6F · The Electrocardiogram: A Two-Cell Model

This is a guest lecture with no slides in the deck. It treats the EKG as a noninvasive window onto the electrical workings of the heart, in three parts: the phenomenology of the EKG, a two-cell model that explains it, and a rational interpretation of EKG abnormalities using that model.

Phenomenology¶

Go back to the 1800s, before modern medicine. Electricity was new, and human biology as a science was new. In that somewhat mystical setting, physiologists began connecting voltage recordings, a very physical science, with the human body. Connect the positive electrode of a galvanometer (an old-fashioned voltmeter) to a person’s left arm and the negative electrode to the right arm, and small but reproducible signals of about 1 millivolt appear in the noise. Strikingly, they coincide with each beat of the heart.

Each heartbeat gives the same stereotyped response: a tiny wiggle, then a longer, stronger wiggle, then a little wiggle again. Even before anyone understood it, there was a deep-seated belief that this signal was intimately related to the electrical workings of the heart. More than a century later that belief has proven well founded. The EKG is laden with mechanistic information about the cellular electrophysiological properties of the heart.

• The P wave, the little blip at the start, relates to atrial depolarization.

• The sharp, tall QRS complex relates to ventricular depolarization.

• The T wave relates to ventricular repolarization.

The EKG is thus an extremely simple but noninvasive and powerful assessment tool for the heart’s electrical function. It predates MRI as a noninvasive tool, and its utility remains undiminished.

The mechanism can get very complicated. A beautifully simple one, still correct in its broad brushstrokes, was posited by two British physiologists, Burdon-Sanderson and Page, in a theory published in 1883 linking the EKG to the cellular electrophysiological events of the heart. The goal here is a mechanistic understanding of the EKG and how it changes with disease states and electrolyte disturbances. The lecture deliberately de-emphasizes pattern recognition, which is probably a maladaptive way to teach this material, in favor of a rational framework that demystifies clinical particulars.

The conduction sequence, briefly¶

The initiating depolarization occurs in the pacemaker cells of the SA node. The signal is conducted to the AV node, which separates the atria and the ventricles. After the AV node, depolarization travels down the common bundle of His into the right and left bundle branches, and finally into the Purkinje fiber network, which signals the actual meat of the heart, the ventricular myocardium.

Think of the AV node, common bundle of His, bundle branches, and Purkinje fibers as a rapid communication network, like the interstate highway. Once the signal gets off into the ventricular myocardium, it is like driving into a local neighborhood. That is where the rubber meets the road, but things are communicated a little less quickly.

Within the meat of the left ventricle, the endocardium depolarizes first and the epicardium depolarizes last. Yet the left ventricular epicardium repolarizes first and the endocardium last. That is the opposite of what you might expect.

Reducing the heart to two cells¶

The dominant signal-generating events of the EKG concern only one part of the heart: the left ventricular apex and free wall. This is simply a mass effect. Most of the electrical meat of the heart is in the ventricular apex and free wall, and there is not enough mass elsewhere to contribute much. So the main features of the EKG can be understood with a simplified two-cell representation.

• Cell A encompasses the endocardium and the endocardial half of the mid wall.

• Cell B encompasses the epicardium and the epicardial half of the mid wall.

By considering the electrical events in cells A and B in detail, you can see how the EKG arises from the action potentials of the two cells.

The frog ventricle experiment¶

In 1883 Burdon-Sanderson and Page used the frog ventricle as their experimental model. The two-cell representation maps onto it with cell A as the base half of the ventricle and cell B as the apical half. A frog has only one ventricle, unlike your left and right, which is a further simplification.

Trace A: the monophasic action potential. Think of it as a poor man’s intracellular action potential. In a monophasic action potential (MAP) recording, the leading electrode presses into the myocardium, causing the membrane immediately below it to be depolarized and unchanging in time. That portion of membrane is insulated from the bath solution. The negative electrode sits in the saline-filled chamber bathing the preparation. The voltage difference between the electrodes gives a scaled-down version of the true transmembrane action potential, and it looks very similar to the cardiac action potentials of the other lectures. This measurement was first made in 1883, and modern versions are obtained with Franz catheters still used in clinical electrophysiology labs today.

Trace B: the frog EKG. The positive electrode of the voltmeter is connected to the apex and the negative electrode to the base. The resulting signal is very similar to the human EKG, except that the frog T wave points downward. That difference comes up later.

Comparing trace A to trace B gives three crucial clues to the genesis of the EKG.

1. The QRS of the EKG corresponds very closely to the depolarizing upstroke of the MAP.

2. The T wave corresponds to the repolarizing phase of the MAP.

3. In some sense, the EKG signal, V_ECG, seems proportional to the time derivative of the MAP voltage. A mysterious but beautiful mathematical correlation.

The deduction from basic physics¶

These clues led Burdon-Sanderson and Page to a deduction from basic physics. The EKG can only respond to voltage differences between the surface of cell A and the surface of cell B, since that is what the electrodes touch. Assume the absolute intracellular voltage of both cells stays at zero.

Transmembrane potential is defined as the potential inside the cytoplasm minus the potential outside the cell. For cell A:

With V_in,A = 0 mV:

By the same reasoning for cell B:

Because the positive electrode is close to cell B, its voltage resembles cell B’s surface voltage. Because of the negative electrode’s placement, its voltage roughly equals cell A’s surface voltage.

The voltage the EKG reports is, by definition, V₊ minus V₋. Substitute step by step:

Testing the theory¶

Align the MAPs of the frog ventricle: a solid curve for the base (cell A) and a dashed curve for the apex (cell B). Numerically subtracting the two traces gives a waveform with striking similarity to the actual EKG in trace B. This was the first inkling that Burdon-Sanderson and Page’s common-sense deduction was true.

The subtraction also explains why the EKG signal is roughly the time derivative of the transmembrane action potential. Taking the time derivative is closely similar to taking the subtracted difference between the two traces; all that is missing is a little Δt for the time delay between them.

Can such a simple theory be true? It makes predictions.

• Warm the base. The base MAP should shorten, and the difference of the MAPs predicts a larger and broader T wave. Trace C of the frog experiment shows this prediction is true.

• Warm the apex. Another investigator, Mines, tested the opposite prediction in 1913. Warming the apex flattened and then turned the T wave upright, also as predicted.

The two-cell model works in spades.

From frog to human¶

Extrapolating back to the human heart needs only a few modifications.

1. Mapping the cells. Cell A corresponds to the left ventricular endocardium-through-mid-wall compartment of the human heart, and cell B to the left ventricular epicardium-through-mid-wall compartment.

2. The upright T wave. The human T wave is upright; the frog’s is upside down. This arises much like the warmed frog apex. Somehow the human heart knows that the action potential duration of cell B must be shorter than that of cell A. In other words, the first part of the ventricle to depolarize is the last to repolarize, and the last part to depolarize is the first to repolarize. The wave of depolarization proceeds in an endocardial-to-epicardial direction, while the wave of repolarization proceeds epicardial-to-endocardial.

3. The P wave. The P wave arises from a small two-cell module in its own right, made of the atria rather than the left ventricle. The P wave is the QRS of the atria. What about the T wave of the atria? Good question. It is generally unresolvable, so it is not considered in the practically measured EKG.

Interpreting EKG abnormalities¶

Armed with the two-cell theory of EKG genesis, you can tap the enormous predictive power of the EKG to gain noninvasive insight into a variety of abnormalities, often explaining EKG changes without recourse to pattern recognition and memory. The abnormalities here are non-geometric: there is no physical abnormality of the heart. They include things like electrolyte disturbances.

1. Ventricular escape beats. If a ventricular beat starts from a site below the bundle of His, left ventricular activation is far less coordinated than usual, with slower conduction velocities. That makes sense: the superhighway is not synchronizing things, and everything goes through local neighborhood streets. The action potentials of cells A and B separate more widely, and sometimes cell B fires before cell A. The graphical prediction is a wide and big QRS complex, or an upside-down QRS complex, with highly variable T wave changes. Seen in excess, this pattern is a real danger sign.

2. Potassium: hyperkalemia and hypokalemia. Hyperkalemia is too-high blood potassium; hypokalemia is too-low blood potassium. Hyperkalemia can arise from a number of causes, including crush injuries, where destroyed tissue releases intracellular potassium. Abnormal external potassium is a dangerous milieu for arrhythmogenesis.

• Hyperkalemia supercharges repolarization driven by some K channels. The gating of the so-called I_Kr (hERG) channels is sensitive to extracellular potassium concentration, [K]_o. Raising [K]_o increases their open probability enough that net outward current increases. If these channels are found at greater density in the epicardial than the endocardial half of the heart, action potential repolarization steepens more in the epicardium than the endocardium. The prediction is tall, peaked T waves, and actual EKG recordings in hyperkalemia show exactly that.

• Hypokalemia gives sluggish repolarization from anemic channels, especially of the hERG variety. The slope of the action potential during repolarization is blunted. The two-cell prediction is a flattened T wave, and the actual EKG in hypokalemia shows just that.

3. Calcium: hypercalcemia and hypocalcemia. With increased serum calcium (hypercalcemia), calcium entry through L-type calcium channels increases, and calcium release from the sarcoplasmic reticulum increases too, because the SR is more heavily loaded. Inactivation of L-type calcium channels is driven by calcium binding to calmodulin that is constitutively tethered to these channels, so inactivation increases. The action potential duration therefore shortens, because the plateau is maintained only while inward L-type calcium current is precisely matched by outward potassium current:

While those two currents are equal and opposite, dV/dt is roughly zero and the membrane holds at the plateau. Shortening the action potential corresponds to a shortened QT interval.

Hypocalcemia, by the same logic, has the opposite effect: a prolonged QT interval.

4. Quinidine. A pharmacological agent used therapeutically that blocks both voltage-gated sodium channels and voltage-gated potassium channels. The sodium channel block slows conduction, separating the action potentials of cells A and B, which widens the QRS complex. The potassium channel block lengthens action potentials and the QT interval. T wave morphology changes variably, as the two-cell model would predict, owing to the potassium channel block.

5. Ischemia. Ischemia is a relative insufficiency of the blood supply to a portion of the heart. In the ischemic region it produces smaller resting potentials and possibly abbreviated, triangular-shaped action potentials. The collapse of resting potential may arise from decreased ATP and decreased sodium-potassium pump activity. The shortened action potential duration may be secondary to a decreased ATP/ADP ratio, which in turn activates ATP-gated potassium channels, K_ATP channels. The two-cell model predicts changes at the ST segment.

• Endocardial ischemia (cell A): ST depression.

• Epicardial ischemia (cell B): ST elevation.

The predicted changes correlate closely with those measured in practice.

6. AV block. The AV node normally provides something like a 100 to 200 ms delay between the moment depolarization reaches it from the atria and SA node and the moment the signal escapes into the bundle of His. The delay allows the atrial kick, the atrium’s final squeeze of blood to fill the ventricle, before the ventricle begins to contract. Without it, the ventricle would be contracting and fighting the atrium as it pushes in the last bolus of blood before a frank heartbeat. In AV block, something goes wrong so that the delay becomes too long. There are three classes.

• First-degree block. Every signal reaching the AV node does finally escape into the bundle of His, but the delay is too long. Measured as the interval between the P wave and the R wave, the PR interval, it exceeds 200 ms (0.2 s). By definition, first-degree AV block is a PR interval greater than 0.2 s. A QRS complex still always follows each P wave. One example is toxicity from digitalis, a drug given to patients in heart failure.

• Second-degree block. Intermittent failure of conduction through the AV node. Sometimes the atrial depolarization gets through, perhaps with a long PR interval; on other beats it fails altogether to get into the bundle of His. Some P waves have no QRS complex following them.

• Third-degree block. The easiest to recognize: complete heart block. No atrial depolarization reaching the AV node gets through to the bundle of His. Ventricular pacemakers, normally quiescent because the SA signals overdrive-suppress them, come alive, and the ventricle beats on its own slower, independent oscillator. The P waves proceed at their own faster rhythm while the QRS complexes, probably ventricular escape beats, occur more slowly and completely independently. One example, rare overall but seen not infrequently in Maryland, is Lyme disease, where the infection attacks the AV node and causes AV block.

Summary¶

The lecture covered three main points: the phenomenological properties of the EKG as a noninvasive window onto the electrical workings of the heart; the two-cell model linking the electrophysiological events of cardiac cells to the macroscopic EKG; and the use of that insight to explain rationally how and why the EKG changes with cellular electrophysiological disturbances such as electrolyte changes, ischemia, or diseases attacking the AV node.