霍金教授辦公室（劍橋大學(xué)）“我書每增加一個(gè)公式，讀者就降低二分之一”——霍金教授醫(yī)學(xué)數(shù)字信號(hào)處理心電圖專家講座第1頁(yè)BME在百年諾貝爾

生理與醫(yī)學(xué)獎(jiǎng)中份額美國(guó)保羅-勞特布爾和英國(guó)彼得-曼斯菲爾德共同取得了年諾貝爾生理學(xué)或醫(yī)學(xué)獎(jiǎng)--核磁共振成像技術(shù)--三維圖象百年總計(jì)(1901-)91（屆次）100%Ⅰ屬于BME范圍1618%Ⅱ與BME親密相關(guān)1314%Ⅲ不采取BME方法、技術(shù)、設(shè)備與材料就不能完成3943%Ⅳ與BME無(wú)關(guān)2325%醫(yī)學(xué)數(shù)字信號(hào)處理心電圖專家講座第2頁(yè)教材作者：美國(guó)威斯康辛大學(xué)電氣與計(jì)算機(jī)工程系教授前IEEE生物醫(yī)學(xué)工程學(xué)會(huì)主席

WillisJ.Tompkins書名：BiomedicalDigitalSignalProcessingISBN：7560925790頁(yè)數(shù)：246醫(yī)學(xué)數(shù)字信號(hào)處理心電圖專家講座第3頁(yè)Lecture2ElectrocardiologyElectrocardiogramECG

第2講心電學(xué)醫(yī)學(xué)數(shù)字信號(hào)處理心電圖專家講座第4頁(yè)心臟機(jī)械收縮之前，先產(chǎn)生電激動(dòng)，心房和心室電激動(dòng)可經(jīng)人體組織傳到體表。心電圖是利專心電圖機(jī)從體表統(tǒng)計(jì)心臟每一心動(dòng)周期所產(chǎn)生電活動(dòng)改變曲線圖形。醫(yī)學(xué)數(shù)字信號(hào)處理心電圖專家講座第5頁(yè)心臟特殊傳導(dǎo)系統(tǒng)由竇房結(jié)、結(jié)間束（分為前、中、后結(jié)間束）、房間束（起自結(jié)間束，稱Bachmann束）、房間交界區(qū)（房室結(jié)、希氏束）、束支（分為左、右束支，左束支又分為前分支和后分支）以及普肯耶纖維（Pukinjefiber）組成。心臟傳導(dǎo)系統(tǒng)與每一心動(dòng)周期次序出現(xiàn)心電改變親密相關(guān)。正常心電活動(dòng)始于竇房結(jié)，興奮心房同時(shí)經(jīng)結(jié)間束傳導(dǎo)至房室結(jié)（激動(dòng)傳，然后循希氏束-左、右束支-普肯耶纖維次序傳導(dǎo)，最終興奮心室。這種先后有序電激動(dòng)傳輸，引發(fā)一系列電位改變，形成了心電圖上對(duì)應(yīng)波段。

醫(yī)學(xué)數(shù)字信號(hào)處理心電圖專家講座第6頁(yè)

心電圖機(jī)是統(tǒng)計(jì)心電圖專用儀器，有單道心電圖機(jī)和多道心電圖機(jī)，多道心電圖機(jī)能夠同時(shí)統(tǒng)計(jì)多導(dǎo)聯(lián)心電，最多有同時(shí)統(tǒng)計(jì)12導(dǎo)聯(lián)，而單道心電圖機(jī)只能次序統(tǒng)計(jì)12個(gè)導(dǎo)聯(lián)，有手控心電圖機(jī)，也有程控、微電腦控制或數(shù)字式心電圖機(jī)，在很多其它儀器中也常有心電統(tǒng)計(jì)電路模塊。三道心電圖機(jī)

次序統(tǒng)計(jì)１２導(dǎo)聯(lián)心電圖后重新排列在一幅紙上運(yùn)動(dòng)心電圖統(tǒng)計(jì)系統(tǒng)醫(yī)學(xué)數(shù)字信號(hào)處理心電圖專家講座第7頁(yè)2.1Electrocardiologicbasis

2.1心電學(xué)基礎(chǔ)2.1.1threebasictechniques

2.1.1三種基本技術(shù)1.StandardclinicalECG（12leads）

1.標(biāo)準(zhǔn)臨床ECG（12導(dǎo)聯(lián)）

2.VCG(3orthogonalleads)

3.MonitoringECG(1or2lead(s))

2.向量心電圖(三維正交導(dǎo)聯(lián))

3.監(jiān)護(hù)ECG(1或2導(dǎo)聯(lián))

醫(yī)學(xué)數(shù)字信號(hào)處理心電圖專家講座第8頁(yè)2.1.2Electrodes

2.1.2電極Figure2.3Asilver-silverchlorideECGelectrode.Manymodernelectrodeshaveelectrolytelayersthataremadeofafirmgelwhichhasadhesiveproperties.Thefirmgelminimizesthedisturbanceofthechargedoublelayer.醫(yī)學(xué)數(shù)字信號(hào)處理心電圖專家講座第9頁(yè)2.1.3心電等效發(fā)生器Figure2.4Boththeelectricalandmechanicalconditionsoftheheartareinvolvedindeterminingthecharacteristicsofthespreadofelectricalactivityoverthesurfaceoftheheart．Amodelofthisactivityiscalledacardiacequivalentgenerator．2.1.3Thecardiacequivalentgenerator

醫(yī)學(xué)數(shù)字信號(hào)處理心電圖專家講座第10頁(yè)Figure2.5Einthovenequilateraltriangle.RAandLAaretherightandleftarmsandLListheleftleg.醫(yī)學(xué)數(shù)字信號(hào)處理心電圖專家講座第11頁(yè)Acurrentdipoleisacurrentsourceandacurrentsinkseparatedbyadistance.Sincesuchadipolehasmagnitudeanddirectionwhichchangethroughoutaheartbeatasthecellsintheheartdepolarize,thisleadstothevectorrepresentation.電流偶極子是相隔一段距離電流源和穴(漏)。當(dāng)心肌細(xì)胞去極化(讀注：實(shí)際應(yīng)包含反極化和復(fù)極化)時(shí)，這么一個(gè)偶極子大小和方向在整個(gè)心搏周期都是改變，這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)是時(shí)變心臟偶極子，Pi(t)

為該矢量正交分量，也稱為標(biāo)量導(dǎo)聯(lián)，X,Y,Z是X,Y,Z方向單位矢量。醫(yī)學(xué)數(shù)字信號(hào)處理心電圖專家講座第12頁(yè)Theforwardsolutionprovidesthepotentialatanyarbitrarypointonthebodysurfaceforagivencardiacdipole.Expressedmathematically，對(duì)于給定心電偶極子，心電正問(wèn)題解提供了體表任意點(diǎn)電位，數(shù)學(xué)上表示為，vn(t)=tnxPx(t)十tnyPy(t)十tnzPy(t)(2.2)Thisforwardso1utlonshowsthatthepotentialvn(t)(i．e．,theECS)atanypointnonthebodysurfaceisgivenbythelinearsumoftheproductsofasetoftransfercoefficients[tni]uniquetothatpointandtheCorrespondingorthogonaldipolevectorcomponents[Pi(t)]．

醫(yī)學(xué)數(shù)字信號(hào)處理心電圖專家講座第13頁(yè)TheECSsaretime-varyingasarethedipo1ecomponents,whilethetransfercoefficientsareonlydependentonthethoracicgeometryandinhomogeneities．Thusforasetofkbodysurfacepotentials(i.e.,1eads)，thereisasetofkequationsthatcanbeexpressedinmatrixform

V=T×P(2.3)

WhereVisakxlvectorrepresentingthetime-varyingpotentials,Tisakx3matrixoftransfercoefficients,Whicharefixedforagivenindividual,andPisthe3x1time-varyingheartvector．心電信號(hào)與偶極子分量一樣是時(shí)變，而傳遞系數(shù)則只決定于胸部幾何形狀和非均勻性。所以，一組k體表電位(即,導(dǎo)聯(lián))，就有

kequations個(gè)方程方程組，并可表示成矩陣形式。

醫(yī)學(xué)數(shù)字信號(hào)處理心電圖專家講座第14頁(yè)Ofcourse,theheartvectorandtransfercoefficientsareunknownforagivenindividual．Howeverifwehadawaytocomputethisheartvector．Wecoulduseitintheso1utionoftheforwardproblemandobtaintheECSforanybodysurfacelocation．Theapproachtosolvingthisproblemisbasedonaphysicalmodelofthehumantorso．Themodelprovidestransfercoefficientsthatrelatethepotentialsatmanybodysurfacepointstotheheartvector.Withthisinformation，wese1ectthreeECSleadsthatsummarizetheintrinsiccharacteristicsofthedesiredabnormalECStosimulate．Thenwesolvetheinverseproblemtofindthecardiacdipolevector.自然，對(duì)于任一個(gè)體心臟向量P和傳遞系數(shù)T

是未知。然而，若我們有計(jì)算心臟矢量方法，就可用之解正問(wèn)題并取得任意體表位置ECS。解這類問(wèn)題方法建立在人體胸廓物理模型基礎(chǔ)上。該模型提供了眾多體表點(diǎn)電位與心臟向量關(guān)系傳遞系數(shù)。用該信息，則只選擇三個(gè)ECS導(dǎo)聯(lián)就能概括欲模擬所希望異常ECS本質(zhì)特征。然后，就解逆問(wèn)題以求出心臟偶極向量。醫(yī)學(xué)數(shù)字信號(hào)處理心電圖專家講座第15頁(yè)Thus,forthreeheartvectorcomponent,therearethreelinearequationsoftheform所以，對(duì)于

三個(gè)心臟向量分量，有以下形式三個(gè)線性方程Px(t)=bx1v1(t)+bx2v2(t)+…+bxkvk(t)(2.5)

P

=B×V(2．4)

WhereBisa3xkmatrixofleadcoefficientsthatisdirectlyderivedfrominvertingthetransfercoefficientsmatrixT.

醫(yī)學(xué)數(shù)字信號(hào)處理心電圖專家講座第16頁(yè)IfweselectkbodysurfaceECSleads[v1(t),v2(t),…，vk(t)]forwhichtheleadcoefficients，T(orB)，areknownfromthephysicalmodelofthehumantorso,wecansolvetheinverseproblemandcomputethetime–varyingheartvector,P,usingEq.(2.4).Oncewehavethesedipolecomponents,wesolvetheforwardproblemusingEq.(2.3)tocomputetheECSforanypointonthebodysurface.假如選擇了K個(gè)體表ECS導(dǎo)聯(lián)[v1(t),v2(t),…vk(t)]，且由人體胸廓物理模型得知了導(dǎo)聯(lián)絡(luò)數(shù)T(或B），則就可由(2.4)式求解逆問(wèn)題并計(jì)算時(shí)變心臟向量P。一旦有了這些偶極分量，則就可用方程(2.3)解正問(wèn)題以計(jì)算任意點(diǎn)ECS.醫(yī)學(xué)數(shù)字信號(hào)處理心電圖專家講座第17頁(yè)2.1.4GenesisoftheECS2.1.4心電起源TimevaryingmotionofthecardiacvectorproducesthebodysurfaceECSforoneheartbeatwithitscharacteristicPandTwavesandQRScomplex.心臟向量時(shí)變運(yùn)動(dòng)產(chǎn)生體表心電，每搏都有其

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

醫(yī)學(xué)數(shù)字信號(hào)處理心電圖專家講座第18頁(yè)Forthepointsintimethatthevectorpointstowardtheelectrodeconnectedtothepositiveterminaloftheamplifier,theoutputECSwillbepositive-going．Ifitpointstothenegativeelectrode，theECSwillbenegative．(Thefollowingstatementisbetterandmoredetailed.“Ifthevectorpointstotheelectrodeconnectedtothenegativeterminaloftheamplifier,theECSwillbenegative”．)

在心臟矢量指向電極連到放大器正端那些時(shí)間點(diǎn)，輸出ECS為正。若心電向量指向電極連到放大器負(fù)端，則輸出ECS為負(fù)。醫(yī)學(xué)數(shù)字信號(hào)處理心電圖專家講座第19頁(yè)Figure2.8Electrocardiogram(ECG)foronenormalheartbeatshowingtypicalamplitudesandtimedurationfortheP,QRS,Twaves.

醫(yī)學(xué)數(shù)字信號(hào)處理心電圖專家講座第20頁(yè)Figure2.9Relationshipbetweenthespreadofcardiacelectricalactivationrepresentatvarioustimeinstantsbyasummingvector(intheupperframes)andthegenesisoftheECS(inthelowerframes).

醫(yī)學(xué)數(shù)字信號(hào)處理心電圖專家講座第21頁(yè)

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.醫(yī)學(xué)數(shù)字信號(hào)處理心電圖專家講座第22頁(yè)

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.

圖2.9(a)中，始于竇房結(jié)、慢運(yùn)動(dòng)心房去極化，產(chǎn)生P波。正如圖2.9(b)所表示，信號(hào)經(jīng)過(guò)房室結(jié)時(shí)被延遲，產(chǎn)生P波后等電區(qū)。然后，當(dāng)Purkinje系統(tǒng)開(kāi)始發(fā)送刺激到心室肌時(shí)，Q波開(kāi)始發(fā)生。在圖2.9(c)中，心室肌快速去極化表現(xiàn)為大而快速運(yùn)動(dòng)矢量，開(kāi)始產(chǎn)生R波。圖2.9(d)說(shuō)明，最大矢量代表了大多數(shù)細(xì)胞去極化時(shí)間點(diǎn)，產(chǎn)生R波峰。圖2.9(e)是激動(dòng)向心室基底部(向圖頂部)傳輸時(shí)心室去極化終末時(shí)相，產(chǎn)生S波。醫(yī)學(xué)數(shù)字信號(hào)處理心電圖專家講座第23頁(yè)2.1.5Thestandardlimbleads

2.1.5標(biāo)準(zhǔn)肢體導(dǎo)聯(lián)I+III–II=0(2.6)

Figure2.10LeadsI,IIandIIIarethepotentialsdifferencebetweenthelimbsasindicated.RAandLAaretherightandleftarmsandLListheleftleg.FromKirchhoff’svoltageslaw,thesumofthevoltagesaroundaloopequalszero.Thus醫(yī)學(xué)數(shù)字信號(hào)處理心電圖專家講座第24頁(yè)2.1.6Theaugmentedlimbleads

2.1.6加壓肢體導(dǎo)聯(lián)

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)醫(yī)學(xué)數(shù)字信號(hào)處理心電圖專家講座第25頁(yè)2.2ECSleadsystems

2.2心電導(dǎo)聯(lián)絡(luò)統(tǒng)

心電學(xué)中有三種慣用基本導(dǎo)聯(lián)絡(luò)統(tǒng)。最通用是12導(dǎo)聯(lián)方法，該法定義了12種電位差集合，組成標(biāo)準(zhǔn)臨床ECG。第二種導(dǎo)聯(lián)絡(luò)統(tǒng)要求了統(tǒng)計(jì)VCG電極位置。經(jīng)典監(jiān)護(hù)系統(tǒng)只分析1或2個(gè)導(dǎo)聯(lián)。

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

醫(yī)學(xué)數(shù)字信號(hào)處理心電圖專家講座第26頁(yè)2.2.112leadECS

2.2.112導(dǎo)聯(lián)心電

醫(yī)學(xué)數(shù)字信號(hào)處理心電圖專家講座第27頁(yè)Figure2.16

Standard12-leadclinicalelectrocardiogram.(a)LeadI.(b)LeadII.(c)LeadIII.Notetheamplifierpolarityforeachoftheselimbleads.(d)aVR.(e)VL.(f)aVF.Theseaug-mentedleadsrequireresistornetworkswhichaveragetwolimbpotentialswhilerecordingthethird.(g)ThesixVleadsarerecordedreferencedtoWilson’scentralterminalwhichistheaverageofallthreelimbpotentials.EachofthesixleadslabeledV1-V6arerecordedfromadifferentanatomicalsiteonthechest.醫(yī)學(xué)數(shù)字信號(hào)處理心電圖專家講座第28頁(yè)醫(yī)學(xué)數(shù)字信號(hào)處理心電圖專家講座第29頁(yè)中心電端C相連。全部單極導(dǎo)聯(lián)皆參考此點(diǎn)電壓。全部輸入端皆采用高輸入阻抗電路。醫(yī)學(xué)數(shù)字信號(hào)處理心電圖專家講座第30頁(yè)12個(gè)標(biāo)準(zhǔn)心電圖導(dǎo)聯(lián)雙極肢體導(dǎo)聯(lián)：I、II、III單極加壓肢體導(dǎo)聯(lián)：aVL、aVR、aVF胸導(dǎo)聯(lián)：V1、V2、V3、V4、V5、V6電極安放位置：肢體導(dǎo)聯(lián)監(jiān)護(hù)導(dǎo)聯(lián)醫(yī)學(xué)數(shù)字信號(hào)處理心電圖專家講座第31頁(yè)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.

醫(yī)學(xué)數(shù)字信號(hào)處理心電圖專家講座第32頁(yè)2.2.2VCSleadsystem2.2.2向量心電導(dǎo)聯(lián)絡(luò)統(tǒng)Figure2.18TheelectrodeplacementfortheFrankvectorECSsystem.Figure2.19Theresistornetworkforcombiningbodysurfacepotentialstoproducethethreetime-varyingscalarleadsoftheFrankVCSleadsystem.

醫(yī)學(xué)數(shù)字信號(hào)處理心電圖專家講座第33頁(yè)Figure2.20Thevectorcardiogramofanormalmalepatient.Thethreetime-varyingscalarleadsforoneheartbeatareshownontheleftandarethex,yandzleadsfromtoptobottom.Inthetopcenteristhefrontalviewofthetipofthevectorasitmovesthroughoutonecomputedheartbeat.Inbottomcenterisatransverseviewofthevectorlooplookingdownfromabovethepatient.Onthefarrightisaleftsagittalviewlookingtowardtheleftsideofthepatient.

醫(yī)學(xué)數(shù)字信號(hào)處理心電圖專家講座第34頁(yè)2.2.3MonitoringECS

leadsystem2.2.3監(jiān)護(hù)心電導(dǎo)聯(lián)絡(luò)統(tǒng)Monitoringapplicationdonotusestandardelectrodepositionsbuttypicallyusetwoleads.Sincetheprincipalgoalofthesesystemsistoreliablyrecogniz