Theoretical modeling of the effects of shock duration, frequency, and strength on the degree of electroporation

Electroporation is becoming an increasingly important tool for introducing biologically active compounds into living cells, yet the effectiveness of this technique can be low, particularly in vivo. One way to improve the success rate is to optimize the shock protocols, but experimental studies are costly, time consuming, and yield only an indirect measurement of pore creation. Alternatively, this study models electroporation in two geometries, a space-clamped membrane and a single cell, and investigates the effects of pulse duration, frequency, shape, and strength. The creation of pores is described by a first order differential equation derived from the Smoluchowski equation. Both the membrane and the cell are exposed to monophasic and biphasic shocks of varying duration (membrane, 10 μs–100 s; cell, 0.1 μs–200 ms) and to trains of monophasic and biphasic pulses of varying frequency (membrane, 50 Hz–4 kHz; cell, 200 kHz–6 MHz). The effectiveness of each shock is measured by the fractional pore area (FPA). The results indicate that FPA is sensitive to shock duration only in a very narrow range (membrane, ≈1 ms; cell, ≈0.25 μs). In contrast, FPA is sensitive to shock strength and frequency of the pulse train, increasing linearly with shock strength and decreasing slowly with frequency. In all cases, monophasic shocks were at least as effective as biphasic shocks, implying that varying the strength and frequency of a monophasic pulse train is the most effective way to control the creation of pores.