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BIOMEDICAL DIGITAL SIGNAL PROCESSING,生物醫(yī)學數(shù)字信號處理,,,1,霍金教授的辦公室（劍橋大學）,“我的書每增加一個公式，讀者就減少一半” ——霍金教授,2,BME在百年諾貝爾 生理與醫(yī)學獎中的份額,美國的保羅-勞特布爾和英國的彼得-曼斯菲爾德共同獲得了2003年諾貝爾生理學或醫(yī)學獎--核磁共振成像技術--三維圖象,3,教材,作者：美國威斯康辛大學電氣與計算機工程系教授 前IEEE生物醫(yī)學工程學會主席 Willis J.Tompkins 書名：Biomedical Digital Signal Processing ISBN：7560925790 頁數(shù)：246,4,Lecture 2 Electrocardiology Electrocardiogram ECG,第2講 心電學,,5,,心臟機械收縮之前，先產(chǎn)生電激動，心房和心室的電激動可經(jīng)人體組織傳到體表。心電圖是利用心電圖機從體表記錄心臟每一心動周期所產(chǎn)生電活動變化曲線圖形。,6,心臟的特殊傳導系統(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（Pukinje fiber）構(gòu)成。心臟傳導系統(tǒng)與每一心動周期順序出現(xiàn)的心電變化密切相關。正常心電活動始于竇房結(jié)，興奮心房的同時經(jīng)結(jié)間束傳導至房室結(jié)（激動傳，然后循希氏束-左、右束支-普肯耶纖維順序傳導，最后興奮心室。這種先后有序的電激動的傳播，引起一系列電位改變，形成了心電圖上相應的波段。,7,,心電圖機是記錄心電圖的專用儀器，有單道心電圖機和多道心電圖機，多道心電圖機可以同時記錄多導聯(lián)的心電，最多有同時記錄12導聯(lián)的，而單道心電圖機只能順序記錄12個導聯(lián)，有手控的心電圖機，也有程控的、微電腦控制或數(shù)字式的心電圖機，在很多其它儀器中也常有心電記錄電路模塊。,8,2.1Electrocardiologicbasis,2.1 心電學基礎,,2.1.1 three basic techniques,2.1.1 三種基本技術,1. Standard clinical ECG（12 leads）,1. 標準臨床 ECG （12 導聯(lián)）,2. VCG (3 orthogonal leads),3. Monitoring ECG (1 or 2 lead(s) ),2. 向量心電圖 (三維正交導聯(lián)),3. 監(jiān)護 ECG (1或2 導聯(lián)),9,2.1.2 Electrodes,2.1.2 電極,,Figure 2.3 A silver-silver chloride ECG electrode. Many modern electrodes have electrolyte layers that are made of a firm gel which has adhesive properties. The firm gel minimizes the disturbance of the charge double layer.,10,,2.1.3 心電等效發(fā)生器,,Figure 2.4 Both the electrical and mechanical conditions of the heart are involved in determining the characteristics of the spread of electrical activity over the surface of the heart．A model of this activity is called a cardiac equivalent generator．,,,,,,2.1.3 The cardiac equivalent generator,,11,,,Figure 2.5 Einthoven equilateral triangle. RA and LA are the right and left arms and LL is the left leg.,,,,,,,,12,A current dipole is a current source and a current sink separated by a distance. Since such a dipole has magnitude and direction which change throughout a heartbeat as the cells in the heart depolarize, this leads to the vector representation.,電流偶極子是相隔一段距離的電流源和穴(漏)。當心肌細胞去極化 (讀注：實際應包含反極化和復極化)時，這樣一個偶極子的大小和方向在整個心搏周期都是變化的，這就導致了向量表示法。,P(t) = Px(t)X 十 Py(t)Y 十 Pz(t)Z (2.1),Where P(t) is the time-varying cardiac vector, Pi(t) are the orthogonal components of the vector also called scalar leads, and X,Y,Z are unit vectors in the x, y, z directions.,式中P(t) 是時變心臟偶極子，Pi(t) 為該矢量的正交分量，也稱為標量導聯(lián)， X,Y,Z 是X,Y,Z方向的單位矢量。,13,The forward solution provides the potential at any arbitrary point on the body surface for a given cardiac dipole. Expressed mathematically，,對于給定的心電偶極子，心電正問題的解提供了體表任意點的電位，數(shù)學上表示為，,vn(t) = tnxPx(t)十tnyPy(t)十tnzPy(t) (2.2),This forward so1utlon shows that the potential vn(t) ( i．e．,the ECS) at any point n on the body surface is given by the linear sum of the products of a set of transfer coefficients [tn i ] unique to that point and the Corresponding orthogonal dipole vector components [Pi(t)]．,14,The ECSs are time-varying as are the dipo1e components, while the transfer coefficients are only dependent on the thoracic geometry and inhomogeneities．Thus for a set of k body surface potentials (i. e., 1eads)， there is a set of k equations that can be expressed in matrix form,V = T×P (2.3),Where V is a k x l vector representing the time-varying potentials, T is a k x 3 matrix of transfer coefficients, Which are fixed for a given individual, and P is the 3 x 1 time-varying heart vector．,心電信號與偶極子分量一樣是時變的，而傳遞系數(shù)則只決定于胸部的幾何形狀和非均勻性。因此，一組 k 體表電位(即, 導聯(lián))， 就有 k equations個方程的方程組，并可表示成矩陣形式。,15,Of course, the heart vector and transfer coefficients are unknown for a given individual．However if we had a way to compute this heart vector．We could use it in the so1ution of the forward problem and obtain the ECS for any body surface location．The approach to solving this problem is based on a physical model of the human torso．The model provides transfer coefficients that relate the potentials at many body surface points to the heart vector. With this information，we se1ect three ECS leads that summarize the intrinsic characteristics of the desired abnormal ECS to simulate．Then we solve the inverse problem to find the cardiac dipole vector.,自然，對于任一個體心臟向量P和傳遞系數(shù)T 是未知的。然而，若我們有計算心臟矢量的方法，就可用之解正問題并獲得任意體表位置的ECS。解此類問題的方法建立在人體胸廓物理模型的基礎上。該模型提供了眾多體表點的電位與心臟向量的關系的傳遞系數(shù)。用該信息，則只選擇三個ECS導聯(lián)就能概括欲模擬的所希望的異常ECS的本質(zhì)特征。然后，就解逆問題以求出心臟偶極向量。,16,Thus, for three heart vector component, there are three linear equations of the form,因此，對于 三個心臟向量的分量，有如下形式的三個線性方程,Px(t) = bx1v1(t) + b x2 v2(t) + … + bxk vk(t) (2.5),P = B×V (2．4),Where B is a 3 x k matrix of lead coefficients that is directly derived from inverting the transfer coefficients matrix T.,17,,If we select k body surface ECS leads [v1(t), v2(t), …， vk(t)] for which the lead coefficients，T (or B)，are known from the physical model of the human torso, we can solve the inverse problem and compute the time–varying heart vector, P, using Eq. (2.4). Once we have these dipole components, we solve the forward problem using Eq. (2.3) to compute the ECS for any point on the body surface.,如果選擇了K個體表ECS導聯(lián)[v1(t), v2(t), … vk(t)] ，且由人體胸廓的物理模型得知了導聯(lián)系數(shù)T (或B） ，則就可由(2.4)式求解逆問題并計算時變的心臟向量P 。一旦有了這些偶極分量，則就可用方程(2.3)解正問題以計算任意點的ECS.,18,2.1.4 Genesis of the ECS,2.1.4 心電的起源,,,Time varying motion of the cardiac vector produces the body surface ECS for one heartbeat with its characteristic P and T waves and QRS complex.,心臟向量的時變運動產(chǎn)生體表心電，每搏都有其 特征性的P、T 波和QRS復合波。,,,Figure 2.7 Basic configuration for recording an electrocardiogram. Using electrodes attached to the body, the ECG is recorded with an instrumentation amplifier. (a) Transverse (top) view of a slice of the body showing the heart and lungs. (b) Frontal view showing electrodes connected in an approximate lead II configuration.,19,,,For the points in time that the vector points toward the electrode connected to the positive terminal of the amplifier, the output ECS will be positive-going．If it points to the negative electrode，the ECS will be negative．(The following statement is better and more detailed. “If the vector points to the electrode connected to the negative terminal of the amplifier, the ECS will be negative”．),在心臟矢量指向的電極連到放大器正端的那些時間點，輸出的ECS為正的。若心電向量指向的電極連到放大器負端，則輸出的ECS為負的。,20,Figure 2.8 Electrocardiogram (ECG) for one normal heartbeat showing typical amplitudes and time duration for the P, QRS, T waves.,21,,Figure 2.9 Relationship between the spread of cardiac electrical activation represent at various time instants by a summing vector (in the upper frames) and the genesis of the ECS (in the lower frames).,,22,In Figure 2.9(a), the slow moving depolarization of the atria which begins at the sinoatrial(SA) node produces the P wave. As Figure 2.9(b) shows, the signal is delayed in the atrioventricular (AV) node resulting in an isoelectric region after the P wave, then as the Purkinje system starts delivering the stimulus to the ventricular muscle, the onset of the Q wave occurs. In Figure 2.9(c), rapid depolarization of the ventricular muscle is depicted as a large, fast-moving vector which begins producing the R wave. Figure 2.9(d) illustrates that the maximal vector represents a point in time when most of the cells are depolarized, giving rise to the peak of the R wave. In Figure 2.9(e), the final phase of ventricular depolarization occurs as the excitation spreads toward the base of the ventricles (to the top in the picture) giving rise to the S wave.,23,In Figure 2.9(a), the slow moving depolarization of the atria which begins at the sinoatrial(SA) node produces the P wave. As Figure 2.9(b) shows, the signal is delayed in the atrioventri-cular (AV) node resulting in an isoelectric region after the P wave, then as the Purkinje system starts delivering the stimulus to the ventricular muscle, the onset of the Q wave occurs. In Figure 2.9(c),rapid depolarization of the ventricular muscle is depicted as a large, fast-moving vector which begins producing the R wave. Figure 2.9(d) illustrates that the maximal vector represents a point in time when most of the cells are depolarized, giving rise to the peak of the R wave. In Figure 2.9(e), the final phase of ventricular depolarization occurs as the excitation spreads toward the base of the ventricles (to the top in the picture) giving rise to the S wave.,圖2.9(a)中，始于竇房結(jié)的、慢運動的心房去極化，產(chǎn)生P波。正如圖2.9(b)所示，信號通過房室結(jié)時被延遲，產(chǎn)生P波后的等電區(qū)。然后，當Purkinje系統(tǒng)開始發(fā)送刺激到心室肌時，Q波開始發(fā)生。在圖2.9(c)中，心室肌的快速去極化表現(xiàn)為大而快速運動的矢量，開始產(chǎn)生R波。圖2.9(d)說明，最大矢量代表了大多數(shù)細胞去極化的時間點，產(chǎn)生R波的峰。圖2.9(e)是激動向心室的基底部(向圖的頂部)傳播時的心室去極化的終末時相，產(chǎn)生S波。,24,2.1.5 The standard limb leads,2.1.5 標準肢體導聯(lián),I + III – II = 0 (2.6),Figure 2.10 Leads I, II and III are the potentials difference between the limbs as indicated. RA and LA are the right and left arms and LL is the left leg.,From Kirchhoff’s voltages law, the sum of the voltages around a loop equals zero. Thus,25,,2.1.6 The augmented limb leads,2.1.6 加壓肢體導聯(lián),Figure 2.11 The augmented limb lead aVL is measured as shown.,From the bottom left loop,i×R+i×R-II=0 (2.8) or i×R=II/2 (2.9),From the bottom right loop,i×R+III+aVL=0 (2.10) Or aVL=i×R–III (2.11),Combining Eqs. (2.9) and (2.11) gives,aVL=II/2–III=(II-2×III)/2 (2.12),From the top center loop,II = III + I (2.13),Substituting gives,aVL=(III–I-2×III)/2=(I–III)/2 (2.14),26,2.2 ECS lead systems,2.2 心電導聯(lián)系統(tǒng),心電學中有三種常用的基本導聯(lián)系統(tǒng)。最通用的是12導聯(lián)方法，該法定義了12種電位差的集合，構(gòu)成標準臨床ECG。第二種導聯(lián)系統(tǒng)規(guī)定了記錄VCG的電極位置。典型的監(jiān)護系統(tǒng)只分析1或2個導聯(lián)。,There are three basic lead systems used in cardiology. The most popular is the 12-lead approach, which defines the set of 12 potential differences that make up the standard clinical ECG. A second lead system designates the location of electrodes for recording VCG. Monitoring systems typically analyze one or two leads.,27,2.2.1 12 lead ECS,2.2.1 12 導聯(lián)心電,,,,,28,,Figure 2.16 Standard 12-lead clinical electrocardiogram. (a) Lead I. (b) Lead II. (c) Lead III. Note the amplifier polarity for each of these limb leads. (d) aVR. (e) VL.(f) aVF. These aug-mented leads require resistor networks which average two limb potentials while recording the third. (g) The six V leads are recorded referenced to Wilson’s central terminal which is the average of all three limb potentials. Each of the six leads labeled V1-V6 are recorded from a different anatomical site on the chest.,29,,30,中心電端C相連。所有單極導聯(lián)皆參考此點電壓。所有輸入端皆采 用高輸入阻抗電路。,31,12個標準心電圖導聯(lián),雙極肢體導聯(lián)：I、II、III 單極加壓肢體導聯(lián)：aVL、aVR、aVF 胸導聯(lián)：V1、V2、V3、V4、V5、V6 電極安放的位置： 肢體導聯(lián) 監(jiān)護導聯(lián),32,,Figure 2.17 The 12-lead ECG of a normal patient. Calibration pulses on the left side designate 1 mV. The recording speed is 25 mm/s. Each minor division is I mm, so the major division are 5 mm. Thus in lead I, the R-wave amplitude is about 1.1 mV and the time between beats is almost 1 S (i. e., heart rate is about 60 bpm). The notes are ID 0042804, S=26, L=×2, C=×1, I, II, III, aVR, aVL, aVF, V1, V2, V3, V4, V5, V6, Patient NO: 4307400 respectively.,33,2.2.2 VCS lead system,2.2.2 向量心電導聯(lián)系統(tǒng),,,Figure 2.18 The electrode placement for the Frank vector ECS system.,Figure 2.19 The resistor network for combining body surface potentials to produce the three time-varying scalar leads of the Frank VCS lead system.,34,,Figure 2.20 The vectorcardiogram of a normal male patient. The three time-varying scalar leads for one heartbeat are shown on the left and are the x, y and z leads from top to bottom. In the top center is the frontal view of the tip of the vector as it moves throughout one computed heartbeat. In bottom center is a transverse view of the vector loop looking down from above the patient. On the far right is a left sagittal view looking toward the left side of the patient.,35,2.2.3 Monitoring ECS lead system,2.2.3 監(jiān)護心電導聯(lián)系統(tǒng),Monitoring application do not use standard electrode positions but typically use two leads. Since the principal goal of these systems is to reliably recognize each heartbeat and perform rhythm analysis, electrodes are placed so that the primary ECS has a large R-wave amplitude. This ensures a high signal-to-noise ratio for beat detection. Since Lead II has a large peak amplitude for many patients, this lead is frequently recommended as the first choice of a primary lead by many manufacturers. A secondary lead with different electrode placements serves as a backup in case the primary lead develops problems such as loss of electrode contact.,,監(jiān)護應用不采用標準電極位置，典型使用兩個導聯(lián)。因該系統(tǒng)的主要目標是可靠識別每一心搏，完成節(jié)律分析，所以電極的放置以能獲得最大R波幅度為準，這樣就能保證檢測心搏時有高的信噪比。因II導聯(lián)對很多病人都有大的峰值，故該導聯(lián)常被很多廠家推薦為首選導聯(lián)。第二種導聯(lián)有各種電極方法，作為主要導聯(lián)發(fā)生問題(如電極接觸不良)時的備用導聯(lián)。,36,2.3 ECS characteristics,2.3 心電信號特征,,Figure 2.21 Bandwidth used in electrocardiography. The standard clinical bandwidth for the 12-lead clinical ECG is 0.005-250Hz. Monitoring systems typically use a bandwidth of 0.5-50Hz. Cardiotachometers for heart rate determination of subjects with predominantly normal beats use a simple bandpass filter centered at 17Hz and with a Q(Q-factor: quality factor) of about 3 or 4.,37,心電圖機原理,體表心電經(jīng)電極、導聯(lián)線送至心電圖機，心電圖機主體從原理上可分為輸入回路、導聯(lián)選擇、放大電路、描筆驅(qū)動和走紙部分，現(xiàn)代心電圖機通常還有程控部分。,38,,,39,,40,導聯(lián)線,導聯(lián)線是連接電極和心電圖機的多股電纜線，各股電纜線應絞合在一起以減小磁場干擾，并屏蔽以減少電場干擾。,41,謝謝！,42,