Time course of transmembrane voltage induced by time-varying electric fields—a method for theoretical analysis and its application

The paper describes a general method for analysis of time courses of transmembrane voltage induced by time-varying electric fields. Using this method, a response to a wide variety of time-varying fields can be studied. We apply it to different field shapes used for electroporation and electrofusion: rectangular pulses, trapezoidal pulses (approximating rectangular pulses with finite rise time), exponential pulses, and sine(RF)-modulated pulses. Using the described method, the course of induced transmembrane voltage is investigated for each selected pulse shape. All the studies are performed at different pulse durations, each for both the normal physiological and the low-conductivity medium. For all the pulse shapes investigated, it is shown that as the conductivity of extracellular medium is reduced, this slows down the process of transmembrane voltage inducement. Thus, longer pulses have to be used to attain the desired voltage amplitude, as the influence of the fast, short-lived phenomena on the induced voltage is diminished. Due to this reason, RF-modulation in such a medium is ineffective. The appendix gives a complete set of derived expressions and a discussion about possible simplifications.