Materials and Methods

Pharmacokinetic Study.

Obtaining PK samples from ocular tissues is a terminal procedure (animals must be sacrificed to collect ocular tissues); thus, the number of experimental animals we could reasonably and ethically use was limited. This limitation is common in preclinical ophthalmology studies. In total, eight beagles (16 eyes) were stratified to receive single topical instillations of either 0.5 or 1.25 μg of PF-04475270 in both eyes. The dosage was formulated in a total dose volume of 50 μl, which was given two times with 25-μl topical drops each time. At specified times, animals were terminated, eyes were surgically removed, and the cornea, AH and iris/ciliary body (ICB) were extracted and homogenized before quantitation. The postdosing times selected for sampling were 0.25, 1, 3, and 6 h for the 0.5-μg dose group and 2, 6, 12, and 18 h after dosing for the 1.25-μg dose group. CP-734432 and PF-04475270 were isolated from homogenized ocular tissues by protein precipitation [80:20 (v/v) acetonitrile/methanol] and quantitated using high-performance liquid chromatography/tandem mass spectrometry. The analytical error was kept within 20%. All animal-related procedures were conducted in accordance with the Association for Research in Vision and Ophthalmology statement for the use of animals in ophthalmic research as well as in compliance with Pfizer Lab Animal Care procedures.

Pharmacodynamic Study.

Male and female normotensive beagles (n = 118 treated eyes) were stratified to receive either a single topical instillation or once-daily multiple topical instillations of PF-04475270. The single-dose study was performed with doses of 0.1, 0.25, 2.5, and 5 μg, and the multiple-dose study was performed with doses of 0.5 and 1.25 μg given once daily for 4 days. The dosage was formulated in a total dose volume of 50 μl, which was given two times as 25-μl topical drops each time. IOP was measured in both eyes of the conscious animal (one eye received the vehicle and the other eye received the test article) using the model 30 classic pneumatonometer (Medtronic, Minneapolis, MN). The postdose times of IOP measurements were 0, 2, 4, 6, and 24 h for the single-dose group and 0, 2, 4, 6, 8, 12, 24, 30, 48, 54, 72, 78, and 96 h for the multiple-dose group. In addition, the 2.5- and 5-μg single dose groups also had their IOP measured at 0.5 h. Because, within each animal, one eye received the vehicle, the other eye received the test article, and the full IOP time course was measured in both eyes, each animal served as its own control. The time-matched IOP percentage of change relative to the vehicle over time was defined as the PD variable for PKPD modeling.

PKPD Modeling.

Five variations (models A–E) of the PK model were explored to describe the CP-734432 PK data set. The PK PF-04475270 was not modeled because it was not readily detectable due to rapid conversion to CP-734432. In model A, CP-734432 was assumed to undergo first-order absorption into the cornea described by the rate constant k_a. First-order bidirectional movements of CP-734432 between the cornea and the AH (k₂₃ and k₃₂) and between the AH and the ICB (k₃₄ and k₄₃) were implemented. In addition, first-order eliminations from the cornea (k₂₀) and the AH (k₃₀) were also assumed. Model B was similar to model A except that k₃₂ was excluded. Model C was similar to model B except that k₄₃ was excluded and k₄₀ was included. Model D was similar to model C except that k₂₀ was excluded. Model E was similar to model D except that k₄₀ was excluded. We ultimately chose a model (model B) that would best balance between reasonable goodness of fit and physiological relevance. The chosen PK model is shown as part of the integrated PKPD model in Fig. 2. Preliminary analysis of the PK data set was performed before modeling using WinNonlin 5.2 (Pharsight, Mountain View, CA) to assess dose proportionality of C_max and area under the curve. Once dose-exposure linearity was verified, the data obtained from the 0.5-μg dose group in the PK study were normalized by a factor 2.5, to reflect the concentrations of the 1.25-μg dose. These normalized data and the original 1.25-μg dose data were combined for simultaneous fitting, using 1.25 μg as dose input for both data sets in the PK model. We found that this method significantly improved model maximum likelihood fitting stability compared with fitting the raw data set, although the latter method would have been in principle more desirable. The volume of distribution in each of the tissue compartments was fixed based on experimentally observed values: 0.15 g, 0.43 ml, and 0.050 g for the cornea, AH, and ICB, respectively.

For modeling the PD data set, first, we assumed that the PD did not exhibit sensitization and described IOP data from the PD study using a basic indirect response model, hereafter model I (Fig. 2) (Dayneka et al., 1993; Sharma and Jusko, 1996). Subsequently, model II, which was an extension of model I, was applied under the assumption that there was time-variant PD. Model II was inspired by an empirical approach to model PD tolerance using a negative feedback loop (Gabrielsson and Weiner, 2000). However, in this situation, we applied a positive feedback loop as an additional component that governs the equilibrium of IOP. In the setup of model II, any perturbation in IOP would directly shift the equilibrium and cause a unidirectional change in M, an assumed “endogenous modulator” (Gabrielsson and Weiner, 2000). Thus, as IOP is increased, M is driven to increase, which further drives up IOP. In our specific scenario, PF-04475270 is rapidly converted to the IOP-lowering therapeutic agent CP-734432, which would lessen the positive signal to the endogenous modulator, resulting in a further time-dependent lowering of IOP. Although this approach to modeling up-regulation is considered empirical, it captures the main feature of decreasing response over time at similar drug concentrations. In both models, CP-734432 concentration in the ICB (the intended site of action) was designated to drive IOP reduction by stimulating its dissipation parameter (k_out, see equations below).

The differential equations used to describe the PKPD model after PF-04475270 administration (model II) are as follows:where A_dep, A_crn, A_ah, and A_icb are the drug amounts in model compartments (depot, cornea, AH, and ICB, respectively); concentrations in the PK compartments (C_rn, C_ah, and C_icb) were fitted by scaling drug amounts, as written in the above-mentioned equations, by their respective volumes of distribution, V_crn, V_ah, and V_icb; k_a is the first-order absorption rate constant from the depot compartment to the corneal compartment; k₂₃, k₃₄, and k₄₃ are first-order distribution rate constants; R is the experimentally measured pharmacodynamic response (IOP), k_in is the zero-order rate constant for the buildup of response; k_out is the first-order rate constant for the response dissipation; S_max describes the capacity for drug stimulation of k_out; SC₅₀ describes the drug concentration corresponding to 50% stimulation of k_out; M is the assumed modulator, which provides the positive feedback to k_in; M₅₀, for M₅₀ > 0, is the value of M that doubles k_in; and k_mod is the rate constant for M production and dissipation. The initial condition (R₀) of eq. 5 is necessarily k_in/k_out × [1 + (M₀/M₅₀)] when one considers C_icb to be zero and dR/dT = 0 when T = 0, before drug administration. It follows that k_in can be derived as k_in = R₀k_out/[1 + (M₀/M₅₀)] so that it is not independently estimated as a parameter. From eq. 6, M₀ is necessarily equal to R₀ when one considers dM/dT = 0 and T = 0. Because the response is expressed as a percentage of baseline, the response at time 0 (R₀), before drug administration, is assumed to have a value of 100 (baseline response). For consistency, the initial level of the modulator (M₀) is also assumed to be 100. Model I is the same as model II, without eq. 6 and with eq. 5 simplified to reflect the absence of the endogenous modulator. Thus, although model II has five unknown parameters (k_out, S_max, SC₅₀, k_mod, and M₅₀), model I has three unknown parameters (k_out, S_max, and SC₅₀).

One issue with analyzing IOP data are the known 24-h circadian rhythm associated with the baseline (Chen et al., 1980). Because only diurnal IOP data were available, we could not incorporate a harmonic component to the baseline effect. To overcome this issue, the IOP data for each of the animal from the drug-treated eye was corrected against IOP data from the vehicle-treated eye on a time-matched basis before fitting. For each time point of the IOP curve in a single animal, the baseline correction was done using the formula IOP_(t) = 100 − 100 × [(IOP_vehicle(t) − IOP_treated(t))/IOP_vehicle(t)]. Due to experimental and between-eye variability within an individual animal, the corrected IOP could be slightly greater than 100 if IOP_treated is greater than IOP_vehicle.

The PK and the PKPD modeling were performed using NONMEM VI (ICON Development Solutions, Ellicott City, MD). Thus, average data from all three ocular tissues were fitted simultaneously to obtain ensemble PK parameter estimates. Although the use of average time points may have some impact on the analysis results, this is typical for ophthalmology studies, in which it is rather unusual to have high-resolution PK measurements, especially in larger animal species. A population-based approach was used instead to fit the PKPD model. The first-order approximation (first-order, METHOD = 0) method, as implemented in NONMEM, was used. Although FOCE-INTERACTION may have been preferable, several attempts to use this method have resulted in run failures typically after ∼48 h of run on our grid server, denoting numerical instability associated with this particular likelihood approximation in this context. The PK parameters for each individual were fixed to the values obtained from the average PK fitting. This assumes that all individuals from the PD data set have identical PK. The PD between-subject variability was assumed to be log-normal; it was estimated for k_out, S_max, and SC₅₀ and, given the expected difficulty to estimate parameters within the modulator submodel, fixed to zero for k_mod and M₅₀. Thus, model II has two more population parameters with respect to model I (the typical values for k_mod and M₅₀). A proportional error model was used for the estimation of the residual variability. In both the PK and the PKPD fits, the parameter asymptotic standard errors (a measure of precision) were directly obtained from the NOMEM output.

Results

Due to robust esterase activity in the eye, levels of intact prodrug PF-04475270 were below the detection limit in the tissues at all the times studied. The mean PK profiles of the active metabolite CP-734432 in dog ocular tissues (cornea, AH, and the ICB) are shown in Fig. 3 along with the PK model fit. CP-734432 was rapidly absorbed into the cornea, as apparent by the early peak and distributed more slowly into the AH and ICB. Exposure in the ICB was slightly lower than in the AH, but approximately 10-fold lower, in terms of C_max, than in the cornea, indicating very little bioavailability to the intended site of action (ICB) after topical dosing. Table 1 lists the resulting parameters from the fit of each variation of the PK model and their relative standard errors (RSEs) expressed as a percentage of the NONMEM-generated standard errors to their respective parameter values. Based on the overall goodness of fit and mechanistic plausibility, model B was selected as the final PK model. From the results of model B fitting, the high estimates of parameters values for k₃₄ and k₄₃ indicate, that the AH and ICB are well equilibrated. Based on the high ex vivo corneal permeability assessment of PF-04475270 (Prasanna et al., 2009), the k_a value, 0.188 h⁻¹, estimated from our model would seem lower than expected. However, because bioavailability fraction was not accounted for, the k_a as represented in this model is a lumped parameter consisting of both k_a and the fraction of the dose absorbed (F), which can be extremely low due to extensive loss of drugs from the corneal surface after topical instillation. The terminal half-life of each tissue as calculated from WinNonlin was extremely short (2–3 h). Due to the short duration of exposure in each of the eye tissues, CP-734432 was not expected to accumulate upon multiple dosing. The repeated dosing simulation in the inset of Fig. 3 shows the ICB concentration quickly reaching steady state without accumulation.

As a preliminary qualitative assessment, mean 24-h IOPs after each dose and their S.E.M. showed that the observed IOP reduction for the multiple-dose profiles was generally more pronounced than after the first dose (Fig. 4) despite projected steady-state PK. Figure 5 presents the composite IOP profiles (100 = 100% of time-matched baseline) for both single-dose and multiple-dose conditions. Figure 5 also shows the fit of model I, which generally overpredicted the IOP observations and therefore underpredicted the extent of the pharmacodynamic response seen with repeated dosing. Model I predicted a steady-state IOP profile consistent with steady-state PK as expected with the standard-indirect response model.

In contrast, model II more robustly captured the persistent decline of the IOP profile seen with multiple dosing, as presented in Fig. 6. The difference in values of the objective function (an approximation of twice the negative log-likelihood) from the NONMEM runs was 67. This difference is greater than ∼6 points, which can be considered statistically significant (P < 0.05) for two nested models (model I and model II) differing by two parameters (Ostermann et al., 2004). Table 2 lists the resulting parameter values and their RSE as provided by NONMEM and expressed as a percentage. Based on visual inspection of the goodness of fit (Fig. 7), model II outperforms model I. Model I tends to overpredict the observed data for the PRED versus DV comparison. Figure 8 (a–c) shows the extended PK and IOP profiles based on model I and model II, which were simulated to test the long-term model behavior, under the conditions of 0.1-, 1-, and 50-μg daily doses using the parameters obtained from fitting. As expected from the standard IRM, model I, reaches an immediate steady-state PD in the presence of steady-state PD. In contrast, model II predicts a time-dependent sensitization before reaching steady state. Both models exhibit dose-response characteristics.

Discussion

PF-04475270 is a preclinically investigated isopropyl ester prodrug of CP-734432, which is a potent and selective agonist for the EP₄ receptor. After topical administration, PF-04475270 was seen to rapidly convert to CP-734432, which quickly gets absorbed into the cornea and subsequently equilibrated into more distal tissues such as the AH and ICB. CP-734432 in ocular tissues exhibits short terminal half-lives (2–3 h), which are characteristic of ophthalmic agents (Urtti, 2006). For example, latanoprost has a half-life of 3.0 h in the AH, 1.8 h in the anterior sclera, 1.8 h in the cornea, and 2.8 h in the ciliary body of rabbits (Ohtori et al., 1998; Sjöquist et al., 1998). Timolol and carteolol have AH half-lives of 1.1 and 1.5 h, respectively, in rabbits (Ohtori et al., 1998; Sjöquist et al., 1998).

Due to its brief duration of exposure in ocular tissues, CP-734432 is not expected to accumulate with multiple dosing. Although accumulation of CP-734432 due to time-dependent PK, i.e., resulting from ocular metabolic enzyme down-regulation, is theoretically possible, this mechanism, to our knowledge, has not been reported. In addition, because the levels of CP-734432 were not detectable in plasma after topical administration, PK accumulation arising from liver metabolic enzyme modulation is also highly unlikely. Notwithstanding, it would be desirable to verify the prediction by directly obtaining PK information from a multiple-dose study. However, we were faced with the usual limitations of animal use, especially for a terminal study using higher species such as dogs.

In this work, several permutations of the PK model were explored to fit the PK data set. Whether the chosen PK model best represents the general mechanism of drug distribution between ocular tissues is debatable and likely depends on the compound. For example, Sakanaka et al. (2004) incorporated a bidirectional movement between the corneal stroma and AH but a unidirectional movement from the AH to the ICB for bunazosin. In contrast, Oh et al. (1995) incorporated a bidirectional movement between the AH and both the fluid compartment of the cornea and the ICB.

Despite the anticipated lack of PK accumulation in the multiple-dose regimens, IOP reduction is more pronounced for days 2, 3, and 4 versus day 1, as summarized in Fig. 4. The progression of IOP lowering in the multidose condition is supportive of our selection of model II. Although the difference between model I and II may seem small upon purely visual inspection of Figs. 5 and 6, it should be pointed out that the goodness of fit improves significantly at later points in the curve. Note from Fig. 4 that at the IOP at the 24-h point of the 1.25-μg dose is less than that of the 0.5-μg dose. This may be attributed to experimental and interanimal variability (see the spread of the data in Fig. 5).

Although taking significantly longer run time than model I, we found that model II was stable and yielded reasonable parameter estimates. The SC₅₀ value of 0.674 ng/g is within the range of the ICB concentrations seen in our PK study (Fig. 3). The estimated k_out value (0.653 h⁻¹) roughly corresponds to the initial slope of log IOP change over time as determined from the observed data (Gabrielsson and Weiner, 2000). For example, on average, IOP drops from 100% baseline to 75% within 0.5 h, yielding a log slope of −0.575, reasonably close to our estimated k_out value. The M₅₀, which represents the amount of M that doubles k_in, was estimated to be 58.2. Because the initial value (M₀) was set at 100, at initial equilibrium condition, it can be shown that the endogenous modulator intrinsically exerts 2.72-fold modulation of k_in, i.e., from eq. 5, we can substitute M and M₅₀ in the first term of the equation, k_in × [1 + (M/M₅₀)], as k_in × [1 + (100/58.2)] = 2.72k_in. Thus, in an unperturbed initial equilibrium, the initial inflow of IOP is 2.72 times k_in. During perturbation, when the drug was given, IOP is driven lower, and the level of M is also lowered, leading to a further drop in IOP, a time-varying component of the model.

To test the behavior of the model, the PD time course was simulated in a longer term multiple-dose condition. As expected, due to the nonlinearity of the system, the PD approaches an eventual steady state as opposed to continually declining. In addition, dose dependence as an inherent characteristic of the standard IRM is retained in this model. This feature of the model is critical in that, first, response sensitization should sensibly exert a physiological limit; and, second, the sensitization component should not fundamentally alter the dose-response nature of the model.

During model development, we have also considered other variations of the PD model. First, under mechanistic consideration, the modulator M would more appropriately be designated to modulate k_out instead of k_in. However, this would probably lead to identifiability issues for M₅₀, SC₅₀, and S_max because, under this model, all of these parameters would simultaneously modify k_out. Second, for simplicity, we could assume M₅₀ to be 1 so that the modulation of k_in due to M is linear. However, including the parameter M₅₀ (which represents the level of M corresponding 50% maximal effect on k_in) improves the interpretability of the effect of M. Last, as opposed to assuming sensitization, the drug potency parameter, SC₅₀, could be specified as changing over time, specifically decreasing, so that the effective potency would increase with repeated dosing. However, such a model would seem less “mechanistic,” and it would not have the advantage of separating the system from the drug specific parameters. In our model, a self-regulating sensitization process is built-in and exists even in the absence of the drug. Thus, we chose, instead, to reversibly adapt a negative feedback model that has been used previously to describe pharmacodynamic tolerance in the context of an IRM by incorporating a positive feedback loop. Such tolerance models have been successfully applied in other situations (Wakelkamp et al., 1996; Gabrielsson and Peletier, 2007).

Because the PK sampling of CP-734432 in ocular tissues was a terminal procedure, we could not match an individual's PK to its respective PD. Instead, the mean PK from a separate set of animals was assumed to drive each individual's PD and the interindividual variability in each of the PD parameters was estimated during the optimization. A consequence of this approach is the lumping of PK variability into the estimated PD variability. Thus, the estimated interindividual variability in the PD parameters can be interpreted to be inclusive of PK variability, although the two cannot be differentiated. However, the structural assessment of the drug's response and sensitization should not be affected by this approach.

The current approach to PKPD modeling of IOP in the presence of scarce PK information may have utility in the clinical drug development setting. Obviously, one cannot feasibly extract eye tissues from humans to collect ocular PK data. However, obtaining PK samples from the AH of a select group of patients is feasible, for example, during cataract surgery (Calissendorff et al., 2002; Yagci et al., 2007), and the mean PK data obtained from such study could be used to drive a population PD model. For example, we have recently used the mean literature PK data of latanoprost obtained from the AH of patients undergoing cataract surgery (Calissendorff et al., 2002) to inform the PD model that describes the time course of IOP in glaucoma patients in clinical trials (data not shown). Thus, our approach is of value in a drug development setting in which ocular PK information is limited but a population-based PD model could reasonably be established. To capture time-dependent sensitization for compounds such as PF-04475270, we would envision clinical IOP data being collected within a multiple-dose/multiday setting to obtain a time course that is amenable to modeling. In addition, more robust methods for nonlinear mixed effect estimation could be considered, among them are stochastic approximation expectation maximization (Lavielle and Mentré, 2007) and Monte-Carlo parametric expectation maximization (Bauer and Guzy, 2004). These methods tend to be based on less stringent approximations to the maximum likelihood problem and could offer a viable alternative.

In summary, we developed an integrated population-based PKPD model to characterize the dog IOP time course that exhibited time-dependent sensitization after topical administration of PF-04475270. To our knowledge, literature modeling reports in which population PKPD approach is used in the field of ophthalmology are relative few. In addition, there are very few modeling examples dealing with sensitization of PD responses. Last, our preclinical approach to modeling population PD data using limited PK data may be applied to model IOP data in the ophthalmology drug development setting. Although the PK may minimally be available to drive the PD, the utility of this model can be tested in the clinic.