· Vincenzo Lambiase · 5 min read
A lead does not look at the heart. It looks along a line. Lead II runs from the right arm to the left leg, and what it writes, millisecond by millisecond, is how far the heart’s electrical arrow points along that line: the arrow’s shadow on it. When the arrow leans toward the left leg the pen goes up, when it leans away the pen goes down, and when the arrow stands square across the line the pen writes nothing at all.
I study medicine, and this is a sentence that is easier to read than to see, so I built it. Lead II is an instrument on this site: the heart’s electrical loop on a dial, and six strips of pink paper that draw themselves as the loop runs. You can take hold of the loop and turn it. This entry is about what it shows, and how it is made.
Six rulers through one point.
The six limb leads are six directions in the plane of the chest, seen face on: lead I at 0°, II at +60°, III at +120°, aVF at +90°, aVL at −30° and aVR at −150°. They are not six cameras around the heart. They are six rulers laid through one point, and the six tracings are one moving arrow measured against each of them.
Two identities follow from the wiring alone: at every instant, I + III = II, and aVR + aVL + aVF = 0. They hold for any heart, because they are arithmetic on three electrodes. The line under the dial does the first sum while the beat runs, and the instrument’s own check finds both identities true to within 10−15 millivolts, the rounding of the machine, on five different hearts. What Einthoven’s triangle adds, with the heart at its centre, is the geometry: the angles above, and an augmented lead reading √3⁄2 of what a limb lead would read along the same direction, about 0.87.
Why one arrow is not enough.
Textbooks often draw the mean electrical axis as a single arrow and read the leads off it. The instrument has a slider that collapses the loop into that arrow while keeping its mean, so you can watch what the arrow throws away. Every lead keeps its net area, to the sixth decimal. But inside each wave all six now write the same curve, only taller, shorter or upside down: the same shape as lead II, to the twelfth decimal.
So the six different shapes of a real tracing, the small q, the tall R and the s after it, are not in the arrow’s direction. They are in its path: where the tip of the arrow travels, and in what order. A mean axis summarises a beat. It does not draw one.
What the loop is made of.
The loop is not drawn by hand. Each wave is a few activation fronts added together, eight in all: two for the atria, right then left; four for the ventricles, the septum first, then the bulk of the walls in two halves, then the base; two for recovery. Each front is a direction with a rise and a fall in time, and the loop is where their sum points, one millisecond at a time, over a beat of 800 milliseconds, 75 a minute.
The intervals are not typed in anywhere. They are measured afterwards, from the strips, the way a reader of paper takes them: PR 157 ms, QRS 84 ms, QT 377 ms. The axis is read twice, once from the mean vector and once from the net areas in I and aVF, and the check requires the two readings to agree: 62.7° both ways. The strips run at 25 mm/s and 5 mm/mV, half the usual height; the step at the start of each is one millivolt.
Two mistakes worth keeping.
Before it went up, the instrument was checked against its own claims, and two of the faults found are worth telling. The printed sum was off by a hundredth of a millivolt: I, III and II were each rounded on their own, and 0.104 and 0.004 print as 0.10 and 0.00 while their sum, 0.108, prints as 0.11. II is now printed as the sum of the two numbers you can see. And turning the loop toward the left drew a q wave deeper than a normal heart writes, because the direction the loop travels was fixed instead of following the axis. Both looked right in a screenshot. Neither was.
What it is not.
There is no field in it for a tracing, a number or a symptom, on purpose. It does not read anyone’s heart; it draws what a loop would produce. A question about a real heart belongs with a doctor who can examine it.
How it is built.
Two scripts and a stylesheet. A model of 176 lines with no page in it, which a 61-line check puts through 49 assertions before every deploy, and 627 lines that draw the dial and the strips in your browser. Nothing is fetched and nothing is kept. The sources are on the page: Waller’s first human electrocardiogram of 1887, Einthoven’s triangle of 1913, Wilson’s central terminal of 1934 and Goldberger’s augmented leads of 1942.
One thing to try.
Turn the loop until lead II’s QRS sits as far below the line as above it. The axis then reads close to −30°, square to lead II’s +60°. aVL now looks almost straight along the arrow, and still lead I writes taller: 1.21 millivolts against 1.16, because an augmented lead reads only √3⁄2 of what a limb lead would.
To hear when the next instrument is out, write to me from the correspondence page.
entry no. 6