Estimating outflow facility through pressure dependent pathways of the human eye

Abstract

We develop and test a new theory for pressure dependent outflow from the eye. The theory comprises three main parameters: (i) a constant hydraulic conductivity, (ii) an exponential decay constant and (iii) a no-flow intraocular pressure, from which the total pressure dependent outflow, average outflow facilities and local outflow facilities for the whole eye may be evaluated. We use a new notation to specify precisely the meaning of model parameters and so model outputs. Drawing on a range of published data, we apply the theory to animal eyes, enucleated eyes and in vivo human eyes, and demonstrate how to evaluate model parameters. It is shown that the theory can fit high quality experimental data remarkably well. The new theory predicts that outflow facilities and total pressure dependent outflow for the whole eye are more than twice as large as estimates based on the Goldman equation and fluorometric analysis of anterior aqueous outflow. It appears likely that this discrepancy can be largely explained by pseudofacility and aqueous flow through the retinal pigmented epithelium, while any residual discrepancy may be due to pathological processes in aged eyes. The model predicts that if the hydraulic conductivity is too small, or the exponential decay constant is too large, then intraocular eye pressure may become unstable when subjected to normal circadian changes in aqueous production. The model also predicts relationships between variables that may be helpful when planning future experiments, and the model generates many novel testable hypotheses. With additional research, the analysis described here may find application in the differential diagnosis, prognosis and monitoring of glaucoma.

Fig 1. Driving pressure and total pressure dependent outflow as a function of intraocular pressure, for a range of values of α (note: CTSL is 1 microlitre/min/mm Hg).

Fig 2. Average outflow facility C¯3p as a function of intraocular pressure and for a range of values of α.

Fig 3. Local (or point) outflow facility C^p as a function of intraocular pressure and for a range of values of α.

These curves may be calculated either using Eq (27), or by taking the derivative with respect to IOP of the total pressure dependent outflow curves shown in Fig 1.

Fig 4. Driving pressure and pressure dependent outflow as a function of intraocular pressure, for a range of values of α.

Pressure dependent outflows are calculated using Eq (18) with a normotensive pressure of 15 mm Hg as the intraocular reference pressure. The data in this figure can employed to help understand or evaluate Eqs (23) and (24).

Fig 5. Average outflow facility C¯15p, as a function of intraocular pressure and for a range of values of α.

The average outflow facility ${\overline{\mathit{C}}}_{\mathbf{15}}^{\mathit{p}}$ is calculated using Eq (28). Note: the average outflow facility curves shown in the figure above are not the same as the average outflow facility curves shown in Fig 2, as the pressure range over which averaging occurs are different in the two figures. For example for α equal to 0.05, at 20 mm Hg the average outflow facility in the above figure is just over 0.4 microlitres/minute/mm Hg, while in Fig 2 it is about just under 0.6 microlitres/minute/mm Hg. The relative difference in the two average outflow facilities increases with increasing α.

Fig 6. Average outflow facility C¯0p as a function of intraocular pressure and for a range of values of α.

These average facility curves are calculated using Eq (26), but wrongly assumes p_T is equal to zero, when in fact p_T equals 3 mm Hg.

Fig 7. Driving pressure and total pressure dependent outflow as a function of intraocular pressure, and for a range of values of α.

The driving pressure (p − p_ref) is calculated using Eq (14) with p_T equal to zero.