Role of Virtual Electrodes in Arrhythmogenesis: Pinwheel Experiment Revisited

Twenty years ago, I published an article with Natalia Trayanova and her student Annette Lindblom about initiating an arrhythmia in cardiac muscle (“Role of Virtual Electrodes in Arrhythmogenesis: Pinwheel Experiment Revisited,” Journal of Cardiovascular Electrophysiology, Volume 11, Pages 274–285, 2000). We performed computer simulations based on the bidomain model, which Russ Hobbie and I discuss in Section 7.9 of Intermediate Physics for Medicine and Biology. A key feature of a bidomain is anisotropy: the electrical conductivity varies with direction relative to the axis of the myocardial fibers.

Our results are summarized in the figure below (Fig. 14 of our article). An initial stimulus (S1) launched a planar wavefront through the tissue, either parallel to (longitudinal, L) or perpendicular to (transverse, T) the fibers (horizontal). As the tissue recovered from the first wave front, we applied a second stimulus (S2) to a point cathodal electrode (C), inducing a complicated pattern of depolarization under the cathode and two regions of hyperpolarization (virtual anodes) adjacent to the cathode along the fiber axis (see my previous blog post for more about how cardiac tissue responds to a point stimulus). In some simulations, we reversed the polarity of S2 so the electrode was an anode (A). This pair of stimuli (S1-S2) underlies the “pinwheel experiment” that has been studied by many investigators, but never before using the anisotropic bidomain model.

We found a variety of behaviors, depending on the direction of the S1 wave front, the polarity of the S2 stimulus, and the time between S1 and S2, known as the coupling interval (CI). In some cases, we induced a figure-of-eight reentrant circuit: an arrhythmia consisting of two spiral waves, one rotating clockwise and the other counterclockwise. In other cases, we induced quatrefoil reentry: an arrhythmia consisting of four spiral waves (see my previous post for more about the difference between these two behaviors).

I began working on these calculations in the winter of 1999, shortly after I arrived at Oakland University as an Assistant Professor. The photograph below is of a page from my research notebook on March 5 showing initial results, including my first observation of quatrefoil reentry in the pinwheel experiment (look for “Quatrefoil!”).

A few weeks later I got a call from my friend Natalia (see my previous post about an earlier collaboration with her). She was organizing a session for the IEEE Engineering in Medicine and Biology Society conference, to be held in Atlanta that October, and asked me to give a talk. We got to chatting and she started to describe simulations she and Lindblom were doing. They were the same calculations I was analyzing! I told her about my results, and we decided to collaborate on the project, which ultimately led to our Journal of Cardiovascular Electrophysiology paper.

Our article was full of beautiful color figures showing the different types of arrhythmias. Below is a photo of two pages of the article. Those familiar with my previous publications will notice that the color scheme representing the transmembrane potential is different than what I usually used. Lindblom and Trayanova had their own color scale, and we decided to adopt it rather than mine. One of the figures was featured on the cover of the March, 2000 issue the journal. Lindblom made some lovely movies to go along with these figures, but they’re now lost in antiquity. I later discovered that a simple cellular automata model could reproduce many of these results (see my previous post for details).

The editor asked Art Winfree to write an editorial to go along with our article (see my previous post about Winfree). I especially like his closing remarks.

This is clearly a landmark event in cardiac electrophysiology at the end of our century. It is sure to have major implications for clinical electrophysiologic work and for defibrillator design.

In retrospect, he was overly optimistic; the paper was an incremental contribution, not a landmark event of the 20th century. But I appreciated his kind words.

Originally published at



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Brad Roth

Brad Roth


Professor of Physics at Oakland University and coauthor of the textbook Intermediate Physics for Medicine and Biology.