Aqueous humor flow in the posterior chamber of the eye with iridotomy
Iridotomy is a procedure in which the hole in the iris is created surgically in order to allow aqueous to flow from the posterior to the anterior chamber. It is done in cases in which there is a concern that this flow might otherwise not occur freely. The problem of the choice of the optimal size and location of an iridotomy is still poorly understood. We study the aqueous flow in the posterior chamber of the eye due to aqueous production in the ciliary body and miosis. This gives us insight on the pressure difference between anterior and posterior chambers and stresses on the surrounding tissues. In this work we propose a mathematical theory, which allows the problem to be solved semi-analytically. Our model is designed to predict the ideal size of the iridotomy that is sufficient to keep the pressure within safe limits and also avoid large velocities to be generated.
The shape of the posterior chamber we derive from ultrasound images. Since the chamber is long and thin, we use lubrication theory to simplify the problem and justify the quasi-steady approach to model miosis. The iridotomy is modeled as a point sink and we work in terms of regularised pressure. To this end, we assume that the flux through the hole is proportional to the pressure drop across the hole and solve the governing equations with finite difference method.
The geometry of the posterior chamber has a significant impact on the pressure and the flow, and in particular the height and the length of the iris-lens channel and the size of the iridotomy. Conversely, the location of the iridotomy does not have a significant effect. During miosis, even the small change of volume in the posterior chamber may cause large velocities of the jet through the iridotomy. We find that there exist the diameter of iridotomy, which maximizes the velocity of this jet. We investigated the possibility of the influence of the jet through the iridotomy on the endothelial cell detachment from the cornea. The result suggests that for the iridotomy located close to the cornea and/or the large change of volume of the posterior chamber after miosis, there is a risk of the detachment of endothelial cells.
The size and the location of the iridotomy is influenced by various geometrical and fluid mechanical factors. The most significant ones are the height and the length of the iris-lens channel, the size of the iridotomy and the presence of the pupillary block. In case of miosis, the intensive flow and/or the cornea located close to the iriditomy cause a risk of the detachment of endothelial cells.