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BIOMEDICAL DIGITAL SIGNAL PROCESSING,生物醫(yī)學(xué)數(shù)字信號(hào)處理,,,1,霍金教授的辦公室（劍橋大學(xué)）,“我的書每增加一個(gè)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(xué)獎(jiǎng)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(xué)或醫(yī)學(xué)獎(jiǎng)--核磁共振成像技術(shù)--三維圖象,3,教材,作者：美國威斯康辛大學(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 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(xué),,5,,心臟機(jī)械收縮之前，先產(chǎn)生電激動(dòng)，心房和心室的電激動(dòng)可經(jīng)人體組織傳到體表。心電圖是利用心電圖機(jī)從體表記錄心臟每一心動(dòng)周期所產(chǎn)生電活動(dòng)變化曲線圖形。,6,心臟的特殊傳導(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（Pukinje fiber）構(gòu)成。心臟傳導(dǎo)系統(tǒng)與每一心動(dòng)周期順序出現(xiàn)的心電變化密切相關(guān)。正常心電活動(dòng)始于竇房結(jié)，興奮心房的同時(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-普肯耶纖維順序傳導(dǎo)，最后興奮心室。這種先后有序的電激動(dòng)的傳播，引起一系列電位改變，形成了心電圖上相應(yīng)的波段。,7,,心電圖機(jī)是記錄心電圖的專用儀器，有單道心電圖機(jī)和多道心電圖機(jī)，多道心電圖機(jī)可以同時(shí)記錄多導(dǎo)聯(lián)的心電，最多有同時(shí)記錄12導(dǎo)聯(lián)的，而單道心電圖機(jī)只能順序記錄12個(gè)導(dǎo)聯(lián)，有手控的心電圖機(jī)，也有程控的、微電腦控制或數(shù)字式的心電圖機(jī)，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(xué)基礎(chǔ),,2.1.1 three basic techniques,2.1.1 三種基本技術(shù),1. Standard clinical ECG（12 leads）,1. 標(biāo)準(zhǔn)臨床 ECG （12 導(dǎo)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(dǎo)聯(lián)),3. 監(jiān)護(hù) ECG (1或2 導(dǎo)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(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)，這樣一個(gè)偶極子的大小和方向在整個(gè)心搏周期都是變化的，這就導(dǎo)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(shí)變心臟偶極子，Pi(t) 為該矢量的正交分量，也稱為標(biāo)量導(dǎo)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(duì)于給定的心電偶極子，心電正問題的解提供了體表任意點(diǎn)的電位，數(shù)學(xué)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(hào)與偶極子分量一樣是時(shí)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(dǎo)聯(lián))， 就有 k equations個(gè)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(duì)于任一個(gè)體心臟向量P和傳遞系數(shù)T 是未知的。然而，若我們有計(jì)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(chǔ)上。該模型提供了眾多體表點(diǎn)的電位與心臟向量的關(guān)系的傳遞系數(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(duì)于 三個(gè)心臟向量的分量，有如下形式的三個(gè)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(gè)體表ECS導(dǎo)聯(lián)[v1(t), v2(t), … vk(t)] ，且由人體胸廓的物理模型得知了導(dǎo)聯(lián)系數(shù)T (或B） ，則就可由(2.4)式求解逆問題并計(jì)算時(shí)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(jì)算任意點(diǎn)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(shí)變運(yùn)動(dòng)產(chǎn)生體表心電，每搏都有其 特征性的P、T 波和QRS復(fù)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(shí)間點(diǎn)，輸出的ECS為正的。若心電向量指向的電極連到放大器負(fù)端，則輸出的ECS為負(fù)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(yùn)動(dòng)的心房去極化，產(chǎn)生P波。正如圖2.9(b)所示，信號(hào)通過房室結(jié)時(shí)被延遲，產(chǎn)生P波后的等電區(qū)。然后，當(dāng)Purkinje系統(tǒng)開始發(fā)送刺激到心室肌時(shí)，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(yùn)動(dòng)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(xì)胞去極化的時(shí)間點(diǎn)，產(chǎn)生R波的峰。圖2.9(e)是激動(dòng)向心室的基底部(向圖的頂部)傳播時(shí)的心室去極化的終末時(shí)相，產(chǎn)生S波。,24,2.1.5 The standard limb leads,2.1.5 標(biāo)準(zhǔn)肢體導(dǎo)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(dǎo)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(dǎo)聯(lián)系統(tǒng),心電學(xué)中有三種常用的基本導(dǎo)聯(lián)系統(tǒng)。最通用的是12導(dǎo)聯(lián)方法，該法定義了12種電位差的集合，構(gòu)成標(biāo)準(zhǔn)臨床ECG。第二種導(dǎo)聯(lián)系統(tǒng)規(guī)定了記錄VCG的電極位置。典型的監(jiān)護(hù)系統(tǒng)只分析1或2個(gè)導(dǎo)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(dǎo)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(dǎo)聯(lián)皆參考此點(diǎn)電壓。所有輸入端皆采 用高輸入阻抗電路。,31,12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 電極安放的位置： 肢體導(dǎo)聯(lián) 監(jiān)護(hù)導(dǎo)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(dǎo)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(hù)心電導(dǎo)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(hù)應(yīng)用不采用標(biāo)準(zhǔn)電極位置，典型使用兩個(gè)導(dǎo)聯(lián)。因該系統(tǒng)的主要目標(biāo)是可靠識(shí)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(zhǔn)，這樣就能保證檢測心搏時(shí)有高的信噪比。因II導(dǎo)聯(lián)對(duì)很多病人都有大的峰值，故該導(dǎo)聯(lián)常被很多廠家推薦為首選導(dǎo)聯(lián)。第二種導(dǎo)聯(lián)有各種電極方法，作為主要導(dǎo)聯(lián)發(fā)生問題(如電極接觸不良)時(shí)的備用導(dǎo)聯(lián)。,36,2.3 ECS characteristics,2.3 心電信號(hào)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(jī)原理,體表心電經(jīng)電極、導(dǎo)聯(lián)線送至心電圖機(jī)，心電圖機(jī)主體從原理上可分為輸入回路、導(dǎo)聯(lián)選擇、放大電路、描筆驅(qū)動(dòng)和走紙部分，現(xiàn)代心電圖機(jī)通常還有程控部分。,38,,,39,,40,導(dǎo)聯(lián)線,導(dǎo)聯(lián)線是連接電極和心電圖機(jī)的多股電纜線，各股電纜線應(yīng)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,