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ComplexityAnalysisofsleepEEGsignalLiLingWangRuipingdept.ofbiomedicalengineeringBeijingJiaotongUniversityBeijing,china100044rpwangbjtu.edu.cnAbstractThecomplexityoftheEEGtimeseriesduringsleepingisinvestigated.TherelationshipsbetweenthesesleepstatesandthecomplexitiesoftheEEGareassessed.Lempel–ZivcomplexityisusedasanovelindexforquantifyingthecomplexityoftheEEGtimeseriesduringdifferentsleepstates.ExperimentalresultsshowthattheLempel–ZivLZcomplexityoftheEEGtimeseriesduringactiveREM,rapideyemovementsleeptendstobehigherthanduringquietNREM,nonrapideyemovementsleep,andthecomplexityduringwakeishigherthanduringsleep.TheLempel–Zivcomplexitycaneffectivelydistinguishthesleepstatesofthebrain.KeywordssleepEEGsleepstatesLempel–ZivcomplexityLZI.INTRODUCTIONTheelectroencephalogramEEGsignalsreflecttheelectricalactivityofthebrain.Sleepstudieshavegrowntoencompassabroadrangeoftechnologiesemployedtostudyanddiagnoseavarietyofsleepdisorders.Thestudyofthebrainelectricalactivity,throughtheelectroencephalographicrecords,isoneofthemostimportanttoolsforthestudyofsleep.Duringsleep,advancedcentralandaseriesofplantsystemchange.In1968,theinstituteofthehumanbrainintheUniversityofCaliforniareleasedthedefinitionofsleepandtechnicalstandards.AccordingtothedifferentformsandfeaturesofEEG,EMGandEOG,sleepisdividedintowakeperiodW,rapideyemovementREM,nonrapideyemovementNREM,includingS1,S2,S3andS4period6.FollowingthenonlinearcharacteristicofsleepEEG,researchershavewitnessedagrowinguseofvariousnonlinearapproachesinfeatureextractionofEEGsignalsintherecentyears,suchasLyapunovexponents,complexity,spectrumentropyetc.Allthesemethodshavetheirrespectivemeritsanddemerits.TheEEGdataofdifferentsleepingstagesareusedtocalculatethecorrespondingcharacteristicparameters.Inthestudy,thesectionⅡgivesthebriefintroductionsofcomplexity,thedataweuseandhowtoanalyzethedata.ThesectionⅢgivesthecalculatedresultsanddiscussions.Finally,thesectionⅣpresentssomeremarksbasedonthestudy1.II.METHODA..ComplexityLempleandZivdefinedthatalimitedlongseriesofcomplexityshouldbethespeedofnewpatternalongwiththesequenceslengthincreased2.Inrecentyears,LZcomplexityhasbeenappliedextensivelyinbiomedicalsignalsanalysisasametrictoestimatethecomplexityofdiscretetimephysiologicsignals10.LZcomplexityhasalsobeenusedtostudybrainfunction,braininformationtransmission,EEGcomplexityinpatientswithdiseases,andsleepEEGsignals.ThecomplexityofEEGsequenceperformsrandomdegreeoftheEEGsequenceandreflectsthesizeoftheinformation2.LZcomplexityanalysisisbasedonacoarsegrainingofthemeasurements.Inthecontextofbiomedicalsignalanalysis,typicallythediscretetimebiomedicalsignalisconvertedintoabinarysequence.Incomparisionwiththethreshold,thesignaldataareconvertedintoa01sequencePasfollows1,2,...,,1,SsssrQsr1Where0,1,dxiTsiotherwise⎧⎪⎨⎪⎩2Usuallythemedianisusedasthethresholdbecauseofitsrobustnesstooutliers.Previousstudieshaveshownthat01conversionisadequatetoestimatetheLZcomplexityinbiomedicalsignals.InordertocomputeLZcomplexity,thesequencePisscannedformlefttorightandthecomplexitycounterisincreasedbyoneuniteverytimeanewsubsequenceofconsecutivecharactersisencountered.Thecomplexitymeasurecanbeestimatedusingthefollowingalgorithm.1LetSandQdenotetwosubsequencesofPandSQbetheconcatenationofSandQ,whilesequenceSQvisderivedfromSQafteritslastcharacterisdeletedvdenotesthe9781424447138/10/25.00©2010Crownoperationofdeletingthelastcharacterinthesequence.Let2sdenotethevocabularyofalldifferentsubsequencesofSQv.Atthebeginning,cn1,S1s,Q2s,therefore,SQv1s.2Ingeneral,1,2,...,,1,SsssrQsrthen1,2,...,SQvsssrifQbelongstovSQv,thenQisasequenceofSQv,notanewsequence.3RenewQtobe1sr,2srandjudgeifQbelongstovSQvornot.4RepeatthepreviousstepsuntilQdoesnotbelongtovSQv.Now1,2,...,QsrsrsriisnotasubsequenceofSQv1,2,...,1sssri−,soincreasecnbyone.5Thereafter,Sisrenewedtobe1,2,...,Ssssri,and1Qsri.TheaboveprocedureisrepeateduntilQisthelastcharacter.AtthistimethenumberofdifferentsubsequencesinPthemeasureofcomplexityiscn.Inordertoobtainacomplexitymeasurewhichisindependentofthesequencelength,cnmustbenormalized.Ifthelengthofthesequenceisnandthenumberofdifferentsymbolsinthesymbolsetisα,ithasbeenprovedthattheupperboundofcnisgivenby1lognancnnε−(3)Wherenεisasmallquantityand0nnε→→∞.Ingeneral,lognnαistheupperboundofcn,wherethebaseofthelogarithmisα,i.e.,limlognncnbnnα→∞(4)Fora01sequence,α2,therefore2lognbnn(5)Andcncanbenormalizedviabn.cnCnbn(6)WhereCn,thenormalizedLZcomplexity,reflectsthearisingrateofnewpatternsinthesequence17810.ComplexitiesofEEGaredifferentcorrespondingtothedifferentsleepstages.Accordingtotheexperienceandanalysis,thecomplexityofEEGsequenceshowstheorderlydegreeofthebrainneuronsprocessinginformationactivities.B.ExperimentDataInthisstudy,theEEGdataisfromMIT/BIHPolysomnographicdatabase.Thisdatabaseisacollectionofrecordingsofmultiplephysiologicsignalsduringsleep.SubjectsweremonitoredinBostonsBethIsraelHospitallaboratory.Therecorddataevery30sisfollowedbyaannotationandthisannotaitoncontainssleepstages,heartconditionsandbreathing.Inthisstudy,wechooseslp01a,slp01b,slp02a,slp02b,slp03,slp04,slp14,slp48toanalyze.TheEEGchannelsareC4A1、C4A1、O2A1、O2A1、C3O1、C3O1、C3O1、C3O1.Thesedatalengthare2h,3h,3h,214h,6h,6h,6h,1016handthesamplingfrequencyis250HZ,markingthecorrespondingsleepingstagesevery30s.C.DATAAnalysisandResultsThestudygot2500pointsfromdifferentsleepingstages10sabouteveryobject,analyzedthesedataandcalculatedthecomplexities.OurprogramisinMATLABandtheresultsobtainedareshowedinTABLE1andFigure.1..TABLE1.ThecomplexityofeachsleepingstageaverageSubjectWakeperiodNREMperiodREMperiodⅠperiodⅡperiodⅢperiodⅣperiodSlp01a0.50120.46120.36510.22580.3206Slp01b0.79460.34540.31830.3564Slp02a0.62760.32460.27540.21670.20320.2122Slp02b0.77930.75630.26640.5508Slp030.39280.36800.26640.20990.2799Slp040.66210.58240.58020.27310.6073Slp140.41090.27990.24380.20320.5057Slp480.78560.51470.50570.18960.3251average0.61930.45300.36470.24290.21450.3947Figure.1.Theanalysisofthecomplexityofeachsleepingstage.Fromthetable1,thereistheconclusionfromWakeperiodtoⅢ、ⅣperiodinNREMperiod,thecomplexitiesareallbythemaximumreducinggradually,then,backtoclosetoⅠperiodandⅡperiodwhenREMperiod.TheFig.1alsocanprovetheconclusion.Wefoundweaknonlinearsignaturesinallsleepstagesinthisstudy.Theresultsshowthatduringsleeptherearevarioustransitionsandthedegreeofchaoticityisdependentonthestageofsleep.ThecomplexityofEEGsequenceshowstheorderlydegreeofthebrainneuronsprocessinginformationactivities.Asaresult,fromshallowtodeepsleep,theoutcomemeansthediminutionoffreedomofbrainactivity.InthecaseofsleepEEGthesleepstagesareconsideredasdistinctpsychophysiologicalstates789.Ⅲ.CONCLUDINGREMARKSInthispaper,thisstudycalculatedcomplexityofsleepingEEGsignalsofeighthealthyadults.Theresultsshowthatthenonlinearfeaturecanreflectsleepingstageadequately.Themethodisusefulinautomaticrecognitionofsleepstages.Butithassomelimitations.Complexityisalsosimplebutlosesinformationdetailsinitspreprocessingoforiginalmeasurementdata1.Duetothecoarseningpretreatmentalgorithmofcomplexityandanalysistimesequencefromonedimensionalangle,thealgorithmofcomplexityiseasytoloseinformation.Theeffectsoftheotherfactorssuchasageandgenderontheperformanceofthenonlinearfeatureextractionmethodarestillunderactivetudy2.Inspiteofthesedifficultiesandshortcoming,complexityisusefulfortheanalysisofsleepEEG.REFERENCES1WeiXingHe,XiangGuoYan,XiaoPingChen,andHuiLiu,NonlinearFeatureExtractionofSleepingEEGSignals,Proceedingsofthe2005IEEE,EngineeringinMedicineandBiology27thAnnualConference.Shanghai,China,September14,2005.2DongGuoYa,WuXiYao,ThecomparisonBetweenApproximateEntropyandComplexityintheStudyofSleepEEG,BeijingUniversityofScienceandTechnolongy.3LuWeimin,LiuFubin,AnalysisoftheNonlinearDynamicsforSleepEEG,ChinaMedicalEquipment,2008,521620.4FuXiaohua,LiHongpei,SleepandHealth,ChinaMedicalJournals,2003,388.5DingBaoxi,ChenZhihua,ZhaoLi,CorrelationAnalysisofEEGData,ProgressinModernBiomedicine,2008,81.6LIUHui,HEWeixing,CHENXiaoping,EEGtimeseriesanalysisusingnonlineardynamicsmethodforsleepmonitoring,JournalofJiangsuUniversityNaturalScienceEdition,Vol.26No.2Mar.2005.7Y.Shen,E.Olbrich,P.A.chermann,P.F.Meier,DimensioncomplexityandspectralpropertiesofthehumansleepEEG,ClinicalNeurophysiology1142003199209.8S.Janjarasjitt,M.S.Scher,K.A.Loparo,NonlineardynamicalanalysisoftheneonatalEEGtimeseriesTherelationshipbetweensleepstateandcomplexity,ClinicalNeurophysiology119200818121823.9ErnestoPereda,DulceMdeLaCruz,SoledadManas,JoseM.Garrido,SantiagoLopzez,JulianJ.Gonzalez,TopographyofEEGcomplexityinhumanneonatesEffectofpostmenstrualageandthesleepstate,NeuroscienceLetters3942006152157.10MateoAboy,Member,IEEE,RobertoHornero,Member,IEEE,DanielAbasolo,Member,IEEE,andDanielAlvarez,InterpretationoftheLemplZivComplexityMeasureintheContextofBiomedicalSignalAnalysis,IEEETRANSACTIONSONBIOMEDICALENGINEERING,VOL.53,VOL.53,NO.11,NOVEMBER2006.
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