A Computational Model of the Ocular Lens
The modelling framework was based on finite volume methods. The intracellular and extracellular solute fluxes were modelled using the Nernst-Plank equation with an extra term to capture solute fluxes due to advection. The modelling framework included equations describing the flux through the Na+ /K+ pumps and K+ channels in the surface membrane, and Na+ and Cl- channels in the fibre cell membrane. The intracellular fluid flow between adjacent fibre cells was modelled by a homogenised transmembrane fluid flow equation and the intracellular fluid flow along the fibre cell was modelled as Poiseuille flow. The extracellular fluid flow was modelled as Couette flow with an extra term to capture electro-osmotic flow. The fluid flow through the fibre cell membrane and surface membrane was modelled as transmembrane fluid flow. The governing equations account for the structural properties of the lens, such as the tortuosity of the extracellular cleft, the intracellular and extracellular volume fractions, and the membrane density.
A one-dimensional model of the Na+ , K+ , Cl- and fluid transport in the frog lens was developed. This model was based on the analytic model developed by Mathias (1985b). The results were consistent with the results from the analytic model and experimental data.
Two versions of the two-dimensional model were developed. In the first model, the parameters were spatially constant except for the distribution of the Na+ /K+ pump currents at the lens surface and the fibre cell angles. The second model was the same, except the extracellular cleft width and fibre cell height was spatially varied to represent the sutures and the diffusion barrier. These models were solved and compared with each other and with experimental data.
Compared to the first, the second model predicted a significantly larger circulation of solutes and fluid between the pole and equator. It predicted a 12-20% increase in the penetration of Na+ , K+ and fluid into the lens. The second model also predicted a 300-400% increase in Cl- penetration and, unlike the first model, a Cl- circulation between the poles and equator. This is significant since Cl- is not an actively transported solute. These results highlight the strong structure-function relationship in the lens and the importance of an accurate spatial representation of model parameters.
The direction of the current, solute fluxes and fluid flow that were predicted by the model were consistent with experimental data but the magnitude of the surface current was a tenth to a third of the values measure by the vibrating probe.
To demonstrate the application of the lens model, the two-dimensional model was used to simulate age-related changes in lens physiology. This was done by increasing the radius of the lens to simulate growth with age. The model predicted an increase in the intracellular Na+ concentration, Cl- concentration and potential, and a decrease in the intracellular K+ concentration with age. These trends were consistent with those observed by Duncan et al. (1989), except for the intracellular K+ concentration, where they reported no change with age.
The two-dimensional model forms a foundation for future developments and applications.
School Location:New Zealand
Source Type:Master's Thesis
Keywords:bioengineering model finite volume methods ocular lens eye
Date of Publication:01/01/2006