Victor H. Barocas, Principal Investigator

Simulation of Controlled Intraocular Drug Delivery

The vitreous and retina—the two primary components of the posterior eye—are particularly difficult to treat with pharmaceutical agents because of poor access by standard delivery techniques. Systemic delivery is impeded by the blood-retinal barrier, topical delivery via eyedrops is prone to washout by the tear film and aqueous humor, and repeated direct intraocular injection is understandably unattractive to many patients. As a result, controlled release systems —such as drugs entrapped in degradable polymers or micropumps attached to drug reservoirs—have emerged as an alternative. Determining the optimal location and delivery rate from the source is a problem that requires three-dimensional simulation of the release, transport, and kinetics of the drug.

This group expected to develop a preliminary model for release from a point source at a set location. This projected work would include techniques being developed in the lab of T. W. Olsen of the Department of Ophthalmology.

At the same time, the research group expected to work on two high-performance computing projects within the area of computational biomechanics. The first project was to deal with coupled mechanics of the Newtonial fluid comprising the aqueous humor, and the iris, an elastic solid, in the anterior portion of the eye. Having previously developed a two-dimensional simulation of this system that can play an important role in certain forms of glaucoma, the researchers looked forward to extending their model to three dimensions. While they would focus on two specific, three-dimensional problems—changes to the aqueous humor flow field when a hole is burnt into the iris by a laser and coupled heat and momentum transfer in the aqueous humor due to evaporative cooling of the cornea—the research group also would seek a novel macroscopic-microscopic finite element approach to the modeling of fibrillar tissues. This approach, although computationally intensive, should offer the potential to provide much more insight into the mechanical behavior of tissues and tissue equivalents, as formed by cells entrapped in a reconstituted biogel. Having demonstrated the effectiveness of their approach on a test problem using workstations, the researchers looked forward to studying real systems, and to performing their work using much greater mesh refinement in three dimensions.

One specific research project conducted in this area over the past year involved a Boussinesq model of natural convection in the human eye and the formation of Krukenberg’s spindle. Here, the cornea of the human eye is cooled by the surrounding air and by evaporation of the tear film. The temperature difference between the cornea and the iris (at core body temperature), causes circulation of the aqueous humor in the anterior chamber of the eye. Others have suggested that the circulation pattern governs the shape of the Krukenberg spindle, a distinctive vertical band of pigment on the posterior cornea surface in some pathologies. These researchers modeled aqueous humor flow in the human eye, treating the humor as a Boussinesq fluid and setting the corneal temperature based on infrared surface temperature measurements. The model predicts convection currents in the anterior chamber with velocities comparable to those resulting from forced flow through the gap between the iris and lens. When paths of pigment particles are calculated based on the predicted flow field, the particles circulate throughout the anterior chamber but tend to be near the vertical centerline of the eye for a greatest period of time. Further, the particles are usually in close proximity to the cornea only when they are near the vertical pigment spindle.

Another study conducted by this research group dealt with coupled macroscopic and microscopic scale modeling of fibrillar tissues and tissue equivalents. Collagen mechanics are crucial to the function and dysfunction of many tissues, including blood vessels, articular cartilage, and bioartificial tissues. Previous attempts to develop computer simulations of collagenous tissue based on macroscopic property descriptions have often been limited in application by the simplicity of the model; simulations based on microscopic descriptions, in contrast, have numerical limitations imposed by the size of the mathematical problem. This method combines the tractability of the macroscopic approach with the flexibility of the microstructural approach. The macroscopic domain is divided into finite elements (as in standard finite element method). Each element contains a microscopic scale network. Instead of a stress constitutive equation, the macroscopic problem is distributed over the microscopic scale network and solved in each element to satisfy the weak formulation of Cauchy’s stress continuity equation over the macroscopic domain. The combined method scales by order 1.1 as the overall number of degrees of freedom is increased, allowing it to handle larger problems than a direct microstructural approach. Model predictions agree qualitatively with tensile tests on isotropic and aligned reconstituted type I collagen gels.

Research Group

Preethi Chandran, Graduate Student Researcher
Brett Hautala, Undergraduate Student Researcher
Jeff Heys, Graduate Student Researcher
Eric Huang, Graduate Student Researcher
Shramik Sengupta, Graduate Student Researcher
David Shreiber, Research Associate
Matthew Stay, Graduate Student Researcher