The Fine Mathematics of a Problematic Heartbeat

The Fine Mathematics of a Troubled Heartbeat
The Fine Mathematics of a Problematic Heartbeat - Credit: Adapted from K. Diagne et al., Phys. Rev. let. 130, 028401 (2023)

Starting from the top, a strong heart leads the way. The sinoatrial node, an oval-shaped piece of tissue in the upper right chamber, is the heart's natural pacemaker. The organ continues to beat in a regular rhythm thanks to the periodic electrical impulses it emits.

But sometimes, the deepest part of the soul has its own thoughts. An ectopic pacemaker can develop in one of the lower chambers, which emits a different set of contradictory signals to regulate the heart's rhythm. This results in a cardiac arrhythmia known as parasystole. If this happens to you, you may feel that your heart is not beating.

If the problem is that the heart is getting too many signals to beat, why skip heartbeats?

The response of heart tissue to electrical stimulation is not linear. After each contraction, there is a refractory period of several hundred milliseconds. If an ectopic pacemaker causes the heart to beat just before a normal pacemaker, the normal beat is blocked and sometimes absent.

Since the ratio of the beat frequencies of normal and ectopic pacemakers can take almost any value, it seems that the beat pattern produced by parasystole can be almost anything.

Physiologist Leon Glass at McGill University in Montreal showed forty years ago that parasystole beats must be surprisingly regular. Indeed, they discovered that the equivalent mathematical problem had already been solved.

As a result, Glass and colleagues showed that there are only three potential values ​​for the number of normal beats between two consecutive ectopic beats for any given value of two pacing periods, with the largest of these values ​​one greater than the sum of the smaller two. Shot intervals and refractory interval determine what these values ​​are. However, there are always only three.

A condensed parasystole model was used in the theoretical research of Glass et al.

The authors ignored the distance between two pacemaker sites and the time it takes for a signal to travel between these two sites, among other approaches. Could such a complex heart system benefit from such a reduced approach?

It has turned out to be possible, as Gil Bub and his colleagues at McGill have now shown. For the parasystole-rhythm problem, they created a mathematical model of the cellular-automaton that explicitly takes into account the spatial propagation of signals. The model continues to produce triplets with the allowable number of interstitial beats. It is also compatible with in vitro studies as well as some ECG data from patients.

Clinical information of a 71-year-old man with suspected parasystole is shown in the left panel of the figure, and the equivalent model simulation is shown in the right panel of the figure. The interval between beats or the interval between heartbeats is plotted on the vertical axis. Longer-than-normal intervals are from normal beats following ectopic beats; Intervals shorter than normal are due to normal beats following ectopic beats. Gaps between two normal beats are represented by blue data points. One of the permissible triads Glass and colleagues predicted is that there will always be 1, 8, or 10 blue and green dots between any successive pairs of red dots.

When it comes to heart conditions, parasystole is more troubling than dangerous, but some research shows that it can eventually lead to heart failure. Ectopic pacemaker can be removed using RF radiation as treatment. The heart can skip due to a number of different conditions that cannot all be treated in the same way. Doctors can analyze patients' irregular heartbeats and guide them to the best course of action with the help of intervening triple beats.


Günceleme: 29/01/2023 12:54

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