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Fig. 1.3. Sketch of a typical ECG, showing the potential variations recorded by one lead during a heart cycle.

Fig. 1.4. A real ECG, from a healthy 30-year old male.

Figure 1.3 shows a very schematic and idealized ECG. In practice, the shape and amplitude of each signal will be different in the three leads, and it might be that not all five signals are visible in all leads. Figure 1.4 shows a real ECG, from lead V1, of a healthy 30-year old male. In this figure, showing several heart beats, the QRS-complexes are easily identified. The P-wave and the T-wave are visible, although they both have fairly low amplitude in this lead.

1.1.1 Physics and Physiology

The current sources that give rise to the ECG are caused by the electrical activation of the heart muscle cells. Because of the conductive properties of the body, these sources result in currents and potential variations that can be recorded on the body surface. The ECG is hence closely connected to cellular electrophysiology, but very useful interpretations of the ECG can be made with little attention to the underlying physiology. For instance, Waller and Einthoven introduced the very powerful simplification of viewing the heart as a dipole embedded in a volume conductor. This approach enables very simple and powerful interpretations of the ECG, and is still an essential part of modern electrocardiology.

The idea is based on the assumption that the body has the properties of a volume conductor, and that the sources of electrical current in the heart can be viewed as dipoles. A volume conductor is simply a three-dimensional conducting medium, while a dipole is a pair of opposite electrical charges with equal magnitude (-q, q), separated by a small distance d. Strictly speaking, a dipole has only two point charges, but various arrangements of multiple charges or charge distributions may also have properties similar to a dipole. A dipole generates an electrical field, and in a volume conductor this electrical field leads to currents throughout the medium. The relation between the electrical field and the current will be described in more detail in Chapter 2. The strength of a dipole, and the strength of the electrical field it generates, is characterized by the dipole moment, which is the product of the charge in each pole and the distance between the poles. The dipole moment has an associated direction, which is the direction from the negative to the positive pole. Denoting the dipole moment by p, we have

Fig. 1.5. The Einthoven triangle, formed by the three lead vectors I, II, and III. The signal recorded in each lead is the projection of the heart vector onto the lead vector.

p = qd, where d is the vector pointing from the negative to the positive pole.

The current sources present during the activation of the heart muscle can be approximated by a number of dipoles, with associated dipole moments. The sum of all the dipole moments gives a vector describing a single dipole, which characterizes the sources of electrical current in the heart. This vector is called the heart vector, and has been a central part of ECG analysis since it was introduced by Einthoven in the early 20th century. The position of the heart vector is assumed to be static, but its strength and orientation varies during the heart cycle.

The potentials recorded by the three Einthoven leads can be interpreted as projections of the heart vector onto the three lead vectors of the Einthoven triangle, as illustrated in Figure 1.5. Hence, the signal amplitude recorded in each lead can be used to construct the heart vector, and in this way it is possible to identify changes in the activation pattern. For instance, the current sources present in the heart during the QRS complex (see Figure 1.3) can be approximated by a dipole that is oriented downwards and to the left. The resulting heart vector is illustrated in Figure 1.5. We see that the vector is almost parallel to lead II, and nearly perpendicular to lead III. As illustrated by the vector projections, we therefore expect to see a large amplitude of the QRS complex in lead II, and a small amplitude in lead III. The amplitude in lead I will have an intermediate value. The directions of the three Einthoven leads have been chosen so that a normal activation pattern gives positive R-waves (the largest signal of the QRS-complex) in all three leads.

A surprisingly large amount of information can be extracted from the three limb leads used by Einthoven. In fact, since the three leads are sufficient to find the direction and strength of the heart vector, one may think that no additional information can be obtained by adding more leads. This would be the case if the heart were truly a dipole oriented in the frontal plane of the body, i.e. the plane defined by the position of the three limb electrodes. However, this simplified view of the heart is not always sufficient. Specifically, the heart vector is not always oriented in the frontal plane of the body, and the dipole approximation does not fully reproduce the complicated electrical activity in the heart. Therefore, more leads have been added, to produce a more accurate picture of the condition of the heart.

As noted above, the electrical potential at a point must always be measured relative to some reference potential, and the three limb leads defined by Einthoven are all bipolar leads. To obtain a good picture of the potential changes in a single point, it will be useful to have an independent reference, or a zero electrode, which changes very little during the course of a heart cycle. This concept was introduced by Wilson [144] and his group, who constructed an independent reference by connecting the three limb electrodes of Einthoven. The idea is that since no electrical charge enters or leaves the body during the heart cycle, the sum of all changes of potential in the body must be zero. Ideally, therefore, one would construct a zero electrode by connecting a large number of electrodes, distributed over the entire body. This would obviously be an inconvenient solution, and the connection of the three limb electrodes has been shown to give a reference electrode with sufficiently small variations. The obtained reference potential is referred to as the Wilson central terminal, and is used to construct unipolar leads, i.e. leads that characterize the potential changes at a single point only.

The six unipolar leads V1-V6 were constructed by placing six electrodes on the front of the chest, as illustrated in Figure 1.6, and recording the potential difference between these electrodes and the Wilson central terminal. Together with the original limb leads of Einthoven, these leads formed a standard nine-lead ECG in 1938. In 1942, three additional leads were introduced by Goldberger [48]; the augmented limb leads aVR, aVL, and aVF. These leads are defined by comparing the potential in each of the three limb electrodes to a reference defined by connecting the two other limb electrodes. They are normally referred to as unipolar leads, although the zero electrode is constructed using only two leads. These 12 leads still form the standard ECG, although there is an ongoing debate regarding the possible advantages of using additional leads; see e.g. [20]. Table 1.1 shows the definition of the 12 leads. The left column shows the name of each lead, the middle column shows the so-called exploring electrode, while the rightmost column lists the leads used to construct the zero electrode. The concept of a lead that consists of an exploring electrode and a zero electrode is common for unipolar leads, and for simplicity we use the same notation for the Einthoven leads.

Figure 1.7 shows a standard 12-lead ECG. One heart cycle is shown for all leads, and the position of each lead is standardized. The bottom line shows the recording of lead II for several heart cycles, included to give a better picture of the heart rhythm. The box-shaped signal to the right on every curve is a calibration artifact resulting from a 1 mV pulse. The position of each lead on the paper is standardized, as is the paper itself. Although barely visible in the figure, the ECG paper is divided into squares. The smallest squares are 1 mm x 1 mm and the larger squares are 5 mm x 5 mm. (The ECG shown in the figure has been scaled, so the dimensions do not match here.) In the horizontal direction each large square represents 0.2 seconds, while in the vertical direction one large square represents 0.5 mV. This standard, with 1 mV being represented by 1 cm, is so well-established that ECG signals are very often described in terms of millimeters rather than millivolts.

Fig. 1.6. The position of the chest electrodes. The leads V1-V6 are constructed by measuring the potential difference between each of these electrodes and the Wilson central terminal.
Table 1.1. The leads of the 12-lead ECG. The notation LL, LA, and RA is used for the left leg, left arm, and right arm electrodes, respectively. The six chest electrodes are denoted 1-6.

Lead

Exploring

Zero

0 0

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