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International Journal of Food Microbiology 162 (2013) 283–296

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International Journal of Food Microbiology

j ourna l homepage: www.e lsev ie r .com/ locate / i j foodmicro

Review

Potential application of quantitative microbiological risk assessment techniques to anaseptic-UHT process in the food industry

Laure Pujol a,b, Isabelle Albert c, Nicholas Brian Johnson d, Jeanne-Marie Membré a,b,⁎a INRA, UMR1014 Secalim, Nantes, F-44307, Franceb LUNAM Université, Oniris, Nantes, F-44307, Francec INRA, UR1204 Mét@risk, Paris Cedex 05, F-75231, Franced Nestlé Research Center, Lausanne, Switzerland

⁎ Corresponding author at: Oniris, UMR1014 Secalim, R44322 Nantes Cédex 3, France. Tel.: +33 2 51 78 55 21; f

E-mail address: jeanne-marie.membre@oniris-nante

0168-1605/$ – see front matter © 2013 Elsevier B.V. Allhttp://dx.doi.org/10.1016/j.ijfoodmicro.2013.01.021

a b s t r a c t
a r t i c l e i n f o
Article history:Received 1 August 2012Received in revised form 8 January 2013Accepted 27 January 2013Available online 1 February 2013

Keywords:Risk-based food safety managementModelling microbial behaviourModelling post-thermal-processrecontaminationProbabilistic risk assessmentCommercial sterilityFood spoilage

Aseptic Ultra-High-Temperature (UHT)-type processed food products (e.g. milk or soup) are ready to eatproducts which are consumed extensively globally due to a combination of their comparative high qualityand long shelf life, with no cold chain or other preservation requirements. Due to the inherent microbialvulnerability of aseptic-UHT product formulations, the safety and stability-related Performance Objectives(POs) required at the end of the manufacturing process are the most demanding found in the food industry.The key determinants to achieving sterility, and which also differentiates aseptic-UHT from in-pack sterilisedproducts, are the challenges associated with the processes of aseptic filling and sealing. This is a complex pro-cess that has traditionally been run using deterministic or empirical process settings. Quantifying the risk ofmicrobial contamination and recontamination along the aseptic-UHT process, using the scientifically basedprocess Quantitative Microbial Risk Assessment (QMRA), offers the possibility to improve on the currentlytolerable sterility failure rate (i.e. 1 defect per 10,000 units). In addition, benefits of applying QMRA are i)to implement process settings in a transparent and scientific manner; ii) to develop a uniform common struc-ture whatever the production line, leading to a harmonisation of these process settings, and; iii) to bringelements of a cost-benefit analysis of the management measures.The objective of this article is to explore how QMRA techniques and riskmanagement metrics may be applied toaseptic-UHT-type processed food products. In particular, the aseptic-UHT process should benefit from a numberof novel mathematical and statistical concepts that have been developed in the field of QMRA. Probabilistic tech-niques such as Monte Carlo simulation, Bayesian inference and sensitivity analysis, should help in assessing thecompliance with safety and stability-related POs set at the end of the manufacturing process. The understandingof aseptic-UHT process contaminationwill be extended beyond the current “As-Low-As-Reasonably-Achievable”targets to a risk-based framework, through which current sterility performance and future process designs canbe optimised.

© 2013 Elsevier B.V. All rights reserved.

Contents

1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2842. The risk-based framework . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 285

2.1. Introduction to risk-based management . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2852.2. Examples of QMRA applied to processed food manufacture . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 286

3. Mathematical models describing the microbial variations at each aseptic-UHT process step . . . . . . . . . . . . . . . . . . . . . . . . . 2873.1. General model framework . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2873.2. Modelling initial contamination level in the product . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2873.3. Modelling bacterial reduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 287

3.3.1. Modelling bacterial reduction in the product line . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2883.3.2. Modelling bacterial reduction in the packaging line . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2883.3.3. Modelling bacterial reduction due to the cleaning procedure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 288

ue de la Géraudière, CS 82225,ax: +33 2 51 78 55 20.s.fr (J.-M. Membré).

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284 L. Pujol et al. / International Journal of Food Microbiology 162 (2013) 283–296

3.4. Modelling bacterial increase . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2893.4.1. Modelling growth . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2893.4.2. Modelling recontamination . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 290

3.5. Modelling other operational steps . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2913.5.1. Modelling mixing step . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2913.5.2. Modelling partitioning step . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 291

4. Probabilistic risk assessment: estimation of the microbial risk . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2924.1. Uncertainty and variability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2924.2. Performing probabilistic risk assessment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 292

4.2.1. Monte Carlo simulation approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2924.2.2. Bayesian inference . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2924.2.3. Sensitivity analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2924.2.4. Second-order Monte Carlo simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 293

5. Risk management: options to control and reduce the microbial risk . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2935.1. Scenario analysis to define performance objective . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2935.2. Setting Microbiological Criteria to assess compliance with Performance Objective . . . . . . . . . . . . . . . . . . . . . . . . . . . 2935.3. Setting performance criteria, process criteria and product criteria to comply with performance objective . . . . . . . . . . . . . . . 293

6. Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 294References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 294

“Non-sterile” phase

Raw Material packaging

(e.g. carton )

Raw Material product

(e.g. raw milk)

UHT treatmentPackaging

sterilisation

Final product storage(warehouse up to consumer place)

“Non-sterile” phase

High care phase

Filling (a2)

Sealing

Cleaning procedure

(b)

Initial level

Microbial reduction

Microbial increase:(a1) growth (a2) recontamination from air and biofilms

(b) Microbial reduction

Microbial increase: growth

Aseptic storage(a1 and a2)

Cleaning procedure

Fig. 1. Schematic process diagram of UHT product from the raw material reception upto final consumer place, with potential microbial contamination variation.

1. Introduction

Aseptic-Ultra-High-Temperature (UHT)-type processed foods areconsumed extensively throughout the world due to their long shelf life(three to six months), no cold chain requirements, and their possibilityto be consumed immediately. The world market for aseptic UHT-typeproducts amounted to 123 billion litres during 2011. Drinking milk ac-counts for 39% of aseptic UHT-type products, beverage (e.g. fruit juice)for 37% and other dairy or food products (e.g. soup) for 24% (WarrickResearch and Zenich International, 2012). Due to stability at ambienttemperature, aseptic-UHT-type processed food products can be manu-factured in one country and consumed in several importing countries.These products are defined as a commercially sterile product whichmeans that the food “must be free ofmicroorganisms capable of growingunder normal non-refrigerated conditions of storage and distribution”(Codex Alimentarius Commission, 1993). A typical value for a tolerablecommercial sterility failure rate is one defect per 10,000 units (Cerfand Davey, 2001). This failure could be due to pathogens (e.g. Bacilluscereus in acai berry juice from Sweden in December 2009) or spoilageagents (e.g. coagulation of and too high count of mesophilic bacteria inUHT milk from Slovenia in June 2012) (European Commission, 2012).

The aseptic-UHT process is relatively complex but can be defined inthree main phases, based on the material and process flow (Fig. 1). Thefirst one is a “non-sterile” phase, in which product ingredients andpackaging raw materials are received and sterilised. A UHT treatmentis applied to the product, and combined or separate thermal or chemicalsterilisation treatments are applied to the packaging line. The second“sterile” phase occurs within a high care area, where aseptic fillingand sealing is performed. The filling and sealing process steps are defin-itively the most challenging in terms of controlling contamination riskto the product; where biofilm formation, air recontamination, and de-fective sealing are significant causes of product sterility failure. Thelast phase encompasses storage in the distribution chain until consump-tion. To comply with the demand of commercial sterility, asepticallydesigned equipment in combination with stringent process settings isrequired.

Traditionally, aseptic-UHT process settings are defined and im-plemented in a deterministic or empirical manner. To move towardsscience-based process settings, risk of microbial contamination andrecontamination along the whole aseptic-UHT process could be quanti-fied. This would allow the contribution of each major process step tosterility failure to be established. That can be done by using the risk-based framework of Risk Analysis (advocated by the World HealthOrganisation and Food Agricultural Organisation (1995b)). It is a sys-tematic and comprehensive methodology to estimate risk associated

with a complex process. Risk analysis is split into three pillars: i) risk as-sessment, or more precisely in our case Microbial Risk Assessment(MRA), which consists of characterising the nature and the likelihoodof hazard; ii) risk management, the evaluation of options to maintainor reduce the risk, and; iii) risk communication, the interaction betweenregulatory authorities, scientists, food producers and consumers. For anaseptic-UHT food process with a commercial sterility target, the foursteps of MRA can be further defined as: i) hazard identification, whichconsists of identifying microbiological agents capable of causing ad-verse health effects (for pathogens) or significant sensory deteriorationof the product (for spoilage agents), and; ii) hazard characterisation, theevaluation of the nature of the adverse effect of pathogens (i.e. publichealth concern) and spoilage agents (i.e. spoilt product); iii) exposureassessment, the quantification of contamination along different path-ways through the whole process to consumption, and; iv) risk charac-terisation, the quantification of the risk in terms of public health(for pathogens) and the probability (“risk”) of non-compliance with acommercial sterility rate (for spoilage agents). The benefits for a food

285L. Pujol et al. / International Journal of Food Microbiology 162 (2013) 283–296

producer of applying Quantitative MRA (QMRA) to an aseptic-UHTprocess is primarily to provide a transparent and scientific basis for pro-cess settings, replacing empirical-based settings. Secondly, QMRA per-mits the harmonisation of process settings, by developing a commonuniform structure; for the manufacturer, this can lead to acceleratedindustrialisation and standardization across UHT production line de-signs and operation, reducing both commissioning and running costs.Lastly, it provides elements for a cost-benefit analysis of the risk man-agementmeasures; their efficiency on the sterility failure rate reductioncan be directly quantified and weighted against their implementationcost.

The objective of this article is to explore how QMRA techniques andrisk management measures may be applied to aseptic-UHT-typeprocessed food products. In the first section of this article, the risk-based framework is presented with some examples of QMRA applica-tions in an aseptic-UHT-type food process. Then, in a second section,themathematicalmodelswithin the disciplines of predictivemicrobiol-ogy, food engineering and statistical science are used to describe thedifferent potential contamination variations in an aseptic-UHT-typeprocess. In a third section, the probabilistic and statistical methodsrequired to estimate the risk, such as Monte Carlo simulation, Bayesianinference and sensitivity analysis are described. Finally, within therisk-based food safety management framework, the main options, tocontrol and reduce the risk when necessary, are discussed.

2. The risk-based framework

2.1. Introduction to risk-based management

Risk analysis activities provide information for the formulationof national policy, advice on issues of public health, and aids in thetransparency of decision-making and communication. Therefore, itis a significant driving force for fair commerce and safe food tradebetween nations. Risk analysis has been advocated by the (WorldHealth Organisation and Food Agricultural Organisation, 1995b) formore than a decade, and recently new concepts have emerged:the Appropriate Level Of Protection (ALOP) and the Food Safety Ob-jective (FSO). ALOP is defined as an expression of a probability ofan adverse health effect in terms of public health statistic (WorldTrade Organization, 1995). An ALOP would be articulated as a state-ment related to the disease burden (e.g. illness or infection incidencerates reported under surveillance programmes), associated with a

RISK ANALYSIS

Risk Communication

Risk Assessment

Risk Management

Fig. 2. FSO: a bridge between ALOPAdapted from ICMSF International C

particular hazard-food combination and its consumption in a country(Stringer, 2004).Whilst expression of an ALOP in terms relevant to pub-lic health serves to inform the public, it is not a useful measure in theactual implementation of food controls throughout the food chain. In-stead, a measurable target for producers, manufacturers and regulatoryauthorities is required; this is the basis of the Food Safety Objective(FSO) concept. FSO is defined as “the maximum frequency and/orconcentration of a microbiological hazard in a food at the time of con-sumption that provides the appropriate level of health protection”(International Commission on Microbial Specification for Foods,2002). The FSO is described as a “bridge” between ALOP and farm-to-fork process steps (Fig. 2). For instance, Perni et al. (2009) havecalculated the FSO in Ready-To-Eat (RTE) food for severalmicroorganisms(i.e. Listeria monocytogenes−0.33 log10 (CFU/g), Salmonella −6.71 log10(CFU/g), Escherichia coli O157 −1.66 log10 (CFU/g), Campylobacter −4.34 log10 (CFU/g), Bacillus cereus 4 log10 (CFU/g), Vibrio −0.60 log10(CFU/g)) based upon the dose–response properties of themicroorganism,severity of the disease and subjective ALOP. Other studies have investi-gated dose–response relationship to specific FSO values (Gkogka et al.,2013; Zwietering, 2005). However, it is important to keep in mindthat ALOPs and FSOs have not yet been established for all pathogens.

On the contrary, the link between the equivalent FSO and ALOP for aspoilage hazard has not been elaborated in the literature. The task ofbuilding such a “link” is greatly aggravated by the almost infinite num-ber of potential spoilage hazard agents capable of contaminating andgrowing within aseptic-UHT products. Each spoilage hazard agent hasa unique profile of hazard characteristics, which differs in “severity” asa function of individual product composition (e.g. formulations andpackaging) and the consumer market (e.g. demography and complaintreporting rates). These effectively contribute to determine the likeli-hood of consumer complaints attributable to spoilage agent, whichitself can be viewed as analogous to the ALOP associated to specificpathogen hazards. The dose–response relationship which links ALOPsto FSOs for pathogen hazards has a counterpart in the consumer com-plaint and sterility failure rate targeted for spoilage hazards. Therefore,a targeted sterility failure rate theoretically can be related by a foodcompany through a measure of consumer satisfaction (e.g. consumercomplaint rates) to define the “link” between line performances andan acceptable quality threshold or target. This effectively could describethe current situation, where a process line, when performingwithin op-erational norms,will produce product “lots” at an acceptable level of ste-rility. Because of the current lack of a clear quantitative link between line

Dose-response

Appropriate level of protection

(ALOP)

Food Safety objective

(FSO)

and farm-to-fork process steps.ommission on Microbial Specification for Foods (2005).


performance and consumer satisfaction, the traditional subjective ap-proach to operational management of spoilage risks in aseptic-UHT pro-cesses can be described with the “As-Low-As-Reasonably-Achievable”concept. Clearly, to advance beyond this qualitative approach foraseptic-UHT processes to one where risk management options are de-fined around FSOs, food company risk managers and decision-makerswill need newALOP-linkedmanagement tools that allow them to assessthe impact, in terms of quality costs and benefits, whenmaking changesto line performance or design. To our knowledge there are no publica-tions in this area ofmicrobial spoilage risk assessment andmanagement.However, theoretical aspects of the relationships between consumersatisfaction, defect rates and process line performance have and continueto be studied; whether integrating quality perceptions and expectations(Linnemann et al., 2006) modelling aspects of quality deterioration (vanBoekel, 2008) or formulating approaches to modelling consumer com-plaint rates (Peleg et al., 2011).

Within the risk-based food safety management metrics, the Perfor-mance Objective (PO) is directly related to the FSO but is set at a stepbefore the time of consumption (e.g. at the point of product release atthe end of themanufacture). The POmay be setwith sufficient stringen-cy to take into account the possible growth of themicroorganismduringthe storage. For instance, Perni et al. (2009) have also studied the rela-tionship between FSO and PO for Salmonella, considering the initial con-centration in the RTE product, the possible growth before cooking, andthe inactivation during cooking. To set a PO is a food safetymanagementdecision. To be operational, FSOs and POs must be translated intocriteria that can be controlled and measured in the food supply chain(Gorris et al., 2006; Gorris, 2005), such as Performance Criteria (PC),Process Criteria (PrC) or Product Criteria (PdC) (Fig. 3). PC is the effectrequired of one or more control measure(s) working in concert tomeet a PO, e.g. a minimum log10 reduction required for inactivation.PrC and PdC are control settings associated with the process and prod-uct formulation, respectively, at a step that can be applied to achieve aPC. For example, time and temperature during the heat treatment arePrCs and pH of the product is a PdC. To better understand these differentconcepts, an ILSI report (Stringer, 2004) gave an example based on thecontrol of Clostridium botulinum in low acid canned foods:

- PrC: 3 min at 121 °C (“botulinum cook”)- PC: 12 D reduction

PerformanceCriteria

(PC)

ProcessCriteria(PrC)

ProductCriteria(PdC)

PerformancObjective

(PO)

Fig. 3. From the Food Safety Objective to the managementAdapted from Gorris (2005).

- PO: b1 spore/1012 g after processing- FSO: b1 spore/1012 g at the time of consumption.

To apply these different risk-based food safety management con-cepts, first, the significant microbial pathways must be identifiedand quantified along the food chain. That is often done in QMRA ofprocessed foods.

2.2. Examples of QMRA applied to processed food manufacture

QMRA in a processed foodmanufacture has been extensively studied(Brown and Stringer, 2002). Many examples of QMRA in food industryare listed on the FoodRisk website (Joint Institute for Food Safety andApplied Nutrition, 2012). At the time of our survey (December, 2012),the available database contained 607 articles (non-exhaustive list)but only 29 were carried out in a processed food manufacture context(e.g. chilled pasteurized foods, cold smoked salmons, RTE vacuumpackedproducts,…etc.). Amongst these 29 studies related to a processedfood context, only nine correspond to, or might be assimilated to,aseptic-UHT processes. However, three of them are highly relevant forcommercial sterility purposes, they are detailed below.

A cross-disciplinary international consortium of specialists fromindustry, academia, and government was organized with the objec-tive of developing a document to illustrate the FSO approach for con-trolling C. botulinum toxin in commercially sterile foods (Andersonet al., 2011). This paper included historical approaches to establishingcommercial sterility; a perspective on the establishment of an appro-priate target FSO; a discussion of control of initial levels, reduction oflevels, and prevention of an increase in levels of the hazard. The initialconcentration was estimated using available data, and in the case ofdata gaps, various options were discussed. For the reduction part ofthe process, microbial inactivation models were used. For themicrobi-al increase, impact of pH, water activity, nitrite, spore injury and com-bination of factor on growth were discussed. The impact of GoodManufacturing Practices (GMPs) in prevention of incipient spoilagewas also discussed. This last factor took into account package integrityand post-process recontamination. For each part described above,gaps are identified and some research activities were recommendedto fill them. Finally, deterministic and probabilistic scenarios wereused to illustrate the impact of various control measure combinations

MicrobialCriteria(MC)

Food Safety objective

(FSO)

e

options: from the “plate” level to the operational level.


on the safety of several commercially sterile productswithin an FSO riskmanagement framework. For instance, in shelf-stable cured luncheonmeat, the authors calculated that the probability that one spore couldgrow and produce toxin was 10−7 at equivalent of 121.1 °C for0.6 min, pH of 7.0, 4.5% of NaCl and 150 ppm of nitrite for an initiallevel in raw meat of less than 0.1 spore per kg.

In Cerf and Davey (2001), a comparison between a Single Value anda Monte Carlo assessment of the risk of non-sterile packs of UHTprocessed milk was made. The number of non-sterile packs obtainedwas compared to the numbers that are anecdotally known to befound in a UHT plant i.e. between 1 and 4 in 104 production units. How-ever, it is important to keep inmind that in their study, the authors haveonly modelled the thermal treatment. More generally, they concludedthat the cause of the non-sterile UHT packs is traditionally attributedto leakage of pack material, or seal, and contamination either duringprocessing or storage and distribution.

Recently, a probabilistic data analysis of an ambient stable soupproduct, heated in a continuous UHT line was performed by Membréand van Zuijlen (2011). The thermal process was based on actual datarather than on generic or conservative rules. The data sets came froma decade of microbiological analysis; the results were illustrated withtwo ingredients, garlic and milk powder. In this case, the sterilizationvalue was estimated then to be 13 min (95th percentile) at 121 °C.

In conclusion, there are significant numbers of studies applyingQMRA in processed foods but only a few in aseptic-UHT lines. Inmost of them, only pathogens have been considered, although risksassociated with spoilage agents are often tangentially mentionedbut not quantified. In QMRA studies, the lack of specific models anddata is often emphasized. In all the studies outlined herein, the micro-bial behaviour during the thermal process step and the potentialgrowth of post-process survival microbes are described. However,consideration or quantification of post-process recontamination isfrequently only mentioned but not quantified.

3. Mathematical models describing the microbial variations ateach aseptic-UHT process step

In this section, mathematical models which permit the quantifica-tion of the contamination level of the product when ready-to-be-consumed, i.e. the output of the exposure assessment part of theQMRA, are presented. Once the contamination level is determined,probability, i.e. risk, of not complying with an FSO can be estimated fora given production line. From this benchmark situation, the effect of var-ious risk reduction measures can be compared quantitatively. Likewise,for commercial sterility assessment, probability of not complyingwith aPO chosen at the product release step can be evaluated and if required,efficiency of different reduction measures can be assessed.

3.1. General model framework

Basically, there are three phases in an aseptic-UHT process (Fig. 1),the first is a “non-sterile” phase with process steps from reception ofingredients and packaging raw materials to bacterial reduction. AUHT treatment is applied to the product and combined or separatethermal or chemical sterilisation treatments are applied to the pack-aging line. The second “sterile” phase occurs within a high care area,where aseptic filling and sealing is performed. The last is the storageuntil consumption. Nonetheless, the aseptic-UHT process is complexand consequently needs to be decomposed into smaller steps toquantify any bacterial contamination pathway.

Nauta (2001) introduced the “Modular Process Risk Model” con-cept where the food pathway is divided into several key smallersteps. This concept has been often used in the risk assessment con-text, for example such studies are reported in Billoir et al. (2011),Malakar et al. (2011) and Nauta et al. (2009). One way to split theprocess in a useful way is to identify the contamination pathway

occurring at each step of the process using the following equation.The International Commission on Microbial Specification for Foods(2002) proposed an equation related to the PO and FSO concepts(Eq. (1)):

H0−∑R þ∑I≤PO or FSOð Þ ð1Þ

It categorises each step from food ingredient to consumer's fork asthree main components or processes through which levels in micro-bial hazards may change:

- H0: is the initial level of hazard, a combination of either the rawmaterials (for the product and the packaging) and the terminallevel of hazard from the preceding step,

- ∑R: is the quantification of microbial inactivation in one or severalof the process steps,

- ∑I: is any increase in the hazard due to either growth orrecontamination.

This framework is a conceptual model rather than amathematicalone, it is a schematic description of the whole process. The termsin Eq. (1) are expressed in decimal logarithm which is usefulfor expressing log-linear inactivation or growth, but not straight-forward for describing a post-process recontamination. Despitethese drawbacks, this concept has been widely applied in QMRAstudies, for example in Anderson et al. (2011), Membré et al.(2007), Sosa Mejia et al. (2011) and Stewart et al. (2003). Moreover,it is also used as a framework in the ILSI report on risk assessmentapproaches to setting thermal processes in food manufacture (Beanet al., 2012).

In the exposure assessment, our mathematical model reviewbelow covers the initial level in raw materials, the sterilisation step(for the product or the packaging), the recontamination pathways(from biofilm or from air), the storage, the mixing and partitioningprocess steps. In aseptic-UHT-type food processes, all contaminationpathways need to be considered due to the respect of the high carearea, even if the probability of occurrence is very low. Dose–responsemodels are excluded here as they are used for modelling the relation-ship between FSO and ALOP, and therefore come under the hazardcharacterization part of the risk assessment.

3.2. Modelling initial contamination level in the product

The first step in a QMRA study is to estimate the initial contaminationlevel in the rawmaterials. Ideally, quantitative data from a large numberof studies on the rawmaterial itself could be used to assess the concentra-tion distribution of the microorganism. Prevalence of the microorganismis often more difficult to establish due to the large variety of samplingplans and microbial detection methods (Jongenburger et al., 2011). Theinitial concentration is often expressed in logarithm of the number ofmicroorganism present per unit. Consequently, the concentration isoften described by a normal, log-normal or some other probability dis-tribution. In the case where data are not informative enough, the prob-ability distribution could be completed with an expert opinion. Thismethod has been already applied byBarker et al. (2005) on the distribu-tion of non-proteolytic C. botulinum spores in potato flakes, coatingflour and other ingredients. They used limited information from statis-tical samples taken by the manufacturer in combination with expertopinions.

3.3. Modelling bacterial reduction

In an UHT-aseptic process line, three types of bacterial reductionoccur. The first, widely explained in the literature, is via the UHT treat-ment of the product, the second is from the sterilisation of the packag-ing, and the last is through the cleaning procedures. These two lastbacterial reduction processes are essential to an aseptic-UHT food


process, because failure of either of these often explains an increase inthe microbial contamination detected. Consequently, they also mustbe considered asmanagement options to control and reducewhen nec-essary the contamination risk (e.g. aminimumefficiency in the bacterialreduction could be set as a PC).

3.3.1. Modelling bacterial reduction in the product lineThe existing models for thermal treatment have been already

discussed extensively by Basset et al. (2012), Brul et al. (2007) andMcKellar and Lu (2004). Consequently, in this review, we have cho-sen to describe only one primary model and one secondary model,and only briefly discuss the others.

In order to model the inactivation kinetics, the primarymodel pro-posed by Bigelow (1921) can be used if it is assumed that the inacti-vation follows a first-order kinetic in isothermal conditions:

log10NN0

� �¼ − tHT

Dð2Þ

where:

- N0: is the bacterial concentration entering in the thermal treat-ment (CFU/ml),

- N: is the bacterial concentration at the end of the heat treatment(CFU/ml),

- tHT: is the time of the heat treatment (s),- D: is the decimal reduction time (s).

This model has been widely used and long established with a loga-rithm transformation (log10 reduction increase linearly with the heattreatment time) (Cerf and Davey, 2001; Malakar et al., 2011; Nauta,2001; Sosa Mejia et al., 2011). More recently, probability distributionshave been introduced in modelling bacterial survival to reflect an as-sumption that lethal events are probabilistic rather than deterministicand to explain that if the heat treatment is sufficiently intensive no mi-croorganisms will survive or recover. For example a Poisson distribu-tion has been used to describe the probability of microbial survivalafter heat treatment (Membré et al., 2007; Nauta, 2001).

The concept of the traditional D-value has appeared insufficient insome cases, because the decrease of the population does not alwaysfollow the Eq. (2); for instance, it might have a lag time before thedecrease could be observed.

Next, the decimal reduction time (D) is described by a secondarymodel which takes into account the process and product charac-teristics. Different secondary model structures were developedto describe D-value with respect to the process (heat treatmenttemperature) and product formulation (pH and water activity(aw)). Amongst them, it has been suggested to extend the gamma-concept (Zwietering et al., 1992), widely used in microbial growth,to the inactivation area (Gaillard et al., 1998; Leguérinel et al.,2000; Mafart et al., 2010):

D ¼ D� � 10T�−THT

zT � 10− pH�−pH

zpH

� �2

� 10a�w−awzaw ð3Þ

where

- D: is the decimal reduction time for conditions of temperature (T),pH and aw (s),

- D*: is the time required at the reference temperature (T*), refer-ence pH (pH*) and reference aw (aw*) to reduce the bacterial con-centration to 1/10th of its value (s),

- THT: is the temperature of the heat treatment (°C),- zT: is the increase of temperature required to reduce the D value to10-fold reduction (°C),

- pH: is the pH of the product,- zpH: is the distance of pH from pH* which leads to a 10-fold reduc-tion of D value,

- aw: is the water activity of the product,- zaw: is the difference of aw from aw*, which leads to a 10-fold in-crease of the D value.

For the temperature parameters, data are abundant and availablein the literature, whereas for pH and aw much less information hasbeen published. This may explain why in the literature, the secondarymodel described in Eq. (3) is mostly applied with only the tempera-ture factor in QMRA studies (Cerf and Davey, 2001; Nauta, 2001;Sosa Mejia et al., 2011).

3.3.2. Modelling bacterial reduction in the packaging lineIn aseptic-UHT product manufacture, microbial contamination

needs to be considered not only in the product line but also in thepackaging line. For the packaging sterilisation, a review of the severaltypes of processes has been listed by Ansari and Datta (2003).

Firstly, there are thermal processes with a sterilisation with satu-rated steam (moist heat) or a combination with super-heated steamand hot air or even heating by extrusion of the packaging (form-fill-seal packaging system). For this kind of sterilisation, the previousmodels (primary and secondary, i.e. Eqs. (2) and (3)) could be ap-plied with the time and temperature of the treatment, as explainedby Ansari and Datta (2003).

Secondly, there are radiation processes with ultra violet (UV),infrared, ionizing or pulsed light sources, or a combination ofhydrogen peroxide and UV rays. In principle all the radiationprocesses kill bacteria in the same exponential manner as withheat (Ansari and Datta, 2003). In the WHO technical report (WorldHealth Organisation, 1999), DIR-values (dose of irradiation needed toproduce a 10-fold reduction in the population of microorganism) aregiven for some vegetative bacteria, spores, yeast and moulds in severaltypes of food products.

Another process type is the thermal or chemical decontaminationmethods, such as hydrogen peroxide or ethylene oxide or peraceticacid or combinations. Hydrogen peroxide, and its combination withheat, is the most widely used for the packaging materials sterilantand consequently the effects have been most thoroughly studied asmentioned in Ansari and Datta (2003).

It seems reasonable to apply a log-linear inactivation model(Eq. (2)) for all types of packaging material sterilisation. For thesecondary model, the relation between the sterilisation agent andthe D-value is not always defined and may be an area of furtherstudy.

This part of the process is not generally quantified in QMRA studies,although microbial contamination through infected packaging mightexplain some sterility failures. The type and quantity of the packagingsterilisation agent could be set as a PrC as an option to control and re-ducewhen necessary the contamination risk. For example, a concentra-tion of hydrogen peroxide of 30%, a temperature of the solution of 70 °Cand a time of immersion of 7 s are settings currently applied in packag-ing sterilisation (Tetra Pak, 2012) and could be then re-interpreted as apotential PrC.

3.3.3. Modelling bacterial reduction due to the cleaning procedureAnother contamination pathway which is not often quantified in

QMRA, is the possible survival of bacteria after the cleaning proce-dure. Indeed, let us consider one batch of contaminated product asan example. If the cleaning procedure is not sufficient to remove orinactivate product residues containing bacteria, the next batch couldbe contaminated.

In aseptic-UHT lines, the cleaning operation could be generallydescribes by three different phases. Cleaning-In-Place (CIP) is anapplication of a chemical agent, either acid or alkaline. Hot waterrinsing is applied on surfaces directly in contact with products.Sterilisation-In-Place (SIP) is the last step of the cleaning procedure,aiming to re-sterilize the production line (Davey et al., 2013). The


Eqs. (2) and (3) could be applied for the SIP step with the time andtemperature.

For the two first steps, a simple model (first-order reaction) as-suming a process combining removal and deposition during cleaningcould be applied (Lelièvre et al., 2002a):

d Ntð Þdt

¼ k1 N0−Nt½ �−k2 Nt−NR½ � ð4Þ

where:

- Nt: is the surface density of spores at time t (CFU/cm2),- k1: is an effective deposition rate constant (/min),- N0: is the initial surface density (CFU/cm2),- k2: is an effective removal rate constant (/min),- NR: is the surface density of permanently adherent spores (CFU/cm2).

The constant deposition rate (k1) depends on cleaning conditionsand on the concentration of removed spores, and is thus dependenton the volume of detergent solution. The constant removal rate (k2)depends on the cleaning procedure conditions and is significantlyinfluenced by the wall shear stress applied during cleaning (Lelièvreet al., 2002b). More generally, the cleanability depends on geometri-cal design of the equipment, fluid hydrodynamic and steel surfaceproperties (Friis and Jensen, 2002; Lei, 2009). The efficiency of thecomplete cleaning procedure could be set as a PC to control and re-duce when necessary the contamination risk.

In conclusion, modelling the effect of the heat treatment step onproduct contamination, and maintaining the link with the complianceto a PO or FSO has been extensively studied, for example in Andersonet al. (2011), Cerf and Davey (2001), Malakar et al. (2011), Membréet al. (2007), Nauta (2001) and Sosa Mejia et al. (2011). However,no study connecting the packaging sterilisation and the cleaning pro-cedure to a risk-based framework has been reported in the literature,to our best knowledge. In other words, studies indicating how the CIPefficiency and the packaging sterilisation contribute quantitatively toa PO or a FSO are missing.

3.4. Modelling bacterial increase

3.4.1. Modelling growthThe growth of microorganisms can occur at several storage steps,

e.g. storage in tank before the filling process or storage of the finalproduct before consumption. Due to growth, products that are con-taminated at a low level and therefore considered safe or ediblemay become, at a certain moment of time, either unsafe or spoilt.The first factor determining whether and when growth of the micro-organisms occurs is the low level in the product surviving the heattreatment. This factor has been widely studied in the literature(Guillier and Augustin, 2006; Kutalik et al., 2005). A study has beendone by Koutsoumanis (2008) on the variability in the growth limitsof individual cells and its effect on the behaviour of microbial popula-tion. The author has concluded that in the case of low inoculum, themodel must take into account not only the distribution of lag timesof growing cells but also the variability in the growth initiation of in-dividual cells. This variability could be included in the lag distributionof the growth model below.

In this article, we have decided to describe one primary model andone secondary model, even if manymodels are available (Basset et al.,2012; Brul et al., 2007; McKellar and Lu, 2004).

Most QMRA models use primary models comprising an exponen-tial growth model without a lag and stationary phase, as for examplein Sosa Mejia et al. (2011). However, including the lag phase is rele-vant when dealing with thermally injured bacterial spores (Stringeret al., 2009). A simple model to do so is the three phase linear

model (Eq. (5)) of Buchanan et al. (1997) as applied in Malakar etal. (2011) for C. botulinum.

LogNtst¼ LogN0 for tst≤tlag

LogNtst¼ LogN0 þ μ � tst−tlag

� �for tlagbtstbtmax

LogNtst¼ LogNmax for tst≥tmax

ð5Þ

where:

- Log Ntst: is the natural logarithm of the population concentrationat time t (Log CFU/ml),

- Log N0: is the natural logarithm of the initial population concen-tration (Log CFU/ml),

- Log Nmax: is the natural logarithm of the maximum populationdensity supported by the environment (Log CFU/ml),

- tst: is the storage time (h),- tlag: is the time when the lag phase ends (h),- tmax: is the time when the maximum population concentration isreached (h),

- μ: is the specific growth rate (/h).

To describe specific growth rate adequately by a secondary model,it must take into account several parameters such as storage temper-ature (Tst) and pH of the product. Several secondary models are avail-able, amongst them the simplified gamma-type models (Ratkowskyet al., 1983; Zwietering et al., 1992) which are interesting to considerfor application in sub-optimal conditions (i.e. low pH and ambientstorage temperatures).

μ ¼ μopt � γ Tstð Þ � γ pHð Þ ð6Þ

where:

- μopt: is the optimal growth rate (/h), when Tst=Topt and pH=pHopt,- γ(Tst): is the effect of the temperature calculated by the modelbelow,

γ Tstð Þ ¼ 0 for Tst≤T min

γ Tstð Þ ¼ Tst−T min

Topt−T min

!2

for T minbTstbTopt

γ Tstð Þ ¼ 1 for Tst≥Topt

ð7Þ

where:○ Tst: is the storage temperature (°C),○ Tmin: is the theoretical minimum temperature below which no

growth is possible (°C),○ Topt: is the optimal temperature for growth (°C),

- γ(pH): is the effect of the pH calculated by the model below,

γ pHð Þ ¼ 0 for pH≤pHmin

γ pHð Þ ¼ pH−pHmin

pHopt−pHmin

!for pHminbpHbpHopt

γ pHð Þ ¼ 1 for pH≥pHopt

ð8Þ

where:○ pH: is the pH of the product,○ pHmin: is the theoretical minimum pH below which no growth

is possible,○ pHopt: is the optimal pH for growth.

The growth of pathogens is often the focus ofQMRA (Anderson et al.,2011; Malakar et al., 2011; Nauta, 2001), whilst the growth of spoilageagents has rarely been quantified or at least just mentioned. Fewmodels have been proposed in the literature concerning the microbialspoilage of food.When it has been possible to focus only on one specificspoilage organism, for instance with fresh fish ormincedmeat, primary


and secondary predictivemicrobialmodels have been developed. Thesemodels estimate microbial log-count as a function of the storage time,for various environmental conditions such as storage temperatureor packaging atmosphere (Dalgaard et al., 2002; Koutsoumanis andNychas, 2000; Vaikousi et al., 2009). In the case of post-processrecontamination, it might be sensible to consider that only one, or afew, species of spoilage microorganism may be reintroduced and havethe ability to grow in the product. In such a case, microbial interactionsmight be neglected, and consequently models developed for individualspecific spoilage organisms can be applied.

In terms of management options to control the sterility failurerate, pH of the product could be set as a PdC. Likewise, the tempera-ture and the time of storage could be set as PrC.

3.4.2. Modelling recontaminationRecontamination is defined as the introduction of any microor-

ganism into the product after an inactivation step, namely post-process recontamination. A survey performed by the World HealthOrganisation and Food Agricultural Organisation (1995a) in Europeindicated that 25% of the food-borne outbreaks could be due torecontamination. Some epidemiological investigations (EuropeanCommission, 2009) on food-borne illnesses have demonstratedthat the presence of vegetative pathogens, such as Salmonella spp. orL. monocytogenes, in consumed products are often due to post-processrecontamination. Recontamination events in aseptic-UHT processesare a primary cause of product sterility failure, and therefore processesmodelling these events would form a key part of any aseptic-UHTQMRA (Agalloco et al., 2004).

Themain objective and challenge whenmodelling bacterial transferis to develop reliablemathematical models capable of predicting, firstly,whether or not transfer takes place, and secondly, what proportion ofbacteria is transferred in relation to certain factors (air pressure leveland cell concentration, …etc.). The Campden & Chorleywood Food Re-search Association group (Smith, 2007) proposed a practical exposureassessment for recontamination from the environment, food contactsurfaces and liquids, and is divided into three steps:

- Step 1: Identifying the vectors involved in the transfer of contam-ination,

- Step 2: Determining the level of contamination in/on transfervectors,

- Step 3: Determining the conditions and frequency of contamina-tion exposure.

An overview of available models has been given in Reij et al.(2004). Moreover, Den Aantrekker et al. (2003b) have built a generalrecontamination model framework. A contaminated source (liquid,equipment or floor) releases cells to the intermediate phase (surface,hands or air) and then cells can be transferred to the product causingrecontamination. This is done with two transfer coefficients: (i) atransfer from the source to the intermediate phase, and (ii) a transferfrom the intermediate phase to the product. Some QMRA studieshave incorporated cross-contamination step, for example, Azizaet al. (2006) and Pérez Rodriguez et al. (2011) but none in theaseptic-UHT-type process.

3.4.2.1. Modelling recontamination from air. The recontamination fromair is a key issue to control for a UHT-aseptic process because the“sterile” product could be exposed to the air, e.g. in the area of thefilling machine (Fig. 1).

Sedimentation of microorganisms is responsible of the post-processrecontamination from air. Den Aantrekker et al. (2003a) studied theprobability of recontamination via the air using Monte Carlo simula-tions as a function of the number of microorganisms in air and particlesettling velocities. The contamination level (Lc) is defined as the numberof CFU which contaminate a product unit, for example a Lc of 10−3

means that 1 out of every 1000 products is contaminated with 1 CFU.It is calculated as follows:

Lc ¼ Cair � vs � A� t ð9Þ

where:

- Lc: is the number of CFU which contaminate a product unit,- Cair: is the concentration of microorganism in the air (CFU/m3),- vs: is the settling velocity (m/s),- A: is the exposed area of a product unit projected on the horizontalplane (m2),

- t: is the exposed time (s).

A seasonal effect was found in the concentration of microbes in theair, with the summer counts higher than was found in the other sea-sons. Regarding the settling velocity, (Den Aantrekker et al., 2003a)conclude that there is no significant difference (p>0.05) betweeneither the product groups, or the seasons, or between bacteria, yeastand moulds, its average value was estimated to 2.70×10−3 m/s. Theauthors have also stated that the high numbers of particles present inthe air correspond to higher concentrations of microorganisms in theair. On the opposite, they have not considered the air flowmovements.

For a UHT-aseptic production line, the filling machine areas arecritical high care areas. In these areas, the air contaminants must beeliminated or at least their concentration (Cair in Eq. (9)) minimized.

Applications of high relative air pressure system or air conditioningsystem are then crucial (Brown, 2005; European Hygienic EngineeringandDesignGroup, 2006;Hayes, 1992; Jacxens et al., 2009). Their impacton the high care area decontamination can be quantified through amass balance. Generally speaking, in food process engineering, a massbalance equation can be written as follows (Zwietering and Hasting,1997):

Flow Inð Þ þ Production rateð Þ ¼ Flow Outð Þþ Variation over the timeð Þ ð10Þ

To quantify the air contamination, parameters such as the sourceof the air, the frequency of air changes, the efficiency of filter andtheir frequency of replacement and the positive pressure appliedhave to be taken into account (BRC Global Standard for Food Safety,2012; Brown, 2005; Graham, 2011; Hayes, 1992). In a risk manage-ment framework, these parameters can be set as a PC or PrC to reducethe contamination risk, e.g. the air change rate could be set between 5and 25 air changes per hour (Brown, 2005).

3.4.2.2. Modelling recontamination from biofilms. Biofilms are definedas communities of microorganisms that attach to surfaces and are aprevalent mode of growth for microorganisms in nature. Bacteriacan adsorb reversibly to surfaces as result of (amongst others) vander Walls forces and electrostatic interaction. When reversiblyadsorbed, the cells are still readily removed by mild rinsing. Bacteriacan also adsorb irreversibly by producing extracellular products, usu-ally polysaccharides that act as anchors between the bacteria and thesurface (Hood and Zottola, 1997), and consequently are more difficultto remove. In this study, both attachment forms are considered as abiofilm.

Marchand et al. (2012) have done a complete review on biofilmformation in milk production including definition of biofilms, mecha-nisms of biofilm formation in dairy plants and efficacy of differentcleaners and sanitizers on dairy biofilms.

In terms of modelling, the contamination through biofilm forma-tion can be explained by a mass balance equation system (Eq. (10))(Den Aantrekker, 2002). Basically, the number of cells in the biofilmphase depends on the number of cells adhering to the surface, the


growth of adsorbed cells and the number of cells detaching from thesurface (Eqs. (11) and (12)).

Accumulationð Þ ¼ Adsorptionð Þ− Desorptionð Þ þ Growthð Þ ð11Þ

dNB

dt

� �¼ kA � XLð Þ− kD � Nn

B

� �þ μB � NBð Þ ð12Þ

where:

- NB: is the number of adsorbed cells (CFU/m2),- kA: is the adsorption coefficient (m/h),- XL: is the concentration of cells in the liquid (CFU/m3),- kD: is the desorption coefficient (m2n.CFU/m2. CFUn.h),- n: is the power factor describing non-linearity for desorption,- μB: is the growth rate in biofilm (/h).

The number of cells in the bulk liquid depends on the number ofcells flowing into the system, the number of cells released from thesurface, growth in the bulk liquid, adsorption of cells to the surfaceand the number of cells flowing out of the system (Eqs. (13) and(14)).

Accumulationð Þ ¼ Inð Þ þ Desorptionð Þ− Outð Þ− Adsorptionð Þþ Growthð Þ ð13Þ

dXL

dt

� �¼ DL � X0ð Þ

þ AL

VL� kD � Nn

B

� �− DL � XLð Þ− AL

VL� kA � XL

� �þ μL � XLð Þ ð14Þ

where:

- XL: is the number of cells in the liquid (CFU/m3),- DL: is the dilution rate (/h),- X0: is the concentration of cells entering the system (CFU/m3),- AL: is the surface area (m2),- VL: is the liquid volume of the system (m3),- μL: is the growth rate in the liquid (/h),- kD, kA, n and NB having the same definitions as above (Eq. (12)).

Writing the mass balance equation related to biofilm contamina-tion as mentioned above has at least three pitfalls:

- generating data or gathering information to inform the parame-ters kA, kD and n is not straightforward,

- biofilm formation is only initiated by a transfer of microorganismsfrom the contaminated food liquid, the possible biofilm formationdue to CIP and SIP survival microorganism is neglected,

- possible death in bulk liquid and biofilm due to sanitation are alsoabsent from the equations above.

The adhesion and detachment kinetics of several strains ofStaphylococcus aureus were studied by Herrera et al. (2007) underthree different experimental static conditions; in the absence of nu-trients (i.e. clear surface), in nutrient-rich media (i.e. readily avail-able nutrients) and dried mussel cooking juice (i.e. presence ofdirt). The detachment kinetic (the detached CFU per mm2) wasmodelled using a logistic equation with the persistence (the num-ber of cells that remain on the surface) and the strength of cell adhe-sion to the surface as parameters. The adherence kinetic wasquantified by an empirical non-linear model consisting of twoterms: a logistic equation that described the adhesion kinetic anda Gompertz equation that defined the detachment and death ofthe cells adhered. The effect of the presence of residues on biofilmwas also studied, and Herrera et al. (2007) concluded that thepresence of dirt (in this case, mussel cooking juice) on surfaces of

processing plants would imply an additional risk of biofilm forma-tion. The accumulation of fouling residues can be prevented byhygienic equipment design, which has been well studied sincethe 90s (EHEDG, 1993; Lelieveld et al., 2003). One way to controlthis potential biofilm contamination could be the setting of PrCassociated to the complexity of the process line: number and clean-ability of pipe corners and valves, number of pipe diameter changes,etc.

3.5. Modelling other operational steps

The models above describe the inactivation, growth and introduc-tion of microorganisms. However, additional important parts of theaseptic-UHT process are the mixing and partitioning steps. Details ofthese steps are described by Nauta (2005).

3.5.1. Modelling mixing stepWhen foods are mixed, various units (n) are joined together

(e.g. powdered ingredients dissolved into a liquid phase). This resultsin microorganisms being redistributed, and consequently the preva-lence is increased. When independent sized units i are mixed, theprevalence is expressed by:

P′ ¼ 1−∏n

i¼11−Pið Þ ð15Þ

where:

- P′: is the new prevalence in the mixed product,- n: is the number of units mixing together,- Pi: is the prevalence in the ith units before mixing.

If n is large, the central limit theorem is applied. It states that, themean of a large number of independent random variables with finitemean and variance, will be approximately normally distributed. Themixing step was used in QMRA studies, for example in Billoir et al.(2011) and Nauta (2001).

3.5.2. Modelling partitioning stepThe partitioning step occurs where a larger food unit is divided into

smaller ones (e.g. at the filling process where milk is distributed intobottles). If the contamination in the large unit is low, some smallerunits can contain zero microorganisms and some contain more thanone microorganism. This assumption could be translated into a Poissondistribution (Nauta, 2005):

N′u∼Poisson N � s=Sð Þ ð16Þ

with:

- N′u: is the number of cells in the smaller unit (CFU/ml),- N: is the number of cells in the large unit (CFU/ml),- s: is the size of the smaller unit (ml),- S: is the size of the large unit (ml).

The partitioning step was used for example in Nauta (2001).To conclude on the modelling section, there are lots of models

available, and the selection of the “best” model depends on the state-ment of purpose, process knowledge and data availability. Moreover,in some cases, more complicated models provide the same result as asimpler one. This approach and philosophy in selection is summa-rized by Zwietering (2009) as “simple is not stupid and complex isnot always more correct”.

The models described above are very helpful for quantifying esti-mates of risk, but there are many assumption and data gaps leading touncertainty. In the section below, approaches to address this issue in aQMRA study are discussed.


4. Probabilistic risk assessment: estimation of the microbial risk

The next step after the modular model has been constructed is tocompute the model. More and more often, probabilistic approaches arepreferred to deterministic ones (with point estimates) for performingQMRA, this is due to the uncertainty and variability inherent to biologicalprocesses (Thompson, 2002).

4.1. Uncertainty and variability

Parameter uncertainty andmodel uncertainty are particularly impor-tant to considerwhen building a probabilistic risk assessment. Parameteruncertainty means uncertainty about the values of input variables,reflecting the lack of information available to estimate these values(e.g. the transfer rate parameters in the mass balance equation forrecontamination). Model uncertainty also means uncertainty due tothe approximation by a functional form of a real phenomenon (e.g. therecontamination by the biofilm formation). Variability differs from un-certainty: variability refers to natural or non-controlled heterogeneitybetween individuals within a population addressed by risk assessment(e.g. D and z values amongst strains of thermotolerant B. cereus). It isnot always possible to separate entirely uncertainty and variability, al-though it is recommended to try as much as possible (Mokhtari andFrey, 2005a). In the probabilistic approach, for example in Gkogka et al.(2013),Malakar et al. (2011) andNauta (2001), probability distributionsare used to describe the uncertainty and variability associated with theinputs.

In the deterministic approach, for example in Sosa Mejia et al.(2011), a single value for each model input is selected. It should be no-ticed that in this case, uncertainty is not systematically neglected. Infact, it can be incorporated in the analysis as a safety margin factor, forexample a 2 log10 process performance added to the peanut inactivationguidance for Salmonella (United States Food and Drug Administration,2009).

Both probabilistic and deterministic approaches are equally valu-able when used in the correct context. The decision-making processmay require iterations of the risk assessment and a mixture of bothapproaches may be used in the same assessment. For example, theprocess may start with a screening assessment, which uses genericnumbers (“defaults”) for many inputs in the deterministic approachand ultimately progress to a highly refined probabilistic analysis.

4.2. Performing probabilistic risk assessment

Probabilistic risk assessment techniques enable an incorporationof inputs as distributions of values with their associated probabilityof occurrence, the risk assessment output is then also a distributionof values with their associated probability of occurrence by propaga-tion through the modelled process. Moreover, uncertainty and vari-ability on the inputs are also propagated to the model output.

4.2.1. Monte Carlo simulation approachMonte Carlo Simulation (MCS) approach involves the random sam-

pling amongst probability distributions values for an input, producingsimulated values, allowing the estimation of the risk. The precision ofthe risk estimate depends on the number of samples. Sometimes, MCSproceed by Latin hypercube sampling, which ensures values from theentire range of the distribution will be sampled proportionally to theprobability density function, even if the number of simulations is rela-tively low. The distribution of the values obtained for the parameteroutcome, therefore, reflects the probability of the values that couldoccur practically in an aseptic-UHT process operation.

In the food chain modelling, each simulation represents one po-tential true event of transmission along the food pathway. Since themodel output is also a probability distribution, MCS enables to evalu-ate the “probabilities” of specified events, and therefore to evaluate

risks. If MCS is to be used and applied in food safety management, itis in all instances important to realise how an ‘event of transmission’is defined and what the input probability distributions represent; interms of both their variability and uncertainty.

This approach have already been used in QMRA studies, for exam-ple in Anderson et al. (2011), Afchain et al. (2008), Cassin et al.(1998), Cerf and Davey (2001) and Nauta (2001).

The model output can be as well compared with real data. In thecase of an aseptic-UHT process risk assessment model, the outputsmight be compared to the sterility failure rate values collected fromcomparable factory lines.

4.2.2. Bayesian inference“The essence of the Bayesian approach is to provide a mathematical

rule explaining how you should change your existing beliefs in the lightof new evidence. In other words, it allows scientists to combine newdata with their existing knowledge or expertise. The canonical exampleis to imagine that a precocious newborn observes his first sunset, andwonders whether the sun will rise again or not. He assigns equal priorprobabilities to both possible outcomes, and represents this by placingone white and one black marble into a bag. The following day, whenthe sun rises, the child places another white marble in the bag. Theprobability that a marble plucked randomly from the bag will bewhite (i.e., the child's degree of belief in future sunrises) has thusgone from a half to two-thirds. After sunrise the next day, the childadds another white marble, and the probability (and thus the degreeof belief) goes from two-thirds to three-quarters. And so on. Gradually,the initial belief that the sun is just as likely as not to rise each morningis modified to become a near-certainty that the sun will always rise”(The Economist group, 2000).

In a Bayesian approach, each model parameter is considered as arandom variable. This randomness includes variability and uncertain-ty. The variability is often modelled by a parametric distribution char-acterized by uncertain hyperparameters. This approach was clearlyexplained in Delignette-Muller et al. (2006). The example of Tmin

(minimal growth temperature) was taken to illustrate the Bayesianapproach. The variability was modelled by a normal distribution,characterized by two hyperparameters, the mean value MTmin andthe standard deviation STmin. In turn, these two hyperparameterswere supposed uncertain, and firstly described by a prior distributionfrom prior knowledge. For each hyperparameter, a posterior distribu-tion was then calculated by the Bayes' theorem using the prior distri-bution and the whole information available in the data set. In aBayesian approach, it is important to realise that the more informa-tive the data set is, the less the impact of the prior distribution hason the posterior distribution. Bayesian inference has been already ap-plied in a risk assessment framework, for example in Albert et al.(2008), Membré and van Zuijlen (2011), Barker et al. (2005) andJaloustre et al. (2011).

4.2.3. Sensitivity analysisSensitivity analysis is widely used in QMRA to i) identify the most

influential variables on the model output, ii) provide a better under-standing and interpretation of the analysis, and iii) identify datagaps and then prioritise future research. Sensitivity analysis mightalso be seen as a prerequisite for model building, to test the robust-ness and the relevance of the model (Saltelli, 2002).

The added value of sensitivity analysis is highlighted in case oflarge and complex models. For example with a QMRA model appliedto aseptic-UHT products, it might be difficult to identify which modelmodules, and inside each of these, which process settings, have thegreatest impact on the commercial sterility failure rate. Moreover,sensitivity analysis helps in identifying and eliminating particularinputs or components of the model which are not essential, i.e. sensi-tivity analysis helps in simplifying complex models on a rational basis(Mokhtari and Frey, 2005a). That is particularly valuable if the QMRA


model is used at the operational level, as the model will be easier toimplement (easier to inform the remaining inputs and then to runthe model) and to use by the risk manager, in the decision-makingprocess.

Frey and Patil (2002) have reported ten different sensitivity anal-ysis methods, grouped in three approaches: mathematical, statisticaland graphical methods. They did not recommend the use of oneover another, but instead to combine several approaches to increaseconfidence in the ranking of key inputs. Likewise, a guideline for se-lection of sensitivity analysis methods applied to microbial food safe-ty process risk models has been set up (Mokhtari and Frey, 2005a).Deterministic sensitivity analysis might be also of interest, at leastat a first stage of model development (Zwietering and Van Gerwen,2000).

4.2.4. Second-order Monte Carlo simulationDue to the differences by nature and by interpretation between

uncertainty and variability, it is often justified to separate them inrisk assessment analysis (Nauta, 2000). Once variability and uncer-tainty are defined by the risk assessor, they can be propagated condi-tionally to each other through a two-dimensional MCS to obtain amore informative model output. By building a confidence intervalaround a risk estimate for different realisations of variability, it is pos-sible to identify if further investigation on uncertainty is requiredbefore making any decision (Mokhtari and Frey, 2005b). In QMRA ap-plied to an aseptic-UHT process, realisations of variability may corre-spond to different process line designs (e.g. filler head geometry, airfilter efficiency) and running procedures (e.g. length of the batch,periodicity of cleaning procedure). Uncertainty may be associated tothe lack of knowledge, for example when characterising the biofilmformation (e.g. lack of information on hygienic equipment design in-fluence on potential microbial interaction and growth rate).

The uncertainty analysis for different realisations of variability hasbeen illustrated with water consumption (Pouillot et al., 2004), theauthors calculated the risk associated to Cryptosporidiosis as a functionof the initial level of the hazard in a water reservoir. Membré et al.(2008) have calculated the risk of having more than 5 log10 of B. cereusin cooked chilled food products for different realisations of variability(e.g. pasteurisation settings, retail market) with a confidence intervalcapturing the uncertainty in their model. The added value of such stud-ies is to select significant risk reductionmeasures despite the uncertain-ty in the QMRAmodel. Cummins et al. (2008) have built a second-orderexposure assessmentmodel for E. coli contamination of beef trimmings.Their second-orderMCS helped them in identifying that the lack of sen-sitivity of themicrobial tests was a significant contributing factor to un-certainty and had to be reduced.

Recently, Pouillot andDelignette-Muller (2010) have presented anRpackage “mc2d”, that is freely and publically available. It helps to buildand study two dimensional (or second-order)MCS inwhich the estima-tion of variability and uncertainty in the risk estimates is separated.Overall, it should be borne in mind that second-order MCS cannot beperformed in absence of a substantial amount of data. Moreover, it isnot straightforward and can be time consuming; it should be fit-for-purpose and deployed only when risk assessors and managershave identified its true benefit: large and complex model, difficultchoice in allocation of resources (to reduce uncertainty), difficulty inhighlighting the impact of process parameters settings in presence ofuncertainty… etc.

5. Risk management: options to control and reduce themicrobial risk

5.1. Scenario analysis to define performance objective

Once the microbial risk is estimated (in the aseptic-UHT process,risk means the probability of non-compliance with a commercial

sterility rate), risk managers have to decide if a risk reduction mea-sure is required and in such a case, to weigh the effect of various mea-sures. Beside sensitivity analysis and second-order MCS, scenarioanalysis is another powerful mathematical tool. A scenario can be de-fined as an outline for any proposed series of events, real or imagined.In other words, a scenario is a series of possible events. ProbabilisticScenario Analysis (PSA) is a methodology for QMRA that has beenused for about sixty years in a variety of fields (Delignette-Mulleret al., 2008). The analysis is designed to allow improved decision-making with a more complete consideration of outcomes and theirimplications. Scenarios have historically been considered determinis-tically. However, because of the extent of inherent variability and un-certainty, it is often difficult to identify the full range of possibleoutcomes of any risk management decision with just a few carefullycircumscribed scenarios.

The PSA methodology of risk assessment can be split into two mainprocesses. The first step is the process of analysing possible futureevents by considering alternative possible outcomes (scenarios). A sce-nario tree is a graphical depiction which provides a useful conceptualframework. The tree will start with one incident or aggravating eventand will then fan out asmore andmore events happen. Once a scenariotree has been developed to depict what can go right or wrong, and howit can happen, the next step is to quantify how likely it is for the eventdepicted in the scenario to occur (Duffy and Schaffner, 2002; Ebel andSchlosser, 2000). The output of a PSA is often a diagram, relatively sim-ilar to a root-cause analysis tools. Root-cause analysis-like PSA tools canaid risk managers to visualize the benefit of developing a QMRAmodeland to have the confidence tomake decisions based upon their outputs.

5.2. SettingMicrobiological Criteria to assess compliance with PerformanceObjective

In the near future, as food safety management moves towardrisk-based food management, food producers will need to provide ev-idence that their foods at the moment they are eaten, comply with anFSO (van Schothorst et al., 2009). For C. botulinum, an example of anFSO might be less than one product unit per 106 or less than oneproduct unit per 109, these figures are based on the comprehensivereport on commercially sterile products compiled by the NationalCenter for Food Safety and Technology experts (Anderson et al.,2011). Setting Microbiological Criteria (MC) to assess such low occur-rences is not realistic. However, MC might be valuable tools to assessthe microbial quality (food spoilage) along the entire aseptic-UHTproduct process, i.e. to assess the compliance with PO set at variouscritical process steps (e.g. on raw materials, mix blends pre-UHTand on product units after filling). In such a case and with a probabi-listic risk assessment model, at least one key question has to be an-swered: what is the percentile (e.g., 99th, 99.9th, 99.99th etc.) usedto verify that the PO is met? (van Schothorst et al., 2009). This ques-tion might be answered internally by a food company, or by consen-sus between UHT-product manufacturers.

Other important considerations for the use of MC as managementtools in a risk-based framework are recommended (Codex AlimentariusCommission, 2009): they should include a statement of themicroorgan-isms of concern and/or their toxins/metabolites and the reason for thatconcern, the analytical methods for their detection and/or quantifica-tion, a plan defining the number of field samples to be taken and thesize of the analytical unit, and, the number of analytical units thatshould conform to these limits.

5.3. Setting performance criteria, process criteria and product criteria tocomply with performance objective

A PC is the effect required of one or more control measure(s) work-ing in concert to meet a PO. The effect might be inactivation (a mini-mum log reduction required) or an inhibition of growth (less than a


given log increase). For example, Advisory Committee on theMicrobiological Safety of Food (2006) recommend a PrC of 70 °Cfor 2 min to achieve a PC or 6 D reduction of E. coli O157H7,Salmonella spp. and L. monocytogenes in meat products. Also, inthe UK, to control non-proteolytic C. botulinum in cooked chilledfoods, the heat-treatment has to deliver a PC of 6-log10 inactivation(Gould, 1999).

PrC and PdC are the control parameters at a step or combination ofsteps that can be applied to achieve a desired reduction or the desiredlimitation on growth and contamination, i.e. to achieve a PC. In cookedchilled foods, the heat-treatment process settings of 90 °C for 10 min,widely used by the food industry, corresponds to a PrC in risk-basedfood safety management, as it enables a PC of 6-log10 inactivation tobe delivered. Other examples of how heat-treatment settings are artic-ulatedwith FSO, PO and PC are provided in a recent review on quantita-tive approaches of thermal food processing (Valdramidis and Van Impe,2012) and also in the ILSI report on risk assessment approaches tosetting thermal processes in food manufacture (Bean et al., 2012).

In an aseptic-UHT process context, the type and quantity of thepackaging sterilisation agent could be set as a PrC. For example, forthe packaging sterilisation, the concentration of the hydrogen perox-ide (30%), the temperature of the solution (70 °C) and also the time ofimmersion (7 s) might be set as a PrC (Tetra Pak, 2012). If the con-tamination came from the air, the efficiency of filter (commonlyHEPA filter) could be translated to a PC (Brown, 2005). Moreover,for contamination by biofilm, the complexity of the line (pipe length,number of valves…etc.) could be expressed in quantitative terms andthen translated into PrCs.

Once defined, PrC and PdC can be translated as Critical ControlPoints or Operational Pre-requisite Plans in a HACCP plan. More gener-ally, a risk-based framework is valuable to demonstrate equivalence ofmanagement options, for example, to demonstrate that a given PO orFSO previously achieved by heat-treatment process as sole controlmea-sure might be achieved by a combination of a milder heat-treatmentand an appropriate change in formulation. An analysis within a risk-based framework can therefore provide new opportunities in foodinnovation.

6. Conclusions

Revisiting aseptic-UHT line process within the QMRA framework isdefinitively valuable since UHT products are extensively and globallyconsumed: 123 billion litres consumed in 2011 (Warrick Research andZenich International, 2012). Moreover, volumes have grown by justover 5% a year since 2008, with South/South East Asia achieving thefastest rise of 22% a year, where ambient stable products are highlydemanded. QMRA, applied to aseptic-UHT products, supports this globalmarket demand; it permits a harmonisation of process settings by devel-oping a uniform common structure independent of the production line.

Another advantage of applying QMRA to aseptic-UHT products liesin the science-based approach. It enables a quantification of the steril-ity failure rate and assesses various options for controlling and reduc-ing it. Currently, the typically applied tolerable sterility failure rate foraseptic-UHT is one defect per 10,000 units and is often obtained withempirical settings. With a modular QMRA model, improvements insterility failure rates can be achieved in a quantitative and transpar-ent manner. Having identified the contamination pathways, Microbi-ological Criteria (including their associated sampling plans) can bebetter targeted. Defining critical process parameters linked to PdCand PrC through QMRA could also allow an eventual move from prod-uct release decisions based on analytical results, to immediate deci-sions based on aspects of process compliance.

However, it is important to keep inmind that risk managers might bereluctant to make their decisions based on probabilistic risk assessmentmodel outputs. Indeed, there is still very limited guidance and supportingdocumentation to explain how risk assessors should communicate the

QMRA outputs to risk managers. In addition, often risk managers donot have the background in probabilistic theory to understand theQMRA model outputs. These factors may hinder or jeopardize the de-ployment of a risk-based food safety management system, and empha-sizes the importance of education and training, and the need for riskcommunication tools in this area. Non-governmental institutes, suchas ILSI Europe or Institute for Food Safety and Health, could act as aforum to promote discussion in this area between the relevantaseptic-UHT process scientists and specialists from academia, govern-mental bodies and food industries. It is the collaboration of risk asses-sors and risk managers from industry and academia within therisk-based framework of QMRA that can lead to a greater understandingof aseptic-UHT process contamination, and so extend the current“As-Low-As-Reasonably-Achievable” sterility failure rates to oneswhere sterility performance can be optimised around defined processsettings and designs.

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