Modeling Cross-Contamination During Poultry Processing

13 Pages·2017·0.63 MB·English

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Mathematics Faculty Publications Mathematics and Statistics Department
1-1-2016
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DDyynnaammiiccss iinn TThhee CChhiilllleerr TTaannkk
Daniel Munther
Cleveland State University, [email protected]
Xiaodan Sun
Xi'an Jiaotong University
Yanni Xiao
Xi'an Jiaotong University
Sanyi Tang
Shaanxi Normal University
Helio Shimozako
York University
See next page for additional authors
Follow this and additional works at: https://engagedscholarship.csuohio.edu/scimath_facpub
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Munther, Daniel; Sun, Xiaodan; Xiao, Yanni; Tang, Sanyi; Shimozako, Helio; Wu, Jianhong; Smith, Ben A.;
and Fazil, Aamir, "Modeling Cross-Contamination During Poultry Processing: Dynamics in The Chiller
Tank" (2016). Mathematics Faculty Publications. 206.
https://engagedscholarship.csuohio.edu/scimath_facpub/206
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AAuutthhoorrss
Daniel Munther, Xiaodan Sun, Yanni Xiao, Sanyi Tang, Helio Shimozako, Jianhong Wu, Ben A. Smith, and
Aamir Fazil
This article is available at EngagedScholarship@CSU: https://engagedscholarship.csuohio.edu/scimath_facpub/206
Modeling(cid:1)cross-contamination(cid:1)during(cid:1)poultry(cid:1)processing:(cid:1)Dynamics
in(cid:1)the(cid:1)chiller(cid:1)tank
Daniel(cid:1)Munther,(cid:1)Xiaodan(cid:1)Sun,(cid:1)Yanni(cid:1)Xiao,(cid:1)Sanyi(cid:1)Tang,(cid:1)Helio(cid:1)Shimozako,
Jianhong(cid:1)Wu,(cid:1)Ben(cid:1)A.(cid:1)Smith,(cid:1)Aamir(cid:1)Fazil
1. Introduction contradictory results. One reason for such issues is that studies
wereconductedatthelaborpilotscaleunderspecificconditions
Poultry contamination by bacterial pathogens such as Salmo thatleavetheirresultsdifficulttosynthesize(Bucheretal.,2012).
nella,CampylobacterandEscherichiacoliO157:H7,continuestopose In this work, part one of a series of studies, we develop a
aseriousthreattopublichealthbothinCanadaandontheglobal mathematicalmodeltogaininsightintothemainmechanismsof
scale. According to the World Health Organization, 25% of food chlorine decay and cross contamination during the chilling pro
borne outbreaks are closely associated with cross contamination cess. This approach is important because of its ability to test
eventsinvolvingdeficienthygienepractices,contaminatedequip mechanistichypothesesaswellastohelpstreamlineexperiments
ment,contaminationviafoodhandlers,processing,orinadequate that would other wise be expensive both financially and tempo
storage(Carrasco,Morales Rueda,&Garcia Gimenoetal.,2012).As rally.Morespecifically,modelinginformedinsightscanbeusedas
processinghasbeenhighlightedasapivotaljunctureinthesupply cost effectivetoolstohelpdescribethemechanismsdrivingcross
chain, both for preventing and potentially promoting cross contamination, and to establish unambiguous, quantifiable links
contamination, researchers have conducted numerous studies, between processing control parameters (such as chiller water
attemptingtodeterminepathogenprevalenceandconcentrationat temperature, wash time, chlorine concentration, carcass towater
variousprocessingstages.However,theunderlyingmechanismsof volumeratio,etc.)andpathogenprevalenceandconcentration.In
crosscontaminationarestillpoorlyunderstoodand,furthermore, turn,thequantifiedconnectionsbetweencontrolparametersand
many studies evaluating the efficacy of intervention strategies pathogendynamicscanprovideinvaluableinformationintermsof
during processing have presented inconsistent and even testingcontrolstrategiestokeeppathogenlevelsbelowthresholds.
While our focus is the chiller process of a typical modernized
Canadianpoultryinspectionprogramplant(highspeed),ourmodel
canbeeasilygeneralizedtochillerprocessesinotherlocales.Also,
272 D.Muntheretal./FoodControl59(2016)271 281
the modeling framework and techniques can be modified to thetank.Thesetwoassumptionsleadtothefollowingequationfor
describesimilarmechanismsintheprocessofdefeathering,evis P,thetotalkgofchickencarcassesinthetankattimet(cid:2)0(min):
cerationandscalding.Wedescribethebackgroundandmodeling
formulation in Section 2. In Section 3 we apply our model to P0 N εdpP; (1)
generic,non pathogenicE.colicontaminationofbroilercarcasses,
discuss detailed parameter estimation, and perform sensitivity where
analysis. Using the results of the sensitivity analysis, we discuss 8
thresholdswithinwhichcross contaminationandchlorinecontrol >>><0; t(cid:3) 1
playalesserroleaswellaswhencross contaminationmayposea ε dp
more significant risk. Also, in Section 3, we compare model pre >>>:1; t> 1:
dictionsforE.colilevelsonpoultryexitingthechillertankwhen dp
freechlorine(FC)inputisusedat50mg/lornotatall.Theseresults
aregivenintermsofUSDAbaselinevalues.Inaddition,weexamine Notethat'isthederivativewithrespecttotimeandthefunction
thedynamicsofFCinactivationviatheorganicloadinchillerred εensuresthatnocarcasseswillleavethetankbeforethe“average”
water,i.e.,chillerwaterthathasbeenexposedtopoultrycarcasses, washtime1/dphaselapsed.
organic material and possibly pathogens. In the final section, we Asthechickensenterandmovethroughthechillertank,they
suggest some quantified rules of thumb for managing cross releasehighamountsoforganicmaterial(intheformofblood,fat,
contamination issues and discuss the feasibility of developing protein,etc.)intothewater.Suchmaterialisimportantbecauseit
morecomplexmodelsandofsimplifyingthecomplexityofcross alterschillerwaterchemistryaswellasmicrobialcounts(Russell,
contaminationmodelsforrelativelyeasyimplementation. 2012). We represent the organic material in the chiller tank at
timet>0byJ(kg).Inordertorelatethistothetotalsuspended
solids(concentration),weconsiderJ/TV,whereTVisthetotaltank
2. Backgroundandchillermodel
volumeinml.Forsimplicity,weassumethattheamountoforganic
materialcomingintothewaterisproportionaltotheincomingrate
Canadahasavarietyofpoultryprocessingoperations,ranging ofchickencarcassesN(kg/min)andthisisrepresentedbyq2(0,1).
from smaller traditional type processing to state of the art, high
Notethatinreality,theamountoforganicmaterialshedfromin
speedoperations.Inthiswork,weconsideratypicalmodernized
dividual carcasses may be independent of one another. Also, we
poultry processing plant (high speed), which covers most of the assume, via the flow through the tank, that the organic material
Canadianslaughterproduction(basedonpersonalcommunication
with CFIA officers, which we will reference from nowon as [P]). spendsonaverage1/dpminutesinthetank.Thereforewebuildthe
followingequationforJ:
Essentially,ourprocessingframeworkinvolvesapoultryslaughter
establishment which operates under the CFIA approved Modern J0 qN εdpJ: (2)
izedPoultryInspectionProgram(MPIP);seeCFIA(2014)formore
information. This perspective leads to several assumptions that
guideourmodelformulation.Theseinclude(1)thetypicalweight
ofacarcassis2kg;(2)thetypicalprocessingspeedis180carcasses/
2.2. Averagemicrobialloadoncarcassesandorganicmaterialin
min;(3)theaveragedwelltimeofcarcassesinthechillertankis
thetank
45 min; (4) red water is not recycled, rather the set up involves
freshwaterintakeatthebeginningofthechillertank,withover
Oneofthekeypurposesofthemodelistounderstandthedy
flowattheend;(5)amaximumof50ppm(mg/l)offreechlorine
namicsoftheaveragemicrobialloadonboththepoultryandthe
(FC)isadded(ifany)atthebeginningofthechillertank,andmixed
organic material in the chiller tank. To do so, we represent the
withincomingfreshwater;and(6)duetomodelsimplificationand
average microbial load (CFU/(kg ml)) on the chicken and organic
alackofdata,weassumethatorganicmatterandmicrobesdonot
bind/attachtothetanksurfaces. materialinthetankattimet>0,byvpandvj,respectively.Notice
Our model is built aroundtwomain types of mechanisms:(i) that the units for vp and vj are (CFU/(kg ml)) since we scale the
those that involve typical processing procedures for immersion averagebacterialoadperkgbythetankvolumeTV.Formodeling
purposes, it is convenient to scale by the tank volume and this
chillinginhighspeedpoultryprocessingfacilitiesinCanadaand(ii)
scaling should not be connected with bacterial concentration
bacteria transfer, bacteria inactivation, and water chemistry dy
measurementstakenfromtypicalrinseproceduresusedtoquan
namics during the chilling process. Refer to Table 2 for a list of
tifythemicrobialloadonapreorpost chillcarcass.Forinstance,
parameterscorrespondingtotype(i)and(ii).Tobeclear,thepa
theUSDAconductedstudiesusinga400mlcarcassrinseinorderto
rametersinvolvedwiththeparticularprocessingassumptionsand
determine E. coli levels on individual poultry carcasses during
dynamics, as in (i), are what specifies our model for Canadian
processingandreportedtheirresultsinunitsCFU/ml(USDA,2012).
poultry programs. The mechanisms under type (ii) are general
Weassumethatthechickensenterthechillerprocesswithan
mechanisms that are expected in a typicallarge scale immersion averagelevelofsCFU/kg.Uponenteringthetank,acertainfraction
chilling procedure that is utilized during poultry processing in
ofthiscontaminationlevelinitiallyshedsintothechillerwater.Let
manylocales,notjustCanada.Therefore,inthissectionaswellas this fraction be r and so 0 < r < 1. Also, as the carcasses move
Section 3, where we apply our model to generic E. coli contami
through the chiller tank, we suppose that continued microbial
nation, data used to quantify the type (ii) mechanisms need not
necessarilybeCanadian. shedding occurs at a rate bvp, where b (1/min) is the shedding
parameter (i.e., the shedding rate is proportional to the current
Wenowformulatethechillermodelinseveralsteps.
averagecontaminationlevelonthepoultry).Inaddition,bacterial
attachmentoccursviacontactbetweenacarcassandmicrobialsin
2.1. Thecarcassdynamicsandtotalsuspendedsolids the chiller water. If we let W (CFU/ml) be the microbial concen
trationinthechillerwaterattimet,thenweassumethisattach
Weassumethattheincomingrateofchickencarcassestothe ment occurs at a rate bW, where b (1/(kg min)) is the binding
tankisN(kg/min)andthechickensspendonaverage1/dp(min)in parameter.
Inadditiontoshedding/binding,weconsidertheinactivationof W' kwCW, where kw (l/(mg min)) is the inactivation rate
microbesoncarcasssurfacesviafreechlorine(FC)contactduring parameter.Notice,thechangeinWattimetisproportionaltoCW,
thechillerprocess.WhiletheeffectivecontactofFCwithcarcass illustratingthecommonmassactionassumptionforsuchchemical
surfaces(andthereforewithmicrobesattachedtocarcasssurfaces) reactions(Deborde&vonGunten,2008).Puttingtogetherthisidea
during immersion chilling is, to our knowledge, not well docu with(i) (iv),theequationforWis:
mented in the literature, there are multiple studies quantifying
VinaancBtirviaetsieonn, 2ra0t0e7s;oZfhmanicgr,oLbueos,iZnhsooulu,tWioanngv,ia&FCM;ilsleneer(,H2e0l1b5li)nagn&d W0 ð1þqÞsTrVNþbvjJþbvpP bPW bJW kwCW g10W(cid:5)3TV;
referencestherein.Ifweletkw>0betheinactivationrateofmi (5)
crobesinthechillerwater,thenwearguethattheinactivationrate
viaFCofmicrobesoncarcasssurfacescanbewrittenasakw,where where the first term (1 þ q)srN/TV reflects the amount of
a2(0,1).Forinstance,inthefreshproduceindustry,studieshave contaminationthatinitiallyshedsfromthepoultryintothewater
concludedthatsurfacecharacteristicscanreduceeffectivecontact andthelasttermgW/10(cid:5)3TV,reflectstheconcentrationofmicrobes
ofchemicalsanitizersduringwashcycleprotocols(Adams,Hartley, that exit the tank with the outflow. Notice, we assume the tank
& Cox, 1989; Gil, Selma, Lo(cid:2)pez Ga(cid:2)lvez, & Allende, 2009). Since volumeTVisconstantintime,soinflow outflow.Assumingthatl
carcass surfaces are irregular and this is an important factor in liters of fresh water are added to the tank per carcass and each
determining contamination levels (Thomas & McMeekin, 1980), carcass on averageweighs m kg, g N(kg/min)*(1 carcass/m kg)
similartotheresultsfromfreshproducestudies,FCcontactwith *l(lfreshwater/carcass) Nl/m(l/min)istheadditionrateoffresh
microbes attached tocarcass surfaces should be significantlyless waterpercarcass.
thanFCcontactwithmicrobesinthechillerwater.Combiningthese IntermsoftheequationforC,wehave:
ideas, the average decrease of the microbial load on carcasses is
gtiiovneanlbtyoathkwevppCro,dwuhcetroefwtheeascsuurmreentthmatictrhoibsiadlecloreaadseanisdptrhoepoFrC C0 c110(cid:5)g3TV dcC kcWC akcvjJC akcvpPC hJJC g10(cid:5)C3TV;
concentrationC(mg/L). (6)
Finally,takingintoaccountthefactthat1/dpistheaveragewash
time (and assuming that the natural death rate of the microbes wherec1(mg/l)istheFCconcentrationoftheinputwater,gisas
attachedtothepoultryandorganicmaterialiszero(Russell,2012)) above,andsoc1g/10(cid:5)3TV(mg/(lmin))measurestherateofincrease
ourequationforvpbecomes: ofFCinthewater.ThenaturaldecayrateofFCinthetankisrep
resentedbydc(1/min).Also,kc(ml/(CFUmin))reflectstherateat
v0p ð1 PTrVÞsNþbW bvp dpvp akwvpC: (3) wcrhobicehsicnhltohreinweaitsero,xaikdcizisedthoerradteegartadwehdicdhuFeCtiosdineagcrtaidvaetdindguemtio
In a similar manner, we can construct an equation for vj as irnaatectaivtawtinhgicmhitchroeboersgoanniccarmcaastsersiuarlfaincetsh,eantdanhkJ(1d/e(ckrgeamseins))thisethFCe
follows:
through chemical binding. For the terms involving kc and hJ we
v0j ð1 JTrÞqsNþbW bvj dpvj akwvjC: (4) atisosnuamletoththatetphreoddeuccrteoasfethineFrCescpoenctcievnetrianttieornacattintgim“espteicsiepsr”o,paonrd
V therefore kc, akc and hJ are types of second order rate constants.
Noticethatthecarcasssurfacetemperaturesduringtheinitial Finally,gC/10(cid:5)3TVillustratesthelossofFCduetooutflowofwater
coolingphaseofchillingmaypromotemicrobialgrowthoncarcass fromthetank.
surfaces.PleaserefertoSection4forreasonsastowhywedonot
includethisdynamicinEquations(3)and(4)forspecificapplica 2.4. Completemodel
tiontoE.colicontamination.
Puttingtogetherthesixequationsabove,ourmodelbecomes:
2.3. Dynamicsinthechillerwater
J0 qN εdpJ;
conTcheenttrwatoiomnainintvhaericahbillelesrwweaetexra,manindeCin(cmlugd/eL)W, t,hteheFCmciocrnocbeinal v0j ð1 JTrÞqsNþbW bvj dpvj akwvjC;
tration in the water. Assuming that red water is not filtered or V
recycled,bacteriadonotmultiplyinthewaterbecauseofthelow P0 N εdpP;
rteemguplaetriaotnusr,e,a(cid:3)n4d(cid:4)CbaasctpeerriaClansuardviaivnalFoiondItnhsepewctaiotenrAgisenecxyp(eCcFtIeAd) v0p ð1PTrÞsNþbW bvp dpvp akwvpC;
V
(Ratkowsky,Olley,McMeekin, & Ball,1982;Wang & Doyle,1998; srN W
wCFaItAe,r2(0d1u4e),toWshdeeeprefnodrsceosninfotuhretwhiantegrs,:e(tic).)m,(iicir)ombeicsroshbeedsiinntwoattheer W0 ð1þqÞ TV þbvjJþbvpP bPW bJW kwCW g10(cid:5)3TV;
abtytaFcChainngdt(oiv)pothueltflryoworroatregaonfiwcamtearteinri/aolu,t(ioiif)tmheictraonbke.sWinhaicletivthateerde C0 c110(cid:5)g3T dcC kcWC akcvjJC akcvpP hJJC g10(cid:5)C3T :
V V
maybeconcentrationdifferencesalongthelengthofthetank,for
(7)
simplicityweassumecompletemixingforthedynamicsin(i) (iv).
Observethatinjuredbacteriacellsmightalsoberepresentedinthis SeeTable1foraconcisedescriptionofthemodel(7)variables.
model, given the assumption that they shed from/adhere to car
cassesatthesameratesasotherintact/viablecells.However,froma 2.5. Modelproperties
modelingstandpointwedonotdifferentiatebetweeninjuredand
viablecells. Notethatsystem(7)ispositivelyinvariantforallnon negative,
Intermsofquantifyingtheabovemechanisms,forinstance,the notidenticallyzeroinitial conditions.Thisessentiallymeans that
inactivation rate for microbes in water due to FC is given by foreachsetofnon negative,notidenticallyzeroinitialconditions,
Table1 (7)approachSontheorderof200e250min,whichmeansduringa
Modelvariables. typical8hshift,ifthereislittlevariationintheaverageE.coliload
Variable Description&units oncarcasses,i.e.szconstant,themodelpredictsthatcontamina
tionlevelsinthewaterandonthepoultryinthetankwillequili
J Amountoforganicmaterialintankattimet(kg)
vj Averagemicrobialloadonorganicmaterialintankattime brate. Practically, this gives us mathematical justification to
t(CFU/(kgml)) simplify the dynamics in the tank and consider only the equilib
P Amountofpoultryintankattimet(kg) riumsolutionSof(7).However,sincetheparametersinvolvedwith
vp Averagemicrobialloadonpoultryintankattimet(CFU/(kgml)) E.colicontaminationarenotpreciselyknown,wewanttounder
W Microbialconcentrationinchillerwaterattimet(CFU/ml)
standhowsensitiveSistothemodelparameters.Thissensitivity
C FCconcentrationinchillerwaterattimet(mg/l)
analysisisvitalformakinginformedconclusionsforE.colicontrol
asweillustrateinthefollowingsections.
Note that s may vary significantly during an 8 h shift and
there exists a unique solution to(7) which stays positive in each
thereforedependingoncertaintimeintervals,contaminationlevels
component for all positive time (i.e. we can meaningfullyascribe
inthechillerwaterandonthepoultrymayvaryinsteadofequili
physical units to each component of the solution). Furthermore,
suchsolutionsto(7)arenotunboundedinfinitetime.Combining brating.Realistically,then,sshoulddependontime.However,in
order to build control strategies and rules of thumb for treating
theseideas,weseethatsystem(7)canunambiguouslydescribethe
suchcases,wefirstseekresultsthatactasareferencepoint.Thatis,
variableswehaveassociatedtoacontinuouspoultrychillingpro
wefirstdeterminearangeforsinwhichcross contaminationplays
cesswithpotentialcross contaminationdynamics.
asignificantroleandgainanunderstandingofwhichparameters
Inaddition,oursystemhasapositiveequilibriumstatewhich
play dominant roles in contributing to cross contamination at
wedenoteby
equilibrium. We do this via sensitivity analysis, assuming s is
(cid:2) (cid:3)
S J(cid:6);v(cid:6);P(cid:6);v(cid:6);W(cid:6);C(cid:6) : constant but randomly selected fromwithin its range. Please see
j p Section 3.1 for details concerning this analysis as well as Section
ThisequilibriumstateSisindependentoftimeandaccordingto 3.2.2andSection4forsituationswheresmayvaryasafunctionof
timeandhowthemodel(7)canbeappliedtoquantitativemicro
numerical calculations (not shown) it attracts all solutions with
bialriskassessment(QMRA).
non negative, not identically zero initial conditions. This means
thatastimeincreases,biologicallyrelevantsolutions(asdescribed
above)movecloserinvaluetoS.Theequationsforeachcoordinate 3.1. ParameterbaselineandrangeestimationforE.coli
ofS,intermsofmodelparameters,aregivenbelow(notethatsome contamination
areimplicitlygivenforthesakeofclarity).
3.1.1. ParametersspecifictoCanadianprocessing
J(cid:6) qN (8) ReferringtoTable2,specificprocessingparametervalueswere
dp obtained from personal communication with CFIA officers, as
referencedby[P].RefertothebeginningofSection2forthedetails
(cid:6) N ofCanadianhighspeedchillingspecifications.Notethattheother
P (9)
dp studiesreferencedforthesesameparametersinTable2confirmthe
uniformityofsomeoftheseassumptionsforimmersionchillingin
v(cid:6) v(cid:6) (cid:4) ð1 rÞdps (cid:5)þ bW(cid:6) (10) otherlocationssuchastheU.S.andBrazil.
p j TV bþdpþakwC(cid:6) bþdpþakwC(cid:6)
3.1.2. AverageE.coliloadonincomingcarcasses
(cid:2) (cid:3)
ð1þqÞsrNþb v(cid:6)J(cid:6)þv(cid:6)P(cid:6) s:Following(Northcuttetal.,2008),wecansetabaselinevalue
W(cid:6) TV j p (11) fors,theaveragemicrobialloadonincomingcarcasses(CFU/kg).
bðP(cid:6)þJ(cid:6)ÞþkwC(cid:6)þ10g3TV From(Northcuttetal.,2008),therinsingproceduretoquantifythe
bacterialloadonpoultrypriortothechillingprocess,indicatesthat
C(cid:6) (cid:4) (cid:5)(cid:6) c1g (cid:7) trhinesaavtee.rGagiveeEn.cao1li0l0evmellfroinrsine,ctohmisintrgancasrlacatesssetosirso1u0g2h.6lyCF1U04/.m6ClFinUtohne
10(cid:5)3TV dcþkcW(cid:6)þakcv(cid:6)jJ(cid:6)þakcv(cid:6)pP(cid:6)þhJJ(cid:6)þ10g3TV theaveragecarcass.Assumingtheaveragecarcassweightis2kg,
s 104.6/2z2(cid:7)104CFU/kg.Forsensitivityanalysis,weestablish
(12) thefollowingrangefors,103to106CFU/kgbasedonE.colidatain
Cavanietal.(2010).
3. ApplicationofmodeltoE.colicross-contaminationduring 3.1.3. ShedrateofE.colifromcarcassestochillerwater
b:FromNorthcuttetal.(2008),wecanestimatebbycomparing
immersionchilling
thepre chillbacterialoadonacarcassandthepost chillbacteria
load.Followingtherinseprocedurein(Northcuttetal.,2008),the
Duetothefactthatthewehavearelativelycompletedatasetfor
pre chillE.coliloadrecoveredfromanaveragesinglecarcasswas
generic E. coli, both bacteria levels and transfer during industrial
chillerprocesses(Cavani,Schocken Iturrino,Garcia,&deOliveira, 102.6CFU/mlandthepost chillloadwas101.1CFU/ml.Byconser
2010; Northcutt, Smith, Huezo, & Ingram, 2008; Tsai, Schade, & vationoftheE.colipopulation,andconsideringa45minaverage
Molyneux,1992)andchlorineinactivation(Helbling&VanBriesen, washtime,weestimatetheshedratetobe:
2007),wetailorourmodeltoaddressthespecificdynamicsasso ln(cid:4)101:1(cid:8)102:6(cid:5)
ciated to the chiller water chemistry and cross contamination of b :077 1=min:
45
broilercarcassescontaminatedwithnon pathogenicE.coli.Forthe
parameterrangesspecifictothissituation,thesolutionsofsystem Intermsofarangeforb,weuse0.04to0.1.Consideringthata
Table2
BaselineparametersvaluesforapplicationtoE.coli.Parameterswithreference[P],correspondtoinformationobtainedfrompersonalcommunicationwithCFIAofficers.
Currentlythereisnodocumenteddataforthesereferencesmarkedwith[P].Parameterslandgareextrapolatedfromguidelinesin(CFIA,2014).
Type Parameter/Reference Description Values/Units
(i) TV Tankvolume 5(cid:7)107ml
(Cavanietal.,2010)
N Carcassprocessrate 360kg/min
(Cavanietal.,2010)
(Northcuttetal.,2008)
1/dp Averagewashtime 45min
[P],(Northcuttetal.,2008)
l Freshwater/carcass 1.7l/carcass
(CFIA,2014)
m Averagecarcassweight 2kg
[P]
g inputwaterrate 306l/min
(CFIA,2014)
c1 inputFCconcentration 0 50mg/l
(USDA,2012;CFIA,2014)
(ii) dc FCdecayrate 4.1(cid:7)10 5min 1
(Li,Gu,Qi,Ukita,&Zhao,2003)
s Prechillcarcassload 2(cid:7)104CFU/kg
(Northcuttetal.,2008)
r Initialshedfraction 0.15
estimated
q Organicmaterialfraction 0.011
(Northcuttetal.,2008)
(Tsaietal.,1992)
b Microbialattachmentrate 0.01(kgmin) 1
(Munther&Wu,2013)
(Northcuttetal.,2008)
b Microbialshedrate 0.077min 1
(Northcuttetal.,2008)
a FractionforFCkillrateoncarcass 0.001 0.1
estimated
kw FCkillrateinwater 216l/(mgmin)
(Helbling&VanBriesen,2007)
kc FCdecayrateviakilling 0.0069ml/(CFUmin)
(Helbling&VanBriesen,2007)
hJ FCoxidationrate 0.0017(kgmin) 1
(Tsaietal.,1992)
carcass undergoes an averagechilling time of 45 min, this corre Usingtherelationshipabove,weseethatkc 0.0069.Fromthe
spondstoa1to2logreductiononthepoultry. rangegivenforthecontacttimeabove,wefindthatkw2[150,300],
while kc ranges from about 0.0048 to 0.0096. Performing similar
calculationswithinactivationofE.coliO157:H7datafrom(Zhang
3.1.4. FCinactivationkinetics etal.,2015),wefindthatkwz276andkcz.02.Hereweusethe
t.t0rha3et2kioc“±na3nt.0lodo0igk9n1wa0:(”cmFtirgvCo/aFmltU)em/H1mi0nel3l.bTCliinhFnUaagct/tmaiisnvl,adoittifVoEtana.nkcBeocrsloiien0isnt.e0asnc3ot2l(u2mtt0iimo0gn7/el)i,onwifsoeFnCgheiacvmvoeeninnctuehbtnaeyt. v(rZeahsruiaelntsgtahcearttoa5sls.l,oi2tgs0110ra5rne).gdBeu,ecfctoiaorunssieimskapcclibhcaiietryveelwydeainffife0xc.2tks5cmswo.0dit0ehl691o0uatmnpdugt/dslooafnsFoiCtt
includeitinthesensitivityanalysis.
ThestudyinHelblingandVanBriesen(2007)indicatesthatE.coliis
IntermsofinactivationofE.colioncarcasssurfaces,weassume
veryreactivewithFCandthe“contacttime”iscalculatedbyinte thattherateisakwandthelossofFCduetothisinactivation,since
gratingtheFCconcentrationcurveoverthetimeinterval[t0,t3],i.e., kc is proportional to kw, is akc. While a is not precisely known,
thetimeintervalittakestoreducethemicrobialconcentrationby
considering the discussion in Section 2.2, weassume that it is at
103. most0.1.Forthesensitivityanalysis,weassumethatarangesfrom
Considering the units of kw and kc, and the fact that it takes 0.001to0.1.
0.032mg/lofFCtoeliminate103CFU/mlofE.coliinoneminute,we
calculate:
3.1.5. Organicmaterialinthechillerwater
kw 3:125(cid:7)104kc: q:FromTsaietal.(1992),thetotalsuspendedsolidsinthechiller
water is 0.35% (i.e. about 3500 mg/l) (this value is similar to the
Also, as bacteria are organic substances, we can model their initialmeasuringstationinthetank(Northcuttetal.,2008)).With
inactivationbyFCusinga secondorderratereaction(Deborde& ourtankvolumegivenbyTV 5(cid:7)107ml,thistranslatestoabout
von Gunten, 2008), W' kwCW. Considering this equation on 175 kg. Using the total suspended solids to estimate the organic
thetimeinterval[t0,t3],wecansolveforkwasfollows: material in the tank, J(t) should equilibrate to about 175 kg. We
(cid:4) (cid:5) know that the positive equilibrium value of J qN/dp without
kw lnðWZ ðt3t0CÞð=sWÞdðst3ÞÞ ln:013023 215:867: filteSriinncge.TNhaisnidmdppliaersethfiaxtedqzfro1m75o/u(4r5p*r3o6c0e)ssin0g.0a1s1s.umptions,we
allowqtovaryfrom0.005to0.03asthismeansthatJvariesfrom
t0
about80to490kg.
3.1.6. FCoxidationrateviaorganicmaterialintank and 3). These input values are then fed into our model (7) and
hJ:Wewanttoestimatetherateofchlorinereactionwiththe linked with the correspondingoutputs for W*, v(cid:6)p and C*. Using a
organicmaterialinthechillerwater.Fromourmodel,weusethe samplesizeofn 1000,wecalculatethepartialrankcorrelation
followingequation: coefficients(PRCCs)correspondingtoeachparameter.Briefly,the
PRCCvaluesquantifythedegreeofmonotonicitybetweenrespec
C0 hJJC: tive parameters and outputs. For more details concerning this
analysis, please refer to (Marino, Hogue, Ray, Krischner, & Zhao,
FromTsaietal.(1992),thechillerwaterisassumedtohavethe
2008). Observe that for a complete uncertainty and sensitivity
total suspended solids at equilibrium, J 3500 mg/l (or 0.35%).
analysis, we should also perform an extended Fourier amplitude
Assuming,asabove,TV 5(cid:7)107ml,wehavethatforlargeenough sensitivity test (eFAST), however, more relevant data for certain
t, JðtÞ≡J J10T6Vmlg 175 kg. Substituting this into the model, we parameterrangesisneededinordertojustifyanextensivesensi
solvetoget tivityanalysis.
Fig.1 illustratesthe PRCC values using thebaseline and range
CðtÞ C0e(cid:5)hJJt: (13) valuesforcorrespondingparameterscomingfromTables2and3.
FromFig.1(A)and(C),wefirstnoticethatW*andv(cid:6) arestrongly
ReferringtothedatainTable5ofTsaietal.(1992),weseethat influenced by s (CFU/kg), the average E. coli load opn pre chilled
chlorine depletion from organic material has both a “fast” and
poultry. This is a logical result, as increasing the pre chiller mi
“slow”kinetic.Forourpurposes,weconsideronlythefastkineticas
crobial load on the poultry will in general lead to an increase in
we have a continuous flow of chlorine and organic material
microbialconcentrationinthechillerwateraswellasoncarcasses
enteringthechilltank.FromTsaietal.(1992),theaverageofthis
duringchilling.WequantifytheaverageE.coliload(duringchill
fast kinetic is 0.29/min with standard deviation 0.10. Combining ing) on the poultry, v(cid:6) (CFU/(kg ml)), as the time independent
thiswiththeratein(13),leadstohJJ 0.29±.10.SinceJ 175kg, expression: p
our baseline value for hJ .0017 and the range is hJ2
[0.0011,0.0022]. Note, the residual chlorine data from Tsai et al.
(1992)isnotthesameasFC,however,weassumethattheresid v(cid:6) (cid:4) ð1 rÞdp (cid:5)sþ bW(cid:6) : (14)
ualchlorineisproportionaltotheFCandthereforethedecayrate p TV bþdpþakwC(cid:6) bþdpþakwC(cid:6)
forbothtypeswillbegivenbyhJ. Equation(14)canbeunderstoodasfollows:thefirsttermcor
respondstotheE.coliloadthatremainsonthepoultryduringthe
3.1.7b.: TBoinedsintigmraatteetohfeE.bcionldiitnogproautletroyfinE.tcaonlki in suspension in the fcrhaicllteiornproofctehses.iTnhcaotmisi,n(g1E.rc)dolpi/(lToVa(dboþndtphþe paokwuClt*r)y)qthuaatndtiofieessnthoet
processwatertothepoultryduringchilling,weadoptthe“trans shed during chilling and is not inactivated by FC contact with
missionrate”perspectivethatiscommontodiseasemodels.Ina carcasssurfaces.ThesecondtermquantifiestheE.coliloadgained
diseasemodelwithawellmixedpopulation,thisrateisbasedon via cross contamination from contaminated chiller water. Recall
the number of successful contacts an infective individual makes that b is the water to carcass transmission parameter,1/b is the
with the susceptible population (Brauer, 2008). For the chilling characteristictimescaleforE.colisheddingfromcarcassesintothe
process,thenumberofcontactsdependson(a)thepoultrytowater chillerwater(itisproportionaltothetimeittakestoshed1e2log10
ratio,(b)theaveragedwelltimeofthepoultryinthetankand(c) CFU)and1/dpistheaveragedwelltimeofacarcassinthechiller
the“path”thecarcassestakethroughthetank.Wesupposethatthe tank.Noticethat1/(akwC*)isthecharacteristictimescaleforFCto
tank is 9 m long (Northcutt et al., 2008) and its volume is inactivateE.colioncarcasssurfaceswhentheFChasreachedthe
TV 5(cid:7)107ml.BecausetheequilibriumamountofpoultryP* N/ equilibriumamountofC*.Combiningthesethreetimescales,we
dp 16200kg,thepoultrytowaterratioisP*/TV 0.324kg/l. observe that 1/(bþdpþakwC*) is the characteristic time scale of
We want to know how many liter “cubes” of contaminated cross contaminationduringan8 hshiftofcontinuousprocessing.
waterthis0.324kgofpoultry“hits”asittravelsthroughthetank. Inotherwords,someoftheE.coligainedfromcross contamination
Assuming the 0.324 kg poultry unit travels straight through the maybeshedorinactivatedbeforethecarcassleavesthechillertank
tank, and because a liter cube of water has a side dimension of andthemodelaccountsforthisbyshorteningtheeffectivecross
0.1 m,thepoultry unit“hits”about90 cubesofwater.Therefore, contaminationtimescalefrom1/dpto1/(bþdpþakwC*).
1 kg of poultry “hits” about 270 L cubes during its 45 min trip Whilev(cid:6) issensitivetomanyparameters,referringtoFig.1(C),
throughthetank.Wedescribebasfollows: we see thapt c1, a, l and q play more influential roles. In terms of
270 hits chlorineefficacy,Fig.1indicatesthatc1(theinputFCconcentration)
b 45 minm; hasastrongeffectonreducingtheE.coliloadoncarcassesduring
kg chilling.Thiseffectiscoupledwiththeimpactofl(theinputoffresh
water/carcass)asincreasinglincreasestheadditionrateofFCtothe
wheremistheprobabilityofsuccessfulE.coliattachment.Currently tank(seeformula(6)).Fromanindustrystandpoint,itisimportant
wehavenodataform,butweestimateittobebetween.02%and2% to note that both c1 and l can be directly controlled during the
success.SeeMunther&Wu(2013)foradiscussionontheproba chillingprocess.Additionally,fromaregulatoryperspective,c1has
bilityofE.coliattachmenttolettuceduringacommercialproduce anupperbound.Considering thislimitation,wewillgiveamore
wash.Inthatcontext,mz1%.Puttingtheseideastogetherindicates detaileddiscussionofFCcontrolaswellasdiscusstheroleofain
thatb2[0.001,0.1]. Section 3.2.3. In terms of water usage and the parameter l, an
interesting study would be to use the model (7) predictions to
3.2. Resultsfromsensitivityanalysis comparethetradeoffsbetweensimultaneouslyminimizingE.coli
loadsintheredwaterandoncarcasssurfacesandthecostasso
InordertounderstandhowparametervariationsaffectW*,v(cid:6) ciatedtowaterconsumption.
p
*
andC (i.e.theequilibriumE.colilevelsinthechillerwater,onthe Fig.1(C)suggeststhatanincreaseinq(thefractionoforganic
poultry and the equilibrium FC level), we use Latin hypercube material the sheds from carcasses intothewater) leads to an in
samplingtobuildamatrixofparameterinputvalues(seeTables2 creaseinv(cid:6).Whileqcannotbedirectlycontrolledduringchilling,as
p
D.Muntheretal./FoodControl59(2016)271 281 277
Table3
Parametersandrangesforsensitivityanalysis.
Parameter/Reference Baseline Range
s 2(cid:7)104CFU/kg 103 106
(Cavanietal.,2010;Northcuttetal.,2008)
r 0.15 0.05 0.30
Estimated
q 0.011 0.005 0.03
(Northcuttetal.,2008;Tsaietal.,1992)
b 0.01(kgmin) 1 0.001 0.1
(Munther&Wu,2013;Northcuttetal.,2008),estimated
b 0.077min 1 0.04 0.1
(Northcuttetal.,2008)
a 0.05 0.001 0.1
estimated
kw 216l/(mgmin) 150 300
(Helbling&VanBriesen,2007;Zhangetal.,2015)
l 1.7l/carcass 1 4
(Northcuttetal.,2008;CFIA,2014)
c1 25mg/l 0 50
(USDA,2012;CFIA,2014)
hJ 0.0017(kgmin) 1 0.0011 0.0022
(Tsaietal.,1992)
Fig.1. PRCCvaluesforparameterswithrespectiveoutput:(A)W*,(B)C*(C)v(cid:6)pand(D)bW*/(bþdpþakwC*).Parametersthataresignificant,(p<0.05)aremarkedwithastar.
in the case of c1 and l, it can be indirectly regulated during pre controlled during processing, we estimate the magnitude of the
chiller processing. See Section 3.2.3 for more details on the rela fraction (1 r)dp/(TV(b þ dp þ akwC*)), the cross contamination
tionship between q, FC control and pre chiller processing term, bW*/(b þ dp þ akwC*), and the E. coli level in water W* as
interventions. follows:foreachfixedc1in[0,50]mg/l,weperformMonteCarlo
simulationstocalculatetherespectivevaluesoftheseterms.Then,
fittinganormaldistributiontotherangeofrespectiveoutputs,we
3.2.1. RulesofthumbforE.colicross contamination
calculatethe95%confidenceinterval.
Under what conditions should we worry about cross
TheresultsareillustratedinFig.2.ExaminingFig.2(A),wesee
ccinootnnottaacmmomiinnpaattaiirooinnng?teItnrhmete.rmSmiansgcneoiftcuE1qd(uethaoteifoinnthp(eu1t4fi)Fr,Cstthciotsenqrcmueensattrniaodtniottnhr)eanccasrlnoatsbeses rthanatgethseov9e5r%acpopnrfiodxeimncaeteilnyte[1rv0a(cid:5)l10fo.4r,1(01(cid:5)8.4]r)adsp/c(1TVv(abriþesdfproþma[k0w,5C0*)]).
Similarly, from Fig. 2(B) and (C), the cross contamination term lesser role in ensuring that cross contamination will not be an
ranges over [10(cid:5)6.75,10(cid:5)3.3] and W* ranges over [10(cid:5)4.4,10(cid:5)3], issue.Thatis,usingmaximumFCinput,comparedtozeroFCinput,
respectively. These results provide quantifiable evidence that FC reducestherangeofs,withinwhichcross contaminationdictates
playsasignificantroleinreducingtheE.coliloadonpoultrybothby themagnitudeofv(cid:6)p,onlybyabout1log10CFU.
directlyinactivatingthebacteriaoncarcasssurfacesandbyinac
tivating the bacteria in the chiller water which reduces the load 3.2.2. Cross contaminationandflocktoflocktransmission
gainedviacross contamination. OuranalysisalsoindicatesthatW*issensitivetob,r,andb,and
However,the questionremains,when shouldweworryabout bW*/(bþdpþakwC*)issensitivetorandb(seeFig.1(A)and(D)).
cross contamination?UsingtheresultsfromFig.2(A)and(B),we ThisinformationcoupledwithourdiscussioninSection3.2.1points
cancomparetheexpressionsforv(cid:6)pwhenc1 0(noFCinput)and to potential cross contamination issues as described in the
whenc1 50(maximumFCinput).First,forc1 0,wehavethat following archetypal situation: Suppose chickens are processed
fromavarietyoffarmsatoneparticularprocessingcenterbutfarm
v(cid:6)z10(cid:5)8:4sþ10(cid:5)3:3 (15) (A), at some juncture, delivers chickens that carry a significantly
p
higherE.coliloadascomparedwiththechickensfromtheother
*
Next,forc1 50,weseethat farms.Itislikelythen,thattheE.coliloadinthechillerwater,W,
will dramatically increase via the shed from farm (A) chickens
*
v(cid:6)z10(cid:5)10:4sþ10(cid:5)6:75 (16) duringchilling.IfthemagnitudeofW ishigherorcomparableto
p themagnitudeofsfromcarcasses nowentering thechillertank,
From Equation (15), if s (cid:3) 105.1, the magnitude of the cross and the chiller water has yet to be replaced, then cross
contamination term plays a dominant role in determining the contamination (flockto flock) may be significant. To obtain rules
overallorderofv(cid:6).Thatis,duringatypical8 hshift,ifnoFCisused, ofthumbforsuchscenarios,thatarebackedbyscientificrigorat
p
cross contaminationhasaprimaryeffectindeterminingtheE.coli the mechanistic scale, our model suggests the need for specific
levelonpost chillerpoultrywhentheaverageE.coliloadonpre experimentstocapturethecomponentsofshedding(randb)and
chillercarcassesisontheorderof5log10CFUorless. cross contamination (b) more precisely. Refer to Section 4 for a
Following the same reasoning, Equation (16) indicates that if moredetaileddiscussion.
s (cid:3) 103.7, then the cross contamination dynamic is again signifi
cant.Inotherwords,duringatypical8 hshift,ifmaximumFCinput 3.2.3. FCcontrolandinactiviation
isused,cross contaminationplaysaleadingroleindeterminingthe While our findings in Section 3.2.1 show that cross
E.colilevelonpost chillerpoultrywhentheaverageE.coliloadon contaminationcanstronglyinfluencetheresultingE.coliloadon
pre chillercarcassesisontheorderof4log10CFUorless.Therefore, chilled poultry, both in the presence or absence of FC input, the
whileFCinputsignificantlyreducesE.colilevelsinthewaterandon results in Figs.1 and 2 demonstrate that FC input is pivotal as a
poultryduringchilling,fromamanagementperspective,itplaysa control.ToquantifythiscontrolonE.colilevels,weagainconsider
(A) (B) (C)
(cid:237)8 (cid:237)3 (cid:237)2.8
(cid:237)3
(cid:237)3.5
(cid:237)8.5
(cid:237)3.2
)) (cid:237)4
)
*C )
w *)C (cid:237)3.4
k
(cid:68) w (cid:237)4.5
+p (cid:237)9 k(cid:68)
+d +p *W) (cid:237)3.6
b d (cid:237)5
d/(T(vp (cid:237)9.5 */(b+W log( (cid:237)3.8
)(cid:85) (cid:69) (cid:237)5.5
(cid:237) ( (cid:237)4
1 g
( o
( l
og (cid:237)6
l (cid:237)4.2
(cid:237)10
(cid:237)6.5
(cid:237)4.4
(cid:237)10.5 (cid:237)7 (cid:237)4.6
0 50 0 50 0 50
c c c
1 1 1
Fig.2. 95%confidenceintervalfor(A)FractionofunshedE.colilevelonpoultryvsFCinputc1,(B)Levelofcross-contaminationonpoultryvsFCinputc1,and(C)E.colilevelinred
waterW*vsFCinputc1.