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SteeperActionPotentialDurationRestitutionSlopeIncreasesRiskofVentricularFibrillationASimulationStudyYiZheng1,2,DamingWei2,,andZuxiangFang11Dept.ofElectronicEngineering,FudanUniversity,Shanghai,PeoplesRepublicofChina2GraduateSchoolofComputerScienceandEngineering,UniversityofAizu,AizuWakamatsu,Fukushima9658580,JapanCorrespondingauthordmweiuaizu.ac.jpAbstractActionpotentialdurationrestitutionAPDRisthoughttoberelevanttothestabilityofcardiacelectrophysiology.VentricularfibrillationVFwassimulatedusingtheWeiHarumimodelbytakingintoaccountpiecewiselinearactionpotentialdurationrestitutionbasedonclinicalfindings.Wefound,inthesimulation,thatheartmodelwithsteeperslopeofAPDRrequiredlessectopicstimulitotriggerVF.ThisresultsuggestedthattheAPDRmayaffectcardiacvulnerabilitytoVF.KeywordsactionpotentialdurationrestitutionventricularfibrillationsimulationI.INTRODUCTIONArrhythmiascausedbycardiovasculardiseasesareprevalenthealthproblemsintheindustrializedcountries1amongwhichtheventricularfibrillationVFisconsideredasthemostmalignantarrhythmianotoriousasthemostcommonmechanismofsuddencardiacdeathSCD24thatannuallyaccountsforover30,000deathsintheUnitedStatesalone5.MacWilliamcharacterizedVFastheventricularmuscleisthrownintoastateofirregulararrhythmiccontractionconsequentlymaketheheartloseitsabilityofpumpingblood6.Despitedecadesofendeavorfromacademiciansandscholars,themechanismunderlyingVFremainscontroversial7,8.LiteraturessuggestthatactionpotentialdurationAPDrestitutionisrelevanttothestabilityofcardiacelectrophysiologyandvulnerabilitytoVFbothinvivo9,10andinvitro11thisisfurtherconfirmedinsimulation1214inducibilityofreentry.NashcombinedclinicalstudywithsimulationtothereemphasizesignificanceofAPDrestitution15.APDrestitutionSeeFig.1isreferredasfunctionbetweenAPDanditsprecedingdiastolicintervalDI16.ResearchershavealsoshownthepossibilityofeliminatingventricularfibrillationbyflattingAPDrestitution12,17thatmayfacilitatetheinventionofnovelantiarrhythmiapharmacy.TheWeiHarumimodel18,19,astateofartheart3Dmodel,withintegrationofAPDrestitutionisutilizedinthisstudytoinvestigatethepossiblecorrelationofslopeofAPDrestitutiontoinducibilityofventricularfibrillation.Itconsistsofover50,000cardiaccellswithrealisticheartandtorsoanatomyaswellaselectrophysiologicalsettingcapableofsimulatingbodysurfacepotentialmapBSPMECGanddepictingactivationpropagationatwholeheartlevel20.Figure1.APDRofendocardiumderivedfromTenscellularmodel21.Thiscurveisobtainedbyapplyingstimulitothemodelcellusingdynamicrestitutionprotocol16.Thestimulationstrengthistwiceofthediastolicthresholdwithandurationofonemillisecond.WorkfromphysiciansindicatesthathighriskpatientswithinducibleVToralternantTWAareconnectedwithsteeperslopeofAPDrestitutionoverthatoflowriskones10,thatinspiresustotakeadvantageoftheWeiHarumimodeltodeterminewhethersteeperslopelinkstohighervulnerabilitytoVF.II.METHODSA.CombinationofpiecewiselinearAPDrestitutionTheoriginalsettingofWeiHarumimodelassumedthatthevariationofactionpotentialdurationislinearwiththeincrementdecrementofcouplingintervalsothatduringsimulationthecellularAPDisdynamicallymodifiedbytheequation1below19APDAPD1DCCIttt⋅Δ1whereCItΔistheincrementdecrementofcardiaccellularcouplingintervalattimet.Researchershavefoundthatwhilepacingsomecardiaccellsatarelativelylonginterval,eachactivatedactionpotentialbycorrespondingstimulationisidenticalcalled11behavior,afterthepacingrhythmexceedscertaincriticalrate,APDbifurcationoccursdoubleperiodicalstimuligenerateThisresearchissupportedbyShanghaiLeadingAcademicDiscipline,ProjectNumberB112andtheGrantinaidforScientificResearch,No.21500297,JapanSocietyforthePromotionofScienceJSPS.9781424447138/10/25.00©2010IEEEtwodifferentactionpotentialsoneshort,onelong22,andthisphenomenonisrecognizedasAPDalternantconsideredasoneofthepotentialtriggersofunidirectionalblockwhichmayconsequentlyinducereentryandevenarrhythmia5.ExpertssuggestthattheAPDshallbeestimatedbyitsfolloweddiastolicintervalwhichistheperiodbetweenonsetofthestimulationandthetimeofAPD9011.TheexperimentalacquiredstandardrestitutioncurvesDIversusAPDareusuallyfittedwiththemonoexponentialfunctions15whileHanetalsuggestedthatpiecewisemonoexponentialfunctioncouldreflecttherestitutionpropertymorefaithfully23.Nevertheless,piecewiselinearfunctionisadaptedinthismodeltodepicttheAPDrestitutionforthesakeofspeedycomputationandstillthissimplicitycanhardlyhampersimulationsfromderivingsatisfyingresults.ThustheAPDisdeterminedbymin11min12212332maxmaxMinimumDIDIAPD⋅⋅⋅⎧⎪⎪⎪⎨⎪⎪⎪⎩2whereDIistheprecedingdiastolicinterval.ItshouldbenotedthatDIcanbenegativesincetheectopicstimulationsmayfallintheactionpotentialwhenthecellhasnotreachedits90repolarization.B.ModificationofabsoluterefractoryperiodsettingInWeiHarumimodel,eachcellularabsoluterefractoryperiodARPisdefinedbyrespectiveconstantplusesgradientdifference.However,Michaeletalpointedoutthatundernormalconditions,APD90andERPwasproportionaltothecyclelengths24,thusinthisstudyARPissettobe90ofcorrespondingAPD90.ThedefinitionofAPD90isthetimebetweenonsetofstimulationand90repolarizationofactionpotential25.C.SimulationofventricularfibrillationinducingRestitutiondataarefromareportbySelvarajetal10,andtheyshowedthatpatientswithcardiomyopathyhighriskofarrhythmiapossessedsignificantlysteepermeanactivationrecoveryintervalequivalenttoAPDrestitutionslopesthanthatoflowriskones.TheparametersofrestitutionofpatientsarelistedrespectivelyinTable1.TheparametersofeachpatientaredividedintothreecataloguesaccordingtotheirlocationsApex,MiddleandBaseofheart10.Twomodelsusingtheseparametersfromrespectivepatientarestudied.VFisinducedbypacingwithatrainofperiodicalectopicstimuliappliedonleftventricularepicardiumoftheheartmodelindicatedbytheblackarrowinFig.226,27.Theonsetofstimulationsistimedtofallinthevulnerableperiodinordertofacilitateinducibilityoffibrillation.InducingoffibrillationisregardedassuccessfuliftheirregularmorphologicalsimulatedECGpersistsaftertheretreatofectopicimpulses.Theentiresimulationlastssixthousandmilliseconds.TABLEI.PARAMETERSOFRESTITUTIONPatientParametersmillisecondLocationMinimumDIminA1B1D1A2B2LowriskApex26000.57260400.08280Middle25400.64254250.1267Base25500.36255470.16264HighriskApex501851.727070.25260Middle402071247120.16258Base302031.33243100.2254PatientParametersmillisecondaLocationD2A3B3DImaxMaximumLowriskApex1250290300290Middle1250.09269300298Base1070.08271300295HighriskApex400.1266300296Middle1350.03276300285Base800.08264300288a.ContinuewithprevioustableFigure2.Acrosssectionlocatedataboutonethirdfromtheapexoftheheartmodel.Theblackarrowindicateddotintherightsideshowsthepositionofectopicstimulation.Figure3.LeadIIofsinusrhythmandVFlikerhythminducedbyminimumectopicstimulifromheartmodelsusingparametersfromrespectivepatients.TheupperpanelindicatesECGsofmodeloflowriskpatientsheart,andtheloweroneindicatesthoseofmodelofhighriskones.Theopenarrowsinthepictureindicatetheonsetandretreattimeofectopicsimulationsinrespectivemodel,notethatthemodelofhighriskpatientsminimumrequiredectopyissignificantlyshortthanthatofmodeloflowriskpatients.Figure4.Insufficientectopicstimulileadingtounsuccessfulventricularfibrillationinductionintheheartmodelofhighriskpatient.Assoonastheectopicsimuliretreat,thesimulatedrhythmautomaticlyrestoresnormalsinusrhythm.III.RESULTFig.3showstheleadIIofsinusrhythmandVFlikerhythmfrombothmodels.Theextrastimulistartabout470msafterthefirstsinuspacingandthecyclelengthisslightlyabove200mscomparablewiththeabsoluterefractoryperiodARP.Theopenarrowsinrespectivediagramsindicatethetimeofonsetandretreatofectopicstimuli,sinusimpulsescontinuetilltheendofthesimulation.Apparentlythesinusrhythmsofbothmodelsareidentical.Formodelofhighriskpatient,atleast9successiveectopicstimuliarerequiredtoinducefibrillationwhileincontrast,themodeloflowriskdemandsatleast13stimuli.Iftheectopicstimuliareinsufficient,theheartmodelcanrestoresinusrhythmitselfasmanifestedinFigure4,suggestingthatheartmodelwithlesssteepAPDrestitutionismorerobustagainstarrhythmia.ThisisconsistentwithsimulationswhichprovethatreentrycanbeterminatedbyflattingAPDrestitutioncurve12,17.IV.CONCULSIONANDDISCUSSIONA.ConclusionPreviouslyYamakiaetalusedWeiHarumitostudyhowrestitutioncanaffectthegenerationofarrhythmiaandcameupwithsimilarconclusion28.Incurrentstudy,morerealisticrestitutionfeatureisintegratedandyieldsresultagreeswiththeclinicalfindings.VFissuccessfullysimulatedwiththreedimensionalheartmodel.Wefindthatheartmodelwithsteeperrestitutionismorevulnerabletoectopy,thusslopeofrestitutionmayplayanimportantroleinstudyingVFandsteeperslopeofAPDRperhapsincreasesthevulnerabilityofhearttotheVF.Itisquitelikelythatsteeprestitutionincreasestheelectrophysiologicalheterogeneityoftheheartwhichisthoughttobeessentialsubstrateforinducingreentryandevenarrhythmia29.AsdescribedinWeissetalspaper5steeprestitutioninducesAPDalternans,formsspatiallydistributedrefractoryperioddifferences,andamplifiesthevariationsofexistedheterogeneity.B.DiscussionDuringventricularfibrillation,eachcellsDIisveryshortsothattheslopeofrestitutionissharp,sincetheslopeofrestitutiondeclinesastheDIincreases,nonlineardynamiccontrolmethodcanbeutilizedtomanipulateDIsandmoveelectricalactivityintoflatrestitutionregion,consequentlystabilizethekineticsofelectricalactivity.Suchprotocolwascertifiedwithfeedbackfeatureandprovenfeasible30.Thesefindingsmayfacilitatethefutureelectricaltherapyagainstarrhythmiaandevendramaticallyreducetheenergydemandedbyconventionaldefibrillation.ACKNOWLEDGMENTTheauthorswouldliketothankDr.XinZhu,Dr.XiaomeiWuandDr.CuiweiYangfortheirvaluableassistancetosimulationstudies.REFERENCES1AMAAHAHeartDiseaseandStrokeStatistics2006Update.2J.ROBERT,SuddenCardiacDeathExploringtheLimitsofOurKnowledge,JournalofCardiovascularElectrophysiologyvol.12,issue3,pp.3041,2001.3E.D.Engelstein,andD.P.Zipes,Suddencardiacdeath,TheHeart,ArteriesandVeins,vol.16,issue9,pp.10811112,1998.4J.N.Weiss,P.S.Chen,Z.Qu,H.S.Karagueuzian,andA.Garfinkel,VentricularFibrillationHowDoWeStoptheWavesFromBreaking,CirculationResearch,vol.87,issue12,pp.11031107,2000.5J.N.Weiss,A.Karma,Y.Shiferaw,P.S.Chen,A.Garfinkel,andZ.Qu,et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