The Effective Conductivity and the Induced Transmembrane Potential in Dense Cell System Exposed to DC and AC Electric Fields

Studying electric potential distribution on the cell membrane and electric conductivity gives us an insight into the effects of the electric field on cells and tissues. Since cells are always surrounded by other cells, we studied how their interactions influence the induced transmembrane potential (TMP) and the effective conductivity in dense cell systems. We numerically and analytically studied the effect of cell organization on the induced TMP and the effective conductivity by organizing cells into simple-cubic, body-centered cubic, and face-centered infinite cubic lattices. We analyzed the general relation between the local quantities (electric field and the induced TMP) and the effective properties such as effective conductivity. We demonstrated that the effective conductivity mainly depends on cell volume fraction, while the induced TMP is affected by cell volume fraction as well as cell ordering. We show that in contrast to some reported results, the phenomenological effective medium theory (EMT) equations cannot be used to determine the local quantities (e.g., the induced TMP) in dense cell systems, whereas the effective properties (e.g., conductivity) can be readily analyzed with EMT equations. We further derive an analytical approximation for the induced TMP in dense cell system exposed to dc and ac electric fields, where dominant factors, which govern the local electric field and the induced TMP, are cell volume fraction and cell ordering. The presented theoretical analysis can be extended also to high frequencies or random distribution of cells.