  Ion transport in biological tissues is crucial in the study of many
biological and pathological problems. Some multi-cellular structures, like
smooth muscles on the vessel walls, could be treated as periodic bi-domain
structures, which consist of intracellular space and extracellular space with
semipermeable membranes in between. With the aid of two-scale homogenization
theory, macro-scale models are proposed based on an electro-neutral (EN)
microscale model with nonlinear interface conditions, where membranes are
treated as combinations of capacitors and resistors. The connectivity of
intracellular space is also taken into consideration. If the intracellular
space is fully connected and forms a syncytium, then the macroscale model is a
bidomain nonlinear coupled partial differential equations system. Otherwise,
when the intracellular cells are not connected, the macroscale model for
intracellular space is an ordinary differential system with source/sink terms
from the connected extracellular space.
