Electrocardiographic Interpretation of Cardiac Muscle and Coronary Blood Flow Abnormalities: Vectorial Analysis

Vectors can Represent Electrical Potentials

To understand how cardiac abnormalities affect the contours of the ECG, one must first become familiar with the concept of vectors and vectorial analysis as applied to electrical potentials in and around the heart. In Chapter 11 , we pointed out that heart current flows in a particular direction in the heart at a given instant during the cardiac cycle. A vector is an arrow that points in the direction of the electrical potential generated by the current flow, with the arrowhead in the positive direction. Also, by convention, the length of the arrow is drawn proportional to the voltage of the potential.

Resultant Vector in the Heart at Any Given Instant

The shaded area and the minus signs in Figure 12-1 show depolarization of the ventricular septum and of parts of the apical endocardial walls of the two ventricles. At the instant of heart excitation, electrical current flows between the depolarized areas inside the heart and the nondepolarized areas on the outside of the heart, as indicated by the long elliptical arrows. Some current also flows inside the heart chambers directly from the depolarized areas toward the still polarized areas. Overall, considerably more current flows downward from the base of the ventricles toward the apex than in the upward direction. Therefore, the summated vector of the generated potential at this particular instant, called the instantaneous mean vector, is represented by the long black arrow drawn through the center of the ventricles in a direction from the base toward the apex. Furthermore, because the summated current is quite large, the potential is large, and the vector is long.

The Direction of a Vector is Denoted in Terms of Degrees

When a vector is exactly horizontal and directed toward the person’s left side, the vector is said to extend in the direction of 0 degrees, as shown in Figure 12-2 . From this zero reference point, the scale of vectors rotates clockwise; when the vector extends from above and straight downward, it has a direction of +90 degrees, when it extends from the person’s left to right, it has a direction of +180 degrees, and when it extends straight upward, it has a direction of −90 (or +270) degrees.

In a normal heart, the average direction of the vector during spread of the depolarization wave through the ventricles, called the mean QRS vector, is about +59 degrees, which is shown by vector A drawn through the center of Figure 12-2 in the +59-degree direction. This means that during most of the depolarization wave, the apex of the heart remains positive with respect to the base of the heart, as discussed later in this chapter.

Axis for Each Standard Bipolar Lead and Each Unipolar Limb Lead

In Chapter 11 , the three standard bipolar and the three unipolar limb leads are described. Each lead is actually a pair of electrodes connected to the body on opposite sides of the heart, and the direction from negative electrode to positive electrode is called the axis of the lead. Lead I is recorded from two electrodes placed respectively on the two arms. Because the electrodes lie exactly in the horizontal direction, with the positive electrode to the left, the axis of lead I is 0 degrees.

In recording lead II, electrodes are placed on the right arm and left leg. The right arm connects to the torso in the upper right-hand corner, and the left leg connects in the lower left-hand corner. Therefore, the direction of this lead is about +60 degrees.

By similar analysis, it can be seen that lead III has an axis of about +120 degrees, lead aVR, +210 degrees, lead aVF, +90 degrees, and lead aVL, −30 degrees. The directions of the axes of all these leads are shown in Figure 12-3 , which is known as the hexagonal reference system. The polarities of the electrodes are shown by the plus and minus signs in the figure. The reader must learn these axes and their polarities, particularly for the bipolar limb leads I, II, and III, to understand the remainder of this chapter.

Vectorial Analysis of Potentials Recorded in Different Leads

Figure 12-4 shows a partially depolarized heart, with vector A representing the instantaneous mean direction of current flow in the ventricles. In this case, the direction of the vector is +55 degrees, and the voltage of the potential, represented by the length of vector A, is 2 millivolts. In the diagram below the heart, vector A is shown again, and a line is drawn to represent the axis of lead I in the 0-degree direction. To determine how much of the voltage in vector A will be recorded in lead I, a line perpendicular to the axis of lead I is drawn from the tip of vector A to the lead I axis, and a so-called projected vector (B) is drawn along the lead I axis. The arrow of this projected vector points toward the positive end of the lead I axis, which means that the record momentarily being recorded in the ECG of lead I is positive. The instantaneous recorded voltage will be equal to the length of B divided by the length of A times 2 millivolts, or about 1 millivolt.

Figure 12-5 shows another example of vectorial analysis. In this example, vector A represents the electrical potential and its axis at a given instant during ventricular depolarization in a heart in which the left side of the heart depolarizes more rapidly than the right side. In this case, the instantaneous vector has a direction of 100 degrees, and its voltage is again 2 millivolts. To determine the potential actually recorded in lead I, we draw a perpendicular line from the tip of vector A to the lead I axis and find projected vector B. Vector B is very short, and this time it is in the negative direction, indicating that at this particular instant, the recording in lead I will be negative (below the zero line in the ECG), and the voltage recorded will be small, about −0.3 millivolts. This figure demonstrates that when the vector in the heart is in a direction almost perpendicular to the axis of the lead, the voltage recorded in the ECG of this lead is very low. Conversely, when the heart vector has almost exactly the same axis as the lead axis, essentially the entire voltage of the vector will be recorded.

Vectorial Analysis of Potentials in the Three Standard Bipolar Limb Leads

In Figure 12-6 , vector A depicts the instantaneous electrical potential of a partially depolarized heart. To determine the potential recorded at this instant in the ECG for each one of the three standard bipolar limb leads, perpendicular lines (the dashed lines ) are drawn from the tip of vector A to the three lines representing the axes of the three different standard leads, as shown in the figure. The projected vector B depicts the potential recorded at that instant in lead I, projected vector C depicts the potential in lead II, and projected vector D depicts the potential in lead III. In each of these, the record in the ECG is positive—that is, above the zero line—because the projected vectors point in the positive directions along the axes of all the leads. The potential in lead I (vector B ) is about half of that of the actual potential in the heart (vector A ), in lead II (vector C ), it is almost equal to that in the heart and, in lead III (vector D ), it is about one-third that in the heart.

An identical analysis can be used to determine potentials recorded in augmented limb leads, except that the respective axes of the augmented leads (see Figure 12-3 ) are used in place of the standard bipolar limb lead axes used for Figure 12-6 .

Vectors That Occur at Successive Intervals During Depolarization of the Ventricles—The qrs Complex

When the cardiac impulse enters the ventricles through the atrioventricular bundle, the first part of the ventricles to become depolarized is the left endocardial surface of the septum. Then, depolarization spreads rapidly to involve both endocardial surfaces of the septum, as shown by the darker shaded portion of the ventricle in Figure 12-7 A . Next, depolarization spreads along the endocardial surfaces of the remainder of the two ventricles, as shown in Figure 12-7 B and C . Finally, it spreads through the ventricular muscle to the outside of the heart, as shown progressively in Figure 12-7 C to E .

At each stage in Figure 12-7 , A to E , the instantaneous mean electrical potential of the ventricles is represented by a red vector superimposed on the ventricle in each figure. Each of these vectors is then analyzed by the method described in the preceding section to determine the voltages that will be recorded at each instant in each of the three standard electrocardiographic leads. To the right in each Figure is shown progressive development of the electrocardiographic QRS complex. Keep in mind that a positive vector in a lead will cause recording in the ECG above the zero line, whereas a negative vector will cause recording below the zero line.

Before proceeding with further consideration of vectorial analysis, it is essential that this analysis of the successive normal vectors presented in Figure 12-7 be understood. Each of these analyses should be studied in detail by the procedure given here. A short summary of this sequence follows.

In Figure 12-7 A , the ventricular muscle has just begun to be depolarized, representing an instant about 0.01 second after the onset of depolarization. At this time, the vector is short because only a small portion of the ventricles—the septum—is depolarized. Therefore, all electrocardiographic voltages are low, as recorded to the right of the ventricular muscle for each of the leads. The voltage in lead II is greater than the voltages in leads I and III because the heart vector extends mainly in the same direction as the axis of lead II.

In Figure 12-7 B , which represents about 0.02 second after onset of depolarization, the heart vector is long because much of the ventricular muscle mass has become depolarized. Therefore, the voltages in all electrocardiographic leads have increased.

In Figure 12-7 C , about 0.035 second after onset of depolarization, the heart vector is becoming shorter, and the recorded electrocardiographic voltages are lower, because the outside of the heart apex is now electronegative, neutralizing much of the positivity on the other epicardial surfaces of the heart. Also, the axis of the vector is beginning to shift toward the left side of the chest because the left ventricle is slightly slower to depolarize than the right ventricle. Therefore, the ratio of the voltage in lead I to that in lead III is increasing.

In Figure 12-7 D , about 0.05 second after onset of depolarization, the heart vector points toward the base of the left ventricle, and it is short because only a minute portion of the ventricular muscle is still polarized positive. Because of the direction of the vector at this time, the voltages recorded in leads II and III are both negative—that is, below the line—whereas the voltage of lead I is still positive.

In Figure 12-7 E , about 0.06 second after onset of depolarization, the entire ventricular muscle mass is depolarized so that no current flows around the heart and no electrical potential is generated. The vector becomes zero, and the voltages in all leads become zero.

Thus, the QRS complexes are completed in the three standard bipolar limb leads.

Sometimes the QRS complex has a slight negative depression at its beginning in one or more of the leads, which is not shown in Figure 12-7 ; this depression is the Q wave. When it occurs, it is caused by initial depolarization of the left side of the septum before the right side, which creates a weak vector from left to right for a fraction of a second before the usual base to apex vector occurs. The major positive deflection shown in Figure 12-7 is the R wave, and the final negative deflection is the S wave.

Electrocardiogram During Ventri-cular Repolarization—The t Wave

After the ventricular muscle has become depolarized, about 0.15 second later, repolarization begins and proceeds until complete, at about 0.35 second. This repolarization causes the T wave in the ECG.

Because the septum and endocardial areas of the ventricular muscle depolarize first, it seems logical that these areas should repolarize first as well. However, this is not the usual case, because the septum and other endocardial areas have a longer period of contraction than most of the external surfaces of the heart. Therefore, the greatest portion of ventricular muscle mass to repolarize first is the entire outer surface of the ventricles, especially near the apex of the heart. The endocardial areas, conversely, normally repolarize last. This sequence of repolarization is postulated to be caused by the high blood pressure inside the ventricles during contraction, which greatly reduces coronary blood flow to the endocardium, thereby slowing repolarization in the endocardial areas.

Because the outer apical surfaces of the ventricles repolarize before the inner surfaces, the positive end of the overall ventricular vector during repolarization is toward the apex of the heart. As a result, the normal T wave in all three bipolar limb leads is positive, which is also the polarity of most of the normal QRS complex.

In Figure 12-8 , five stages of repolarization of the ventricles are denoted by progressive increase of the light tan areas—the repolarized areas. At each stage, the vector extends from the base of the heart toward the apex until it disappears in the last stage. At first, the vector is relatively small because the area of repolarization is small. Later, the vector becomes stronger because of greater degrees of repolarization. Finally, the vector becomes weaker again because the areas of depolarization still persisting become so slight that the total quantity of current flow decreases. These changes also demonstrate that the vector is greatest when about half the heart is in the polarized state and about half is depolarized.

The changes in the ECGs of the three standard limb leads during repolarization are noted under each of the ventricles, depicting the progressive stages of repolarization. Thus, over about 0.15 second, the period of time required for the entire process to take place, the T wave of the ECG is generated.

Atrial Depolarization—The P Wave

Depolarization of the atria begins in the sinus node and spreads in all directions over the atria. Therefore, the point of original electronegativity in the atria is at about the point of entry of the superior vena cava where the sinus node lies, and the direction of initial depolarization is denoted by the black vector in Figure 12-9 . Furthermore, the vector remains generally in this direction throughout the process of normal atrial depolarization. Because this direction is generally in the positive directions of the axes of the three standard bipolar limb leads I, II, and III, the ECGs recorded from the atria during depolarization are also usually positive in all three of these leads, as shown in Figure 12-9 . This record of atrial depolarization is known as the atrial P wave.

Vectorcardiogram

As noted previously, the vector of current flow through the heart changes rapidly as the impulse spreads through the myocardium. It changes in two aspects. First, the vector increases and decreases in length because of increasing and decreasing voltage of the vector. Second, the vector changes direction because of changes in the average direction of the electrical potential from the heart. The vectorcardiogram depicts these changes at different times during the cardiac cycle, as shown in Figure 12-10 .

In the large vectorcardiogram of Figure 12-10 , point 5 is the zero reference point, and this point is the negative end of all the successive vectors. While the heart muscle is polarized between heartbeats, the positive end of the vector remains at the zero point because there is no vectorial electrical potential. However, as soon as current begins to flow through the ventricles at the beginning of ventricular depolarization, the positive end of the vector leaves the zero reference point.

When the septum first becomes depolarized, the vector extends downward toward the apex of the ventricles, but it is relatively weak, thus generating the first portion of the ventricular vectorcardiogram, as shown by the positive end of vector 1. As more of the ventricular muscle becomes depolarized, the vector becomes stronger and stronger, usually swinging slightly to one side. Thus, vector 2 of Figure 12-10 represents the state of depolarization of the ventricles about 0.02 second after vector 1. After another 0.02 second, vector 3 represents the potential, and vector 4 occurs in another 0.01 second. Finally, the ventricles become totally depolarized, and the vector becomes zero once again, as shown at point 5.

The elliptical figure generated by the positive ends of the vectors is called the QRS vectorcardiogram.

Determining the Electrical Axis From Standard Lead Electrocardiograms

Clinically, the electrical axis of the heart is usually estimated from the standard bipolar limb lead ECGs rather than from the vectorcardiogram. Figure 12-11 shows a method for performing this estimation. After recording the standard leads, one determines the net potential and polarity of the recordings in leads I and III. In lead I of Figure 12-11 , the recording is positive, and in lead III, the recording is mainly positive but negative during part of the cycle. If any part of a recording is negative, this negative potential is subtracted from the positive part of the potential to determine the net potential for that lead, as shown by the arrow to the right of the QRS complex for lead III. Then, each net potential for leads I and III is plotted on the axes of the respective leads, with the base of the potential at the point of intersection of the axes, as shown in Figure 12-11 .

To determine the vector of the total QRS ventricular mean electrical potential, one draws perpendicular lines (the dashed lines in the figure) from the apices of leads I and III, respectively. The point of intersection of these two perpendicular (dashed) lines represents, by vectorial analysis, the apex of the mean QRS vector in the ventricles, and the point of intersection of the lead I and lead III axes represents the negative end of the mean vector. Therefore, the mean QRS vector is drawn between these two points. The approximate average potential generated by the ventricles during depolarization is represented by the length of this mean QRS vector, and the mean electrical axis is represented by the direction of the mean vector. Thus, the orientation of the mean electrical axis of the normal ventricles, as determined in Figure 12-11 , is 59 degrees positive (+59 degrees).