HRVdeprep

SoftwareforadvancedHRVanalysis

Juha-PekkaNiskanen,MikaP.Tarvainen,PerttuO.Ranta-aho,andPasiA.Karjalainen

4.9.2002

ReportNo.2/2002

ThismanuscripthasbeensubmittedtoComputerMethodsandProgramsinBiomedicine

UniversityofKuopio•DepartmentofAppliedPhysics

P.O.Box1627,FIN-70211Kuopio,Finland

SoftwareforadvancedHRVanalysis

Juha-PekkaNiskanen∗,MikaP.Tarvainen,PerttuO.Ranta-aho,

PasiA.Karjalainen

4.9.2002

AbstractAcomputerprogramforadvancedheartratevariability(HRV)analysisispresented.Thepro-gramcalculatesallthecommonlyusedtime-andfrequency-domainmeasuresofHRVaswellthenonlinearPoincar´eplotandbothparametricandnonparametricspectrumestimates.Theprogramgeneratesanin-formativeprintablereportsheetwhichcanbeexportedtovariousfileformatsincludingportabledocumentformat(PDF).ResultscanalsobesavedasanASCIIfilefromwhichtheycanbeimportedtoaspread-sheetprogramsuchasMicrosoftExcel󰀁.TogetherwithamodernheartratemonitorcapableofrecordingRRintervalsthisfreelydistributedprogramformsacompletelow-costHRVmeasuringandanalysissystem.Heartratevariability,Analysissoftware,Computerprogram,HRV

1Introduction

Heartratevariability(HRV)describesthevariationsbetweenconsecutiveheartbeats.Theregu-lationmechanismsofHRVoriginatefromsympatheticandparasympatheticnervoussystemsandthusHRVcanbeusedasaquantitativemarkerofautonomicnervoussystem[1].Stress,certaincardiacdiseases,andotherpathologicstatesaffectonHRV.AgoodreviewofphysiologicaloriginsandmechanismsofHRVcanbefoundin[2].

InHRVanalysiseithertheheartrateasafunctionoftimeortheintervalsbetweensuccessiveQRScomplexesneedtobedetermined.InthispaperwhenwetalkaboutHRVweactuallymeanthevariabilityofRRintervals(i.e.intervalsbetweenconsecutiveRpeaks).

HRVanalysismethodscanbedividedintotime-domain,frequency-domain,andnonlinearmethods.Inthefollowingthesemethodsarediscussedshortly.DenotionsanddefinitionsforHRVparametersinthispaperandinthedevelopedsoftwarefollowtheguidelinesgivenin[1].1.1

Time-domainmethods

Thetime-domainparametersarethemostsimpleonescalculateddirectlyfromtherawRRintervaltimeseries.ThesimplesttimedomainmeasuresarethemeanandstandarddeviationoftheRRintervals.ThestandarddeviationofRRintervals(SDNN)describestheoverallvariationintheRRintervalsignalwhilstthestandarddeviationofthedifferencesbetweenconsecutiveRRintervals(SDSD)describesshort-termvariation.ForastationarytimeseriesSDSDequalstotherootmeansquare(RMS)ofthedifferencesbetweenconsecutiveRRintervals(RMSSD).

TherearealsoothercommonlyusedparameterslikeNN50whichisthenumberofconsecutiveRRintervalsdifferingmorethan50ms.ThepNN50isthepercentagevalueofNN50intervals.TheprefixNNstandsfornormal-to-normalintervals(i.e.intervalsbetweenconsecutiveQRScomplexesresultingfromsinusnodedepolarizations).Inpractice,RRandNNintervalsusuallyappeartobesame.

Furthermore,therearesomegeometricmeasuresliketheHRVtriangularindexandTINNthataredeterminedfromthehistogramofRRintervals[1].

Niskanen,MikaP.Tarvainen,PerttuO.Ranta-aho,andPasiA.KarjalainenarewithUniversityof

Kuopio,DepartmentofAppliedPhysics,P.O.Box1627,FIN-70211Kuopio,Finland

∗Juha-Pekka

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1.2Frequencydomainmethods

TheRRintervaltimeseriesisanirregularlytime-sampledsignal.Thisisnotanissueintime-domain,butinthefrequency-domainithastobetakenintoaccount.Ifthespectrumestimateiscalculatedfromthisirregularlytime-sampledsignal,implicitlyassumingittobeevenlysampled,additionalharmoniccomponentsaregeneratedinthespectrum.Therefore,theRRintervalsignalisusuallyinterpolatedbeforethespectralanalysistorecoveranevenlysampledsignalfromtheirregularlysampledeventseries.

Inthefrequency-domainanalysispowerspectraldensity(PSD)oftheRRseriesiscalculated.MethodsforcalculatingthePSDestimatemaybedividedintononparametric[e.g.fastFouriertransform(FFT)based]andparametric[e.g.basedonautoregressive(AR)models]methods[3].ThePSDisanalyzedbycalculatingpowersandpeakfrequenciesfordifferentfrequencybands.Thecommonlyusedfrequencybandsareverylowfrequency(VLF,0-0.04Hz),lowfrequency(LF,0.04-0.15Hz),andhighfrequency(HF,0.15-0.4Hz).Themostcommonfrequency-domainparametersincludethepowersofVLF,LF,andHFbandsinabsoluteandrelativevalues,thenormalizedpowerofLFandHFbands,andtheLFtoHFratio.Alsothepeakfrequenciesaredeterminedforeachfrequencyband.FortheFFTbasedspectrumpowersarecalculatedbyintegratingthespectrumoverthefrequencybands.Theparametricspectrum,ontheotherhand,canbedividedintocomponentsandthebandpowersareobtainedaspowersofthesecomponents.Adetaileddescriptionofthiscanbefounde.g.in[4].ThispropertyofparametricspectrumestimationhasmadeitpopularinHRVanalysis.1.3

Nonlinearmethods

ItisrealistictopresumethatHRValsocontainsnonlinearpropertiesbecauseofthecomplexregulationmechanismscontrollingit.Theinterpretationandunderstandingofmanynonlinearmethodsis,however,stillinsufficient.

OnesimpleandeasytocomprehendnonlinearmethodisthesocalledPoincar´eplot.ItisagraphicalpresentationofthecorrelationbetweenconsecutiveRRintervals.ThegeometryofthePoincar´eplotisessential.Acommonwaytodescribethegeometryistofitanellipsetothegraph[5].Theellipseisfittedontothesocalledline-of-identityat45◦tothenormalaxis.Thestandarddeviationofthepointsperpendiculartotheline-of-identitydenotedbySD1describesshort-termvariabilitywhichismainlycausedbyrespiratorysinusarrhythmia(RSA).Thestandarddeviationalongtheline-of-identitydenotedbySD2describeslong-termvariability.1.4

Aimofthisstudy

InthisstudywepresentacomputerprogramforadvancedHRVanalysisforWindowsoperatingsystems.Theprogramcalculatesallthecommonlyusedtime-andfrequency-domainparametersofHRVaswellthenonlinearPoincar´eplotandbothparametricandnonparametricspectrumestimates.ItalsofeaturesadvanceddetrendingoptionsforRRseriesandaninformativeprintablereportsheetwhichcanalsobeexportedtovariousfileformatsincludingportabledocumentformat(PDF).CombinedwithamodernheartratemonitorcapableofrecordingRRintervalsthisfreelydistributedprogramformsacompletelow-costHRVmeasuringandanalysissystem.

2Background

WehavebeendevelopingaMatlab1basedsoftwarepackageforevent-relatedbiosignalanalysisincollaborationwiththeKuopioUniversityHospitalandtheBrain@Work-LaboratoryoftheFinnishInstituteofOccupationalHealth.Thesoftwarepackageconsistsofamainbrowserfordifferentbiosignalsandofvariousanalysistools.ThepresentedHRVanalysissoftwareforWindowshasoriginatedfromtheHRVanalysistoolofthissoftwarepackage.

ThegrowinginterestinHRVandtheabsenceoffreeandprofessionalHRVanalysisprogramshaveledusontoportingtheexistingMatlabbasedprogramtoastandalonewindowsapplication.Ouraimhasbeentodevelopafreeandfull-featuredHRVanalysissoftwareforphysiciansand

1Matlab

isaregisteredtrademarkoftheMathworksInc.http://www.mathworks.com

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othermedicalexpertsinresearchorclinicalfield.Therearesomecommercialprogramsavailableforthiskindofanalysis,suchastheNevrokard󰀁HRVSystem(MedistarInc.),buttheircostissometimestoohighformanyapplications.

TableI:Variablescalculatedbytheprogramwithshortdescription

VariableMean&STDRRMean&STDHRRMSSDNN50pNN50

Unitss1/minmscount%

DescriptionStatisticalMeasuresMeanandstandarddeviationoftheselectedRRintervalseriesMeanandstandarddeviationoftheselectedheartrateseriesTherootmeansquareofdifferencesofsuccessiveRRintervalsNumberofconsecutiveRRintervalsthatdiffermorethan50ms

ThepercentagevalueofconsecutiveRRintervalsthatdiffermorethan50ms

GeometricMeasuresTheintegralofthesampledensitydistributionofRRintervalsdividedbythemaximumofthedensitydistribution

RRtriangularindexTINN

ms

SD1SD2

PeakfrequencyPower

Baselinewidthoftheminimumsquaredifferencetriangular

interpolationofthemaximumofthesampledensitydistributionofRRintervals

NonlinearMeasures(Poincar´eplot)msThestandarddeviationofpoincar´eplotperpendiculartotheline-of-identity

msThestandarddeviationofpoincar´eplotalongtheline-of-identitySpectralMeasures(parametricandnonparametric)HzPeakfrequenciesofthepowerspectraldensityestimateforVLF,LF,andHFfrequencybandsms2,%andn.u.

ThepowersforVLF,LF,andHFfrequencybandsinms2andinpercentagevalue.ForLFandHFbandsthepowerisalsorepresentedinnormalizedunits(n.u.).

RatioofLFandHFfrequencybandpowersin[ms2]

LF/HF%

3Programdescription

TheprogramwasoriginallydevelopedusingMatlab6.1(Release12.1).Thefinalversionoftheprogramhasbeencompiledtoastand-aloneC-languageapplicationusingtheMatlabCompilerSuite2.3andthefreeBorlandC-Builder5.5compiler.ThustheprogramisnowindependentfromMatlabanddoesnotrequireMatlabinstallationtorun.

ThepresentedHRVanalysissoftwarecalculatesallthecommonlyusedtime-andfrequency-domainmeasuresofheartratevariability.AllthecalculatedparametersaresummarizedinTableI.Theemphasisinthedevelopmentoftheprogramhasbeenoncompleteheartratevariabilityanalysiscombinedwitheaseofuse.Thuswehaveimplementedaneasy-to-usegraphicaluserinterfacefortheprogram(Fig.1).

Aftertheanalysistheprogramgeneratesaneasytointerpretprintableone-pagereportsheet(Fig.3)whichcanalsobeexportedtovariousfileformats.ThemostimportantresultsoftheanalysiscanalsobesavedasanASCIItextfilefromwhichtheyareeasytoimporttootherprogramsforlateranalysis.3.1

Inputformatfordata

Therearenumerousdifferentelectrocardiogram(ECG)measuringdeviceswithmanymoreorlessproprietaryfileformats.Thuswritingasupportforeveryprogramwouldbeanendlessjob.HowevermostoftheECGmeasuringprogramscanexporttheRRtimeseriesinsomecommonlyuseddataformat.OneoftheseuniversaldataformatsisasimpleASCIItextfile.HencewehavechosentohavetheRRintervaldataasacolumnvectorinASCIIformat.

SupportforASCIIfilesopensnewkindofpossibilitiessincethereexistssomeinexpensiveandeasilyavailableproductsforheartratemonitoring2.

2One

oftheseproductsisthePOLAR󰀁S810heartratemonitorusedinthesamplerunsofthisarticle.

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Fig.1:Theuserinterfaceoftheprogram.

3.2Theuserinterface

ThedevelopedHRVanalysissoftwareisoperatedwithagraphicaluserinterfaceconsistingofonlyonewindowshowninFig.1.

Theuserinterfaceisdividedintothreesegments:thedatabrowsersegmentonthetopoftheuserinterface,analysisoptionssegmentonthelowerleft-handside,andresultsviewsegmentonthelowerright-handsideoftheuserinterface.3.2.1

Databrowser

ThedatabrowsersegmentdisplaysthemeasuredRRintervaltimeseries.Theselectedpartorpartsofthedataareshownasapatchoverthedata.Anestimatefortrendintheselectedpartofthedataisshownoverthepatch.Thepatchismovableandresizablewithmouse.Thex-axislimitofthedataviewcanbechangedbymodifyingthevaluebesidetheRangetext.Thenameoftheselecteddata-fileisdisplayedoverthedatabrowser.

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3.2.2Analysisoptions

Theanalysisoptionssegmentoftheprogramuserinterfacehasbeendividedintofivesubcategories.TheleftsideofthesegmentcontainsFrequencyBands,DetrendingofRRseries,andInterpolationofRRseriesoptions.TherightsidecontainsRRSampleSelectionandSpectrumEstimationoptions.Eachoftheseoptionsaredescribedbelow.

FrequencyBands:Thefrequencylimitsforverylowfrequency(VLF),lowfrequency(LF),andhighfrequency(HF)bandsarealterable.TheUseDefaultsbuttonrestoresthefrequencybandsintotheirdefaultvalueswhichare0-0.04HzforVLF,0.04-0.15HzforLF,and0.15-0.4HzforHFband.

DetrendingofRRSeries:SometimestheRRintervaltimeseriesincludesadisturbinglow

ntrendcomponent.nfrequencynbaselineDetrendingoptionscanbeusedtoremovethiskindoftrend

components.Detrendingoptionsincluderemovalofthefirstorsecondorderlineartrendorthetrendcanberemovedusingthesocalledsmoothnesspriorsmethodpresentedin[6].

InterpolationofRRSeries:RRintervaltimeseriesisanirregularlytime-sampledseriesandshouldthereforebeinterpolatedpriortospectrumestimation.Theprogramusescubicinterpola-tionatthedefaultrateof4Hz.

RRSampleSelection:ThepartoftheRRseriestobeanalyzedcanbeselectedbyeditingtheStartandEndvaluesorbyjustmoving/resizingthepatchovertheRRseries.Theanalyzedsegmentcanalsobeformedbymergingtwoormoresmallersegments.Thenumberofsegmentsislimitedto20segments.

SpectrumEstimation:Thissubcategoryisdividedintotwoparts:Welch’sPeriodogram(FFTbasedspectrum)andARSpectrum(autoregressivemodelingbasedspectrum).Thenumberofpointsinfrequencydomaincanbechangedforbothspectrumestimates.ForWelch’speriodogramalsothewidthandoverlapoftheHanningwindowcanbeadjustedinpoints[3],andforARspectrumtheorderofthemodelcanbechanged.ThesocalledFBLS-method(forward-backwardlinearleastsquaresmethod)isusedforthecalculationoftheAR-modelparameters[3].ThedefaultvaluesoftheseoptionsaresetfortheRRinterpolationrateof4Hz.

Allthedefaultvaluesfordifferenttunableparametersintheanalysisoptionssegmentcanbecustomized,byeditingacommentedASCIIconfigurationfile(namedhrvparam.dat)locatedintheinstalldirectoryoftheprogram.3.2.3

Resultsview

Theresultsviewsectionisforviewingcalculatedparametersandspectrumsforprevailingoptions.Itcontainsfourbuttonswhichcontrolthedisplayedresults(Fig.2).ChoosingtheARSpectrumoption,theautoregressivespectrumestimateisdisplayedalongwithtableofcalculatedparametersforthespectrum(Fig.2(a)).ThepowersandpeakfrequenciesfortheARspectrumarecalculatedfromthedistinctcomponents.TheFFTSpectrumbuttondisplaystheWelch’speriodogramand,correspondingly,atableofparameterscalculatedfromtheperiodogram(Fig.2(b)).TheStatisticsbuttondisplaysatableofcalculatedtime-domainparameters(Fig.2(c)).UnderthetableRRintervalandheartratehistogramsaredisplayed.ChoosingthePoincareplotoption,thenonlinearPoincar´eplotalongwithcalculatedparametersisdisplayed(Fig.2(d)).3.2.4Meusadtoolbarbuttos

Therearethreeusermenusandsixtoolbarbuttonslocatedintheupperleft-handcorneroftheprograminterfacewindow(Fig.1).TheFilemenuincludesOpen,Save,SaveAs,andQuitcommands.TheSavecommandsavesthenumericresultsoftheanalysistoafileinASCIIformat.Columnsofthefileareseparatedwithcommassothattheresultscouldeasilybeimportedtoe.g.aspreadsheetprogramsuchasMicrosoftExcel󰀁forfurtherinspection.Open,Save,andQuitcommandsarealsoavailableastoolbarbuttons.

TheReportmenuhasReportSheetoptionwhichopenstheprintablereportsheetwindow(Fig.3).Reportsheetwindowoptionisalsoincludedasatoolbarbutton.

TheHelpmenuhasAboutoptionwhichopenstheaboutdialog.Theaboutdialogcontainstheversionnumberoftheprogramandcontactinformation.Theaboutdialogcanalsobeinvoked

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(a)(b)

(c)(d)

Fig.2:Differentoptionsoftheresultsviewsegmentoftheprogramsuserinterface.(a)ARspectrumestimationresults,(b)FFTbasedspectrumestimationresults,(c)time-domainparametersanddistributionhistograms,(d)Poincar´eplotresults.

withatoolbarbutton.Thereisalsoatoolbarbuttonforshowing/hidingtheRRintervaldatamarkers.3.3

Thereportsheet

Theprogramgeneratesaninformativeprintablereportsheetaftertheanalysishasbeenmade.Thereportincludesinonepagealltheparameterscalculatedbytheprogram.AscreenshotofthereportsheetispresentedinFig3.

Therearesevenbuttonsinthereportpagetoolbar.Inorderfromlefttoright:Export,Print,ZoomIn,ZoomOut,Restoreoriginalview,Moveviewablearea,andClose.ThePrintbuttonopenstheprintdialogoftheoperatingsystemandtheClosebuttonclosesthereportwindow.TheExportbuttonopensaspecificexportdialog.SupportedfileformatsintheexportdialogaresummarizedinTableII.Version6.53oftheGNUGhostscriptisusedforexportingthereportsheettosomeofthefileformatsanditisincludedintheprogramdistribution.GNUGhostscript

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Fig.3:Reportsheetgeneratedbytheprogram.

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isdistributedwiththeGNUGeneralPublicLicense.

TableII:Supportedfileformatstoexportthereportsheet

FileFormatExtensionPortableDocumentFormat.pdfEnhancedMetafile.emfBitmapfile.bmpEncapsulatedPostscript.epsJPEGimagefile.jpgTIFFimagefile.tifPortableNetworkGraphicsfile.pngPaintbrush24-bitfile.pcxPortableBitmapfile.pbmPortableGraymapfile.pgmPortablePixmapfile.ppm

3.4Hardwarespecifications

HRVanalysissoftwarewillrunonall32-bitwindowsoperatingsystems(thatis,windows

98/Me/NT/2000/XP).Itshouldworkalsoinwindows95environmentalthoughithasnotbeentested.TheprogramrequiresaPCsystemwithabout30MBofharddiskspace,aPentiumclassorhigherprocessorwithx86architecture,minimumof32MBRAManddesktopresolutionof800x600(although1024x768orhigherisrecommendedforusability).ForcomputationsitusesmainlyMatlablibrarieswhichareincludedintheprogramdistribution.

4Sampleruns

AsatestcasewemeasuredHRVfromahealthyyoungfemaleatrestinalyingposition.AsameasuringdeviceaPOLARS810heartratemonitorwasused.ItiscapableofautomaticallystoringconsecutiveRRintervalsanditisveryinexpensivecomparedtoothercommercialECGorRRintervalmeasuringdevices.TheresolutionofPOLARVantageNVheartratemonitor,whichisanalogoustoS810butwithlowermemorycapacity,wasstudiedin[7].TheinaccuracyoftheRRintervalmeasurementswasshowntobelessthan3mswhichissufficientforHRVanalysis.Thetimingaccuracyofthebuild-inQRSdetectionsystemwasstudiedin[8].

PriortoHRVanalysis,themeasuredRRintervaldatawaspreprocessedforartifactsusingthePolarPrecisionPerformanceTMsoftwarethatcamewiththeheartratemonitor.ThemeasuredpreprocessedRRintervaldatacanbeseeninthedatabrowsersegmentoftheuserinterfaceinFig.1.Foranalysisasegmentfrom140to340secondswasselected.ObtainedresultsfortheselectedRRepocharepresentedinthereportsheetinFig.3.ThelowfrequencytrendcomponentintheRRserieswasremovedusingthesmoothnesspriorsbasedapproach.Thesmoothnesspriorsmethod[9]operateslikeatime-varyingfiniteimpulseresponse(FIR)high-passfilteranditiseasytoapplytodifferentoccasions,sinceithasonlyoneadjustableparameter.

Theeffectofthedetrendingprocedureonthespectrumestimatesandonfewpopulartime-domainparametersispresentedinFig.4andTableIII.ThespectrumestimatesoftheoriginalanddetrendedRRseriesarecomparedinFig.4(b).FortheWelch’speriodogrammethod,theVLFcomponentisproperlyremovedwhilethehigherfrequencycomponentsarenotsignificantlyalteredbythedetrending.ButwhenARmodelsofrelativelyloworderareused,whichisusuallydesirableinHRVanalysisinordertoenabledistinctdivisionofthespectrumintoVLF,LF,andHFcomponents,theeffectofdetrendingisremarkable.IntheARspectrumoftheoriginalRRseriestheLFandHFcomponentsarealmostentirelyobscuredbythestrongVLFcomponent.However,fromthedetrendedRRseriesspectrumtheLFandHFcomponentsareclearlyevidentandmorecongruentwiththeWelch’speriodogram.

Theeffectofthedetrendingprocedureonafewcommonlyusedtime-domainparametersisshowninTableIII.ThedetrendinghasnaturallyastrongeffectonSDNNandonlyasmalleffectonRMSSDandpNN50whichdescribetheshort-termRRvariability.Finallyitshouldbeemphasizedthatwhenusinganydetrendingmethodoneshouldmakesurethatthedetrendingdoesnotloseanyusefulinformationfromthelowerfrequencycomponents.

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1.2RRI (s)10.80.60.20DetrendedRRI−0.2140240Time (s)3400.050.040.030.020.01PSD (s/Hz)200.050.040.030.020.01000.25Frequency (Hz)0.5VariableSDNNRMSSDpNN50Units(ms)(ms)(%)Original82.1271.9040.71Detrended68.5371.4041.59

5Futureplans

Infutureversionsweintendtoaddread-supportforNeuroScancontinuousCNTfiles(NeuroScanInc.),BiopacAcqKnowledgefiles(BiopacSystemsInc.),andpossiblyforsomeotherfileformats.ThiswillalsoincludesupportforviewingrawECGdataandautomaticdetectionofQRS-complexesforcalculatingRRintervals.ThesefeaturesarealreadyimplementedintheMatlabversionofthesoftware.

WearealsoplanningtoporttheapplicationtoLinuxandotherUnixbasedsystems.

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6Discussion

WehavepresentedacomputerprogramforadvancedHRVanalysisforWindowsoperatingsys-tems.Theprogramcalculatesallthecommonlyusedtime-andfrequency-domainparametersandthenonlinearPoincar´eplot.Advancedspectrumestimationmethodsanddetrendingoptionsareincludedaswell.Theprogramgeneratesaninformativeandeasytointerpretprintableone-pagereportsheetthatcanbeexportedtovariousdifferentfileformatsincludingtheportabledocumentformat(PDF).ThemostimportantresultsoftheanalysiscanalsobesavedasanASCIItextfilefromwhichtheyareeasytoimporttoaspreadsheetprogramsuchasMicrosoftExcel󰀁forlateranalysis.Theuserinterfaceoftheprogramfunctionswithonlyonewindowwhichsimplifiestheuseoftheprogramconsiderably.Thissoftwareisaimedatphysiciansandothermedicalexpertsforclinicalorresearchuseanditisavailablefreeofchargeuponrequest.

HRVanalysishasalongtimebeenconsideredonlyasa”researchtoy”,butnowadaysithasalsogainedgrowinginterestintheclinicalfieldaswell.ThishasraisedaneedforinexpensivemethodsforadvancedHRVanalysis.ThepresentedHRVanalysissoftwareforwindowstogetherwithmodernheartratemonitorabletorecordRRintervalscreatesacompletelow-costHRVmeasuringandanalysissystem.

7Availability

TheHRVanalysissoftwareforWindowsisavailablefreeofchargeuponrequest.Ifyouareinterestedindownloadingandusingthesoftwarepleasevisithttp://venda.uku.fi/research/biosignaloremailtoPasi.Karjalainen@uku.fiforfurtherinstructions.

Acknowledgments

ThisworkhasbeendoneincollaborationwithKuopioUniversityHospitalandtheBrain@Work-LaboratoryoftheFinnishInstituteofOccupationalHealth.

References

[1]TaskforceoftheEuropeansocietyofcardiologyandtheNorthAmericansocietyofpacing

andelectrophysiology.Heartratevariability–standardsofmeasurement,physiologicalinter-pretation,andclinicaluse.Circulation,93(5):1043–1065,March1996.[2]G.G.Berntson,J.T.BiggerJr.,D.L.Eckberg,P.Grossman,P.G.Kaufmann,M.Malik,H.N.

Nagaraja,S.W.Porges,J.P.Saul,P.H.Stone,andM.W.VanDerMolen.Heartratevariability:Origins,methods,andinterpretivecaveats.Psychophysiol,34:623–8,1997.[3]S.L.Marple.DigitalSpectralAnalysis.Prentice-HallInternational,1987.

[4]P.Tikkanen.CharacterizationandapplicationofanalysismethodsforECGandtimeinterval

variabilitydata.PhDthesis,UniversityofOulu,DepartmentofPhysicalSciences,DivisionofBiophysics,1999.[5]M.Brennan,M.Palaniswami,andP.Kamen.DoexistingmeasurespfPoincar´eplotgeometry

reflectnonlinearfeaturesofheartratevariability.IEEETransBiomedEng,48(11):1342–1347,November2001.[6]M.P.Tarvainen,P.O.Ranta-aho,andP.A.Karjalainen.Anadvanceddetrendingmethodwith

applicationtoHRVanalysis.IEEETransBiomedEng,49(2):172–175,February2001.[7]KinnunenH.andHeikkil¨aI.ThetimingaccuracyofthePolarVantageNVheartratemonitor.

JournalofSportsSciences,16:s107–s110,1998,AbstractintheFirstInternationalConferenceonHeartRateMonitoringandExercise.[8]AnttiRuha,SamiSallinen,andSeppoNissil¨a.Areal-timemicroprocessorQRSdetectorsystem

witha1-mstimingaccuracyforthemeasurementofambulatoryHRV.IEEETransBiomedEng,44(3):159–167,March1997.

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[9]W.Gersch.Smoothnesspriors.InNewDirectionsinTimeSeriesAnalysis,PartII,pages

113–146.Springer-Verlag,1991.

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