A Computational Biophysical Model for Use in Ophthalmology
Abstract
Despite their use in ophthalmology for more than a century, there are no fundamental biophysical models that account for the dissolution rate of intra-ocular gas bubbles in vivo, as a function of their initial size and composition. Any physical model that reliably predicts the evolution of these bubbles would be extremely useful for planning treatment, by predicting their size over time, and their periods of clinical usefulness. A fundamental, computational, biophysical model is developed here with these purposes in mind. The model is fundamental in the sense that the underlying rate equations are derived using linear response theory, wherein the driving force is a solute chemical potential difference. It is computational because the rate equations for the bubble volume and composition are fully coupled and must be integrated numerically and simultaneously. It was rendered clinically relevant by fitting its two adjustable parameters (two rate constants) to recently acquired live human eye data on intra-ocular air bubble dissolution rates. The model consists of an explicitly four-component, dome-shaped gas bubble, comprised of N2, O2, H2O and CO2, which exchanges N2 and O2 with circulating venous blood in the capillaries of the eye. The calibrated model provided an excellent fit to the available data, and interpolated nicely through three points not used for the calibration. It was used to show that by selecting different N2/O2 ratios in the initially injected gas, one can generate intra-ocular gas bubbles with significantly different predicted periods of clinical usefulness. This potentially useful predictive capability does not exist in current clinical practice.
