While electrical stimulation with pulses of milli- or microsecond duration is possible without electroporation, stimulation with nanosecond pulses typically entails electroporation, and nanosecond pulses can even cause electroporation without stimulation. A recently proposed explanation for this intriguing finding is that stimulation requires not only that a threshold membrane potential is reached, but also that it is sustained for a certain time $t_{\mathit{min}}$, while electroporation occurs almost immediately after a higher threshold potential is reached. Here we analytically derive stimulation and electroporation thresholds for membranes that satisfy these assumptions. We analyze the safety factor, i.e. the ratio between electroporation and stimulation threshold and its dependence on pulse duration, membrane charging time constant, and $t_{\mathit{min}}$. We find that the safety factor is sharply reduced if both the pulse duration and the membrane charging time constant are below $t_{\mathit{min}}$. We discuss different approaches to get models with varying $t_{\mathit{min}}$ that could be used to experimentally test this theory and cardiac applications.

虽然可以在没有电穿孔的情况下使用持续时间为毫秒或微秒的脉冲进行电刺激，但使用纳秒脉冲的刺激通常需要电穿孔，而纳秒脉冲甚至可以在没有刺激的情况下引起电穿孔。最近对这一有趣发现提出的解释是，刺激不仅需要达到阈值膜电位，而且还需要持续一段时间${吨}_{\mathit{分钟}}$，而电穿孔几乎在达到更高的阈值电位后立即发生。在这里，我们分析得出满足这些假设的膜的刺激和电穿孔阈值。我们分析了安全系数，即电穿孔和刺激阈值之间的比率及其对脉冲持续时间、膜充电时间常数的依赖性，以及${吨}_{\mathit{分钟}}$. 我们发现如果脉冲持续时间和膜充电时间常数都低于安全系数${吨}_{\mathit{分钟}}$. 我们讨论了获得不同模型的不同方法${吨}_{\mathit{分钟}}$ 可用于实验测试该理论和心脏应用。