I had to cut the title a bit short, because it’s a long one.

Hubmed Page: What can nonlinear dynamics teach us about the development of ventricular tachycardia/ventricular fibrillation?

This short article (3 pages) describes in a very readable way how nonlinear dynamics may be applied to understand beat-to-beat alternans of action potential duration and amplitude. While the actual methods used are not written, the concept is well-conveyed. I’ve not yet had a course in nonlinear dynamics, so some of the terminology was a bit beyond my understanding. I don’t know anything about eigenmodes, for example.

After providing a brief background of nonlinear dynamics, the authors elaborate on how they used nonlinear dynamics to develop a realistic model of calcium cycling and alternans in the canine myocardium. All-in-all, it’s not a terribly informative paper. Like many articles that mention fibrillation and tachycardia, it comes up short of actually linking the found mechanisms to clinical application and human disease. It is, however, a nice introduction to the topic, and the references look promising. If you have an interest in cardiac arrhythmias, and aren’t very familiar with this sort of analysis, I recommend you read it over and consider further study of the topic.

Hubmed Page: Reentry in heterogeneous cardiac tissue described by the Luo-Rudy ventricular action potential model (with abstract)
The primary focus of this article is the effect of a gradient of action potential duration (APD) on spiral wave dynamics. The authors ran several simulations of a spiral wave using the Luo-Rudy I ionic model, and tracked the drift of the spiral wave’s phase singularity with respect to a gradient of APD. As the abstract says, spiral wave drift was in the direction of longer rotation period (analogous to longer APD, in this case), which is right in line with what should be expected. Higher-frequency rotation should push the spiral wave center (phase singularity) away, regardless of the phenomenon underlying that higher frequency. The article is a medium-length read at six pages. While it seems somewhat redundant, in that every test yielded approximately the same results, this leant strong support to the conclusions of the paper — no caveats or qualifications were necessary. The conclusions of this article are important to the study of arrhythmias in regional disease, where gradients of electrophysiological disease exist along the borders between normal and diseased tissues.
The paper does not, unfortunately, delve into the details of why high-frequency rotation pushes away low-frequency rotation. A similar phenomenon was explained to me this past fall by Dr.Valentin Krinski with regard to two interacting spiral waves or periodic sources. I’m currently struggling to find the bridge — the relationship between different frequencies in different parts of the same spiral wave, and different frequencies in different spiral waves.

If you know why this is, kindly leave a comment. In the mean time I’ll be puzzling over it.