Mathematical Modeling of Coupled Ion and Water Transport in Biological Tissues

The coupling of ion and water transport has been recognized as an important subject of research in modern physiology, but much less attention has been paid to its mathematical modelling and analysis. In this thesis, we focus on mathematical modelling of the coupled ion and water transport in the lens of the eye and optic nerve. The choice of these two important parts of the vision system is made based on the fact that their physiology has been well studied and there is a large amount of experimental data.

For the lens of the eye, we introduce a general non-electroneutral (full) model to study microcirculation in the lens driven by its flows through ion channels and transporters. Through the numerical simulations, we show the full model can match with the experiment studying the effect of connexins on hydrostatic pressure very well. Furthermore, we obtain a simplified model based on physiological data and compare results with those in the literature. The simplified model can be reduced further to the first-generation models and provides a good approximation of the full model with a deeper understanding of the physiological process.

For optic nerve, our research focuses on potassium clearance in the narrow extracellular space outside nerve cells, a classical subject of biophysics research. Through a tridomain mathematical model, we capture general properties by which the central nervous system controls potassium concentration in the narrow extracellular space. We calibrate our full model (including water) with experiments in the literature and compare our full model with the corresponding electro-diffusion (without water) model. We explore how the magnitude of potassium clearance changes during and after neural stimulation and how the water flow generated by osmosis plays an important role in glial buffering.