Dynamical Modeling of Cellular Response to Short-Duration, High-Intensity Electric Fields

The interaction of ultra-short duration, high-intensity electric fields with biological cells has recently begun to generate significant interest due to the possibility for non-thermal manipulation of cellular functions. It is clear that a full understanding requires a dynamical model for both electroporation and the electrostatic potential evolution. Here, dynamical aspects related to electroporation are reviewed. The simple model used in the literature is somewhat incorrect and unphysical for a variety of reasons. Our model for the pore formation energy, E(r), includes a dependence on pore population, density, a variable surface tension, and is dynamic in nature. It is shown that membranes can survive a strong electric pulse and recover provided the pore distribution has a relatively large spread. If, however, the population consists predominantly of larger radii pores, then irreversibility can result. Physically, such a distribution could arise if pores at adjacent sites coalesce. Results show that a finite time delay exists for pore formation, and can lead to a transient overshoot of the transmembrane potential V _mem beyond 1.0 V. Pore resealing is shown to consist of an initial fast process, a 10^-4 s delay, followed by a much slower closing at a time constant of about 10^-1 s. This establishes a time-window for effective killing by a second pulse.