医学数字信号处理-心电图(详细)

医学数字信号处理-心电图(详细)第一页，共42页。霍金教授的办公室（剑桥大学）“我的书每增加一个公式，读者就减少一半”——霍金教授第二页，共42页。BME在百年诺贝尔

生理与医学奖中的份额美国的保罗-劳特布尔和英国的彼得-曼斯菲尔德共同获得了2003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(1901-2000)91（届次）100%Ⅰ属于BME范畴1618%Ⅱ与BME密切相关1314%Ⅲ不采用BME方法、技术、设备与材料就不能完成的3943%Ⅳ与BME无关的2325%第三页，共42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第四页，共42页。Lecture2ElectrocardiologyElectrocardiogramECG

第2讲心电学第五页，共42页。心脏机械收缩之前，先产生电激动，心房和心室的电激动可经人体组织传到体表。心电图是利用心电图机从体表记录心脏每一心动周期所产生电活动变化曲线图形。第六页，共42页。心脏的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）构成。心脏传导系统与每一心动周期顺序出现的心电变化密切相关。正常心电活动始于窦房结，兴奋心房的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-普肯耶纤维顺序传导，最后兴奋心室。这种先后有序的电激动的传播，引起一系列电位改变，形成了心电图上相应的波段。

第七页，共42页。

心电图机是记录心电图的专用仪器，有单道心电图机和多道心电图机，多道心电图机可以同时记录多导联的心电，最多有同时记录12导联的，而单道心电图机只能顺序记录12个导联，有手控的心电图机，也有程控的、微电脑控制或数字式的心电图机，在很多其它仪器中也常有心电记录电路模块。三道心电图机

顺序记录１２导联心电图后重新排列在一幅纸上运动心电图记录系统

第八页，共42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)

第九页，共42页。2.1.2Electrodes

2.1.2电极Figure2.3Asilver-silverchlorideECGelectrode.Manymodernelectrodeshaveelectrolytelayersthataremadeofafirmgelwhichhasadhesiveproperties.Thefirmgelminimizesthedisturbanceofthechargedoublelayer.第十页，共42页。2.1.3心电等效发生器Figure2.4Boththeelectricalandmechanicalconditionsoftheheartareinvolvedindeterminingthecharacteristicsofthespreadofelectricalactivityoverthesurfaceoftheheart．Amodelofthisactivityiscalledacardiacequivalentgenerator．2.1.3Thecardiacequivalentgenerator

第十一页，共42页。Figure2.5Einthovenequilateraltriangle.RAandLAaretherightandleftarmsandLListheleftleg.第十二页，共42页。Acurrentdipoleisacurrentsourceandacurrentsinkseparatedbyadistance.Sincesuchadipolehasmagnitudeanddirectionwhichchangethroughoutaheartbeatasthecellsintheheartdepolarize,thisleadstothevectorrepresentation.电流偶极子是相隔一段距离的电流源和穴(漏)。当心肌细胞去极化(读注：实际应包含反极化和复极化)时，这样一个偶极子的大小和方向在整个心搏周期都是变化的，这就导致了向量表示法。

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)

为该矢量的正交分量，也称为标量导联，X,Y,Z是X,Y,Z方向的单位矢量。第十三页，共42页。Theforwardsolutionprovidesthepotentialatanyarbitrarypointonthebodysurfaceforagivencardiacdipole.Expressedmathematically，对于给定的心电偶极子，心电正问题的解提供了体表任意点的电位，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)]．

第十四页，共42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的，而传递系数则只决定于胸部的几何形状和非均匀性。因此，一组k体表电位(即,导联)，就有

kequations个方程的方程组，并可表示成矩阵形式。

第十五页，共42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

是未知的。然而，若我们有计算心脏矢量的方法，就可用之解正问题并获得任意体表位置的ECS。解此类问题的方法建立在人体胸廓物理模型的基础上。该模型提供了众多体表点的电位与心脏向量的关系的传递系数。用该信息，则只选择三个ECS导联就能概括欲模拟的所希望的异常ECS的本质特征。然后，就解逆问题以求出心脏偶极向量。第十六页，共42页。Thus,forthreeheartvectorcomponent,therearethreelinearequationsoftheform因此，对于

三个心脏向量的分量，有如下形式的三个线性方程Px(t)=bx1v1(t)+bx2v2(t)+…+bxkvk(t)(2.5)

P

=B×V(2．4)

WhereBisa3xkmatrixofleadcoefficientsthatisdirectlyderivedfrominvertingthetransfercoefficientsmatrixT.

第十七页，共42页。IfweselectkbodysurfaceECSleads[v1(t),v2(t),…，vk(t)]forwhichtheleadcoefficients，T(orB)，areknownfromthephysicalmodelofthehumantorso,wecansolvetheinverseproblemandcomputethetime–varyingheartvector,P,usingEq.(2.4).Oncewehavethesedipolecomponents,wesolvetheforwardproblemusingEq.(2.3)tocomputetheECSforanypointonthebodysurface.如果选择了K个体表ECS导联[v1(t),v2(t),…vk(t)]，且由人体胸廓的物理模型得知了导联系数T(或B），则就可由(2.4)式求解逆问题并计算时变的心脏向量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的ECS.第十八页，共42页。2.1.4GenesisoftheECS2.1.4心电的起源TimevaryingmotionofthecardiacvectorproducesthebodysurfaceECSforoneheartbeatwithitscharacteristicPandTwavesandQRScomplex.心脏向量的时变运动产生体表心电，每搏都有其

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

第十九页，共42页。Forthepointsintimethatthevectorpointstowardtheelectrodeconnectedtothepositiveterminaloftheamplifier,theoutputECSwillbepositive-going．Ifitpointstothenegativeelectrode，theECSwillbenegative．(Thefollowingstatementisbetterandmoredetailed.“Ifthevectorpointstotheelectrodeconnectedtothenegativeterminaloftheamplifier,theECSwillbenegative”．)

在心脏矢量指向的电极连到放大器正端的那些时间点，输出的ECS为正的。若心电向量指向的电极连到放大器负端，则输出的ECS为负的。第二十页，共42页。Figure2.8Electrocardiogram(ECG)foronenormalheartbeatshowingtypicalamplitudesandtimedurationfortheP,QRS,Twaves.

第二十一页，共42页。Figure2.9Relationshipbetweenthespreadofcardiacelectricalactivationrepresentatvarioustimeinstantsbyasummingvector(intheupperframes)andthegenesisoftheECS(inthelowerframes).

第二十二页，共42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.第二十三页，共42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，始于窦房结的、慢运动的心房去极化，产生P波。正如图2.9(b)所示，信号通过房室结时被延迟，产生P波后的等电区。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，心室肌的快速去极化表现为大而快速运动的矢量，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的时间点，产生R波的峰。图2.9(e)是激动向心室的基底部(向图的顶部)传播时的心室去极化的终末时相，产生S波。第二十四页，共42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第二十五页，共42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)第二十六页，共42页。2.2ECSleadsystems

2.2心电导联系统

心电学中有三种常用的基本导联系统。最通用的是12导联方法，该法定义了12种电位差的集合，构成标准临床ECG。第二种导联系统规定了记录VCG的电极位置。典型的监护系统只分析1或2个导联。

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

第二十七页，共42页。2.2.112leadECS

2.2.112导联心电

第二十八页，共42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.第二十九页，共42页。第三十页，共42页。中心电端C相连。所有单极导联皆参考此点电压。所有输入端皆采用高输入阻抗电路。第三十一页，共42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电极安放的位置：肢体导联监护导联第三十二页，共42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.

第三十三页，共42页。2.2.2VCSleadsystem2.2.2向量心电导联系统Figure2.18TheelectrodeplacementfortheFrankvectorECSsystem.Figure2.19Theresistornetworkforcombiningbodysurfacepotentialstoproducethethreetime-varyingscalarleadsoftheFrankVCSleadsystem.

第三十四页，共42页。Figure2.20Thevectorcardiogramofanormalmalepatient.Thethreetime-varyingscalarleadsforoneheartbeatareshownontheleftandarethex,yandzleadsfromtoptobottom.Inthetopcenteristhefrontalviewofthetipofthevectorasitmovesthroughoutonecomputedheartbeat.Inbottomcenterisatransverseviewofthevectorlooplookingdownfromabovethepatient.Onthefarrightisaleftsagittalviewlookingtowardtheleftsideofthepatient.

第三十五页，共42页。2.2.3MonitoringECS

leadsystem2.2.3监护心电导联系统Monitoringapplicationdonotusestandardelectrodepositionsbuttypicallyusetwoleads.Sincetheprincipalgoalofthesesyste