An approach to electrical modeling of single and multiple cells

Previous theoretical approaches to understanding effects of electric fields on cells have used partial differential equations such as Laplace's equation and cell models with simple shapes. Here we describe a transport lattice method illustrated by a didactic multicellular system model with irregular shapes. Each elementary membrane region includes local models for passive membrane resistance and capacitance, nonlinear active sources of the resting potential, and a hysteretic model of electroporation. Field amplification through current or voltage concentration changes with frequency, exhibiting significant spatial heterogeneity until the microwave range is reached, where cellular structure becomes almost "electrically invisible." In the time domain, membrane electroporation exhibits significant heterogeneity but occurs mostly at invaginations and cell layers with tight junctions. Such results involve emergent behavior and emphasize the importance of using multicellular models for understanding tissue-level electric field effects in higher organisms.