Assessing delivered pulse-energies by a nonlinear model

Short-duration and high-amplitude electric pulses have recently been used for two different biological tasks: stimulating physiological actions such as heart rate or defibrillation and invoking cell annihilation, as in cancer treatment or atrial fibrillation ablation, by electroporation. However, the physics behind the influence of such pulses has been controversial due to the linear methods used in the analyses. We present the results of a simple nonlinear model to study this situation. Results for the specific nonlinear model show that, below a certain pulse duration, stimulating threshold levels increase rapidly, while the delivered energies reach the lowest plateau. This renders former energy estimates based on linear models, which show a distinct minimum in the calculated delivered energy at a certain amplitude which is invalid for the real nonlinear case. It is notable that these results explain why short high-amplitude pulses are more beneficial to the patient than lower and longer ones in pacing. However, these pulses should not be too high, since no additional energy reduction is achieved and electroporation processes could occur. To further reduce the tissue burden, a train of pulses is necessary, but delivered energies become higher. Considering this case, we clarify the difficulty of reaching threshold at the end of the nth pulse for n > 2 not previously reached and find the "best" conditions for such a train of pulses.