Electrical properties of tissues from a microscopic model of confined electrolytes

Objective. In the presence of oscillatory electric fields, the motion of electrolyte ions in biological tissues is often limited by the confinement created by cell and organelle walls. This confinement induces the organization of the ions into dynamic double layers. This work determines the contribution of these double layers to the bulk conductivity and permittivity of tissues. Approach. Tissues are modeled as repeated units of electrolyte regions separated by dielectric walls. Within the electrolyte regions, a coarse-grained model is used to describe the associated ionic charge distribution. The model emphasizes the role of the displacement current in addition to the ionic current and enables the evaluation of macroscopic conductivities and permittivities. Main results. We obtain analytical expressions for the bulk conductivity and permittivity as a function of the frequency of the oscillatory electric field. These expressions explicitly include the geometric information of the repeated structure and the contribution of the dynamic double layers. The low-frequency limit of the conductivity expression yields a result predicted by the Debye permittivity form. The model also provides a microscopic interpretation of the Maxwell-Wagner effect. Significance. The results obtained contribute to the interpretation of the macroscopic measurements of electrical properties of tissues in terms of their microscopic structure. The model enables a critical assessment of the justification for the use of macroscopic models to analyze the transmission of electrical signals through tissues.