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1、DecompositionofHeartbeatTimeSeries:ScalingAnalysisoftheSignSequenceYAshkenazy1,PChIvanov1,2,SHavlin3,C-KPeng2,YYamamoto4,ALGoldberger2,HEStanley11CenterforPolymerStudiesandDepartmentofPhysics,BostonUniversity,Boston,Massachusetts02215,USA2HarvardMedic
2、alSchool,BethIsraelDeaconessMedicalCenter,Boston,Massachusetts02215,USA3Dept.ofPhysicsandGondaGoldschmiedCenter,Bar-IlanUniversity,Ramat-Gan,Israel4TokyoUniversity,GraduateSchoolofEducation,EducationPhysiol.Lab.,BunkyoKu,7-3-1Hongo,Tokyo1130033,JapanA
3、bstract0.7(a)0.6Thecardiacinterbeat(RR)incrementtimeseriescanbe0.5RR[s]decomposedintotwosub-sequences:amagnitudeseries0.1andasignseries.Weshowthatthesignsequence,asimple(b)binaryrepresentationoftheoriginalRRseries,retainsRR0∆fundamentalscalingproperti
4、esoftheoriginalseries,isrobustwithrespecttooutliers,andmayprovideuseful0.1(c)informationaboutneuroautonomiccontrolmechanisms.RR
5、
6、∆01.Introduction1(d)RR)∆0Manybiologicalandphysicalsystemsexhibitcomplex−1sign(dynamicscharacterizedbylong-rangecorrelation
7、properties01020304050(scalinglaws)[1,2,3].Forexample,apparentlynoisyBeatnumbernormalcardiacinterbeat(RR)intervaltimeseriesobeyFigure1.Anillustrationofthemagnitude/signscalinglawsandtheRRincrementseriesshowslong-rangedecomposition.(a)TheRRtimeseries(he
8、althysubject)anticorrelations[4].Moreover,thesescalingexponentsmayversusbeatnumberfor50beats.(b)Theincrement,∆RRhavediagnosticandprognosticutility[5,6].oftheRRtimeseriesshownin(a).(c)MagnitudeofInapreviousreport[7]weshowedthattwocomponentstheincrement
9、softhesuccessiveheartbeatintervalsoftheoftheheartinterbeatintervalincrementseries,namelyseriesshownin(a).Patchesofless“volatile”incrementsthemagnitude(“volatility”)andsign,canbeofhelpinwithsmallmagnitude(beatnumber20-35)arefollowedbyunderstandingtheun
10、derlyingdynamicswhichrelatetopatchesofmorevolatileincrementswithlargemagnitudecorrelationpropertiesintheoriginalheartbeattimeseries(beatnumber35-50),suggestingthatthereiscorrelationin(Figs.1and2).Theheartbeatincrementmagnitudeseriesthemagnitud
