A Scaling Law for Bioelectric Effects of Nanosecond Pulses

Experimental studies of bioelectric effects caused by single intense, ultrashort (nanosecond and even subnanosecond), square wave pulses indicate that the product of electric field amplitude and pulse duration, i.e., the electrical impulse, can be considered a similarity or scaling factor. An explanation for this scaling law is based on the assumption that any bioelectric effect in this parameter range of intense nanosecond pulses is caused by membrane charging. In particular, it is assumed that electrical charge transferred to the plasma membrane (which, for electroporated membranes is related to the current through the membrane) is a measure of the intensity of the bioelectric effect. For multiple pulses, bioelectric effects caused by ultrashort pulses were found to scale with the square root of the pulse number. This square root dependence on the pulse number points to a statistical motion of cells between pulses with respect to the applied electric field, and can be explained using the random walk theorem. It will only hold if the time between pulses is short compared to the recovery time of the cell membrane, and long compared to the time for considerable, thermally induced changes in the cell position, with respect to the electric field direction. The validity of the scaling law is limited to pulse durations larger than the dielectric relaxation time of the cytoplasm (on the order of 500 ps), and durations less than the charging time constant of cell membranes (on the order of 100 ns for eukaryotic cells). For single pulses with durations close to the characteristic charging time, the bioelectric effects are expected to scale with electrical energy density, rather than the electrical impulse.