HOMOGENIZATION THEORY OF ION TRANSPORTATION IN MULTICELLULAR TISSUE

The transport of ions in biological tissues plays a crucial role in studying many biological and pathological problems. Certain multi-cellular structures, such as smooth muscles on vessel walls, can be considered as periodic bi-domain structures consisting of intracellular and extracellular spaces separated by semipermeable membranes. To model these structures, macroscale models are proposed based on an electro-neutral (EN) microscale model with nonlinear interface conditions, using an unfolding operator. The membranes are treated as combinations of capacitors and resistors, while also taking into account the connectivity of the intracellular space. If the intracellular space is fully connected and forms a syncytium, the macroscale model is a bidomain nonlinear coupled partial differential equations system. Otherwise, if the intracellular cells are not connected, the macroscale model for the intracellular space is an ordinary differential system with source/sink terms from the connected extracellular space. The first-order error estimates for these models are achieved with proper regularity assumptions.

Duke Scholars

Author Shixin Xu DKU Faculty