Comparison of adaptive neuro-fuzzy inference system (ANFIS) and Gaussian processes for machine learning (GPML) algorithms for prediction of skin temperature in lower limb prostheses

Contents lists available at ScienceDirect

Medical

Engineering

and

Physics

journal homepage: www.elsevier.com/locate/medengphy

Comparison

of

adaptive

neuro-fuzzy

inference

system

(ANFIS)

and

Gaussian

processes

for

machine

learning

(GPML)

algorithms

for

the

prediction

of

skin

temperature

in

lower

limb

prostheses

Neha Mathur

a,∗

_{, Ivan Glesk}

a

_{, Arjan Buis}

b

a_{Department of Electronic and Electrical Engineering, University of Strathclyde, 204 George Street, Glasgow G11XW, UK} b_{Department Biomedical Engineering, University of Strathclyde, Glasgow G40NW, UK}

a

r

t

i

c

l

e

i

n

f

o

Article history: Received2June2015 Revised21March2016 Accepted5July2016

Keywords: ANFIS Fuzzylogic

Gaussianprocessformachinelearning Lowerlimbprosthetics

Modeling Temperature

a

b

s

t

r

a

c

t

Monitoringoftheinterfacetemperatureatskinlevelinlower-limbprosthesisisnotoriouslycomplicated. Thisisduetotheflexiblenatureoftheinterfacelinersusedimpedingtherequiredconsistentpositioning ofthetemperaturesensorsduringdonninganddoffing.Predictingthein-socketresiduallimb tempera-ture bymonitoringthe temperaturebetweensocket and linerrather thanskinand linercould bean importantstepinalleviatingcomplaintsonincreasedtemperatureandperspirationinprostheticsockets. Inthiswork,weproposetoimplementanadaptiveneurofuzzyinferencestrategy(ANFIS)topredictthe in-socketresiduallimbtemperature.ANFIS belongstothefamilyoffusedneurofuzzysysteminwhich thefuzzysystemisincorporatedinaframeworkwhichisadaptiveinnature.Theproposed methodis comparedto ourearlier work usingGaussian processes formachine learning. By comparingthe pre-dictedandactualdata,resultsindicatethatboththemodelingtechniqueshavecomparableperformance metricsandcanbeefficientlyusedfornon-invasivetemperaturemonitoring.

© 2016TheAuthor(s).PublishedbyElsevierLtdonbehalfofIPEM. ThisisanopenaccessarticleundertheCCBYlicense.(http://creativecommons.org/licenses/by/4.0/)

1. Introduction

Manyamputeescomplainofincreasedtemperatureand perspi-rationwithintheirprostheticsocket[1,2].Themostaccurate tem-peraturereadingwouldbeobtainedbyplacingthesensordirectly incontactwiththeskin,however,thiswouldcreatepracticality is-sueswithprostheticuseinadomestic situationsuch as, protrud-ingleadwiring,consistentpositioningofsensorsandpossibleskin irritation anddiscomfort. Onthe other hand, embedding sensors andwiresintothehardprostheticsocketduringthe manufactur-ing process forprostheticsocketswould eliminateanyissues de-scribed earlier.Inaddition,therewouldbe nodamageto the de-viceduringthedonninganddoffinganditslongevitywouldnotbe marred.Wedescribetheroutewhereinthein-socketresiduallimb temperature can be accurately predicted by monitoring the tem-perature between theliner andthe socket usingartificial neuro-fuzzy inference system (ANFIS). The predictive modeling results are thencompared withGaussian processesformachine learning (GPML)previouslydevelopedbyPeeryetal.[3].

∗ _{Correspondingauthor.}

E-mail address: [email protected](N.Mathur).

ANFIS are a class of adaptive networks that incorporate both neural networks and fuzzy logic principles. Neural networks are supervisedlearningalgorithmswhichutilizeahistoricaldatasetfor the prediction offuture values. In fuzzy logic, the control signal isgeneratedfromfiringthe rulebase.Thisrulebaseisdrawn on historicaldataandisrandominnature.Thisimpliesthatthe con-troller’soutputisalsorandomwhichmaypreventoptimalresults. The use of ANFIS can make the selection of the rule base more adaptive to the situation. In this technique, the rule base is se-lectedutilizingtheneuralnetworktechniquesviatheback propa-gationalgorithm.Toenhanceitsapplicabilityandperformance,the propertiesoffuzzylogic,i.e.approximatinganon-linearsystemby settingIF-THENrulesisinheritedinthismodelingtechnique.This integratedapproach,makesANFIStobeauniversalestimator[4].

Thegoalofthe Gaussianprocess techniqueontheother hand istoinferacontinuousfunctionf(x) fromatrainingsetof input-outputpairsinsupervisedlearningcontext.A,Gaussianprocessis acollectionofrandomvariables,anyfinitenumberofwhichhave joint Gaussian distributions [5]. The key assumption in Gaussian process modeling is that the data can be represented as a sam-ple froma multivariate Gaussian distribution. Therefore, it could betotallyspecifiedbythemeanandcovariancefunction.A Gaus-sianprocessmodelcanbethoughtofasapriorprobability distri-butionoverfunctionsinBayesianinference.Thisenablesdeducing

http://dx.doi.org/10.1016/j.medengphy.2016.07.003

thehyperparametersforthemodelwhicharean indicationofthe precisionandrelevanceoftheinputparametersforpredictingthe output.Thus,theaiminGaussianprocessmodelingistoselectthe modelparametersforwhichtheprobabilityofthetrainingdatais maximized[5].Inthis paper,we investigatetheuseof ANFISand Gaussianprocessalgorithmsinthecontextofpredictingthe resid-uallimbskintemperatureoftheamputee.

2. Method

IthasbeenrecordedbyKluteetal.[6]thatenvironmental fac-tors like temperature, humidity, and also the activitylevel of an amputee affecttheir residual limb temperature. Also, itwas sug-gested by Klute et al. [7] that some prosthetic materials act as insulatorsasrestrict thetransfer ofheatandmaybethe causeof thermaldiscomfortintheresiduallimb.Thus,ifthethermal prop-ertiesoftheprostheticmaterialsareknownthentheresiduallimb temperaturecanbe predictedbymonitoring thetemperature be-tweenthelinerandthesocket.Inordertoinvestigatethe temper-atureprofilecorrelation of theresidual limband thesocket-liner interface,a68year-oldmaletransitibialtraumaticamputee weigh-ing70kg wasaskedto take partina laboratory test.The details ofinvestigation weresimilar toasdescribedbyMathur etal.[3]. In summary, the subject wore a 6mm Polyurethane liner (Otto-BockTechnogel)witha4mmthick socketmadeofthermosetting lay-upmaterialandwasdressedinshortsandt-shirtwithoutany extralayerofclothingontheprosthesis.According toKluteetal.

[7]thethermalconductivities ofmaterials used intheprosthesis oftheamputeesubjectwere– Polyurethaneliner0.19W/m°Kand Thermosettingsocketmaterial0.14W/m°K.

Tomonitorandrecord theresiduallimbandliner-socket tem-peratures, four K –type thermocouples via a data logger (type HH1384;Omega Engineering)were used.One thermocouple was tapedonthelateralsideofthelimbandtheotheronthemedial. Theremainingtwothermocoupleswere tapedonthe correspond-inglateralandmedialpositions onthe liner-socketinterface.The schematicandtheactual setup oftheprosthesis withthe sensor placement are indicated in Fig. 1. Data fromthese four thermo-coupleswasrecordedatasamplingrateof0.5Hzatadefined am-bienttemperature(dataset A). Thiswasrepeatedagain aftertwo months to confirm the influence of ambient temperatureon the

Table1

Experimentalprotocolfortheamputeetestsubject.

Activity Time(min)

Resting/sitting 10

Walkingonthetreadmillatself-selected speedof0.62m/s

10

Finalrest 15

residual limb skin temperature(dataset B). Detailsof the 35min experimentalprotocolareasindicatedinTable1.

Thetemperatureprofilesofthelinerandtheresiduallimbskin wererecordedinaclimatecontrolledchamberwithzerowind ve-locityand40% humiditylevelsforambienttemperaturesof10°C, and then the same protocol was repeated for 15°C, 20°C, and 25°C. The results indicated that for any given ambient temper-ature, the liner temperature profile follows that of the in-socket residuallimbtemperature.Thissuggestedapossibilitytoapply su-pervised machine learningalgorithms tomodel theresidual limb temperature of the amputee as a function of liner temperature. Timeaveragingof5sisdoneontherecordeddatatohelpin iden-tifyingthetrendbetterandsmoothout thefluctuations. Different modeling techniques for machine learning were utilized and the results from the Gaussian processes model and ANFIS technique arecompared inthisstudy.Since, thetemperatureprofilesofthe residuallimbarealmostsimilarfortheambienttemperaturepairs of 10°C, 15°C and 20°C, 25°C, the predictive model atambient temperaturesof10°Cand25°Careonlydiscussedinthisstudy.

3. Adaptiveneurofuzzyinferencestrategy

ANFISbelongstoa familyofhybridsystem,calledastheterm ‘neurofuzzynetworks’[8]inheritingthepropertiesofbothneural networksand fuzzylogic. Neural networkscan easily learn from the data. However, it is difficult to interpret the knowledge ac-quired by it, as meaning associated with each neuron and each weightitquitecomplextocomprehend.Incontrast,fuzzylogic it-self cannot learnfrom thedata.But fuzzy-based modelsare eas-ilyunderstood as it utilizes linguisticterms rather than numeric and the structure of IF-THEN rules. Linguistic variables are de-finedasvariableswhosevaluesarewordsorsentencesinanatural

a

b

[image:2.595.335.521.76.133.2] [image:2.595.103.489.514.714.2]

Fig.2. Blockdiagramofaneuro-fuzzy(ANFIS)controller.

languagewithassociateddegreesofmembership.Thefuzzysetin which linguistic variables belongs isan extension of a ‘crisp’ set where an element could have full or no membership. However, fuzzy sets allow partial membership as well, which implies that anelementmaypartiallybelongtomorethanoneset[9].Inother words,foracrispset,themembershiplevelofanelementxinset

Acanbeexpressedbyacharacteristicfunction

μ

A

(

x

)

,suchthatif

μ

A

(

x

)

=

1 if x

A implyingfullmembership

0 if x ∈/A implyingnon-membership (1)

But fora fuzzysetA the membershipfunction

μ

A

(

x

)

can take

values in the interval [0, 1].The basic structure ofthe developed ANFIScontrollerforthepredictionofresiduallimbskin tempera-tureconsistsoffourparts,whichare,fuzzification,rulebase, infer-enceengineandthede-fuzzificationblocksasseeninFig.2.

IntheANFIScontroller,thecrispinputsignal(linertemperature inourcase)isconvertedtofuzzyinputsbythemembership func-tion. The membership function patternused inour ANFISmodel isGaussian.ThefuzzyinputsalongwiththeGaussianmembership function are then fed into the neural network block. The neural networkblockconsistsofarulebasewhichisconnectedtothe in-ferenceengine.Backpropagationalgorithmisusedtotrainthe in-ference enginefortheproperselectionofrulebase.Oncetrained, proper rulescan begeneratedandfiredfromthe neuralnetwork blocktoyieldoptimaloutput.Thelinguisticoutputfromtheneural network block isthen converted into crisp output (residual limb skin temperature) by the defuzzifier unit [10]. The structure of the neuro-fuzzy model consistsof differentadaptive layers. Each of theselayers hasnodes withan associated network oftransfer functions,throughwhichthefuzzyinputsareprocessed.The out-put from these nodes are then combined to yield a single crisp output astheconfigurationoftheANFISpermitsonlyoneoutput of themodel. Thiscrispoutput is fedbackasinput to themodel andcomparedwiththesetvalue.Ifthereisanydeviation,the er-rorsignal sogeneratedbecomestheinputtotheANFIScontroller, therebymaintainingstabilityinthesystem[11].

ANFIS, supports the Takagi–Sugeno based systems [12]. The structureoftheadaptivenetworkiscomposedoffivenetwork lay-ersi.e.layer1tolayer5(withnodesandconnections)asshownin

Fig.3.Assumingthatthesystemisdefinedtohavetwoinputsx1

andx2,one outputz andfuzzysetA1,A2, B1,B2;then fora first

orderTakagi–Sugenofuzzymodel,havingtwoIF-THENrulesinthe commonruleset,canbe writtenusingthefollowingEqs.(2)and (3)[13].

Rule1:If x 1 is A 1and x 2 is B 1 then f 1= p 1x 1+q 1x 2+r 1 (2)

Rule2:If x 1 is A 2and x 2 is B 2 then f 2= p 2x 1+q 2x 2+r 2 (3)

Layer 1: This layer is called as the fuzzification layer. Here the crisp input signal is fed to the node i which is associated witha linguistic labelAi or Bi−2. Thus, themembership function

O1,i

(

X

)

determines the membership level (full, none or partial)

of the given input. The output of each node is calculated using

Eqs.(4)and(5).O1,i

(

X

)

isthegeneralizedGaussian shaped

mem-Fig.3. ArchitectureofafirstordertworuleTakagi–SugenotypeANFIS.

bershipfunctionusedinourmodeldevelopment.

O 1,i=

μ

Ai

(

x 1

)

for i =1,2 (4)

O 1,i=

μ

Bi−2

(

x 2

)

for i =3,4 (5)

Layer 2: Thenodes inthis layerare fixed andlabeled asO2,i.

Theoutputofeachnodeistheproductofalltheincomingsignals asintheEq.(6).

O 2,i=w i=

μ

Ai

(

x 1

)

μ

Bi

(

x 2

)

for i =1,2 (6)

Theoutputofeachnoderepresentsthefiringstrengthofarule. Also,knownasthemembershiplayer,itactsontheinputvariables fromlayer1asmembershipfunctionsto representthemintheir fuzzysets.

Layer3:Eachnodeinthislayercalculatestheratioofthe indi-vidualrule’sfiringstrengthtothesumofallrulesfiringstrengths as in the Eq. (7). wi represents the normalized firing strength.

Hence,thislayerisalsoknownastherulelayer.

O 3,i=w i=

w i

w 1+w 2

for i =1,2 (7)

Since,eachnodeinthislayercalculatesthenormalizedweights, the output signal can be thought of as the normalized firing strengthofagivenrule.

Layer 4: This layer known as the defuzzification layer. It cal-culatestheindividual outputvalues y fromtheinferring ofrules fromtherulebase.Individualnodesofthislayerareconnectedto therespectivenormalizationnode inlayer 3andalsoreceive the inputsignal.Eachnodeofthislayerisadaptiveinnaturewiththe nodefunctiongivenby theEq.(8)wherepi,qi,riisaset of

con-sequentparametersofrulei.

O 4,i=w if i=w i

(

p ix 1+q ix 2+r i

)

(8)

[image:3.595.329.547.54.356.2] [image:3.595.48.293.55.142.2]

Fig.4. EpochsandtrainingerrorinANFISforambienttemperatureof10°Cat lat-eralside.

thenodesofthedefuzzificationlayertoproducetheoverallANFIS outputasinEq.(9).

overalloutput=O 5,i=

i

w if i=

iw if i

iw i

(9)

Thisarchitectureoftheadaptivenetworkisusedtodevelopthe ANFISmodelforthepredictionofin-socketresiduallimb temper-atureandisdiscussedinthenextsection.

4. Modelgenerationandprediction

TheANFISmodelisdesignedusingMATLAB’sFuzzyLogic Tool-box and the GUI editor which was used for analyzing its per-formance [14]. The optimized sets of rules were generated using the grid partition method. The architecture of the realized AN-FISmodelhadthefollowing specifications;numberofnodes: 84, numberoflinearparameters:20,numberofnonlinearparameters:

[image:4.595.301.553.58.266.2] [image:4.595.40.279.59.254.2]

Fig.5. Illustrationofpredictionwith ANFISforambienttemperatureof10°Cat lateralside.ThepredictedFISoutputisindicatedbyredandthetestdatais rep-resentedbythebluecrosses.(Forinterpretationofthereferencestocolorinthis figurelegend,thereaderisreferredtothewebversionofthisarticle.)

Fig.6. EpochsandtrainingerrorinANFISforambienttemperatureof10°Cat me-dialside.

40,numberoftrainingdatapairs: 210,numberoftest datapairs: 99 andnumberof fuzzyrules: 20. The adaptivenetwork utilizes thehybridmethodtooptimizethemembershipfunctionsandthe parameters so that the prediction error is minimized. Dataset A is used to train the model andthe predictive ability ofANFIS is testedondatasetB.Duringthetrainingprocessofthemodel,the input dataismappedanumberoftimesto minimizethe predic-tionerror.Thenumberofiterationsrequiredformappingisknown as epochs. It is observed from Fig. 3 that 50 iterations (epochs) arerequiredtotrainthemodelondatasetAwithaminimalerror of0.15341.It canbe observedfromFig. 4that thetrainedmodel is then tested on 100 data points from dataset B to validate it.

Figs.4–7illustratethepredictiveabilityofANFISforambient tem-peratureof10°C atlateralandmedialsideofresiduallimb.They aregeneratedinthesimilarwayforlateralandmedialsideofthe residuallimbat25°C.

[image:4.595.301.554.495.703.2] [image:4.595.40.282.503.703.2]

a

b

Fig.8. PredictedresiduallimbskintemperaturefromANFISmodelisshownalongwiththeactualskintemperatureatlateralandmedialsidesin(a)and(b),respectively, atambienttemperatureof10°C.Theactualmeasuredresiduallimbtemperatureisindicatedasthecheckingdatawhereasthepredictedresiduallimbtemperatureisthe FISoutput.Theaxislabelsimply:indexisthetimeinsecondsandtheoutputisthetemperatureinCelsius.

5. Obtainedresults

Ouraimwastousethemodeltopredicttheresiduallimbskin temperature fromthe linertemperature andcompare theresults with direct skin temperaturemeasurements. Hence, the input to themodelisthelinertemperatureobtainedfromrunningthe ex-periment in the climate chamber and the output of the model wouldbethepredictedresiduallimbskintemperature.Totestthe predictive capability ofa modelwe developed, themodel isfirst ‘trained’ ononeset ofdata andthen is‘tested’onpreviously un-seendatawecollectedindependently.Finally,theresultsare com-paredforitsaccuracy.

It isseenfromthat theskintemperatureisdependent onthe ambient temperature. Hence, individual Gaussian process models andANFIS modelsfor thelateral andmedialside of theresidual limbweredesigned, usingtheprincipleasdescribedinthe previ-oussectionforambienttemperaturesof10°Cand25°C.

The actual skin temperature obtained by the ANFIS model is shown in Figs. 8 and 9 for two very different ambient tem-peratures of 10°C and 25°C, respectively. For both these exper-iments, done at different ambient temperatures, our predictive modelusing ANFISprovides a simple,effective,andpractical ap-proach to determine the unknown skin temperature of the sub-ject within the prosthetic device from the actual liner measure-ments.Boththedevelopedpredictivemodelsleadtoresultswhich have an accuracy of ±0.5°C. However, this study needs to be extended on a greater population in order to define a generic behavior.

6. Discussionandtestresults

[image:5.595.82.519.56.501.2]

a

b

Fig.9. PredictedresiduallimbskintemperaturefromANFISmodelisshownalongwiththeactualskintemperatureatlateralandmedialsidesin(a)and(b),respectively, atambienttemperatureof25°C.Theactualmeasuredresiduallimbtemperatureisindicatedasthecheckingdatawhereasthepredictedresiduallimbtemperatureisthe FISoutput.TheoutputlabelimpliestemperatureinCelsius.

Table2

PerformancecomparisonofANFISandGPMLmodels.

MAE RMSE

ANFIS GPML ANFIS GPML

Trainingdata 0.1427 0.0879 0.1534 0.0910

Testdata 0.07412 0.0946 0.07583 0.102

temperaturefrom the linertemperature values ofdataset B. The performanceofboththemodelswascomparedbythemean abso-luteerror(MAE), rootmeansquarederror(RMSE), andR2 _criteria

areshowninTables2and3.

The MAEindicates how closethepredictions are tothe even-tualoutcomeswhichisgivenby

MAE= 1

n

n

i=1

|

f i−y i

|

=

1 n

n

i=1

|

e i

|

(10)

Table3

R 2_{criteriacomparisonofANFISandGPML}

models.

Modellingtechnique R 2

ANFIS 0.9802

GPML 0.97

As seen in Eq. (10), the mean absolute error can be defined as the average of absolute errors; the absolute error given by

[image:6.595.71.517.60.518.2] [image:6.595.65.251.585.639.2] [image:6.595.363.493.595.632.2]

involvessquaringthedifference betweenthepredictedand corre-sponding observedvalues,averaging it overthe sampleandthen finallytakingitsaverage.Thiscanbewrittenas

RMSE=

1 n n

i=1

e i2 (11)

RMSEhasaquadraticerrorrule,wheretheerrorsaresquared beforebeingaveraged.Asaresult,arelativelyhighweightisgiven tolargeerrors[15].Thiscouldbeusefulwhenlargeerrorsare un-desirable in a statistical model.From Table 2 it can be deduced thatfortheGaussianmodeltheMAEandRMSEisslightlyloweras comparedtoANFIS.Butinordertodiscriminatebetweenthe mod-els for their predictive performance, the errormetrics should be capabletodifferentiateamongstthemodelresults.Inthiscontext, theMAEmightbeaffectedbylargeaverageerrorvaluesby ignor-ing some large errors. The RMSE isgenerally better in reflecting the modelperformance differences[16] asitgives higherweight totheunfavorableconditions.ThedifferencebetweentheRMSEof theGaussianmodelandANFISisnotimmenseandhenceboththe modelshavecomparableperformancemetrics.

Anothermeasureofgoodness-of-fitofthemodelistheR2

cri-teria.Highervaluesareindicativethatthepredictivemodelfitsthe datainabetterway.Bydefinition,R2_{istheproportionalmeasure}

of variance of one variable that can is predicted from the other variable. Thus ideallythevaluesofR2 _{toapproach oneis always}

desirable. However, a highR2_{tellsyou that the curve came very}

close to thepoints butin reality it doesnot always indicate the modelquality[17].FromTable3,bothGaussianandANFISmodels havesimilarR2 _{valueswhichareindicatorsthatinboth the}

mod-eling techniques,the predictioncapabilityissimilar. UsingtheR2

criteriainconjunctionwiththeMAEandRMSE,itcanbefairly de-ducedthattheGaussianandANFISmodelscanbeaccuratelyused forthepredictionofresiduallimbtemperature.

7. Conclusion

This studyaddressesthe challengesof non-invasively measur-ingthein-socketresiduallimbtemperaturebycomparingtwo dif-ferentmodelingtechniques,namelyANFISandGaussianprocesses. The temperature profile of the residual limb skin is dependent on the ambient temperature and the activity level of the sub-ject.Thedataobtainedatambienttemperaturesof10°Cand25°C were used to develop an ANFISmodel.The results fromthe AN-FISmodelwereencouraging.Thesewerecomparedwiththe previ-ouslydevelopedGaussianmodel.Theperformancemetricsofboth the models indicatethat they are very similar intheir predictive abilitywithanaccuracyof±0.5°C.Howeverthisapproachhas cer-tainlimitationsaswell.Theresiduallimbtemperatureprofilewill differforeveryamputeeastherearevariationsinphysiological re-sponses (suchasdifferencesincapillarydilatation)andvariations inpropertiesoftheskinparameters(suchasthickens/composition oftheskinlayers).Becauseofthevarying residuallimb tempera-tureprofileinindividuals,thesemachinelearningalgorithmshave to be personalizedby trainingthem with individual datasets for eachoftheamputeesubjects.Thisstudywhichwasconductedon one amputee subjecta number of times, verified the success of

proposed approach withan accuracy of ±0.5°C. Thus, thiswork will be used to figure out the envelopein estimating the statis-ticalpoweri.e.howmanypeople are neededtomake themodel clinicallysignificantandwillbeusefulinextendingitonagreater populationinordertodefineagenericbehavior.Alsothe tempera-tureprofileoftheresiduallimbisdependentontheambient tem-perature;it putsa constraintondrawing upa generalizedmodel forallambienttemperatures.Thiscouldpotentiallyberesolvedby usinginterpolation orextrapolationtechniquesin themodelata giventemperaturetopredicttheresiduallimbtemperatureprofile atanotherambienttemperatureprovidedthattheactivitystateof thesubjectisknown.

Conflictofinterest

None.

Acknowledgments

This work was supported by the Engineering and Physical Sciences Research Council under the Doctoral Training Grant EP/K503174/1 andthe Centre for Excellencein Rehabilitation Re-search(CERR). Thisinvestigationwasimplemented following eth-icalapprovalgranted bytheUniversityofStrathclydeEthics Com-mittee(RefUEC13/04).Also, supportfortheclimatechamberwas givenbyUniversityofGlasgow.

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