医学数字信号处理心电图专家讲座

霍金教授办公室（剑桥大学）“我书每增加一个公式，读者就降低二分之一”——霍金教授医学数字信号处理心电图专家讲座第1页BME在百年诺贝尔

生理与医学奖中份额美国保罗-劳特布尔和英国彼得-曼斯菲尔德共同取得了年诺贝尔生理学或医学奖--核磁共振成像技术--三维图象百年总计(1901-)91（届次）100%Ⅰ属于BME范围1618%Ⅱ与BME亲密相关1314%Ⅲ不采取BME方法、技术、设备与材料就不能完成3943%Ⅳ与BME无关2325%医学数字信号处理心电图专家讲座第2页教材作者：美国威斯康辛大学电气与计算机工程系教授前IEEE生物医学工程学会主席

WillisJ.Tompkins书名：BiomedicalDigitalSignalProcessingISBN：7560925790页数：246医学数字信号处理心电图专家讲座第3页Lecture2ElectrocardiologyElectrocardiogramECG

第2讲心电学医学数字信号处理心电图专家讲座第4页心脏机械收缩之前，先产生电激动，心房和心室电激动可经人体组织传到体表。心电图是利专心电图机从体表统计心脏每一心动周期所产生电活动改变曲线图形。医学数字信号处理心电图专家讲座第5页心脏特殊传导系统由窦房结、结间束（分为前、中、后结间束）、房间束（起自结间束，称Bachmann束）、房间交界区（房室结、希氏束）、束支（分为左、右束支，左束支又分为前分支和后分支）以及普肯耶纤维（Pukinjefiber）组成。心脏传导系统与每一心动周期次序出现心电改变亲密相关。正常心电活动始于窦房结，兴奋心房同时经结间束传导至房室结（激动传，然后循希氏束-左、右束支-普肯耶纤维次序传导，最终兴奋心室。这种先后有序电激动传输，引发一系列电位改变，形成了心电图上对应波段。

医学数字信号处理心电图专家讲座第6页

心电图机是统计心电图专用仪器，有单道心电图机和多道心电图机，多道心电图机能够同时统计多导联心电，最多有同时统计12导联，而单道心电图机只能次序统计12个导联，有手控心电图机，也有程控、微电脑控制或数字式心电图机，在很多其它仪器中也常有心电统计电路模块。三道心电图机

次序统计１２导联心电图后重新排列在一幅纸上运动心电图统计系统医学数字信号处理心电图专家讲座第7页2.1Electrocardiologicbasis

2.1心电学基础2.1.1threebasictechniques

2.1.1三种基本技术1.StandardclinicalECG（12leads）

1.标准临床ECG（12导联）

2.VCG(3orthogonalleads)

3.MonitoringECG(1or2lead(s))

2.向量心电图(三维正交导联)

3.监护ECG(1或2导联)

医学数字信号处理心电图专家讲座第8页2.1.2Electrodes

2.1.2电极Figure2.3Asilver-silverchlorideECGelectrode.Manymodernelectrodeshaveelectrolytelayersthataremadeofafirmgelwhichhasadhesiveproperties.Thefirmgelminimizesthedisturbanceofthechargedoublelayer.医学数字信号处理心电图专家讲座第9页2.1.3心电等效发生器Figure2.4Boththeelectricalandmechanicalconditionsoftheheartareinvolvedindeterminingthecharacteristicsofthespreadofelectricalactivityoverthesurfaceoftheheart．Amodelofthisactivityiscalledacardiacequivalentgenerator．2.1.3Thecardiacequivalentgenerator

医学数字信号处理心电图专家讲座第10页Figure2.5Einthovenequilateraltriangle.RAandLAaretherightandleftarmsandLListheleftleg.医学数字信号处理心电图专家讲座第11页Acurrentdipoleisacurrentsourceandacurrentsinkseparatedbyadistance.Sincesuchadipolehasmagnitudeanddirectionwhichchangethroughoutaheartbeatasthecellsintheheartdepolarize,thisleadstothevectorrepresentation.电流偶极子是相隔一段距离电流源和穴(漏)。当心肌细胞去极化(读注：实际应包含反极化和复极化)时，这么一个偶极子大小和方向在整个心搏周期都是改变，这就造成了向量表示法。

P(t)=Px(t)X十Py(t)Y十Pz(t)Z(2.1)WhereP(t)isthetime-varyingcardiacvector,Pi(t)aretheorthogonalcomponentsofthevectoralsocalledscalarleads,andX,Y,Z

areunitvectorsinthex,y,zdirections.式中P(t)是时变心脏偶极子，Pi(t)

为该矢量正交分量，也称为标量导联，X,Y,Z是X,Y,Z方向单位矢量。医学数字信号处理心电图专家讲座第12页Theforwardsolutionprovidesthepotentialatanyarbitrarypointonthebodysurfaceforagivencardiacdipole.Expressedmathematically，对于给定心电偶极子，心电正问题解提供了体表任意点电位，数学上表示为，vn(t)=tnxPx(t)十tnyPy(t)十tnzPy(t)(2.2)Thisforwardso1utlonshowsthatthepotentialvn(t)(i．e．,theECS)atanypointnonthebodysurfaceisgivenbythelinearsumoftheproductsofasetoftransfercoefficients[tni]uniquetothatpointandtheCorrespondingorthogonaldipolevectorcomponents[Pi(t)]．

医学数字信号处理心电图专家讲座第13页TheECSsaretime-varyingasarethedipo1ecomponents,whilethetransfercoefficientsareonlydependentonthethoracicgeometryandinhomogeneities．Thusforasetofkbodysurfacepotentials(i.e.,1eads)，thereisasetofkequationsthatcanbeexpressedinmatrixform

V=T×P(2.3)

WhereVisakxlvectorrepresentingthetime-varyingpotentials,Tisakx3matrixoftransfercoefficients,Whicharefixedforagivenindividual,andPisthe3x1time-varyingheartvector．心电信号与偶极子分量一样是时变，而传递系数则只决定于胸部几何形状和非均匀性。所以，一组k体表电位(即,导联)，就有

kequations个方程方程组，并可表示成矩阵形式。

医学数字信号处理心电图专家讲座第14页Ofcourse,theheartvectorandtransfercoefficientsareunknownforagivenindividual．Howeverifwehadawaytocomputethisheartvector．Wecoulduseitintheso1utionoftheforwardproblemandobtaintheECSforanybodysurfacelocation．Theapproachtosolvingthisproblemisbasedonaphysicalmodelofthehumantorso．Themodelprovidestransfercoefficientsthatrelatethepotentialsatmanybodysurfacepointstotheheartvector.Withthisinformation，wese1ectthreeECSleadsthatsummarizetheintrinsiccharacteristicsofthedesiredabnormalECStosimulate．Thenwesolvetheinverseproblemtofindthecardiacdipolevector.自然，对于任一个体心脏向量P和传递系数T

是未知。然而，若我们有计算心脏矢量方法，就可用之解正问题并取得任意体表位置ECS。解这类问题方法建立在人体胸廓物理模型基础上。该模型提供了众多体表点电位与心脏向量关系传递系数。用该信息，则只选择三个ECS导联就能概括欲模拟所希望异常ECS本质特征。然后，就解逆问题以求出心脏偶极向量。医学数字信号处理心电图专家讲座第15页Thus,forthreeheartvectorcomponent,therearethreelinearequationsoftheform所以，对于

三个心脏向量分量，有以下形式三个线性方程Px(t)=bx1v1(t)+bx2v2(t)+…+bxkvk(t)(2.5)

P

=B×V(2．4)

WhereBisa3xkmatrixofleadcoefficientsthatisdirectlyderivedfrominvertingthetransfercoefficientsmatrixT.

医学数字信号处理心电图专家讲座第16页IfweselectkbodysurfaceECSleads[v1(t),v2(t),…，vk(t)]forwhichtheleadcoefficients，T(orB)，areknownfromthephysicalmodelofthehumantorso,wecansolvetheinverseproblemandcomputethetime–varyingheartvector,P,usingEq.(2.4).Oncewehavethesedipolecomponents,wesolvetheforwardproblemusingEq.(2.3)tocomputetheECSforanypointonthebodysurface.假如选择了K个体表ECS导联[v1(t),v2(t),…vk(t)]，且由人体胸廓物理模型得知了导联络数T(或B），则就可由(2.4)式求解逆问题并计算时变心脏向量P。一旦有了这些偶极分量，则就可用方程(2.3)解正问题以计算任意点ECS.医学数字信号处理心电图专家讲座第17页2.1.4GenesisoftheECS2.1.4心电起源TimevaryingmotionofthecardiacvectorproducesthebodysurfaceECSforoneheartbeatwithitscharacteristicPandTwavesandQRScomplex.心脏向量时变运动产生体表心电，每搏都有其

特征性P、T波和QRS复合波。Figure2.7Basicconfigurationforrecordinganelectrocardiogram.Usingelectrodesattachedtothebody,theECGisrecordedwithaninstrumentationamplifier.(a)Transverse(top)viewofasliceofthebodyshowingtheheartandlungs.(b)FrontalviewshowingelectrodesconnectedinanapproximateleadIIconfiguration.

医学数字信号处理心电图专家讲座第18页Forthepointsintimethatthevectorpointstowardtheelectrodeconnectedtothepositiveterminaloftheamplifier,theoutputECSwillbepositive-going．Ifitpointstothenegativeelectrode，theECSwillbenegative．(Thefollowingstatementisbetterandmoredetailed.“Ifthevectorpointstotheelectrodeconnectedtothenegativeterminaloftheamplifier,theECSwillbenegative”．)

在心脏矢量指向电极连到放大器正端那些时间点，输出ECS为正。若心电向量指向电极连到放大器负端，则输出ECS为负。医学数字信号处理心电图专家讲座第19页Figure2.8Electrocardiogram(ECG)foronenormalheartbeatshowingtypicalamplitudesandtimedurationfortheP,QRS,Twaves.

医学数字信号处理心电图专家讲座第20页Figure2.9Relationshipbetweenthespreadofcardiacelectricalactivationrepresentatvarioustimeinstantsbyasummingvector(intheupperframes)andthegenesisoftheECS(inthelowerframes).

医学数字信号处理心电图专家讲座第21页

InFigure2.9(a),theslowmovingdepolarizationoftheatriawhichbeginsatthesinoatrial(SA)nodeproducesthePwave.AsFigure2.9(b)shows,thesignalisdelayedintheatrioventricular(AV)noderesultinginanisoelectricregionafterthePwave,thenasthePurkinjesystemstartsdeliveringthestimulustotheventricularmuscle,theonsetoftheQwaveoccurs.InFigure2.9(c),rapiddepolarizationoftheventricularmuscleisdepictedasalarge,fast-movingvectorwhichbeginsproducingtheRwave.Figure2.9(d)illustratesthatthemaximalvectorrepresentsapointintimewhenmostofthecellsaredepolarized,givingrisetothepeakoftheRwave.InFigure2.9(e),thefinalphaseofventriculardepolarizationoccursastheexcitationspreadstowardthebaseoftheventricles(tothetopinthepicture)givingrisetotheSwave.医学数字信号处理心电图专家讲座第22页

InFigure2.9(a),theslowmovingdepolarizationoftheatriawhichbeginsatthesinoatrial(SA)nodeproducesthePwave.AsFigure2.9(b)shows,thesignalisdelayedintheatrioventri-cular(AV)noderesultinginanisoelectricregionafterthePwave,thenasthePurkinjesystemstartsdeliveringthestimulustotheventricularmuscle,theonsetoftheQwaveoccurs.InFigure2.9(c),rapiddepolarizationoftheventricularmuscleisdepictedasalarge,fast-movingvectorwhichbeginsproducingtheRwave.Figure2.9(d)illustratesthatthemaximalvectorrepresentsapointintimewhenmostofthecellsaredepolarized,givingrisetothepeakoftheRwave.InFigure2.9(e),thefinalphaseofventriculardepolarizationoccursastheexcitationspreadstowardthebaseoftheventricles(tothetopinthepicture)givingrisetotheSwave.

图2.9(a)中，始于窦房结、慢运动心房去极化，产生P波。正如图2.9(b)所表示，信号经过房室结时被延迟，产生P波后等电区。然后，当Purkinje系统开始发送刺激到心室肌时，Q波开始发生。在图2.9(c)中，心室肌快速去极化表现为大而快速运动矢量，开始产生R波。图2.9(d)说明，最大矢量代表了大多数细胞去极化时间点，产生R波峰。图2.9(e)是激动向心室基底部(向图顶部)传输时心室去极化终末时相，产生S波。医学数字信号处理心电图专家讲座第23页2.1.5Thestandardlimbleads

2.1.5标准肢体导联I+III–II=0(2.6)

Figure2.10LeadsI,IIandIIIarethepotentialsdifferencebetweenthelimbsasindicated.RAandLAaretherightandleftarmsandLListheleftleg.FromKirchhoff’svoltageslaw,thesumofthevoltagesaroundaloopequalszero.Thus医学数字信号处理心电图专家讲座第24页2.1.6Theaugmentedlimbleads

2.1.6加压肢体导联

Figure2.11TheaugmentedlimbleadaVLismeasuredasshown.

Fromthebottomleftloop

i×R+i×R-II=0(2.8)ori×R=II/2(2.9)Fromthebottomrightloop

i×R+III+aVL=0(2.10)OraVL=i×R–III(2.11)CombiningEqs.(2.9)and(2.11)givesaVL=II/2–III=(II-2×III)/2(2.12)

Fromthetopcenterloop

II=III+I(2.13)

SubstitutinggivesaVL=(III–I-2×III)/2=(I–III)/2(2.14)医学数字信号处理心电图专家讲座第25页2.2ECSleadsystems

2.2心电导联络统

心电学中有三种惯用基本导联络统。最通用是12导联方法，该法定义了12种电位差集合，组成标准临床ECG。第二种导联络统要求了统计VCG电极位置。经典监护系统只分析1或2个导联。

Therearethreebasicleadsystemsusedincardiology.Themostpopularisthe12-leadapproach,whichdefinesthesetof12potentialdifferencesthatmakeupthestandardclinicalECG.AsecondleadsystemdesignatesthelocationofelectrodesforrecordingVCG.Monitoringsystemstypicallyanalyzeoneortwoleads.

医学数字信号处理心电图专家讲座第26页2.2.112leadECS

2.2.112导联心电

医学数字信号处理心电图专家讲座第27页Figure2.16

Standard12-leadclinicalelectrocardiogram.(a)LeadI.(b)LeadII.(c)LeadIII.Notetheamplifierpolarityforeachoftheselimbleads.(d)aVR.(e)VL.(f)aVF.Theseaug-mentedleadsrequireresistornetworkswhichaveragetwolimbpotentialswhilerecordingthethird.(g)ThesixVleadsarerecordedreferencedtoWilson’scentralterminalwhichistheaverageofallthreelimbpotentials.EachofthesixleadslabeledV1-V6arerecordedfromadifferentanatomicalsiteonthechest.医学数字信号处理心电图专家讲座第28页医学数字信号处理心电图专家讲座第29页中心电端C相连。全部单极导联皆参考此点电压。全部输入端皆采用高输入阻抗电路。医学数字信号处理心电图专家讲座第30页12个标准心电图导联双极肢体导联：I、II、III单极加压肢体导联：aVL、aVR、aVF胸导联：V1、V2、V3、V4、V5、V6电极安放位置：肢体导联监护导联医学数字信号处理心电图专家讲座第31页Figure2.17The12-leadECGofanormalpatient.Calibrationpulsesontheleftsidedesignate1mV.Therecordingspeedis25mm/s.EachminordivisionisImm,sothemajordivisionare5mm.ThusinleadI,theR-waveamplitudeisabout1.1mVandthetimebetweenbeatsisalmost1S(i.e.,heartrateisabout60bpm).ThenotesareID0042804,S=26,L=×2,C=×1,I,II,III,aVR,aVL,aVF,V1,V2,V3,V4,V5,V6,PatientNO:4307400respectively.

医学数字信号处理心电图专家讲座第32页2.2.2VCSleadsystem2.2.2向量心电导联络统Figure2.18TheelectrodeplacementfortheFrankvectorECSsystem.Figure2.19Theresistornetworkforcombiningbodysurfacepotentialstoproducethethreetime-varyingscalarleadsoftheFrankVCSleadsystem.

医学数字信号处理心电图专家讲座第33页Figure2.20Thevectorcardiogramofanormalmalepatient.Thethreetime-varyingscalarleadsforoneheartbeatareshownontheleftandarethex,yandzleadsfromtoptobottom.Inthetopcenteristhefrontalviewofthetipofthevectorasitmovesthroughoutonecomputedheartbeat.Inbottomcenterisatransverseviewofthevectorlooplookingdownfromabovethepatient.Onthefarrightisaleftsagittalviewlookingtowardtheleftsideofthepatient.

医学数字信号处理心电图专家讲座第34页2.2.3MonitoringECS

leadsystem2.2.3监护心电导联络统Monitoringapplicationdonotusestandardelectrodepositionsbuttypicallyusetwoleads.Sincetheprincipalgoalofthesesystemsistoreliablyrecogniz