A Simplified Electrical-Based Model for Electroporation Dynamics

Abstract

Calculating pulsed electric field (PEF)-induced pore formation using the Smoluchowski equation (SME) can be computationally expensive, even when reduced to the asymptotic SME (ASME). These issues are exacerbated when incorporating additional physical phenomena, such as membrane temperature gradients or shock waves, or incorporating pore formation into multiscale models starting from an external stimulus at the organism level. This study presents a rapid method for calculating the membrane-level effects of PEFs by incorporating a semi-empirical equation for transmembrane potential (TMP)-dependent membrane conductivity into a single-shell model for calculating the TMP. The TMP calculated using this approach and the ASME agreed well for a range of electric field strengths for various PEF durations and AC frequencies below and above the threshold for pore formation. These results demonstrate the feasibility of rapidly predicting TMP, which is easily measured, during pore formation strictly from electrical properties and dynamics without needing to explicitly calculate pore dynamics, as required when using the SME and ASME.

Keywords

• Bioelectrics
• electroporation
• Laplace’s equation
• Smoluchowski equation
• transmembrane potential