of aprobability of inactivating, PHT, and, a probability of inhibiting, PR(Fig. 4).

What-if scenarios were then generated for heat-treatment set at a F0value of 0.3, 0.4 and 0.5 min. These relatively low values were con-sistent high organoleptic quality maintenance of this delicate product.The model output was the number of human cases per year (Fig. 5).What-if scenarios are here run for the setting F0 on which the operatorhas a control, it is presented in the x-axis of the graph.

This case-study illustrates the possibility of optimizing/revisitingheat-treatment settings of food product using a QMRA model. In thecase of foie gras, at F0 of 0.5 min, the number of human cases per yearin France (65 million inhabitants) was estimated to zero (5th percentile:0, 95th percentile: 1) showing a very low public health risk. This resultwas in agreement with epidemiological data (Membré et al., 2015). Incontrast, an F0 value of 0.3 min was not enough safe:> 100 cases es-timated per year (Fig. 5).

3.2. Determining product shelf-life for various food formulation

The present case illustrates how a risk-modeling process can be used

to address a food quality issue in industry: how to determine productshelf life according to various formulations?

Brioche-type product has a best-by-date around 21 days, it isslightly acidic with a pH around 5.2, and has a low water activity (aw)around 0.86, preventing bacterial growth. The first step when de-termining shelf-life is to identify the main causes of product spoilage. Inthe present case, due to the processing conditions (cooking and thenpackaging), a mold contamination is possible. Although aw is known tobe a key factor influencing mold growth (Guynot et al., 2005; Huchetet al., 2013; Rosso & Robinson, 2001), to maintain the organolepticproperty and particularly the spongy texture, aw cannot be dropped toomuch in this type of food product. Note that in the risk-based foodsafety management terminology, aw is a product criterion, it corre-sponds to a setting as the operator can change it.

To respect consumer's preference, there is no preservative added tobrioche. In case of an in-factory mold post-process contamination, moldgrowth might then potentially occur. If that happens, mycelium pro-liferation will start after a certain time required to have the sporegerminate and outgrow (Dagnas & Membré, 2013). If the total storagetime (retail + home) is shorter than this germination and outgrowthtime, there is a low risk of spoilage. The Risk of mold spoilage could bethen determined as follows:

= ≤Risk Ind storage timePr( )λ (6)

where

– Indλ is the time for a spore to germinate and outgrow (individual lagtime as only few spores on the product),

– Storage time corresponds to the total time of storage (retail + home),it depends on the best-by-date setting but also of consumer's habits.

Note that best-by-date is a fixed value for a given product even if isexpected to vary according to product formulation. The storage time isa variable value as not all consumers are going to eat the product at thesame time, and obviously not necessarily at its best-by-date. A generalrule has been recently suggested for European countries (Roccato,Uyttendaele, & Membré, 2017): the storage time varies according anexponential distribution (Eq. (7)):

Storage time~ Exp (best‐by‐date/4) (7)

To facilitate the product sale on a national market, it is interestingfor an industrial perspective to extend the shelf-life (here defined as atime between manufacture release and best-by-date). The best-by-dateis set by the product manufacturer, in the model it is a setting. A pro-blem of shelf-life determination is a relatively complex problem tosolve: a longer shelf-life will leave more time for mold spores to ger-minate and grow, unless aw is dropped. There are then combinations of

Fig. 4. Probability of inactivating or inhibiting C. botulinum spores for various heat-treatment settings.

Fig. 5. Number of human cases per year in France (65 million inhabitants): estimationbased on the QMRA model developed by Membré et al. (2015) using a Monte Carloprocedure (Latin Hypercube sampling, 100 million iterations).


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shelf-life and aw which lead to the same level of spoilage risk.Mathematically, these combinations could be estimated using a sec-ondary model (for the individual mold spore lag time) as explainedbelow.

The individual lag time, Indλ, is variable as all spores do not haveexactly the same lag time (Koutsoumanis & Aspridou, 2017). Itsvariability is described by a Normal distribution (Dagnas, Gougouli,Onno, Koutsoumanis, & Membré, 2017) (Eq. (8)):

Ind Ind Ind~Normal( , )λ mean λ sd λ (8)

The mean of the individual lag time, Indmean λ, depends on aw andstorage temperature, T, this relationship is quantified using a secondarypredictive model (Dagnas et al., 2017) (Eq. (9)).

=Ind λ x γ a x γ T1 1 ( ) ( )mean opt w (9)

γ(aw) and γ(T) are gamma terms describing the effect on lag time ofaw and temperature, respectively. Their mathematical expression isprovided in Eqs. (10) and (11).

=⎧⎨⎩

≤

≤ ≤−−( )γ a

a a

a a( )

0,

, 1w

w w min

a aa w min w1

2w w min

w min (10)

=

⎧

⎨⎪

⎩⎪

≤

≥

≤

≤

− −− − − − − + −γ T

T T

T T

T T

T

( )

0,

0,

,

min

T T T TT T T T T T T T T T T

max

min

max

( ) ( )( )[( )( ) ( )( 2 )]

min maxopt min opt min opt opt max opt min

2

(11)

where

– aw min is the minimum aw below which no growth is possible,– Tmin is the minimum temperature below which no growth is possible(°C),

– Topt is the optimal temperature for growth (°C),– Tmax the maximal temperature above which no growth is possible(°C).

The storage temperature, T, varies with the region and the season.In France for example, it is reasonable to consider two periods: aroundsummer (no heating) or around winter (heating) season. At heatingseason, the temperature is around 19 °C. It is described here by a Pertdistribution: T ~ Pert (16,19,22). At no heating season, the temperaturevaries more, it is also described with a Pert, but right skewed: T~ Pert(18,21,30).

Finally, when plugging all these pieces of information in Eq. (6), the

Risk of spoilage is calculated for various aw and best-by-date. Iso-riskcurves could be then generated and expressed relatively to the riskcalculated for the current product formulation and shelf-life (aw 0.86,21 days). This model can be used to determine the shelf-life (Fig. 6). Forinstance, if the aw is dropped to 0.85 without altering the organolepticproperty, then, the shelf-life can be extended to 28 days (at the samelevel of risk as the current product). On the opposite, if the aw is raisedto 0.88, then the shelf-life has to be much shorter (aw 0.88, 10 days,RR = 1) unless a Risk of spoilage 10% higher is acceptable (aw 0.88,21 days, RR = 1.1). Note that in the iso-curve plot, the x-axis and y-axiscorrespond to settings on which the operator has a control.

This case-study illustrates the possibility of using quantitative MRAtools to solve a spoilage issue. The difficulty here is then to defineclearly what the risk is. This requires an agreement between risk as-sessors, decision makers and modelers. This example illustrates onceagain the benefit of developing probabilistic models: it enables to runrealistic scenarios. In case of shelf-life determination, it is then possibleto consider that different consumers are storing their product for dif-ferent times, and not at the same time (as done in deterministic ap-proach).

4. Conclusion

In industry, operators face safety and spoilage issues. Althoughdifferent per nature, they could be tackled by similar quantitative tools.Firstly, they can be analyzed with a common methodology which canbe summarized as following: define clearly the scope of the model,develop the model, run simulation and what-if scenario and finallycommunicate results through user-friendly graphs. This “scope-model-simulation-communication” method comes directly from the MRA fra-mework. The second common points between safety and (microbial)quality issues faced in the industry is the type of mathematical modelsused: predictive microbiology is a valuable tool to estimate the level ofmicroorganism at a given time along the farm-to-fork continuum asfunction of various process (e.g. heat-treatment time) and product cri-teria (e.g. aw). Finally, even if not deployed in all types and sizes ofindustry, probabilistic techniques allowing the inclusion in models ofrealistic inputs rather than worst-case values, are beneficial to decisionmakers when tackling safety or spoilage issues. Definitively, all thesequantitative MRA techniques provide an added-value to industry op-erating under the risk-based food safety management framework. Wecould expect to see more and more applications in the next future.

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0.80

0.82

0.84

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8212417

Wa

te

r a

ctivity

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