NOTE

If you are unfamiliar with the anatomy of the eye, you may find the horizontal section shown at the end of this page (reproduced from Britannica.com) helpful.
 

Ocular Biomechanics and Transport

Our group's main goal is to understand the functional consequences of conservation of mass and momentum within the eye.  Within that broad mission, we are focusing (ha, ha) primarily on two questions:  (1) How does the aqueous humor affect the contour of the iris in healthy and pathological cases, and (2) If drug is delivered to the vitreous by some method (e.g., injection or implantation), where will the drug go over time?

AQUEOUS HUMOR DYNAMICS AND IRIS CONTOUR

Aqueous humor flows the the extreme anterior part of the eye, turning over the contents roughly every 1.5-2 hr.  The primary path for aqueous humor flow is from the ciliary body along the posterior surface of the iris, through the pupil, across the anterior surface of the iris, and finally out of the eye via the trabecular meshwork (see figure below).  Although the iris engages in active deformation to control the amount of light passing through the pupil, it is also subject to passive deformation from the pressure in the aqueous humor.  Since the aqueous humor is flowing from posterior to anterior, the pressure must be highest on the posterior side, causing the iris to be pushed anteriorly by the humor.  This is a relatively small effect in normal eyes but can be quite pronounced in certain pathological cases, and in some cases the iris even exhibits a confusing posterior deflection.

We are developing a finite element simulation of the coupled iris - aqueous humor problem.  The problem is referred to as "coupled" because there is a fluid (the aqueous humor) interacting with a flexible solid (the iris), and neither problem can be solved independently of the other.  We solve the Navier-Stokes equations for the fluid flow and the linear elastic equations for the solid deformation, giving us in the end a solution that includes both the iris contour and the aqueous humor velocity field (see figure).  The color scale in the figure shows the pressure, and you can see that almost all of the pressure drop occurs in the pinch where the iris is nearest the lens.

Our current interest is in using the finite element simulation to explore pathological cases and to try to understand how transient phenomena, such as blinking and accommodation (lens motion during focusing) affect aqueous humor and iris dynamics.  We are also working with Dr. M. D. May of the Department of Ophthalmology at the University of Colorado Health Sciences Center, using ultrasound biomicroscopy to get better experimental data on the contour of the iris under various circumstances.  We are also interested in extending our axisymmetric results to three dimensions, which requires more sophisticated computational tools.

This work is supported by the Whitaker Foundation.


 
(Click to enlarge)


 

INTRAVITREAL TRANSPORT

The retina is a particularly difficult tissue to reach with drugs.  Systemic delivery (e.g., pills or intravenous injection) is hindered by the blood-retina barrier, which makes it extremely difficult for drugs to enter the retina from the blood (N.B. - the blood-retinal barrier is less selective than the more famous blood-brain barrier, but it is still a major impediment to systemic delivery of retinal drugs).  Topical delivery (drops) is ineffective because the drug is swept away by the aqueous humor (see above for more details on aqueous humor flow).  Direct intravitreal injection is efficient but unattractive to patients, especially for long-term treatment.  One emerging option is controlled delivery, in which the drug of interest is entrapped in a polymer or surrounded by a membrane, and the drug is released over a long period of time, possibly weeks to months.  The challenge of controlled delivery, however, is designing a treatment strategy that can get the optimal dose of drug to the target with minimal peripheral loss.  In some cases, the drugs are toxic at high dose, whereas in other cases, delivery of as much drug as possible is desired.

Our group is developing simulation tools to design better controlled delivery strategies.  The key is understanding transport  phenomena within the vitreous, which has required experimental determination of diffusivity within vitreous and, more importantly, assessing whether there is significant convection within the vitreous.  Although there is strong evidence that the flow of aqueous humor into the vitreous is a small fraction of total aqueous flow (most exits through the trabecular mesh), even a very small amount of convecting posterior flow could be significant since diffusion is so slow.  The modeling of intravitreal transport is further complicated by experimental evidence that the retinal pigment epithelial cells actively pump chemical species out of the vitreous.  These complications are particularly challenging because they (directly or indirectly) involve active processes and are thus not amenable to study in non-living samples.

Those difficulties notwithstanding, we are currently developing three-dimensional models of aqueous humor flow and drug distribution within the vitreous, with typical results shown in the figure below.  The solid region represents an isosurface of constant drug concentration a given period of time after implantation.  Current research involves testing the model against experimental results, studying novel delivery systems (with Dr. T. W. Olsen of the Department of Ophthalmology at Minnesota and with Prof. T. W. Randolph of the Department of Chemical Engineering at the University of Colorado), and improving our physical description of the system.


 


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