A mathematical model of corneal endothelium pump function

The corneal endothelium plays a critical role in maintaining the transparency of the cornea by regulating water transport through the ‘pump and leak’ mechanism. This study presents a mathematical model to analyse fluid and ion pumping across the endothelium, accounting for two proposed mechanisms of the endothelial pump: local osmosis and electro‑osmosis. The model incorporates four key ions (Na+, K+, Cl− and HCO−3 ) and considers transcellular and paracellular transport pathways. The model predicts a water flux from the stroma to the anterior chamber as observed in experiments with isolated endothelium. Electro‑osmosis is found to contribute minimally to water transport compared with local osmosis, which is the dominant mechanism. The magnitude of water flux depends on the cell membrane and tight junction permeability to water. Global sensitivity analysis reveals that water flux is also highly influenced by the tight junction permeability to different ion species, and to a smaller extent, to the permeability of cell membrane to some ions, with the specific effect depending on the ion species. The model captures experimental observations, including responses to ion channel inhibitors. This work provides a framework for understanding the factors governing fluid regulation in the cornea.