Comparison of Model Calculated and Experimental Data

Figures 4 and 5 show the model calculated concentration profiles for fluorescein at 15 hours and for fluorescein glucuronide at 24 hours, respectively, after a spherical central injection (A), and a cylindrical injection displaced towards the hyaloid membrane (B). The concentration profiles for the injection displaced towards the lens and the injection displaced towards the retina were qualitatively similar to the concentration profile produced by the central injection.

Qualitatively, the contour profiles calculated using the model are similar to those found experimentally by Araie and Maurice (8). In Figure 4, the

Figure 3 Injection positions studied using the model. Four extreme and distinct injection positions were studied to determine the sensitivity of the model calculated retinal permeability to the initial location of the injected drug.

concentration contour lines are parallel to the retina as expected, since the flux of fluorescein across the retina was the dominant elimination mechanism. For each injection position along the symmetry axis, the maximum model calculated concentrations were next to the lens, on the symmetry axis as shown in Figure 4A. In the case where fluorescein was injected closer to the hyaloid membrane (Fig. 4B), the maximum model calculated concentration was next to the lens; however, it is displaced slightly, closer to the site of the injection.

In Figure 5, the model calculated concentration contour lines are perpendicular to the retina since fluorescein glucuronide is eliminated mainly across the hyaloid membrane. Araie and Maurice (8) found that the concentration of fluorescein glucuronide in the vitreous was approximately the same next to the retina and next to the lens on the symmetry axis of the vitreous at 24 hours. However, the model calculated that the concentration next to the retina (12.1 mg mL"1) was slightly higher than the concentration next to the lens (10.4 mg mL"1) for all injection positions. For the hyaloid-displaced injection, the maximum concentration was shifted slightly towards the injection site, similar to that noted for the hyaloid-displaced

Figure 4 Model calculated concentration profile for fluorescein at 15 hours for a spherical central injection (A) and a hyaloid-displaced injection (B). The dominant elimination route for fluorescein is across the retina; therefore, the concentration contour lines are parallel to the retina surface. The concentration profile for the lens-displaced injection and the retina-displaced injection were qualitatively similar to the central injection.

Figure 4 Model calculated concentration profile for fluorescein at 15 hours for a spherical central injection (A) and a hyaloid-displaced injection (B). The dominant elimination route for fluorescein is across the retina; therefore, the concentration contour lines are parallel to the retina surface. The concentration profile for the lens-displaced injection and the retina-displaced injection were qualitatively similar to the central injection.

Figure 5 Model calculated concentration profile for fluorescein glucuronide at 24 hours for a spherical central injection (A) and a hyaloid-displaced injection (B). Fluorescein glucuronide has a very low retinal permeability; therefore, the concentration contour lines are perpendicular to the retina. The concentration profile for the lens-displaced injection and the retina-displaced injection were qualitatively similar to the central injection.

Figure 5 Model calculated concentration profile for fluorescein glucuronide at 24 hours for a spherical central injection (A) and a hyaloid-displaced injection (B). Fluorescein glucuronide has a very low retinal permeability; therefore, the concentration contour lines are perpendicular to the retina. The concentration profile for the lens-displaced injection and the retina-displaced injection were qualitatively similar to the central injection.

injection of fluorescein. If the hyaloid membrane was the only elimination route, theory would suggest that the maximum concentration would be next to the retina on the symmetry axis, since this is the point where a drug molecule must travel furthest to be eliminated.

In Figure 6, the model calculated concentration gradients of fluorescein between the lens and the retina along the symmetry axis are compared with the experimental data of Araie and Maurice (8). In each case, the concentrations have been normalized with respect to the concentration found next to the lens. Considering that the concentration gradients were calculated by fitting only the experimental concentration measured 1 mm adjacent to the

« \ E ---Lens Displaced Cylindrical Injection o 0.2 —

« \ E ---Lens Displaced Cylindrical Injection o 0.2 —

—----- Retina Displaced Cylindrical Injection

--------- Hyatold Displaced Cylndrlcal Injection

012345678 Distance From Lens (mm)

Figure 6 Concentration gradient between the lens and retina 15 hours after an intravitreal injection of fluorescein. Concentrations have been normalized with respect to the concentration next to the lens. The experimental bars represent the minimum and maximum distance from the center of curvature of the retina that each specific experimental concentration contour line was observed (8). The model calculated profiles were produced using the retinal permeabilities shown in Table 1. The retinal permeabilities were calculated by fitting only the experimental concentration observed 1 mm adjacent to the lens measured at 15 hours. However, the model was able to accurately fit the entire profile.

lens, the fact that the model-calculated concentration gradients follow the experimentally observed gradient provides strong validation of the model and its inherent assumptions. Of particular note is that even 15 hours after the intravitreal injection, significant variations in the concentration profiles were observed when different injection locations were considered. At earlier times after the injection, the concentration variations would be much larger, which suggests that injection position is an important variable that must be controlled when performing animal experiments and in clinical treatment.

For each of the simulated injection positions, Table 1 shows the model calculated retinal permeabilities of fluorescein and fluorescein glucuronide that were determined by fitting the experimental data and compares them to values calculated by other published models and found in vitro by Koyano (9) using an excised rabbit retina. As mentioned earlier, the retinal permeability for a compound is a constant. The different values obtained from the various simulations occurred because the retinal permeability was the only parameter with an unknown value that could be adjusted to fit the experimental data. Since the injection position affects the concentration gradients in the vitreous, different estimates for retinal permeabilities were obtained. The estimated fluorescein retinal permeabilities were much lower when the injection was displaced towards the retina or the hyaloid membrane. In the former case, fluorescein was placed closer to the retina, producing a higher initial concentration gradient of fluorescein across the retina than obtained from a central injection. Since the concentration gradient is higher, a lower

Table 1 Comparison of Finite Element Model Calculated Retinal Permeabilities and Other Published Values

Retinal permeability (cm/s)

Fluorescein

Position of injection and other published values Fluorescein glucuronide

Fluorescein

Position of injection and other published values Fluorescein glucuronide

Central Injection

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