Numerical solution of coupled transport equations applied to corneal hydration dynamics

Area of Science:

• Ocular Physiology
• Biophysics
• Mathematical Modeling

Background:

• Corneal hydration is crucial for vision and is regulated by epithelial and endothelial transport.
• Previous theories, like the 'pump-leak' hypothesis, require quantitative validation.
• Understanding corneal hydration dynamics is essential for diagnosing and treating corneal diseases.

Purpose of the Study:

• To develop a quantitative model for corneal hydration regulation.
• To integrate transport and permeability properties of corneal layers using finite element analysis.
• To validate the 'pump-leak' hypothesis with a refined mathematical model.

Main Methods:

• Employed finite element analysis to integrate coupled flow equations based on non-equilibrium thermodynamics.
• Measured in vitro rabbit corneal thickness changes in response to osmotic challenges.
• Fitted experimental data to the mathematical model to determine membrane coefficients and transport rates.

Main Results:

• Accurate prediction of corneal hydration dynamics requires accounting for trans-stromal pressure and solute gradients.
• The refined model accurately predicted experimental observations, including stromal swelling in hibernating mammals.
• Identified stromal fluid flow retardation and solute gradients as significant factors in hydration dynamics.

Conclusions:

• Corneal stromal hydration is accurately explained by the balance between dissipative flows and active endothelial HCO3 transport.
• The 'pump-leak' hypothesis is supported by quantitative evidence from the developed model.
• Tissue gel properties play a critical role in coupled transport across corneal cell layers.