"Catheter Ablation Outcome Prediction in Persistent Atrial Fibrillation Using Weighted Principal Component Analysis"

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Pleasecitethisarticleinpressas:M.Meo,etal.,Catheterablationoutcomepredictioninpersistentatrialfibrillationusingweightedprincipal ContentslistsavailableatSciVerseScienceDirect

Biomedical Signal Processing and Control

j o u r n al ho m e p a g e :w w w . e l s e v i e r . c o m / l o c a t e / b s p c

Catheter ablation outcome prediction in persistent atrial fibrillation using weighted principal component analysis

Marianna Meo

^a,^∗

, Vicente Zarzoso

^a

, Olivier Meste

^a

, Decebal G. Latcu

^b

, Nadir Saoudi

^b

aLaboratoired’Informatique,SignauxetSystèmesdeSophiaAntipolis(I3S),UniversitéNiceSophiaAntipolis,CNRS,France

bServicedeCardiologie,CentreHospitalierPrincesseGrace,Monaco

a r t i c l e i n f o

Articlehistory:

Received22June2012

Receivedinrevisedform1February2013 Accepted11February2013

Available online xxx Keywords:

Atrialfibrillation(AF) Catheterablation(CA) Electrocardiogram(ECG) Spatialdiversity

Weightedprincipalcomponentanalysis (WPCA)

a b s t r a c t

Radiofrequencycatheterablation(CA)isincreasinglyemployedtotreatpersistentatrialfibrillation(AF), yetselectionofpatientswhowouldpositivelyrespondtothistherapyiscurrentlyacriticalproblem.Sev- eralparametersofthesurface12-leadelectrocardiogram(ECG)havebeenanalyzedinpreviousworksto predictAFterminationbyCA.Nevertheless,theyareaffectedbysomelimitations,suchasmanualcom- putationandtheexaminationofasingleECGleadwhileneglectingcontributionsfromotherelectrodes.

AFspatio-temporalorganizationhasbeendescribedonsurfaceECGbymeansofthenormalizedmean squareerror(NMSE)betweenconsecutiveatrialactivity(AA)signalsegmentsandtheirreduced-rank approximationsbasedonprincipalcomponentanalysis(PCA).However,thesefeaturesdonotshowto becorrelatedwithCAoutcome.Inthisstudy,suchdescriptorsareadequatelyadaptedandappliedtoCA outcomeprediction.AnNMSEindexisputforward,computedoverthesetofeightlinearlyindependent ECGleadsafterAAsignalrank-1approximationsdeterminedbyweightedprincipalcomponentanal- ysis(WPCA).Thefinalpredictorisabletodiscriminatebetweensuccessful(70.76±17.74)andfailing CAprocedures(37.54±20.01)beforeperformingtheablation(p-value=0.0013,AUC=0.91).Thepro- posedWPCA-basedtechniqueemphasizesthemostdescriptivecomponentsofAFelectrophysiology byselectivelyenhancingcontributionscomingfromthemostrepresentativeECGleads.Ourinvestiga- tionconfirmsthatECGspatialdiversityexploitationinthisWPCA-basedframeworknotonlyendowsthe NMSEindexwithclinicalvalueinthecontextofCAoutcomeprediction,butitalsoimprovesclassification accuracyandincreasesrobustnesstoECGleadselection.

1. Introduction

Atrialfibrillation(AF)isasustainedcardiacarrhythmiachar- acterizedbyrapidanddisorganizedatrialactivationsinducinga lossofatrialmechanicalefficacy.Severaltheorieshavebeensug- gestedtoexplainAFelectrophysiologicalmechanisms,soastoput forthasystematicproceduralprotocolforitstreatment.AFactiv- ityhasbeenfirstregardedastheresultofinteractions between multiplewanderingatrialwavelets[1,2].Ontheotherhand,itis commonlyacknowledgedthatpulmonaryveins(PVs)significantly contributetoAFmaintenanceandevolution,especiallyinparox- ysmalformsofthisdisease[3].Inspiteofmajoradvancesinits treatment,AFremainsasignificantcauseofcardiovascularmor- bidityandmortality,especiallythosearisingfromstrokeandheart failure.

∗Correspondingauthor.Tel.:+33492942741.

E-mailaddresses:[email protected](M.Meo),[email protected](V.Zarzoso), [email protected](O.Meste),[email protected](D.G.Latcu),[email protected] (N.Saoudi).

Radiofrequencycatheter ablation (CA)hasbecome thefirst- linestrategy [4] for thetreatment of this disease.However,as theprecisepathophysiologyof AFdynamicshasnotbeencom- pletelyclarifiedyet,itisstillquestionablewhetherCAeffectively suppressesabnormalrhythmsources,andhowitaffectsheartelec- tricalsubstrate.DifferentCAtechniqueshavebeendeveloped,yet noneofthemiswidelyconsideredaseffectiveforthetreatmentof persistentAF.Theirperformanceisstillfarfromsatisfactory,and theyarelesseffectivethanequivalentproceduresforparoxysmal AF.Sincethiscardiacinterventionalprocedureisprofoundlyinflu- enced byoperator’sexperience and patient’shealth conditions, resultsreportedbyclinicalcentersarequitedisparateandnoteas- ilycomparable[5–7].ItfollowsthatitsefficacyinterminatingAF andavoidingitsrecurrenceisnotguaranteedforallpatients.This situationexplainstheincreasingtendencytoattemptanapriori selectionofpatientswhocanundergoCAandexperiencedurable sinusrhythm(SR)restoration.Severalparametersextractedfrom thesurfaceECGhavebeenproposedaspotentialpredictorsofCA outcome[8,9].Forexample,prolongationofatrialfibrillationcycle length(AFCL)canbeassociatedwithAFterminationbyCA[10].In otherstudies[8],ithasbeenarguedthatthehighertheamplitude 1746-8094/$–seefrontmatter© 2013 Elsevier Ltd. All rights reserved.

http://dx.doi.org/10.1016/j.bspc.2013.02.002

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Pleasecitethisarticleinpressas:M.Meo,etal.,Catheterablationoutcomepredictioninpersistentatrialfibrillationusingweightedprincipal ofthefibrillatorywaves(f-waves)observedonthesurfaceECG,the

morelikelyproceduralsuccess.

Inparallel,anotherlineofresearchaimsatnoninvasivemeas- ures of AF spatio-temporal complexity, with the underlying assumptionsthattreatmentmodalitiesshouldbechosenandther- apyoutcomecouldbepredictedonthebasisofthesemeasures.In [11],anoninvasivemeasureofAForganizationisassessedbythe normalizedmeansquareerror(NMSE)valuesbetweentheatrial activity(AA)signalanditsrank-3approximationsdeterminedby principal component analysis(PCA) in lead V1 [11]. Thisargu- mentissupportedbythehypothesisofacorrelationbetweenAF organizationandthenumberandinteractionsofatrialwavefronts throughtheheartsubstrate.ThechoiceofV1 is justifiedbythe factthatitpresentsthemaximumatrial-to-ventricularamplitude ratioamongallECGleads[12].In[13],CAperformancewasshown toinfluenceAFspatio-temporalorganization,anditseffectcanbe quantifiedbyvariationsinNMSEvalues.

Nevertheless,suchparametersare affectedbyseveralshort- comings.Inthefirstplace,someclassicalECG-baseddescriptorsare manuallycomputed[8,10],sotheyaresubjecttooperators’subjec- tivityandthuspronetoerrors.Furthermore,asmostofthemare measuredinonlyoneECGlead,theydonotaccountforinforma- tionthatmaybeprovidedbyotherelectrodes.Indeed,ECGanalysis isnotalwaysstraightforward,andvisualinspectiondoesnotcap- tureAFfeaturesunderlyingthewholeensembleofleads;hence, thelimitations ofclassicalsingle-leadtechniques,whichdo not fullyexploitmultileadECGspatialdiversity.However,AFspatio- temporalcomplexity as definedin [11] hasnotbeenshown to correlatewithCAoutcome.

Ourinvestigationfocuses onthepotentialapplication ofthe spatio-temporalorganizationofAAmeasuredonthestandardECG bytheNMSEindexasatooltodiscriminatebetweensuccessfuland failingCAproceduresbeforeapplyingthetherapy.Contributions providedfromtheeightindependentECGleadsareexpressedin terms onNMSE betweensuccessivesegmentsof theactual AA signaland theirrank-1 approximations computedby weighted principalcomponentanalysis(WPCA),andtheyarefinallycom- binedin asingleparametercapableofpredictinglong-termCA outcome.Thankstothisdecomposition,thespatialvariabilityof thestandardECGistakenintoaccount,andthemostsignificant ECGleadsarealsoautomaticallyenhancedbyassigningdifferent weightstodatabasedontheirestimatedrelevance.

2. Methods

2.1. Characteristicsandacquisitionmodalitiesofthe persistent-AFdatabase

Twentypatients(19males,60±11years)withamedianper- sistentAFepisodeduration of4.5months(2–84)wereenrolled in thepresent study. Theyall underwent CAat theCardiology DepartmentofPrincessGraceHospitalinMonaco,performedwith theaidofPruckaCardiolabandBiosenseCARTOelectrophysiology measurementsystems.Theyallgavetheirinformedconsent.Sur- face12-leadECGrecordingswereacquiredatthebeginningofthe procedure,atasamplingrateof1kHz.Anexampleofthesignal recordedontheleadV1foroneofthepatientsisshowninFig.1.

CAwasaccomplishedaccordingtothesequentialstepwiseprotocol [14],whosemajoractionsconsistin1)circumferentialPVisolation, 2)fragmentedpotentials’ablation,and3)non-PVtriggers,roofline andmitralisthmuslinerightatrialablation.

ThemostrecentHRSExpertConsensusStatementguidelinesfor CAtrials[14]recommendthatimmediatelyafterCAperformance, thereisathree-month“blankingperiod”duringwhichanyfibrilla- toryepisodesarenotregardedassymptomsofAFrecurrence,butas

0 200 400 600 800 1000 1200 1400 1600 1800 2000

−0.6

−0.4

−0.2 0 0.2 0.4

Time (ms)

Voltage (mV)

f − waves

T T T

QRS QRS QRS

Fig.1.ExampleofECGrecordingduringAFanditscharacteristicwaves.Boxes highlightTQintervalswhichareconcatenatedtoformtheAAsignalYAAinEq.(1).

aphysiologicalreactionduringrecoveryfromCA.Afterthisblank- ingperiod,ifthepatientremainsfreeofarrhythmiarecurrences, proceduralAFterminationisconsideredeffectivelyaccomplished.

ProceduralsuccessisdefinedasfreedomfromECG/Holterdocu- mentedsustainedAFrecurrence(>30s)duringfollow-up,afterthe 3-monthblankingperiod.ImmediatelyafterperformingCA,AFcan beconvertedeitherdirectlytoSRortointermediatetachyarrhyth- mia,exclusivelybyablationorafter anelectricalcardioversion.

For itsclinical interest, a long-termcriterion is adopted in our investigationtodistinguishbetweensuccessfulandineffectiveCA procedures.Inourexperimentalframework,afteramedianfollow- upof9.5months,CAwassuccessfullyaccomplishedinn_S=13outof n_P=20patients(65%),whereasn_F=7procedureswerenoteffective.

Afollow-upofmmonthswasavailableatthetimeofouranaly- sis,wheremrangedbetween4and19monthsdependingonthe patient.

Some patientsreceived a pharmacological treatment subse- quent toCA procedure, mainlyamiodarone (forsome patients, solatolandflecaine).Threepatientsunderwentasecondablation.

In thiscase, only ECGsignals related tothefirstprocedureare takenintoaccountinourstudy.Asopposed topreviousstudies [8,9],terminationofAFduringCAwasnotachievedinallpatients.

Nevertheless,thisisnotdetrimentaltoouranalysis,sinceAFter- minationbyCAisnotpredictiveoflong-termoutcome[15],which istheeventwithclinicalinterest.

2.2. ECGpreprocessingandatrialactivitysegmentation

A fourth-orderzero-phase Chebyshev type IIbandpassfilter with−3dBattenuationbandbetween0.5Hzand30Hzhasbeen appliedtostandardECGrecordingsofourdatabase,whoselength isabout1min.ThispreprocessingstageallowsAFcontentenhance- ment,whosedominantfrequencytypicallyrangesbetween3and 12Hz, aswell as removal of baseline wandering and highfre- quencynoisesuchasmyoelectricartifactsand50Hzpowerline interference.Automaticdetectionof ECGfiducial pointsis then accomplished, in order to segment TQ intervals. R wave time instantsaredetectedonleadV1usingthePan–Tompkins’algorithm [16].Then,Qwaveonsetisdefined40msbeforethesubsequentR wave,thisbeingthetypicaldurationofthiswaveinthesecondi- tions(anabnormalQwavedenotespresenceofinfarct).Finally, TwaveoffsetisidentifiedwithanimprovedversionofWoody’s methodandautomaticallycomputedaftervisualinspectionand selectionoftheleadexhibitingthemostvisibleTwaves(ingeneral,V2andV3)[17].Suchintervalsarefinallymean-correctedand

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Pleasecitethisarticleinpressas:M.Meo,etal.,Catheterablationoutcomepredictioninpersistentatrialfibrillationusingweightedprincipal concatenated,soobtainingthe(L×N)datamatrixY_AArepresenting

AAcontentonly:

YAA=[y_AA(1)···y_AA(N)]∈R^L^×^N (1) wherevectory_AA(t)=[y1(t),...,y_L(t)]^TrepresentsthemultileadAA signalatthesampleindext,Lstandsforthenumberofleadsused, andNthenumberofsamplesoftheAAsignaly_!(n)foreachlead

!=1,2,...,L.

TheredundancyinECGleads[18]promptedustodiscardlead IIIandGoldberger’saugmentedleads(aVR,aVL,aVF),sinceleadsI andIIcanfullycharacterizeheartelectricalactivityonthefrontal plane.Finally,all precordial leadshavebeen introducedtoo,in order torecordthe electricpotentialchanges in theheart in a cross-sectionalplane.ThisyieldsatotalofL=8leads,thatis,I,II, V₁–V₆.

2.3. Atrialactivitycomplexity

Severalparameters describingdifferentaspectsof AFspatio- temporal organization have been proposed and analyzed in previousworks,accordingtovariousdefinitionsofthisconcept.The rationaleistoinvestigateevidencesofsomeunderlyingstructure inatrialactivityduringAF.Thewidevarietyofdifferentcriteriathat havebeenproposedintheliteraturemakesitdifficulttocompare andinterpretallsuchindices.

ThedegreeoforganizationofAFwavefrontspropagatinginside theatria hasbeentraditionallyexaminedonintracardiacrecor- dings. In [19] thelevel of spatial correlation betweenmultiple activationsequencesiscorrelatedwithAFpresence,andenables selectionofantiarrhythmicdrugtherapyforSRmaintenance.In [20],AFmorphologycharacterizationbasedonPCAandautomatic clusteringprovidesa quantitativetool for AFclassification.The studydescribedin[21]alsoproposesmoreadvancedtechniquesfor featureextractionandSVM-classificationtoperformthesametask.

Otherapproachesfocusontemporalregularityofatrialactivations andassess AFcomplexity accordingtothelevelof beat-to-beat variability[22].Morerecently,time-frequencyanalysishasbeen appliedtoendocavitarianrecordingsin[23].Despitetheireffec- tiveness,suchstrategiesareallquiteinvasiveanddonotprovidea prioripredictionsofCAoutcome.

Bycontrast,noninvasiverecordingscaneasilyprovidemeasures ofheartelectricalactivity.Somenonlinearmeasuresbasedonsam- pleentropy[24]computedonsurfaceECGhavealsobeenexploited topredictspontaneousparoxysmalAFtermination[25].In[26],it isalsostatedthatmoreorganizedAFpatternsasquantifiedbythis indexpredictAFterminationbyelectricalcardioversion.Themain drawbackoftheseindicesisthattheyarecomputedinonlyoneECG lead,thuspotentialinformationaboutAFcomplexityprovidedby theremainingleadsisnotexploited.

Recentattempts toexploitECGspatialproperties havebeen madein[27]bycombiningfrequencyandcomplexitymeasures, allowingthedistinctionbetweenpersistentandlong-standingAF.

Also,in[28]wavefrontpropagationmapsextractedonBSPMrecor- dingshavebeenusedforvisualclassificationofAFcomplexitytypes accordingtoKonings’criteria[1]onBSPMrecordings.Basedonthis approach,aquantitativemultileadanalysisiscarriedoutin[11].

Thisstudyunderlinesthat AAspatio-temporal organizationcan beeffectivelyrepresentedbythefirstfewprincipalcomponents (PCs)determinedbyPCA,retainingmostofthetotalvariance,by quantifyingthesimilaritybetweentheprincipalsubspacesofthe AAsignalalongconsecutivetimesegments.Forsakeofcomplete- ness,themathematicaldescriptionofthiscomplexitymeasureis summarizednext,asitconstitutesanimportantingredientofthe presentwork.

ThemultileadAA signalYAA issplitinto Sequal-lengthseg- ments,eachcontainingN_S=[N/S]samples,sothatY_AA=[Y⁽¹⁾,Y⁽²⁾,

..., Y^(S)], with Y^(s)=[y((s−1)NS+1), y((s−1)NS+2), ..., y(sNS)], s=1,...,S.TheAAsignalY^(r) isexaminedinacertainreference segment r=/ s and decomposedby PCAaccordingtothelinear modelY^(r)=M^(r)X^(r),r=1in[11].Subsequently,afixednumbern ofcolumnsM^(r)_n isextractedfromthemixingmatricescomputed byPCAinthisreferenceinterval.Suchcolumns,theso-calledprin- cipaldirections,weighttherelativespatialcontributionofthePCs totheECGleads.Afterthesesteps,theAAsignalisestimatedinall othersegmentss=/ rbyprojectingY^(s)onthesubspacespanned bythecolumnsofM^(r)_n ,thusyielding:

Y^(s,r)_n =M^(r)_n [M^(r)_n ^TM^(r)_n ]⁻¹M^(r)_n ^TY^(s) (2) thatis,theorthogonalprojectionofY^(s)onthespanofM^(r)_n .Hence, theapproximationqualitycanbeevaluatedbymeansofthenor- malizedmean square error NMSE^(s,r)_!,n between theinput signal y^(s)_! (t)onthe!thleadanditsprojection ˆy^(s,r)_!,n(t)foundinthe!th rowofEq.(2):

NMSE^(s,r)_!,n =

!

N

t=1[y_!^(s)(t)−yˆ^(s,r)_!,n(t)]²

!

N

t=1[y^(s)_! (t)]² (3)

with!=1,···,L.In[11],themeanNMSEiscomputedbyassuming thefirstsegmentasareference(r=1),andaveragingEq.(3)over theremainingsegments(s=2,...,S).

Nonetheless,in[11]theNMSEintroducedinEq.(3)ismerely computedonasinglelead,sospatialvariabilitytypicalofmulti- leadrecordingsisnotentirelyexploited.Inparticular,despitethe proximityofleadV1totherightatrialfreewall,thereistheriskof notconsideringfurtherusefulinformationprovidedbyotherECG leads.Inaddition,asallaforementionedparameters,thissingle- leadindexprovedunabletopredictCAoutcome[13].

In order to render a more general perspective of AF com- plexityoverallleadsand providetheNMSEindexwithfurther clinicalvaluewithrespecttoCAoutcomeprediction,severalalter- nativestrategies havebeenputforward.In[29]somestatistical descriptorscombiningNMSEcontributionsfromseveralECGleads depending onAA signal variance were ableto assess thelevel ofspatio-temporalrepetitivenessoftheAAsignalduringseveral steps ofthe ablationand predictits outcome. NMSE computa- tionwasrepeatedforeachsegment,forallpossiblecombinations between estimatedand referencesegments r, s=1, ..., S, with r=/ s.Theanalysispresentedin[30]putsforwardthecomputa- tionofreduced-rankrepresentationsofAFcomplexitymeasures bymeansofthenonnegativematrixfactorization(NMF).Despite theiradvantages, thesestrategies proveeffectiveonly inshort- termprediction,sotheyarenotabletorenderthemechanisms ofelectricalremodelingoftheheartsubstratealteredbyCAover longerfollow-upperiodsanddiscriminatebetweentheclassesof interest.Resultsfromtheseworksencouragedustodesignamore robustmethodologycapableofselectivelyemphasizingthemost relevantcontributionsfromECGobservationstoimproveclassifica- tionaccuracyintheCAoutcomepredictioncontext.Moreprecisely, weaimatcharacterizingtheNMSEindexinamultileadframework soastopredictCAoutcomebyapplyingtheweightedPCAofthe atrialsignalmatrix.

2.4. Weightedprincipalcomponentanalysis

Asmentionedintheprevioussection,apossiblestrategyaim- ingattheexploitationofthemultivariatepropertiesofthestandard ECGconsistsinsearchingforareducedsetofuncorrelatedcompo- nentsretainingasmuchofitsspatialvariabilityaspossible.Inorder toachievethisobjective,PCAhasbeenwidelyappliedtotheECG, duetoitsnon-parametricnature,simplicityofimplementationand

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Pleasecitethisarticleinpressas:M.Meo,etal.,Catheterablationoutcomepredictioninpersistentatrialfibrillationusingweightedprincipal versatility[31–34].However,PCAissometimesnotrecommended

inECGprocessing.Asitgivesthesamerelevancetoallobservations, thelow-rankrepresentationtendstobequitesensitivetooutliers andcanbecomeunstable.Thisissueaffectseverydecomposition methodbasedontheminimizationofacriterionfunctioninthe ordinaryleastsquares(OLS)sense.Toavoidtheselimitations,we putforwardamorerobustmultivariateanalysisaimingatdecom- posingthemultileadAAsignaldefinedinEq.(1)andsplitintoS segments.

Theapproachproposedistheweightedprincipalcomponentanal- ysis(WPCA),fittingthedatamodelY^(r)byminimizingaweighted leastsquares(WLS)lossfunction[35]asintheschemedescribed next.AccordingtotheWLSapproach,eachentryoftheinputmatrix Y^(r)definedinareferencesegmentrisseparatelyweightedwith afixed,nonnegativequantity.Theseleveragingfactorscanbecol- lectedina matrixW^(r) havingthesamedimensionsasY^(r).The generalformoftheWLSlossfunctioncanbewrittenas:

h(Y^(r)|Y^(r),W^(r))= %(Y^(r)−Y^(r))∗W^(r)%²F

=

"

L

!=1

"

N

m=1

[w_!,m^(r) (y^(r)_!,m−yˆ^(r)_!,m)]² (4)

where*denotestheHadamard(orelementwise)product,whereas theoperator||·||_FstandsfortheFrobeniusnorm.Inourexperi- mentalframework,theoutputmodelY^(r)=M^(r)X^(r)consistsofthe WPCAvectorscontainedintheL×nmatrixM^(r),andthen×N_S matrix X^(r) representing thePCs, stored in decreasing order of variance.AsinclassicalPCA,someorthogonalityconstraintsare imposedonM^(r)andX^(r)inordertoreducetheambiguitiesinthe model.

2.5. Assignmentoftheweightmatrix

Specialconsideration mustbepaidtotheassignmentofthe weightscollectedinmatrixW^(r).Indeed,anaccuratechoiceofthese valuescangiverisetoakindoffilteringactionwhichenhances not only theleads, but also thetime samplesgiving themost content-bearingcontributionswhilediscardingthosethatdonot yieldsignificantinformationorcanpolluteatrialobservations.In ourapplication,alltemporalsamplesonthesameleadareequally treated.Also,weaimatemphasizingleadswithmorestableand regularwaveformswhilereducingtheinfluenceofthosecharacter- izedbyhighertemporaldispersion,quantifiedintermsofenergy.

WeassumethattheinputsignalY^(r)canbemodeledas:

Y^(r)=Y^(r)_S +Y^(r)_N (5)

namely,asthesumofa meaningfulcomponentY^(r)_S (describing AFinourapplication)andanoisycomponentY^(r)_N,duenotonly todataacquisitionnoise, butalsotoelementsdiscardedbythe reduced-rankWPCA-approximation.OurhypothesisisthatY^(r)_N = (Y^(r)−Y^(r)_S )ischaracterizedbyahighdegreeofspatio-temporal variabilitywhichcanalter orhideinformativeelementscoming fromYSineachlead.Thistermcanberegardedastheargumentof theWLScriteriondefinedinEq.(4)tobeminimizedaccordingto thealgorithmdescribedinthesequel.Hence,onewayofreducing itsinfluenceontheoverallsignalisbyweighingeachleadbythe inverseofAAsignalvariance,thusgivingmoreimportancetothe leastpowerfulelectrodes.Asaresult,eachrowofW^(r)isweighted bytheinverseofthestandarddeviation"^(r)_! associatedwiththe correspondinglead!=1,...,LinY^(r)andcomputedoneachsegment r=1,...,S:

W^(r)=[("₁^(r))⁻¹("₂^(r))⁻¹...("_L^(r))⁻¹]^T1 (6)

where1isarowvectorwithTunitentries.Itiswellworthnoting thatclassicalPCAisaspecialcaseofWPCA,wheretheelementsof theweightmatrixareallequalto1.Onceaweightmatrixhasbeen chosen,WPCAcanbecarriedoutusingthealgorithmsummarized intheAppendix.Hence,thechoiceofdecomposingeachreference timeintervalinkeepingwiththeWPCAmodelY^(r)=M^(r)X^(r).Inour application,thismodeliscomputedineachreferencetimeinter- val.Insuchacontext,AAsignalestimationqualitypersegmentis quantifiedbytheNMSEdefinedinEq.(3).Differentweightmatrices W^(r)willgenerallyleadtodifferentmodelsM^(r)X^(r),thusresulting indifferentNMSEvalues.Thepredictivevalueofdifferentformsof W^(r)willbetestedinSection3.

2.6. AssessingatrialactivitycomplexityfromtheNMSEvalues AfterWPCAperformance,weinvestigatehowtoproperlycom- bine NMSE values computed on each ECG lead and condense informationinauniquepredictorofCAoutcome.Withreferenceto Section2.3,AFcomplexityevaluationineachsegmentisfollowed bythecomputationofthemeanvalue#_!,nandthestandarddevi- ation"_!,n oftheNMSEinEq. (3)overallpossiblecombinations ofestimatedandreferencesegments(s,r), foreachlead![29].

Parameter#_!,nassessesglobalsegmentestimationperformance, whereas"_!,nquantifiesAForganizationinter-segmentvariability.

Finally,contributionsfromallleadsanalyzedarecombinedintothe interleadNMSEweightedsum:

#

#n=

"

L

!=1

#_!,n

"_!,n² /

"

L

!=1

1

"_!,n² (7)

whoseweightsarerepresentedbyNMSEinversevariancevalues 1/"_!,n² perlead; contributionscomingfromECGleadsrendering more regularand less dispersive patterns are consideredtobe morerelevant.Afurtherinterpretationof"_!,ncanbegiveninterms ofuncertainty:lowvaluesofthisparameterdepictamorestable reconstructionacrosstimesegments,whereashighvaluesdenote higherprojectionerroruncertainty.Accordingly,leadsguarantee- inga morerobust AA contentcharacterization have a stronger influenceinthecomputationoftheoutputdescriptor.Thechoiceof suchweightscanbefurtherjustifiedifweconsiderthatthecom- plexityinformationisreflectedontheensembleofECGleadsas asetofindependentrandomvariables.Thebestlinearminimum- varianceunbiasedestimatorofthecomplexitydescriptorwillthus begivenbytheweightedmeanofEq.(7)[36].Asaresult,greater weightisgiventovaluescomingfromlower-variancedistributions.

Theflowchartresumingthemainprocessingstagesofourmethod isrepresentedinFig.2.

2.7. ChoiceofNMSEcharacteristicparameters

SomeconsiderationsaboutthetuningofNMSEcharacteristic parametersshouldbementioned,i.e.,thenumberSofAAsegments whichneedtobeprocessed,besidesthenumberofspatialtopogra- phiesnusedforAAsignalestimation.ConcerningthevalueofS, experimentalevidencein[29]showsthatinmostpatientsNMSE decreasesandremainsconstantafteracertainthresholdSvalue.

SincetheerrorvariationflattensfromS≈4segments,wesetthis valuepriortosignaldecomposition.Thischoiceisalsosupported inthepresentstudybytheevolutionof^#

#

^WPCA8 asafunctionof thenumberofsegmentsS,assumingthattheirsizeisfixedand equaltoN_Sandtakingintoaccountconstraintsderivedfromthe ECGrecordinglengthavailableinourdatabase.AsFig.3shows,the indexkeepsquiteaconstantvaluewhenSincreases.Inaddition, evenwhensegmentlengthN_S changes,parametervariationsare quitelimited(below10%),asshowninFig.4.Thisresultconfirms therobustnessofthepredictorputforwardtothechoiceoftuning

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Pleasecitethisarticleinpressas:M.Meo,etal.,Catheterablationoutcomepredictioninpersistentatrialfibrillationusingweightedprincipal Fig.2.FlowchartofthealgorithmyieldingtheproposedCAoutcomepredictor

#

^#^WPCA8.

Fig.3. Evolutionof

#

^#^WPCA⁸âsâ^functionôf^the^numberôf^segments^S.

parametersandsupportsourchoiceofsettingauniquevalueforS forallpatientsinordertosimplifythealgorithm.

Concerning estimation performance, as WPCA rationale assumesthatthefirstPCretainsthemostoftheAAglobalvariance, therank-1approximationofAAobservationsbyprojectingthem overthedominantPCiscomputed.Indeed,suchareconstruction allowsnotonlyunderliningthemostdescriptivecomponentsin terms of variance, but also suppressingirrelevant and/ornoisy

Table1

AssessmentofWPCAconvergencecharacteristics:averagenumberofiterationsfor convergence$=10⁻⁵.

NS s

1 2 3 4

1000 96 84 114 93

2000 92 100 92 96

3000 84 90 92 103

4000 85 98 101 112

Fig.4. Evolutionof

#

^#^WPCA⁸âsâ^functionôf^the^numberôf^samples^per^segment^N^S^.

elementsthatcandeterioratesignalcontent.Furtherexperimental resultsarepresented later inthepaper(Section3)and support thechoiceofsettingn=1,sothecorrespondingsubscriptwillbe omittedinthesequelforconvenience.Finally,asWPCAisaniter- ativealgorithm(describedintheAppendix),astoppingcriterion hasbeenintroduced,basedona convergencetolerance$=10⁻⁵ defined beforeEq. (9). In order toassess WPCA computational Table2

Assessmentof WPCAconvergence characteristics:averagefinalvalue ofWLS convergencecriterionC^*(Eq.(9)afterconvergence,with$=10⁻⁵)[n.u.].Values normalizedbyascalingfactorequalto10⁻⁶.

NS s

1 2 3 4

1000 9.0 8.8 9.1 8.9

2000 8.8 9.0 8.6 9.2

3000 8.6 9.1 9.1 8.7

4000 9.0 8.9 8.9 9.0

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Pleasecitethisarticleinpressas:M.Meo,etal.,Catheterablationoutcomepredictioninpersistentatrialfibrillationusingweightedprincipal Table3

InterpatientstatisticalanalysisandCAoutcomepredictionperformance(n.u.:normalizedunits).

SuccessfulCA FailingCA p-Value AUC Bestcut-off

#

^#^WPCA⁸^[n.u.] ^70.76^±^17.74 ^37.54^±^20.01 ^0.0013 ^0.91 ^40.64

#

^#^WPCA¹²^[n.u.] ^63.03^±^18.12 ^61.64^±^20.87 ^0.88 ^0.47 ^53.76

#

^#^PCA⁸^[n.u.] ^65.68^±^19.27 ^37.59^±^21.88 ^0.0082 ^0.84 ^45.57

#

^#^PCA¹²^[n.u.] ^65.85^±^28.41 ^44.09^±^27.49 ^0.12 ^0.76 ^45.57

NMSEWPCA8[n.u.] 54.24±25.89 50.24±23.04 0.74 0.57 45.64

NMSEWPCA₁₂[n.u.] 85.67±14.62 86.78±17.41 0.75 0.54 95.32

NMSEPCA₈[n.u.] 45.56±26.93 30.35±26.93 0.19 0.64 49.03

NMSEPCA₁₂[n.u.] 67.80±22.11 80.73±14.48 0.18 0.69 69.00

D(V1)[mV] 0.08±0.03 0.06±0.01 0.03 0.80 0.05

SampEn(Ls,rs^(A))[n.u.] 2.82±0.39 3.06±0.43 0.21 0.70 3.12

SampEn(Ls,rs^(B))[n.u.] 2.42±0.38 2.66±0.43 0.20 0.70 2.73

SampEn(Ls,rs^(C))[n.u.] 2.14±0.37 2.39±0.42 0.20 0.70 2.44

AFCLV₁[ms] 139.63±19.66 121.75±23.83 0.09 0.71 129.87

load,thenumberofiterationsforconvergenceandthefinalvalue of WLS convergence criterion C^* (introduced in Eq. (9) in the Appendix)arecomputedforafixedN_Svalue.Thesevaluesarefirst computedoneachsegments=1,...,4andthenaveragedoverthe 20-patientdatabase.TestresultsarereportedinTables1and2.

Wecanremarkthat bothparametervalues donot significantly changewhenpassingfromasegmenttothefollowingone,and thatcomputationalburdenisrelativelylowintermsofiterations.

Asimilar resultis obtainedwhen considering variationsin the numberofsamplespersegmentN_S.Thisfurtherevidencesupports therobustnessofourmethodtothechoiceoftuningparameters, asthealgorithmconvergestosatisfactoryresultsinallcases.

2.8. Statisticalanalysisandclassificationperformanceassessment As displayed in Table 3, categories under examination are referredtoas“SuccessfulCA”and“FailingCA”.Allparametersare expressedasmean±standarddeviation.First,Lilliefors’testwas runtoverifydatanormality.Differencesbetweensuccessfuland failingCAprocedureswerestatisticallydeterminedbyanunpaired Student’st-testifdataweresampledfromaGaussiandistribution, aWilcoxonranksumtestotherwise.Thep-valuesoutputbyeach unpairedtestareobtainedunderaconfidencelevel˛=0.05,and theyarereportedinTable3aswell.Binaryclassificationaccuracy ofeachfeatureisquantifiedbytheareaunderitsreceiveroperator curve(ROC),orareaundercurve(AUC),whosevalueiscorrelated withthemaximizationofsensitivityandspecificity,i.e.,thetrue positiveandtruenegativerates,respectively.

3. Results

Our8-leaddescriptor^#

#

^WPCA8iscomparedwithits12-leadcoun- terpart^#

#

^WPCA12.Moreover,thefinalweightedmeanofNMSEvalues hasalsobeencomputedforeachleadsubsetafterperforminga rank-1approximationbyclassicalPCA,thusobtaining

#

^#^PCA8 and

#

#_PCA₁₂,respectively.Acomparisonbetweenmultileaddescriptors andconventionalsingle-leadmethodsisdrawnaswell.Accord- ingly,AAamplitudeD(V1)iscomputedonleadV1accordingtothe algorithmproposedin [37,38].Moreover,atrialfibrillationcycle length (AFCL), widely known as a predictor of AFtermination byCA,isalsodeterminedonthesameelectrode. Itsmeasureis manuallydeterminedas describedin [39].Morespecifically,its valueisobtainedbyaveragingtemporaldistancebetween30con- secutivef-waves, thusgiving AFCLV₁ as output.In addition,we examinea single-lead complexity measure basedonthe NMSE valuecomputedonV₁eitherbyapplyingWPCAorclassicalPCA.

Suchdecompositionsareaccomplishedboth onthefullensem- bleofECGleadsandthereduced8-leadsubset,thusresultingin NMSEWPCA₈,NMSEWPCA₁₂,NMSEPCA₈ andNMSEPCA₁₂,respectively,

asoutputs.Aparallelwithanon-linearcomplexitydescriptor,the sampleentropy SampEn [24,26,40],hasbeendrawnas wellon V1.Twoparametershavetobetunedpriortoitscomputation:Ls

andr_s.ParameterL_sisdefinedasthelengthofthesequencesthe ECGrecordingissplitinto.Suchsegmentsarethencompared,and thetoleranceforacceptingmatchesisassessedbythethreshold r_s.Thisparameterischosenasa fractionoftheAAinputsignal standarddeviationonV1,denoted"_V₁,soastoassurethetransla- tionandscaleinvarianceofSampEn.Parametervalueshavebeen tunedaccordingtotheguidelinesgivenin[24],sowesetLs=2 besidesthreevaluesofr_s,namely,r_s^(A)=0.1"V₁,r_s^(B)=0.15"V₁and r_s^(C)=0.2"V₁.

Thegeneralization powerof ouranalysis toanindependent datasetisvalidatedbymeansofaleave-one-outcross-validation technique.More precisely, AUCvalues have beencomputed on everypossiblesubsetof19patients,andthenaveragedoverthe 20subsets.AUCvaluesdescribingtheclassificationpowerofeach descriptorareshowninTable3,besidesthecorrespondingoptimal cut-offpoints,providingboththehighestsensitivityandthehigh- estspecificityonthewhole20-patientdatabase.Fig.5plotsthe

2 3 4 5 6 7 8

0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

L

AUC

PCAWPCA

Fig.5.AUCvaluescharacterizing

#

^#^WPCALpredictionperformanceasafunctionof thesizeLofthesubsetofthe8independentECGleads(S=4,n=1).WPCA:rank-1 decompositionoftheatrialsignalintheECGleadsubsetsaccordingtotheWPCA approach;PCA:rank-1decompositionoftheatrialsignalintheECGleadsubsets accordingtothePCAapproach.

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Pleasecitethisarticleinpressas:M.Meo,etal.,Catheterablationoutcomepredictioninpersistentatrialfibrillationusingweightedprincipal Table4

ECGleadsubsetswithoptimalpredictionperformanceof

#

^#^WPCA⁸^.

Numberofleads(L) Leads

2 I,V1

3 I,II,V2

4 I,V2,V3,V5

5 [I,II,V2,V4,V5]

[I,II,V1,V3,V6]

6 I,II,V2,V3,V4,V6

7 I,II,V1,V2,V3,V4,V5

AUCvaluesdescribingtheclassificationperformanceof^#

#

^WPCALas afunctionofthenumberLofleadsretainedintheanalysis.For eachvalueofLrangingfrom2upto8,

#

^#PCALvaluehasbeencom- putedforall8!/((8−L)!L!)possibleensemblesofleads.Foreach leadcombination,CAoutcomepredictionperformancehasbeen assessedfromthecorrespondingvaluesof^#

#

WPCAL,andvalidated bytheleave-one-outtechnique.ForeachsizeL,theminimum,max- imumandmeanAUCvaluesoverallL-leadsubsetswereobtained asafunctionofthesubsetdimensionL,andtheirrelatedranges ofvaluesaredisplayedinFig.5.Theleadcombinationswiththe bestpredictionperformanceforeachsubsetdimensionareshown inTable4.TheapplicationofPCAonasinglelead(L=1)hasbeen excludedfromthistest,sinceinthiscasethemethodisequivalent tosingle-leadanalysis.

In ourapplication,wedeal withmultivariatedecomposition techniquesbasedonthemaximizationofthevarianceoftheAA signal,conveyinginformationaboutAFspatio-temporaldistribu- tion.Hence,anothercrucialpointofourinvestigationistheeffect ofsuchtechniquesonAAsignalenergycontent.Morespecifically, theinputAAsignalvariancehasbeendeterminedoneachECGlead, yieldingtheatrialpowerdistributionrepresentedbythevector

!²_AA=["_AA²₁,"_AA²₂,...,"_AA²_L]^T,withL=8.Effectsofthemultilead weightingschemeonthedecompositionsoftheobservedAAsig- nalare alsocompared to those obtainedby standard PCA.The rank-1approximationsYcomputedbyWPCAandPCAyieldatrial powerdistributionvectors!²_WPCAand !²_PCA,respectively.These

I II V1 V2 V3 V4 V5 V6

0 0.5 1 1.5 2 2.5 x 10⁻³

Lead Signalvarianceσ2(mV2)

σ²_AA σ²_PCA σ²_WPCA

Fig.6.EffectsofthemultileadweightingschemeonAAreconstruction.!²_AA:vari- anceoftheinputAAsignalperlead;!²_PCA:varianceperleadoftherank-1AAsignal approximationbyPCA;!²_WPCA:varianceperleadoftherank-1AAsignalapproxi- mationbyWPCA.

I II V1 V2 V3 V4 V5 V6

0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Lead

AUC

σ_AA² σ_PCA² σ_WPCA²

Fig.7.AssessmentofCAoutcomepredictionperformanceofsingle-leadenergy descriptors.!²_AA:energyoftheinputAAsignalperlead;!²_PCA:energyperleadofthe rank-1AAsignalapproximationbyPCA;!²_WPCA:energyperleadoftherank-1AA signalapproximationbyWPCA.

parameters have beencomputed over thewhole persistent AF databaseandaveragedoverallpatients;theirspatialdistribution is plotted in Fig.6. Thisfigureevaluates theenergy contentof data reconstructions computedby each decomposition, as well astheircapability ofeffectively approximatingtheoriginalsig- nal.Followingthisline,thisevaluationhasbeenaccomplishedin theframeworkofCAoutcomepredictionaswell.Inparticular,we testedwhetherAAsignalenergy"_AA² associatedwitheachleadcan effectivelyperformasapredictoroftheablationresult;hence,the quantificationoftheirclassificationaccuracyoneachECGleadby meansoftheAUCcriterion,whosevaluesaredisplayedinFig.7.

Thesameanalysisis ledontheenergyvaluescomputedonthe rank-1approximationsoutputbyPCAandWPCA,"_PCA² and"_WPCA² , respectively,alsoplottedinFig.7.Finally,furthertestsconfirmthe validityofthemodelintroducedinEq.(5)byassessingCAoutcome predictionperformanceonthebasisofdifferentdefinitionsofthe weightmatrixW^(r)aswillbediscussedinSection4.5.

4. Discussion

This work investigates noninvasive measures of AA spatio- temporal variabilityand theirlinktoCAoutcome predictionin persistent AF. The main resultscan be summarized as follows.

Firstly,spatialvariabilityofthestandardECGprovestobeause- fultooltodescribeAFcontentandofferawiderperspectiveabout theevolutionofthediseaseduringCA,thushelpingitsoutcome prediction.Inthesecondplace,anindexconventionallyemployed asaclassifierofAForganizationtypeishereincharacterizedsoas toassessCAeffect.InformationaboutAAsignalcomingfrommul- tipleECGleadsisexploitedbyapplyingWPCA,whichefficiently compressesAFcontentinaunique,significantPC,thereby min- imizingtheimpactofpollutingsignalcomponents.Theweights usedinWPCAseemtoautomaticallyenhancetheroleofthemost descriptiveECGleads,unlikePCA,whichequallyweightsallECG leads.Thisfilteringactionisalsoperformedbyselectingthe8-lead ensembleintroducedinSection2.2,sosuppressinglineardepend- enciesbetweencertainleadsduetotheirspatiallocation.These aspectsarediscussedinmoredetailinthesequel.

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Pleasecitethisarticleinpressas:M.Meo,etal.,Catheterablationoutcomepredictioninpersistentatrialfibrillationusingweightedprincipal 4.1. CAoutcomepredictionintheWPCAmultileadframework

Our experimental results point out the advantages of the multileadstrategywhichconsiderablyoutperformsconventional predictorscomputedinonlyoneECGlead.Concerningsingle-lead AFcomplexitymeasuresdeterminedbyPCAondifferentsetsofECG leads,i.e.,NMSEPCA₈ andNMSEPCA₁₂,notonlystatisticallysignifi- cantinterpatientdifferencescannotbeobserved,butAUCvalues relatedtotheirdiscriminationcapabilityarealsoextremelylow.

Similarconclusionscanbedrawnwhenexaminingtheequivalent parametersobtainedinV₁whenapproximatingdatabymeansof WPCA(NMSE_WPCA₈,NMSE_WPCA₁₂).Theseresultscouldbeexplained bythelimitedoutlookofsingle-leadcomplexitymeasures,which ignoreinterleadrelationships. Relevantinformation fromother electrodesisneglected,thusreducingdiscriminationcapabilities.

Furthermore,asleadV1isclosetotherightatrialfreewall,there istheriskofneglectingusefulinformationaboutotherimportant anatomicalareas,suchastheleftatrium(LA)andthePVs,which playacrucialroleinAFinitiationandmaintenance[41].In[42], itisshownthatV1istheleadthatbestexplainsleftatrialactiv- ityintwosubjectsaffectedbyatrialtachycardiaconfinedtothe LA.However,AFmechanismsaregenerallymorecomplex,andour resultsinSection4.5indicateinanycasethat,concerningCAout- comeprediction,leadV₁ doesnotdepictimportantinformation aboutablationeffectsthatcouldbepresentinotherleads.Also,con- cerningnonlinearAFcomplexityindicessuchassampleentropy, nostatisticallysignificantinterclassdifferencescanberemarked, regardlessofthevalues of tuningparameters.Notonly sample entropyindexisaffectedbythesameshortcomingstypicalofthe othersingle-leadfeatures,butitisalsonecessarytosetvaluesof itstuningparameterspriortoitscomputation.

By contrast,by meansof WPCA, ECG spatialdiversity high- lightsstatisticallysignificantdifferencesbetweenthecategories examined. As displayed in Table 3, higher values of the mul- tilead descriptor ^#

#

^WPCA8 are significantly correlated with CA success.AsitsmathematicaldefinitioninEq.(7)shows,theNMSE inter-segmentvarianceprovidesa quantitativecriterion forthe assessmentofthespatio-temporalvariabilityoftheAAsignal:leads exhibitingmorestableandrepetitivepatternsgiveamorerelevant contributiontotheweightedmean^#

#

^WPCA8,sotheyhavestronger influence.Theinter-segmentvariance actsasa leadselector: it enhancesECGelectrodeswherenotonlythesignalshowsthemost stablewaveform,butitisalsolikelytoyieldamoreaccuratesignal estimation,withalowerdegreeofuncertainty.

4.2. AcomparisonwithstandardclinicalpredictorsofCAoutcome Inthefirstplace,selectionofpatientstobetreatedbyCAis guidedbyconsiderationsaboutsomeclinicaldata,suchasLAdiam- eterandAFduration.Indeed,itiswidelyknownthatwhentheLA ismarkedlydilatedCAislesslikelytobeeffective,asalargerLAis linkedtoamoreadvanceddegreeofthepathology.Similarremarks canbemadeaboutAFduration,correlatedwithitschronification level[14].In[43]itisdemonstratedthatCAoutcomepredictionin paroxysmalAFisnotablyimprovedbytheknowledgeaboutsome features,primarilythepresenceofnon-PVdriversanddominant frequenciesbothinrightandleftatrium.Nevertheless,themost oftheseparametersareinvasivelyacquiredandknownonlyatthe momentoftheprocedure.Thismotivatestheinterestinpredic- tivefeaturesthatcanbeextractedwithoutrisktothepatientina cost-efficientmanner,asthosederivedfromtheECG.

AnalysisoftheAAamplitudeasrenderedbyD(V1)arousesdif- ferentremarks.Actually,wecannoticethesatisfactoryabilityto distinguishbetweensuccessful and failingablations, as wellas theeffective reproduction ofresults manuallyreported in pre- viousworksusingadifferentpersistentAFdatabase[8].Such a

descriptorcaneffectivelycaptureAAsignalamplitudecharacter- isticsifthepatternissufficientlyregularand f-wavesareeasily detectable,althoughinterpolationoperationscanbehamperedby residualspuriouspeaksortooirregularpatterns.Whatismore,no informationaboutAFspatio-temporal repetitivenessisprovided bythisfeature.

The study presented in [39] assesses the predictive role of AFCL measured on surface ECG for CA of persistent AF.

However, as its value is manually acquired, there is a lack of reproducibility and prediction reliability. Moreover, experimental results show that such parameter, defined as AFCL_V₁, does not underline statistically significant differences between the categories under examination using lead V1. Further- more, as it is usually determined in only one electrode, it is affected by the shortcomings typical of single-lead predic- tors.Inaddition,correlationbetweenECG-basedparametersand intracardial measures hasnot beenconfirmed in somestudies [44].

4.3. WeightedandstandardPCA:acomparison

EventhoughstandardPCAiscapableofdiscriminatingbetween successfulandfailingCAproceduresaswell,resultsconcerning

#

#_WPCA₈showthatclassificationqualitycanbefurtherimprovedby ouraprioriknowledgeaboutatrialobservationsintheformofthe weightsusedinWPCA.Onfurtheranalysis,AAstandarddeviation measuredoneachECGelectrodeprovestobeareliableindex,since itdoesnotonlyweightAFtemporaldispersion,butitisalsoasta- tisticalmeasureofuncertainty.Indeed,ifAApatternsoncertain leadsare excessivelyirregular and/orvariable, thecorrespond- inginversestandarddeviationvaluesautomaticallyreducetheir influence.Thisselectiveaction seemstoboostthecompression powerofthedecomposition.Morespecifically,theeffectofpossi- bleredundanciesisalreadyreducedbeforecomputingtheiterative minimizationalgorithm byselectingthe8 linearlyindependent ECGleads,sothatthemostdiscriminantAAcomponentsareput intoevidencemoreeasily.InFig.5theAUCcriterionquantifiesthe classificationperformanceof^#

#

^WPCALand^#

#

^PCALasafunctionofthe numberofECGleadsexploitedforthepredictionselectedamong the8independentleads.ClassificationresultsobtainedusingWPCA outperformthosebyPCA,especiallyassizeLincreases.Thisfigure alsoconfirmsthebenefitsderivedfromthespatialvariabilityof thestandardECG.Thehigherthenumberofleadsemployed,the moreaccurateCAresultprediction,assessedbyhighermeanAUC values.

Furtheradvantagesderivedfromtheweightingframeworkare displayedin Fig.6.First of all,it canbenoticedthat thetrend of!²_WPCAvaluesisverysimilartothatof!²_AA.Inaddition,!²_WPCA values are closerto!²_AA thanthose obtainedwhen performing classicalPCA(!²_PCA),therebyquantifyingalowererrorofrecon- struction of theoriginal data. Energy values obtained after AA signalapproximation,eitherbyPCAorWPCA,arelowerthanthose computeddirectlyoninputdatabecauseofthelow-rankrepre- sentationeffect.ItcanbeinferredthatWPCAcanbetterpreserve energycontentoftheAAsignalandcondenseitmoreefficiently inasingle,maximum-variancePCthanconventionalPCA.Differ- encesbetweenthesedecompositionsintermsoftheamountof informationretainedbytherank-1approximationareparticularly evidentinV₁andV₂,whichrepresentthereferenceleadsforAF analysisinmedicalpractice,owingtotheirproximitytotheright atrium.NotehowWPCAsignificantlyenhances,inanautomated fashion,therelevanceoftheseleadsintheAAsignaldecomposi- tion.Theuseoftheseenergy-descriptorsinsingle-leadprediction doesnotprovidesatisfactoryresults,asshowninFig.7.Indeed, theirpredictionperformanceispoor,andalsohighlydependenton

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Pleasecitethisarticleinpressas:M.Meo,etal.,Catheterablationoutcomepredictioninpersistentatrialfibrillationusingweightedprincipal theleadconsidered.Ingeneral,theseresultsconfirmtheneedfor

anadequatecombinationofatrialsignalcontributionsfromdiffer- entECGleadsinamorerobustmultileadframework,capableof filteringoutuninformativeAAsignalfeaturesandexploitingECG spatialvariability.However,theimportanceoftheircontribution issignificantlyreducedwhenapplyingPCA,thuslosingrelevant informationaboutAFenergycontentintheassociatedheartsites.

Conversely,theWPCAschemecaneffectivelyimproveCAoutcome predictionbyreinforcingthemostdiscriminativefeaturesofinput datathankstothepriorknowledgeaboutAAsignalenergydistri- bution.

4.4. Alternativedefinitionsoftheweightmatrix

The choiceof the inverse standard deviation values as W^(r) weightsconfirmsourhypothesisaboutAA signalrepresentation illustratedinSection2.5.Conversely,otherweightingschemesare notabletogivecomparableclassificationresults.Forexample,the weightmatrixdependingonAAstandarddeviationvaluesperlead W^(r)=["₁^(r),"₂^(r),...,"_L^(r)]^T1doesnotmanagetoproperlyempha- sizeECGleadcontributions,thusshowingaweakpredictivepower (AUC=0.53,p-value=0.98).Theseresultsseemtocorroborateour AFmodel,as AAmaximum-power componentsseemunableto selectivelyenhancethemostinformativecontributionsbymeans oftheweightingstructure.

Infurtherexperiments,alternativeweightmatricesW^(r) have alsobeen tested. For instance,one of the attempted strategies consists in giving more weight to leads better explained by a reduced-rankPCAapproximation,thusdefiningW^(r) elementsas afunctionoftheinversevalueofstandarddeviationoftheerror between original data and rank-1 PCA approximation per lead (W^(r)=[("1(r)

N)⁻¹,("2(r)

N)⁻¹,...,("L(r)

N)⁻¹]^T1).However,nosignif- icant differences between effective and failing CA procedures havebeenfoundinthiscase(AUC=0.67,p-value=0.69).Inother tests,wehypothesizethatW^(r) componentsdependonthevalue ofthestandarddeviationitself(W^(r)=["1(r)

N,"2(r)

N,...,"L(r) N]^T1), although similar poor results are obtained (AUC=0.63, p- value=0.37). This leads us to conclude that focusing onnoisy componentsthatmaybepresentintheAAsignaldoesnotactu- allyimprovetheselectiveactionoftheweightingscheme,whereas consideringvarianceofthewholesignalgivesmoreemphasistoits mostinformativecomponents,thusimprovingpredictionaccuracy.

4.5. ECG-leadselection

Classificationperformanceof multileadCApredictors proves tobemoreaccuratewhenreduced-rankapproximationsarecom- putedonthesubsetof8independentleadsratherthanthewhole standard ECG.Thisresult is inlinewithrecent previousworks [38]. In clinical centers,all leadsof the standard ECG are ana- lyzedsothatprojectionsoftheresultantvectorsin2orthogonal planesatdifferentanglescanbecompared,soimprovingpattern recognition[18].However,WPCAcomputationoverthesubsetof 8independentleadsdefinedaboveseemstoincreasetheefficacy ofitsfilteringaction,aspartofredundantinformationisalready suppressedbeforethedecomposition,andthemodelcapturesthe naturalvariationunderlyingthedatamoreeasily.Theseconsid- erationsjustifythefactthatdescriptorsextractedfromthewhole ECG,namely,^#

#

^WPCA12and^#

#

^PCA12,areoutperformedbytheir8-lead counterparts.

Table4displaysthegroupsofleadswhichbesthelpdiscrim- inatingbetweensuccessfuland failingprocedures,and givethe mostrelevantcontributiontothecomputation oftheweighted mean

#

^#^WPCA8 in the prediction scenario. Some considerations can be made about the role of certain leads in CA outcome

1 2 3 4 5 6 7 8

0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

n

AUC

Fig.8. AUCvaluesdescribing

#

^#^WPCA8predictionperformanceasafunctionofthe ranknoftheWPCAdecomposition.

prediction. In particular, we can remarkthat leadV1 doesnot providethemaincontributiontoCAoutcomeprediction.Infact, otherleads,suchasI,II,V2,recurmorefrequently.Thisevidence isincontrastwithstandardmedicalpractice,anditcanbeprob- ably explained by theplacement of lead V1, not close enough tocriticalsitesresponsibleforAFgenesisandmaintenancesuch asthePVsandtheLA,commonlyacknowledgedaspotentialAF sources.Thisseemstobeconfirmedbytherecurrenceofatleast one lead closeto theleft side of theheart in each L-size sub- set,forinstance,V5 andV6.Wecanconcludethatthepresence ofleadsrepresentingheartelectricalactivityonmultipleplanes supportsthehypothesisthatclinicalinformationcomingfrommul- tipleelectrodelocationscanimproveablationoutcomeprediction ascomparedtoclassicalsingle-leadapproaches,asdiscussedin Section4.1.

4.6. Benefitsofreduced-rankWPCAapproximationstotheAA signal

Fig.8illustratestheadvantagesprovidedbydatacompression carried out by WPCA,and seemsto justify thechoiceof rank- 1approximations(n=1)madeinSection2.7.Indeed,AUCvalues relatedtoourmultileadpredictor^#

#

^WPCA8havebeencomputedby varyingthenumberofPCsnretainedintheWPCAtruncationin Eq.(2),whichrangesfrom1(thevaluesetforouralgorithm)to8 (full-rankdecomposition).ThequalityofCAoutcomeprediction considerablyworsenswhen increasingthetruncationrank,and

#

#WPCA₈ exhibitsweakdiscriminatingcapabilitieswhenassuming morethan4PCs.ThefewerPCsemployedinthedecomposition,the bettertheclassificationperformance,asifthedominantPCspre- servedthediscriminativepowerofthecomplexityindex.Indeed, noisyand/orredundantelementsaretypicallyascribedtothevery lastPCs,whilepreservingthemostrepresentativefeaturesofthe AAsignalinthedominantones.Asimilarbenefitofrankreduction wasobtainedin[38]inthecontextofshort-termCAoutcomepre- dictionbasedonamplitudeparameterscomputedfromlow-rank PCAapproximation.

4.7. LinkswithAFspatio-temporalcomplexity

Asourresearchdemonstrates, CAoutcome predictionbased onWCPAof multileadECGsignalsproves tobeeffective.How- ever,theproperlinkbetweentheNMSE-basedpredictorproposed andAFspatio-temporalcomplexitycannotbeestablishedinthe presentworkforlackofsimultaneousinvasiverecordings.Such a connectioncanonly besuggestedbytheresultspresentedin [11],whichshowedthecorrelationbetweentheNMSEmeasure in V1 and AF organization. Accordingly, the potential relation