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 t his technique can be low, particularly in vivo. One way to improve the succ ess rate is to optimize the shock protocols, but experimental studies are c ostly, time consuming, and yield only an indirect measurement of pore creat ion. Alternatively, this study models electroporation in two geometries, a space-clamped membrane and a single cell, and investigates the effects of p ulse duration, frequency, shape, and strength. The creation of pores is des cribed by a first order differential equation derived from the Smoluchowski equation. Both the membrane and the cell are exposed to monophasic and bip hasic shooks of varying duration (membrane, 10 mus-100 s; cell, 0.1 mus-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 shoo k 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, approximate to 1 ms; cell, approximate to 0.25 mus). In contrast, FPA is se nsitive to shock strength and frequency of the pulse train, increasing line arly with shuck strength and decreasing slowly with frequency. In all cases , monophasic shooks 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. (C) 2000 Elsevier Sci ence S.A. All rights reserved.