purpose. To develop pharmacokinetics models to describe the disposition of small lipophilic molecules in the cornea and retina after periocular (subconjunctival or posterior subconjunctival) administration.

methods. Compartmental pharmacokinetics analysis was performed on the corneal and retinal data obtained after periocular administration of 3 mg of celecoxib (a selective COX-2 inhibitor) to Brown Norway (BN) rats. Berkeley Madonna, a differential and difference equation–based modeling software, was used for the pharmacokinetics modeling. The data were fit to different compartment models with first-order input and disposition, and the best fit was selected on the basis of coefficient of regression and Akaike information criteria (AIC). The models were validated by using the celecoxib data from a prior study in Sprague-Dawley (SD) rats. The corneal model was also fit to the corneal data for prednisolone at a dose of 2.61 mg in albino rabbits, and the model was validated at two other doses of prednisolone (0.261 and 26.1 mg) in these rabbits. Model simulations were performed with the finalized model to understand the effect of formulation on corneal and retinal pharmacokinetics after periocular administration.

results. Celecoxib kinetics in the BN rat cornea can be described by a two-compartment (periocular space and cornea, with a dissolution step for periocular formulation) model, with parallel elimination from the cornea and the periocular space. The inclusion of a distribution compartment or a dissolution step for celecoxib suspension did not lead to an overall improvement in the corneal data fit compared with the two-compartment model. The more important parameter for enhanced fit and explaining the apparent lack of an increase phase in the corneal levels is the inclusion of the initial leak-back of the dose from the periocular space into the precorneal area. The predicted celecoxib concentrations from this model also showed very good correlation (*r* = 0.99) with the observed values in the SD rat corneas. Similar pharmacokinetics models explain drug delivery to the cornea in rat and rabbit animal models. Retinal pharmacokinetics after periocular drug administration can be explained with a four-compartment (periocular space, choroid-containing transfer compartment, retina, and distribution compartment) model with elimination from the periocular space, retina, and choroid compartment. Inclusion of a dissolution–release step before the drug is available for absorption or elimination better explains retinal *t* _{max}. Good fits were obtained in both the BN (*r* = 0.99) and SD (*r* = 0.99) rats for retinal celecoxib using the same model; however, the parameter estimates differed.

conclusions. Corneal and retinal pharmacokinetics of small lipophilic molecules after periocular administration can be described by compartment models. The modeling analysis shows that (1) leak-back from the site of administration most likely contributes to the apparent lack of an increase phase in corneal concentrations; (2) elimination via the conjunctival or periocular blood and lymphatic systems contributes significantly to drug clearance after periocular injection; (3) corneal pharmacokinetics of small lipophilic molecules can be explained by using similar models in rats and rabbits; and (4) although there are differences in some retinal pharmacokinetics parameters between the pigmented and nonpigmented rats, the physiological basis of these differences has yet to be ascertained.

^{ 1 }Because it is a safer approach, the periocular route of drug delivery is gaining importance as an alternative to the intravitreous route for the treatment of posterior segment ocular disorders. The periocular routes include the subconjunctival, subtenon, peribulbar, and retrobulbar modes.

^{ 2 }Although these routes deliver drugs to the posterior segment tissues including the retina and the vitreous, the bioavailability of the route is not clearly established. Literature on the pharmacokinetics of periocular injections is relatively sparse compared with that on the topical or intravitreous modes of administration. Understanding the pharmacokinetics is essential for determining the dose regimen and for designing novel drugs and delivery systems.

^{ 3 }Tsuji et al.

^{ 4 }described the pharmacokinetics of a small lipophilic steroid (prednisolone) in tissues of the anterior and posterior segments. However, the model development procedure was not described, and there were no statistical goodness-of-fit criteria mentioned, and thus the use of their model is limited. Lee and Robinson

^{ 5 }developed a model that describes the pharmacokinetics in the vitreous after periocular administration.

^{ 5 }The model was developed with the data of Tsuji et al.

^{ 4 }Most of the posterior segment disorders affect the retina and/or the choroid, and no model has been developed to date to describe the pharmacokinetics of the drugs in the retina. There is significant drug delivery to the anterior segment after subconjunctival administration.

^{ 6 }

^{ 7 }

^{ 8 }However, attempts to model the pharmacokinetics of drugs in the cornea after subconjunctival or other periocular modes of administration have been few.

^{ 9 }

^{ 10 }The modeling software allows for both the forward-modeling approach (simulation) and backward-modeling approaches (parameter estimations using curve fitting). Thus, the purpose of this study was to use Berkeley Madonna and the compartment approach to pharmacokinetic modeling, to explain the pharmacokinetics of small lipophilic molecules in the cornea and retina after periocular administration.

^{ 11 }in pigmented Brown Norway (BN) rats after posterior subconjunctival injection. The corneal model was validated by using the pharmacokinetic data that Ayalasomayajula and Kompella

^{ 12 }obtained in nonpigmented Sprague-Dawley (SD) rats after a similar injection, and further comparisons and validations were performed with the prednisolone corneal pharmacokinetics data of Tsuji et al.

^{ 4 }after subconjunctival injection in albino rabbits. The retinal model developed with the BN rat data

^{ 11 }was validated with the SD rat data of Ayalasomayajula and Kompella.

^{ 12 }

*n*is the number of observations,

*Y*

_{ i }is the observed value;

*Y*

^{′}_{ i }is the model-predicted value,

*Y*

^{″}_{ i }is the mean of the observed values, and

*p*is the number of model parameters.

*Y*

_{ i }is the observed value,

*Y*

_{ i }″ is the mean of the observed values,

*X*

_{ i }is the predicted value, and

*X*

_{ i }″ is the mean of the predicted values.

^{ 11 }and then validated the same with data from nonpigmented rats.

^{ 12 }There is significant delivery of drugs to the cornea after subconjunctival administration.

^{ 6 }The cornea is devoid of circulation, and hence very little drug is expected to reach the cornea from the circulation. Our earlier studies showed that ∼97% of drug delivery to the cornea after periocular administration is mainly by local pathways, as opposed to delivery via systemic circulation.

^{ 12 }Hence, we started with a simple model whereby the drug had a local delivery pathway from the site of administration to the cornea after periocular administration (Fig. 1A) . This base model consisted of two compartments, one representing the periocular site (which is made up of the periocular space and the tissue) and the other representing the cornea. It has been demonstrated in several studies that there is a significant loss of drug from periocular administration due to the presence of the conjunctival circulation and lymphatics.

^{ 13 }

^{ 14 }

^{ 15 }Hence, in our base model, we assumed an elimination pathway for the drug from the subconjunctival/periocular site. Also, it is possible that drugs are eliminated from the cornea possibly through tear turnover and blinking. Therefore, we assumed a corneal elimination pathway for the drugs. We assumed first-order kinetics wherein the rates of disposition are proportional to drug concentration. The model fit with this simple two-compartment model is shown in Figure 1A . The model fit to the experimental data was poor (

*R*

^{2}: 0.41; AIC: 286.5) for the later time points and the estimates of the model parameters are therefore of little value. A visual examination of the elimination phase in the experimental corneal data of celecoxib clearly shows the existence of a distribution phase (bi- or multi-phasic kinetics). Studies have indicated the existence of a possible distribution compartment for pilocarpine in the anterior segment tissues.

^{ 16 }Theoretical discussions of modeling have described the existence of a distribution compartment comprising the aqueous.

^{ 17 }Therefore, we introduced a distribution compartment for the drug in the cornea. This distribution compartment is most likely a combination of aqueous humor and other anterior segment tissues such as the iris ciliary body. When the curve-fitting procedure was performed with this new model, the data-fits significantly improved at the later time points (Fig. 1B) . The overall fit also improved significantly (

*R*

^{2}: 0.5; AIC: 280.7). However, some initial data points could not be fit by either of the models described.

*R*

^{2}: 0.29; AIC: 291.3) without a distribution compartment was better than that obtained with the inclusion of a distribution compartment (

*R*

^{2}: 0.1; AIC: 327.4; Figs. 1C 1D ). We considered an additional model in which there are three elimination pathways, one from the periocular space, one from the cornea, and one from the distribution compartment (aqueous humor; Fig. 1G ). However, the fit with this model was worse than the fit with any of the models described herein.

^{ 18 }

^{ 19 }

^{ 20 }This leak-back is dependent on the method and location of subconjunctival injection and on the volume injected, with greater volumes leading to greater leak-back. In our experience, we have consistently observed that a fraction of the injected volume immediately accesses the cornea as the needle is withdrawn after posterior subconjunctival administration to rats. A similar leak-back has been reported in rabbits.

^{ 18 }

^{ 19 }Sasaki et al.

^{ 18 }

^{ 19 }have demonstrated that tilosolol as well as larger molecules (11 kDa FITC-dextran) leak out into the tear film after subconjunctival administration, which means that there is an initial bolus or higher delivery of dose to the cornea that should be incorporated in the model. To account for this initial drug load on the cornea, we used the models in Figure 1C , but allowed the initial concentration in the cornea to be an additional parameter to be estimated by the software. With this modification, the model was refit to the data (Fig. 1E ;

*R*

^{2}: 0.91; AIC: 225.2). There was a significant improvement in the model fits with this approach. The data fit the model well and the correlation coefficient between the observed and predicted values was excellent (

*r*= 0.99).

^{ 21 }and Lee et al.

^{ 22 }have demonstrated that episcleral implants of cyclosporine can deliver high levels of the drug to the rabbit cornea. The implants also show beneficial therapeutic effects in the lachrymal glands of other species including the canine model. Further, the authors reported that the levels in the cornea after episcleral implant administration are higher at all the time points than those predicted by diffusion alone. Hence, it was speculated that processes other than simple diffusion, most likely ocular circulation and lymphatics, lead to higher drug levels in the cornea after periocular implant administration. A similar or another unknown mechanism of convection may contribute to high drug levels in the cornea. This mechanism and a leak-back along the needle tract from the site of administration may have contributed to high corneal levels of celecoxib after subconjunctival administration of celecoxib suspension in our studies. We collected the first tissue sample at 15 minutes, unlike the 3-hour time point of Robinson et al.

^{ 14 }Further, the visible bleb at the site of injection disappeared in about an hour in our study. It is likely that a leak-back contributed to high drug levels in early samples. By 3 hours in the celecoxib studies, the drug levels were in the declining phase (∼40% of the peak levels). The other differences between the two studies are the formulation (an implant may not have a leak–back, whereas a suspension would) and also the species (rabbit versus rat).

^{ 12 }in which they used a similar dose and volume of injection of celecoxib for the periocular administration. However, they used the SD rats, a nonpigmented strain. When our model-predicted values for pigmented BN rats were compared with the values obtained by Ayalasomayajula and Kompella, a very good correlation was observed (Fig. 2 r= 0.99). Thus, the corneal pharmacokinetics were similar for celecoxib between the two strains of rats (Table 1) .

^{ 4 }in rabbits. They assessed three subconjunctival doses, 2.61, 0.261, and 26.1 mg, of prednisolone. A soluble salt of prednisolone, prednisolone sodium succinate, was used in this study. We used our optimum cornea model in rats to fit the rabbit data with a 2.61-mg dose of prednisolone and then used the data with 0.261 and 26.1 mg doses for further validation of the model. Since prednisolone sodium succinate was administered as a solution, we assumed that the entire dose was immediately available at the periocular site and that there was no dissolution/release step. The data-fit to the prednisolone levels in the cornea is shown in Figure 3 . It is evident that our model resulted in a very good fit for the rabbit prednisolone data and the correlation coefficient between the observed and predicted data was excellent (

*r*= 0.99). We further validated this model at two other doses (0.261 and 26.1 mg). We generated the pharmacokinetic profiles at these two doses and compared the experimental and the model-predicted data. The comparisons of the two doses between the model-predicted and the experimental data are shown in Figure 3 . If the slopes of the curves obtained at different doses are similar, it indicates that the model predictions and the constants calculated are independent of concentrations in the dose range examined (0.261–26.1 mg). A similar validation was made by Lee and Robinson

^{ 5 }to explain the vitreous pharmacokinetics after subconjunctival administration of prednisolone. We also found a very good correlation between the observed and the model-predicted data. Therefore, the model generated with the 2.61-mg dose was validated with the 0.261- and 26.1-mg doses. Thus, a similar model can be used to describe the corneal pharmacokinetics in both rats and rabbits after periocular administration.

^{−1}, which is comparable to the values reported in rabbits for other small lipophilic drugs such as lidocaine, benoxinate, and proparacaine.

^{ 23 }

^{ 24 }

^{ 25 }Further, the model predicted a high elimination from the periocular site, which has been well-demonstrated with several drugs, including macromolecular drugs.

^{ 26 }It is extremely difficult to estimate the precision (mean ± SEM) of the parameter estimates in nonlinear regression modeling, unless the software provides these precisions using an algorithm. The drawback of Berkeley Madonna as software for pharmacokinetics modeling is that it does not provide the precision (mean ± SEM) of the parameter value. However, even the software used by Lee and Robinson

^{ 5 }(Model Maker; Family Genetix, Ltd., Wallingford, UK) has the same drawback. It would be ideal to know how precisely these parameters are estimated to make any significant statistical comparisons from two different studies. However, assuming that the parameter estimates are accurate, some reasonable conclusions can be made from our modeling studies. We initially modeled the prednisolone pharmacokinetics using the Lee and Robinson

^{ 5 }values for elimination rate constant from the periocular site (0.128 minute

^{−1}). However, if the subconjunctival elimination rate constant is fixed at that value, a poor data fit results. Hence, instead of fixing the value of that parameter, we allowed it to float and let the software determine its estimate. The values predicted by Berkeley Madonna for the elimination rate constant from the periocular site (0.072 minute

^{−1}) were somewhat different from those obtained by Lee and Robinson (0.128 minute

^{−1}). There are two possible explanations. First, the software used is different (present study, Berkeley Madonna; Lee and Robinson, Model Maker) and we do not know whether the integration method used is similar, as Lee and Robinson did not mention that in their study. The software algorithm as well as the hardware can contribute to the differences in the parameter estimates in modeling.

^{ 27 }Second, for estimating the value of the subconjunctival elimination rate constant Lee and Robinson used the vitreous pharmacokinetic data of prednisolone, whereas we used the corneal pharmacokinetic data to estimate the value. When we modeled the vitreous data of prednisolone using the model of Robinson and Lee but using Berkeley Madonna software, the parameter estimates were close for the elimination from the periocular site (0.143 vs. 0.128 minute

^{−1}). It is also possible that there is some missing element in obtaining similar values for parameters such as the elimination rate constant from the periocular tissue based on independent fits to corneal and vitreous concentration profiles.

^{ 28 }which is approximately 20 to 100 times that of celecoxib.

^{ 29 }

^{ 30 }Prednisolone sodium succinate used in the study by Tsuji et al.

^{ 4 }is expected to increase the drug’s solubility further to 50 to 100 mg/mL. The formulation administered in the rabbit study was thus a solution, whereas in the studies by Cheruvu et al.

^{ 11 }and Ayalasomayajula and Kompella,

^{ 12 }the formulation administered was a suspension of celecoxib. Thus, the differences in elimination from the periocular tissue could either be due to the differences in the species or differences in the formulation. It is known that the suspension form of the drug can sustain the drug levels better than the solution form. Indeed, a periocular (posterior juxtascleral) suspension of anecortave acetate (a lipophilic, very poorly water-soluble drug) has been shown to sustain drug levels for a prolonged period in preclinical studies as well as in humans.

^{ 31 }

^{ 32 }

^{ 31 }

^{ 32 }

^{ 33 }

^{ 34 }

^{ 35 }

^{ 36 }

^{ 37 }

^{ 38 }

^{ 39 }

^{ 40 }It is important to know the retinal pharmacokinetics of drugs, as it is the target organ for the above-mentioned disorders. Models have been developed to describe the vitreous pharmacokinetics after periocular administration. Lee and Robinson

^{ 5 }described a three-compartment model with a parallel elimination pathway to describe the pharmacokinetics of prednisolone in the vitreous after subconjunctival (periocular) administration. In a subsequent study, they proposed a simplified version of their model, to perform simulation studies to understand the kinetics of sustained drug delivery systems in the vitreous.

^{ 41 }No attempt has been made to model the retinal drug concentrations after periocular or even intravitreous modes of administration. We used the data of Cheruvu et al.,

^{ 11 }and developed a model describing the pharmacokinetics of drugs in the retina after periocular administration. As described in the corneal model’s development, we started with the simplest model wherein the drug directly penetrates the retina after periocular administration. The absorption constant for the retina is a hybrid of the absorption across the sclera–choroid and the RPE. This model is similar to the simple vitreous model proposed by Lee and Robinson.

^{ 41 }The data from the retinal celecoxib concentrations in BN rats were fitted to this model by using the curve-fitting procedure. The data-fits are shown in the Figure 5A . As can be seen, data at several time points were not fit well by the model (

*R*

^{2}: 0.65; AIC: 260), and the fits can definitely be improved. By evaluating the terminal (elimination) phase in the retinal kinetics of celecoxib, it can be seen that the drug follows multiphasic disposition from the retina. To model this, we included a distribution compartment into which the drug was distributed from the retina. This distribution compartment could be a combination of vitreous and probably the lens in the rat. However, inclusion of this distribution compartment did not lead to any significant improvement in the data-fits (Fig. 5B ;

*R*

^{2}: 0.63; AIC: 263.3). One important observation is that in both cases, the

*C*

_{max}was not well fit, and the

*t*

_{max}was achieved later than the model predicted. These findings indicate a lag phase in the kinetic profile. Since the formulation used was a suspension, a dissolution step is required before the drug becomes available for absorption. This process of dissolution/release may explain the greater than predicted

*t*

_{max}. We modified the model to include the dissolution step. With the revised model without a distribution compartment associated with retina, the

*t*

_{max}predicted by the model and the actually observed

*t*

_{max}were quite close (Fig. 5C)and the fit was better (

*R*

^{2}: 0.86; AIC: 231.3). However, the last few data points were underpredicted by the model, suggesting the existence of a distribution compartment. When the distribution compartment was added to the retina, the fits improved significantly and the model-predicted values fit well to the observed concentrations at all the time points (

*R*

^{2}: 0.9; AIC: 223.3; Fig. 5D ).

*C*

_{max}was slightly underpredicted by the model. We considered two more types of models to improve the

*C*

_{max}prediction. The drug has to cross the sclera and the choroid-RPE to reach the retina after periocular administration. In this process, there is a possibility that some of the drug is eliminated by the episcleral and choroidal circulation and lymphatics. Hence, instead of using a hybrid rate constant for absorption (which combines absorption in sclera, choroid, and retina) an inclusion of a transfer compartment that could be either the choroid or a combination of the sclera-choroid-RPE may lead to a better fit. Further, since the drug can be eliminated from the sclera-choroid-RPE (transfer compartment/choroidal compartment), we used a third parallel elimination pathway from the choroid. The structural model is shown in Figure 5E . When the data were fit to this revised model, an excellent data-fit was obtained (

*R*

^{2}: 0.92; AIC: 218.4). All the time points were well fit by this model. Further, this model predicted the

*C*

_{max}better than the previous models. There was good correlation between the observed and the model-predicted data. We included a distribution compartment for the choroidal compartment, to evaluate whether this would further improve the goodness of fit. However, no further improvement was achieved by inclusion of this compartment (data not shown). Thus, the model in Figure 5Ewas initially selected as the model to describe retinal pharmacokinetics after periocular administration. The elimination from the retina could be due to retinal blood flow or metabolism of the drug in the retina. There is not much evidence that a significant drug metabolism can take place in the neural retina. The RPE has metabolic activity, but we have included the RPE as a part of the transfer compartment, as the retinal concentrations measured in the studies are concentrations in the neural retina. Also, the blood flow to the choroid is significantly greater than the blood flow to the retina in many species including the rat, rabbit, cat, and the dog.

^{ 42 }

^{ 43 }

^{ 44 }

^{ 45 }In addition, the choroidal vessels are leakier and the choroidal vessels perform much of the retinal perfusion in mammals. It has been demonstrated by cryotherapy that choroidal blood flow does not play a significant role in the removal of triamcinolone acetonide after periocular administration.

^{ 14 }It has been argued that cryotherapy does not cause damage to the episcleral and conjunctival circulation but does affect the choroidal circulation. However, no actual measurements have been made of the choroidal and conjunctival blood flow with and without the cryotherapy. Also, only one time point was evaluated, and no statistical comparisons were performed. It is possible that the drug is eliminated via the choroid even when given intravitreously.

^{ 46 }

^{ 47 }Several previous modeling attempts have used the choroid as a perfect sink and have good fit between the model-predicted and observed data for intravitreous kinetics.

^{ 48 }

^{ 49 }

^{ 50 }

^{ 51 }Hence, we evaluated an additional model that did not have elimination from the retina. We assumed that the drug is distributed from the choroidal compartment (transfer compartment) into the retina but is eliminated primarily through the choroidal compartment and the periocular tissue. The fits to the revised model are shown in Figure 5F . The difference between Figures 5E and 5Fis the presence or absence of the retinal elimination pathway, respectively. The model in Figure 5E(

*R*

^{2}: 0.92; AIC: 218.4) with an elimination pathway in the retina results in a better fit than the model in Figure 5F(

*R*

^{2}: 0.89; AIC: 228). There are species differences in the retinal circulation, with humans and rodents having a holangiotic retina and rabbits having a merangiotic retina.

^{ 52 }

^{ 53 }The model in Figure 5Fwithout the retinal elimination pathway may be more representative of the rabbit physiology. Based on the statistical goodness-of-fit criteria model described in Figure 5Ewas selected as the finalized model to describe retinal pharmacokinetics after periocular administration in the rat model.

*C*

_{max}. One potential explanation is that there is a systemic recirculation component contributing to retinal drug levels. We included such a possibility in the models to improve the prediction of

*C*

_{max}and to enhance the overall data-fit. We considered four recirculation models, which are essentially those shown in Figures 5C 5D 5E 5F , but with the addition of a systemic circulation compartment that communicates with the vascularized tissues in the back of the eye and eliminates the drug from the system (Fig. 6) . None of the recirculation models evaluated resulted in a better fit to the data than the models described herein (Fig. 6) . Also, the predicted

*C*

_{max}values with the recirculation models were not as good as those predicted by the model in Figure 5E . Hence, the model in Figure 5Ewas selected as the final model. We validated the model in Figure 5Eusing the retinal pharmacokinetics data in nonpigmented SD rats. The model resulted in an excellent fit to the observed data (

*r*= 0.99; Fig. 7 ). Thus, a similar model can be used to describe the pharmacokinetics of celecoxib in the pigmented and nonpigmented rat retina although the parameter estimates can differ.

^{−1}), therefore in our retinal modeling, we did not fix the value of the periocular elimination rate constant. However, the values obtained for the elimination rate constant for celecoxib from the periocular tissue from either the corneal or retinal pharmacokinetics data of celecoxib were very close (0.123 minute

^{−1}with retinal data versus 0.135 minute

^{−1}with corneal data). The estimates for the other parameters are shown in Table 3 . The parameter estimates indicate that the elimination rate constant of celecoxib from the periocular site was approximately threefold greater than its elimination from the choroidal compartment (transfer compartment; 0.123 vs. 0.035 minute

^{−1}). Further, the choroidal elimination rate constant for celecoxib was 18-fold greater than the retinal elimination rate constant (0.035 vs. 0.002 minute

^{−1}). Using animal models, Robinson et al.

^{ 14 }showed that the conjunctival circulation and lymphatics play a much greater role in the elimination of drugs after periocular administration compared with the clearance by the choroidal circulation. This route is even believed to be responsible for the clearance of macromolecules from the periocular site, as was shown in the case of albumin by Bill,

^{ 54 }

^{ 55 }who demonstrated that the albumin is eliminated partly by the conjunctival circulation and lymphatics. We also found that the conjunctival circulation and lymphatics could be playing a role in the clearance of small (20 nm) nanoparticles.

^{ 56 }Also Liu et al.

^{ 57 }demonstrated that the conjunctival lymphatics play a role in clearing latex particles, ultimately leading to accumulation of the latex particles in the cervical lymph nodes after subconjunctival administration.

^{ 58 }Similarly, others have demonstrated that the RPE is a significant barrier to the transscleral delivery of drugs to the retina, and the resistance of the RPE is higher to hydrophilic drugs than to lipophilic drugs.

^{ 59 }However, our model suggests that if the drug or delivery system is directly injected into the transfer compartment, the retinal availability would significantly increase, because a significant portion of the elimination by the subconjunctival and episcleral circulations can be avoided. Recently, Kim et al.

^{ 15 }using MRI, demonstrated that periocular administration does not lead to significant drug levels in the posterior segment intraocular tissues; however, if the drug is administered by an intrascleral infusion, significant drug levels can be seen in the posterior intraocular tissues. We used the finalized model (Fig. 5E)to fit the celecoxib retinal pharmacokinetics data in nonpigmented rats. Very good data fits were obtained and there was a good correlation between the predicted and observed values (Fig. 6) . The predicted parameter estimates for the nonpigmented rats are shown in Table 3 . The elimination rate constant from the periocular space appeared to be similar between the BN and SD rats (0.123 vs. 0.115 minute

^{−1}). All other parameters were also similar, with the only major differences being in the parameter K30 (elimination rate constant from the retina), which was approximately 100-fold greater in the BN rats than in the SD rats (Table 3) . We also observed that the dissolution/release rate constant for celecoxib is similar based on corneal data as well as retinal data in both the rat strains (Tables 1 3) . As discussed in the section on corneal modeling, the precision of the parameter estimates is not known, and hence no conclusive statement can be made about the statistical significance of these differences. With more data and use of software programs with built-in features for calculating the precisions, this problem can be solved. We tried to use another pharmacokinetic modeling software (WinNonlin 1.5; Pharsight Corp., Mountain View, CA) in our modeling, because it provides precision of the parameter estimates. However, the software algorithm failed to converge with some of the modeling strategies in the present analysis. It has been shown that there are significant differences in retinal AUC of celecoxib after periocular administration to BN and SD rats, with the levels being higher in SD rats than in the BN rats. From the parameter estimates in the two species, we cannot determine which parameter influenced this difference in the retinal AUCs. It could be a single parameter or a combination that leads to the observed differences. The binding of the drug to melanin can be included in each of the modeling compartments where melanin is present. To keep the approach simple and to minimize the number of parameters, we did not include this component in our modeling strategy.

*C*

_{max}and a lower

*t*

_{max}. The suspension dosage form had a lower

*C*

_{max}but it sustained the drug levels better than the solution dosage form (Fig. 8 , inset). During the longer-term simulation over a 60-day period with the three different formulations, similar to the cornea, the sustained-release dosage form maintained the drug levels in the retina within 1 order of magnitude for most of the 60-day period. With the solution and suspension dosage forms, on the other hand, there was a rapid initial decline followed by a gradual decline in the drug levels over several orders of magnitude (Fig. 8) . Thus, it can be inferred from the model simulations that solution and suspension dosage forms of celecoxib do not sustain significant levels of drugs in the cornea or retina for a prolonged period. However, with a sustained-release system releasing drug at a much slower rate, tissue levels can be maintained for prolonged periods.

^{ 60 }data on drug quantification in the retina are sparse. We are currently establishing the reliability of Fluorotron measurements for pharmacokinetics analysis. Although Fluorotron allows the measurement of only fluorescein and related fluorophores, other noninvasive techniques such as magnetic resonance imaging assess only the disposition of contrast agents or contrast agent–labeled solutes, which may not be truly reflective of the solute’s disposition. For any modeling study, tissue data should be analyzed by using reliable analytical methods such as HPLC analysis, as was the case with the data used in this study. In future, more such data will enable better mathematical modeling of the pharmacokinetics of drugs in various layers of the posterior eye after periocular administration.

**Figure 1.**

**Figure 1.**

**Figure 2.**

**Figure 2.**

Symbol | Meaning | BN Rats | SD Rats |
---|---|---|---|

K10 | Elimination rate constant from periocular site | 0.135 | 0.134 |

K12 | Absorption rate constant for cornea | 1.5e-4 | 1.3e-4 |

K20 | Elimination rate constant from the cornea | 0.177 | 0.154 |

Krel | Dissolution/release rate constant from the formulation | 0.024 | 0.025 |

**Figure 3.**

**Figure 3.**

Symbol | Meaning | Value (min^{−1}) |
---|---|---|

K10 | Elimination rate constant from the periocular site | 0.072 |

K12 | Absorption rate constant for cornea | 2.11e-7 |

K20 | Elimination rate constant from the cornea | 0.065 |

**Figure 4.**

**Figure 4.**

**Figure 5.**

**Figure 5.**

**Figure 6.**

**Figure 6.**

**Figure 7.**

**Figure 7.**

Symbol | Meaning | BN rats | SD rats |
---|---|---|---|

K10 | Elimination rate constant from periocular site | 0.123 | 0.115 |

K12 | Absorption rate constant for sclera-choroid-RPE (transfer compartment) | 3.61e-4 | 6.81 e-4 |

K20 | Elimination rate constant from the sclera-choroid-RPE (transfer compartment) | 0.035 | 0.038 |

K23 | Absorption rate constant for retina from the sclera-choroid-RPE (transfer compartment) | 0.061 | 0.031 |

K30 | Elimination rate constant form the retina | 0.002 | 1.28 e-5 |

K34 | Rate constant for transfer to the distribution compartment from the retina | 0.045 | 0.046 |

K43 | Rate constant for transfer to the retina from the distribution compartment | 0.001 | 0.001 |

Krel | Rate constant for the release of the drug from the formulation (suspension) | 0.017 | 0.018 |

**Figure 8.**

**Figure 8.**