A model for tear film thinning with osmolarity and fluorescein

Purpose. We developed a mathematical model predicting dynamic changes in fluorescent intensity during tear film thinning in either dilute or quenching regimes and we model concomitant changes in tear film osmolarity. Methods. We solved a mathematical model for the thickness, osmolarity, fluorescein concentration, and fluorescent intensity as a function of time, assuming a flat and spatially uniform tear film. Results. The tear film thins to a steady-state value that depends on the relative importance of the rates of evaporation and osmotic supply, and the resulting increase of osmolarity and fluorescein concentrations are calculated. Depending on the initial thickness, the rate of osmotic supply and the tear film thinning rate, the osmolarity increase may be modest or it may increase by as much as a factor of eight or more from isosmotic levels. Regarding fluorescent intensity, the quenching regime occurs for initial concentrations at or above the critical fluorescein concentration where efficiency dominates, while lower concentrations show little change in fluorescence with tear film thinning. Conclusions. Our model underscores the importance of using fluorescein concentrations at or near the critical concentration clinically so that quenching reflects tear film thinning and breakup. In addition, the model predicts that, depending on tear film and osmotic factors, the osmolarity within the corneal compartment of the tear film may increase markedly during tear film thinning, well above levels that cause marked discomfort.