Synchronization of Triggered Waves in Atrial Tissue.

When an atrial cell is paced rapidly, calcium (Ca) waves can form on the cell boundary and propagate to the cell interior. These waves are referred to as "triggered waves" because they are initiated by Ca influx from the L-type Ca channel and occur during the action potential. However, the consequences of triggered waves in atrial tissue are not known. Here, we develop a phenomenological model of Ca cycling in atrial myocytes that accounts for the formation of triggered waves. Using this model, we show that a fundamental requirement for triggered waves to induce abnormal electrical activity in tissue is that these waves must be synchronized over large populations of cells. This is partly because triggered waves induce a long action potential duration (APD) followed by a short APD. Thus, if these events are not synchronized between cells, then they will on average cancel and have minimal effects on the APD in tissue. Using our computational model, we identify two distinct mechanisms for triggered wave synchronization. The first relies on cycle length (CL) variability, which can prolong the CL at a given beat. In cardiac tissue, we show that CL prolongation leads to a substantial amplification of APD because of the synchronization of triggered waves. A second synchronization mechanism applies in a parameter regime in which the cell exhibits stochastic alternans in which a triggered wave fires, on average, only every other beat. In this scenario, we identify a slow synchronization mechanism that relies on the bidirectional feedback between the APD in tissue and triggered wave initiation. On large cables, this synchronization mechanism leads to spatially discordant APD alternans with spatial variations on a scale of hundreds of cells. We argue that these spatial patterns can potentially serve as an arrhythmogenic substrate for the initiation of atrial fibrillation.