Model Development

A detailed description of the model equations and solution methods are presented elsewhere (20). The tissues included in the model were the vitreous, retina, posterior surface of the lens, and the posterior chamber of the aqueous humor (Fig. 2). Mass transport by both convection and diffusion was accounted for in the aqueous humor. Due to the viscous nature of the vitreous, especially in the rabbit eye, only diffusive mass transport was considered in the vitreous.

The only unknown variables in the model were the initial distribution of drug solution in the vitreous following injection (initial condition) and the retinal permeability. The initial distribution of the injected drug solution is a variable that could affect the elimination ofdrug from the vitreous. Therefore, rather than simulating only a central injection, four extreme initial conditions were considered. These conditions covered a range ofpossible positions where the injected drug solution may have been placed in the in vivo experiments performed by Araie and Maurice (8): (a) a central injection, (b) an injection placed next to the lens on the symmetry axis, (c) an injection placed next to the retina on the symmetry axis, and (d) an injection placed close to the hyaloid membrane (Fig. 3). The model simulated the shape of the injected solution as a sphere in cases 1-3 and a cylinder of equal height and diameter for case 4. In reality, a drug solution injected into the vitreous will not take the shape of a perfect sphere or a cylinder. Complex and poorly characterized shapes that depend on drug solution and vitreous properties as well as the injection procedure may be observed (7). These complex shapes would be difficult to incorporate in the finite element model, so for the purpose of studying the effect of injection position, a simpler shape was selected. The concentration profiles produced by the model using each initial condition were fit to the concentration profiles observed by Araie and Maurice (8), resulting in four

Surface of Ciliary Body radius = 7 8 mm

Hyaloid Membrane (thickness = 0 1 mm)

Figure 2 Cross section view of the model. In addition to the vitreous, the model includes the posterior aqueous compartment and the surrounding retina layer. The aqueous compartment was included to properly account for drug loss across the hyaloid membrane.

Surface of Ciliary Body radius = 7 8 mm

Post erior Chamber of Aqueous Humour

Hyaloid Membrane (thickness = 0 1 mm)

Figure 2 Cross section view of the model. In addition to the vitreous, the model includes the posterior aqueous compartment and the surrounding retina layer. The aqueous compartment was included to properly account for drug loss across the hyaloid membrane.

possible values of retinal permeability that best fit the experimental profiles. By simulating extreme injection positions, the range of retinal permeabilities calculated by the model should include the actual retinal permeability. If the actual injection position used by Araie and Maurice was precisely known, a single retinal permeability could be calculated using the model.

Was this article helpful?

0 0

Post a comment