Spiral waves of excitation are common in many physical, chemical, and biological systems. In physiological systems like the heart, such waves can lead to cardiac arrhythmias and need to be eliminated. Spiral waves anchor to heterogeneities in the excitable medium, and to eliminate them they need to be unpinned first. Several groups focused on developing strategies to unpin such pinned waves using electric shocks, pulsed electric fields, and recently, circularly polarized electric fields (CPEF). It was shown that in many situations, CPEF is more efficient at unpinning the wave compared to other existing methods. Here, we study how the circularly polarized field acts on the pinned spiral waves and unpins it. We show that the termination always happens within the first rotation of the electric field. For a given obstacle size, there exists a threshold time period of the CPEF below which the spiral can always be terminated. Our analytical formulation accurately predicts this threshold and explains the absence of the traditional unpinning window with the CPEF. We hope our theoretical work will stimulate further experimental studies about CPEF and low energy methods to eliminate spiral waves.

中文翻译：

---

可激发介质数学模型中圆极化电场解旋波的理论

螺旋激励波在许多物理，化学和生物系统中都很常见。在诸如心脏的生理系统中，此类波可导致心律不齐，需要消除。螺旋波锚定在可激发介质中的异质性，要消除它们，首先需要将其解开。几个小组致力于开发使用电击，脉冲电场以及最近的圆极化电场（CPEF）来消除此类固定波的策略。结果表明，在许多情况下，与其他现有方法相比，CPEF能够更有效地解开潮流。在这里，我们研究圆极化场如何作用于固定的螺旋波并将其解除固定。我们表明终止总是发生在电场的第一次旋转内。对于给定的障碍物尺寸，存在CPEF的阈值时间段，在该阈值时间段以下始终可以终止螺旋。我们的分析公式可以准确地预测此阈值，并说明没有使用CPEF的传统解锁窗口。我们希望我们的理论工作能激发有关CPEF和低能方法消除螺旋波的进一步实验研究。