Estimating three-dimensional outflow and pressure gradients within the human eye

In this paper we set the previously reported pressure-dependent, ordinary differential equation outflow model by Smith and Gardiner for the human eye, into a new three-dimensional (3D) porous media outflow model of the eye, and calibrate model parameters using data reported in the literature. Assuming normal outflow through anterior pathways, we test the ability of 3D flow model to predict the pressure elevation with a silicone oil tamponade. Then assuming outflow across the retinal pigment epithelium is normal, we test the ability of the 3D model to predict the pressure elevation in Schwartz-Matsuo syndrome. For the first time we find the flow model can successfully model both conditions, which helps to build confidence in the validity and accuracy of the 3D pressure-dependent outflow model proposed here. We employ this flow model to estimate the translaminar pressure gradient within the optic nerve head of a normal eye in both the upright and supine postures, and during the day and at night. Based on a ratio of estimated and measured pressure gradients, we define a factor of safety against acute interruption of axonal transport at the laminar cribrosa. Using a completely independent method, based on the behaviour of dynein molecular motors, we compute the factor of safety against stalling the dynein molecule motors, and so compromising retrograde axonal transport. We show these two independent methods for estimating factors of safety agree reasonably well and appear to be consistent. Taken together, the new 3D pressure-dependent outflow model proves itself to capable of providing a useful modeling platform for analyzing eye behaviour in a variety of physiological and clinically useful contexts, including IOP elevation in Schwartz-Matsuo syndrome and with silicone oil tamponade, and potentially for risk assessment for optic glaucomatous neuropathy.