Fibrillation as a wave phenomena

## Fibrillation as a wave phenomena

By Jos Claerbout's father

My cardiac summary page sums the view of cardiac clinicians. Here we touch the the view of cardiac researchers, namely, biophysicists, mathematicians, engineers, electrophysiologists, and pharmacologists. Their view is based in the mechanics of wave phenomena. Being a teacher, and being one who deals professionally with seismic waves, I present a summary of their view here. For a more technical and professional view, I suggest you do a web search on the words cardiac spiral waves.

There are many kinds of waves: acoustic, light, radio, seismic, ocean, and more. From a mathematical perspective, all these waves are solutions to the same family of differential equations. Mathematics can unify disparate physical phenomena. What might seem like a mere analogy has a deeper basis. Once you scale everything properly, the different wave types behave the same way.

In most situations, waves lose energy as they propagate. Sometimes, however, waves amplify as they propagate. This rather rare circumstance is said to be "negative viscosity" or "active media". Live heart muscle widely understood an example of active media.

A more simply understandable active media is the earth's atmosphere on a hot summer afternoon. Air at ground level is hot and ready to rise. It cannot rise everywhere at once. Somewhere the air must come down. It will rise first at some local hot spot which forms a virtual chimney drawing hot air in from the sides at the bottom. In-rushing air carries a certain angular momentum. The angular momentum is the product of the angular velocity times the distance from the chimney. The in-rushing air conserves this angular momentum. As inrushing air approaches the chimney center, its radial distance to the chimney decreases. Angular momentum conservation thus requires that the rotational velocity increase inversely with the radius. This produces a "dust devil" (or a tornado). [Conservation of angular momentum causes the accelerating rotation often observed as professional ice skaters pull their arms close in to their torso.]

The center of the tornado or dust devil meanders from place to place. If it were to sit in one place too long, it would use up all the energy available in that place.

A sheet of heart muscle is thought likewise to be an active medium with negative viscosity. Instead of wind, there are ion flows. These flows relate to the way the heart uses energy.

There is a mathematical theory for waves in negative viscosity media. This theory predicts spiraling waves. Spiral waves have been demonstrated experimentally in a variety of biological and nonbiological systems (heart, brain, retina, various social amoeba, and autocatalytic chemical reactions). In heart muscle, it is not the muscle itself moving; it is the electrical pattern of the ion flows.

If you saw the dust devil from above, you might see something like the spiraling wave in a sheet of heart muscle. Using voltage-sensitive dyes, these spiral waves have been observed in mammalian heart muscle. I'm not sure if the spiral waves have been observed in human heart tissue. I'm not sure if the spiral waves can be observed in living animals. Once the spiraling begins, the center of rotation, like that of the dust devil, can meander from place to place. When the center collides with obstacles, it may split into multiple spirals. In heart muscle, the spiral rotates at a rate of about ten complete circumnavigations per second.

The heart muscle is actually three-dimensional. The waves in 3-D are said to be "scroll waves." An epileptic attack may be another form of spiral waves.

Here are some pictures of spiral waves in sheep's heart muscle. Here are some numerical experimental spiral waves. Here is a nice tutorial. Search on cardiac spiral wave movies.

Fibrillation does not seem to be exactly the same thing as spiral waves. I'm not sure about what the difference is, but heart attack seems to have three stages.

1. Spiral waves -- might be ventricular tachycardia (VT), a rapid contraction of the heart muscle which lasts a few seconds before
2. fibrillation- the break up of a spiral into many spirals and chaos. This is the heart quivering but not pumping.
3. ischemia -- this is when the heart muscle itself lacks enough fresh blood and it starts to die.
Above is about all I understand, and I'm not sure which parts are somebody's speculation and which parts are generally assumed to be true. I'll add more bits here as I learn them. If you know I've made any errors, please tell me by sending email to: claerbout at stanford dot edu.

#### Speculation and Hope

Thinking beyond what I have read, it seems to me altogether possible, indeed normal and almost certain, that many spiral waves would start but then simply dissipate before they resonate to crisis stage. A person like my son might have had numerous cardiac events, perhaps monthly, perhaps daily, or hourly events that dissipated before becoming noticible.

This hypothesis cries out for equipment for continuous monitoring, to see the "foreshocks", to identify hearts at risk, and to measure the efficacy of drugs to stabilize it. With the modern electronics revolution, we might come to see it.

At present there is a heart monitor called a Holter monitor that records a continuous electrocardiogram. Since the Holter measurements are all outside the body, however, they may be too remote to detect the spiral waves which are on the heart itself.

As more and more professionals become web aware, we quickly find new things, such as the Society of Pacing and Electrocardiology who are having a big meeting including a session on "Correlation of Surface ECG with Intracardiac Electrograms".

 to my son Jos to Death in Young Athletes