Modeling coupled single cell electroporation and thermal effects from nanosecond electric pulse trains

Abstract

A distributed circuit approach is used to simulate the development of electric potentials across a cell membrane and the resulting poration dynamics for ∼700 ns duration voltage pulses. Besides electric field effects, temperature increases from a pulse train are included on an equal footing to probe heating effects. The results show (i) strong heating and power dissipation at the membrane in keeping with previous simpler models, (ii) an initial spike in the membrane temperature within 100 ns timescales, (iii) a monotonic increase in membrane temperature with successive pulses to about 8 K over twelve pulses within roughly 10 μs, and (iv) large temperature gradients in excess of 2 × 107 K/m at the polar membrane region indicative of a strong source for thermo-diffusive transport. Our results suggest that inherent heating during repeated pulse application may be used to tailor excitation sequences for maximal cellular transport, broaden the permeabilization beyond the polar regions for greater transmembrane conduction, and lower the electric field thresholds for greater efficiency in longer duration irreversible electroporation protocols. More generally, the present analysis represents an initial step toward a comprehensive analysis-based optimization for tumor treatment that could select waveforms for tissues, factor in heating effects (whether for synergistic action or to ascertain safe operating limits), and engineer temporal manipulation of wavetrains to synchronize with timescales of selective bio-processes of interest for desired transient responses.