Date Published: April 9, 2019
Publisher: Public Library of Science
Author(s): David W. Smith, Chang-Joon Lee, William Morgan, Bruce S. Gardiner, Reuben O’Dea.
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.
Glaucoma is the most significant cause of irreversible blindness world-wide, with some 70 million people affected . While glaucoma is a group of diseases, there is a crucially important association between the initiation and progression of glaucoma and an elevated intraocular pressure (IOP). The only proven treatment of glaucoma is the reduction of IOP [1–3].
Having described and calibrated ‘the model’ for the normal human eye in the upright position, we can now explore the implications of this model in more detail.
This paper describe the development and calibration of an axisymmetric, three dimensional fluid outflow model for the human eye. The fluid outflow in the model is pressure dependent, being regulated according to the model described in detail in . The geometric anatomic details for the model human eye (S1 Table), as well as parameters employed for the model human eye (see Table 1), have been inferred from data reported in the literature.
In this paper we build a 3D PDE model for pressure dependent outflow from the human eye, starting from the previously published ODE model by . We calibrate the model using the data available in the literature, which fortunately includes the data published by [30, 37] on the pressure distributions through the optic nerve head for the dog. This enables us to develop a reasonably accurate model of flow through the optic nerve head to the cerebrospinal fluid in the subarachnoid space surrounding the optic nerve. Assuming anterior outflow pathways are operating normally, we employ the model to explain why and by how much IOP becomes elevated upon the introduction of a silicone oil tamponade into the vitreous chamber. Then assuming outflow across the retinal pigment epithelium is normal, we employ the model to explain by how much IOP becomes elevated in Schwartz-Matsuo syndrome. This is the first time a pressure-dependent outflow model has successfully modelled both these conditions, which helps build confidence in its predictive capability. We calculate the TLPG in the upright and supine postures, and during day and night. Based on the data of  we define a macroscale factor of safety against acute interruption of axonal transport, and find that the estimated factor of safety varies with posture and the time of day. Based on the measurements by , which were been successfully incorporated by  in their model of axonal transport along the optic nerve of the mouse, the known mechanics of dynein motors, and our model estimated true fluid velocity along retinal ganglion cell axons, we compute another factor of safety for acute interruption of axonal transport of neurofilaments. For the normal eye, we find the two factors of safety, estimated by independent methods, both generate similar estimates for the factor of safety, being between about 1.5 and 2.0 during the daytime and 2.7 and 3.5 during the night-time. Interestingly, and perhaps reassuringly, the magnitude of the estimates for the factor or safety are similar to those estimated for bone fracture and employed in engineering design. For the case of normal tension glaucoma, the model estimates a factor of safety that are less than one, suggesting that glaucomatous disease progression is likely. While much remains to be discovered, we believe that the fluid outflow model for the human eye presented here may prove itself useful for many applications that are of both physiological interest when interpreting eye behaviour and clinical interest when managing eye disease.