6G · The Electrocardiogram: Geometry and Electrical Axis
This guest lecture, with no slides in the deck, picks up from the previous one (6F). Everything there was obtained with a single pair of electrodes, positive on the left arm and negative on the right arm, the so-called lead I configuration. That ignored geometry. Considering geometry lets you gauge the electrical position of the heart in the body, another useful diagnostic.
Why geometry matters¶
As a gedanken experiment, think of cells A and B as the heart placed in a giant vat of conductive saline.
Traditional placement. The positive electrode sees mostly the negative of cell B’s transmembrane potential, and the negative electrode sees mostly the negative of cell A’s transmembrane potential.
A diabolical placement. Position the electrodes so that V+ and V− both see an intermediate potential between the negatives of cell A’s and cell B’s transmembrane potentials. The EKG signal, the difference between V+ and V−, is then zero, even though the heart is still beating and generating electrical signals.
An intermediate placement. A geometric interpretation predicts the strength of the QRS. Draw an arrow from cell A to cell B whose length is proportional to the full strength of the QRS. Draw a line between the negative and positive electrodes. Project the cell-A-to-cell-B arrow onto this inter-electrode line. The projection gives the size of the QRS deflection.
With a standard set of leads you can work out the electrical axis, the main electrical direction of the heart. Changes in the axis often point to disease states, and should be used in a clinical, correlative manner to corroborate suspicions about clinical abnormalities.
The standard leads¶
Frontal plane leads I, II, and III.
Lead I: positive electrode on the left arm, negative on the right arm. The lead used so far.
Lead II: positive electrode on the left leg, negative electrode still on the right arm.
Lead III: negative electrode on the left arm, positive electrode on the left leg.
Reasoning from cells A and B in the vat of conductive medium, you can begin to predict how the size of the QRS changes between the lead I, II, and III configurations.
Augmented limb leads. For ease of reading there are three more frontal plane leads. These are not truly new placements. They are electronically manufactured to correspond to different frontal leads, for the convenience of the electrophysiological reader, created from the signals of leads I, II, and III.
aVR: positive electrode on the right arm. The negative electrode is a phantom, electronically made as the average of negative electrodes on the left leg and left arm. It is as if you physically placed the negative electrode somewhere around the left thigh, an intermediate placement. You do not actually do this.
aVL: positive electrode on the left arm. The negative electrode is the electronic average of negative electrodes on the left leg and right arm, as if placed somewhere around the right thigh.
aVF: positive electrode on the left leg. The negative electrode is the electronic average of negative electrodes on the left arm and right arm.
Together, leads I, II, III, aVR, aVL, and aVF form the six frontal leads.
Precordial leads. Here the negative electrode is again a phantom: the electronic average of negative electrodes on the left arm, right arm, and left leg. It acts as if it sits in the middle of the body, in the middle of the heart. The positive electrode is real, placed at very specific locations on the front of the patient’s chest. There are six placements, V1 through V6, with landmarks registered relative to the intercostal spaces.
Geometrically, the frontal plane leads give the electrical direction of the heart projected onto the patient’s frontal plane. The precordial leads give the electrical axis in the other plane, projecting transversely out from the chest. V1 through V6 are very important at times, but they are somewhat esoteric and not normally read on the floor; they are left for the cardiology consult. The rest of this lecture focuses on determining the electrical direction of the heart in the frontal plane, using the frontal plane leads.
Finding the axis: the geometric method¶
Measure the height of the QRS wave in two leads. Pick one in which the signal is close to the largest and most positive, and a second in which it is about half as large.
Mark the measured heights on the circle of axes, using arbitrary length units chosen to make the most of the scale of your axes.
Draw perpendicular lines through each marking.
Connect the center of the circle of axes to the intersection of the two perpendicular lines.
The vector drawn in step 4 is the axis of the heart: its main electrical direction lies along that vector. In the lecture’s example, the axis is about 95°.
The geometric method fits very nicely with the cosine math of the vat-and-electrode thinking, and it is very good as a teaching tool. In practice few people use it.
Finding the axis: the inspection method¶
A more practical, quicker method.
Find a lead in which the wave of interest is almost zero: isoelectric, deflecting upward as much as downward. Say this lead has an axis of X degrees. The axis of the wave must be perpendicular, or nearly perpendicular, to that lead.
Decide which way it is perpendicular. It could be one way or the other, so examine a second lead to discriminate whether the wave’s axis is X + 90° or X − 90°.
In the example, aVL is isoelectric. The axis of aVL is −30°, so the heart’s axis must be perpendicular to aVL.
Now inspect whether the vector points toward the positive end of lead II (+60°) or the negative end (−120°). In this example lead II is positive, so the estimated mean QRS axis is +60°. With this you can see the axis of the heart in a quick jiffy.
What the axis tells you¶
As a rough rule of thumb:
Electrical axis and associated conditions
Axis | Name | Examples |
|---|---|---|
0° to 90° | Normal | |
90° to 180° | Right axis | Right ventricular hypertrophy |
0° to −30° | Mild left axis deviation | Obesity, stocky build, ascites |
−30° to −120° | Severe left axis deviation | Left ventricular hypertrophy, left bundle branch block |
Right axis and right ventricular hypertrophy. Many workers who spent their lives in the steel mills at Bethlehem Steel suffered lung diseases, perhaps from asbestos inhalation. The lung disease creates a high resistance to blood flow through the lungs, so the right heart works very hard and develops right ventricular hypertrophy. Many of these people could have right axis deviation.
Mild left axis deviation and obesity. The gut is so big and full of fat that the heart is shifted leftward, physically and electrically, mildly. A stocky build may be a euphemistic term for the same thing.
Mild left axis deviation and ascites. In liver failure there is protein mishandling and osmotic mismatch, and fluid essentially bleeds into the space surrounding the gut. Through mass and hydraulic pressure it pushes the heart up through the diaphragm, moving it to the left physically and electrically.
Severe left axis deviation and left ventricular hypertrophy. Too much of the left side of the heart drives the electrical wave.
Severe left axis deviation and left bundle branch block. The block stops rapid communication through the left side of the heart, slowing conduction and separating cell A and cell B further. From the geometric interpretation you would expect a fatter, perhaps taller, broader QRS, and a left axis deviation.
The detailed genesis of the QRS is left to the interested student, better done in the quiet of your own room with the reading materials.
Summary¶
This lecture moved from the non-geometric two-cell picture to how geometry and lead placement shape the signal you see. By judiciously comparing the patterns and sizes of signals across leads, you gain insight into the main electrical direction, or disposition, of the heart, and can correlate the electrical axis with clinical conditions such as obesity, stocky build, ascites, and left or right ventricular hypertrophy.