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Source: Adapted from Ref. 8.

Source: Adapted from Ref. 8.

4. Ocular Pharmacokinetic Models

Various approaches to modeling pharmacokinetic data from ocular studies have been developed. These primarily involve (a) classical, empirical com-partmental modeling, (b) physiological modeling, and (c) noncompartmen-tal modeling employing statistical moment theory. Critical to pharmacokinetic modeling is an adequate description of the concentration versus time curve. Unfortunately, the rationale for selecting the number and timing of sample intervals is not always clear. In many cases, a sampling scheme may be dictated by bioanalytical sensitivity, practicality, or even economics. However, Schoenwald (8) has provided general sampling guidelines that may prove useful in properly designing ocular studies (Fig. 4).

Not only are an appropriate number of time intervals necessary, but there should also be a sufficient number of replicates per time point. Rabbits studies have used as few as 4 and as many as about 20 eyes per time interval, depending on the study objectives. Higher numbers are preferred for bioequivalence studies. Moreover, because the animal is typically euthanized for ocular tissue/fluid sampling, each animal subject (e.g., rabbit or monkey) yields at most two data points (one/eye) per interval. Mean concentrations, derived from individual animal data, are then used to calculate the pharmacokinetic parameters. A statistical approach to this sparse sampling scheme has been developed for comparison of area under the concentration-time curves (62,63).

a. Classical Empirical Pharmacokinetics. Classical modeling uses compartments, representing kinetically homogeneous groups of tissues/organs, linked together by various rate constants. For ocular pharmacoki-netics, the simplest model is one employing a single compartment as shown in Figure 5a. However, this model fails to account for precorneal loss. The model in Figure 5b corrects for this but is still very simplified and treats the cornea as a homogeneous tissue, lumping all precorneal

Figure 5 Schematics of various models of topical ocular drug pharmacokinetics FD = Bioavailability times dose; C = cornea; PC = precorneal area; AH = aqueous humor; AC = anterior chamber; R = reservoir; Epi = corneal epithelium; Str = corneal stroma; Endo = corneal endothelium. (Adapted from Refs. 4, 44, 64.)

Figure 5 Schematics of various models of topical ocular drug pharmacokinetics FD = Bioavailability times dose; C = cornea; PC = precorneal area; AH = aqueous humor; AC = anterior chamber; R = reservoir; Epi = corneal epithelium; Str = corneal stroma; Endo = corneal endothelium. (Adapted from Refs. 4, 44, 64.)

rate constants together into one. The model in Figure 5c divides the anterior segment of the eye into cornea and aqueous humor, although this still excludes precorneal loss and does not adequately describe disposition beyond entry into the aqueous. Makoid and Robinson proposed a four-compartment caternary model for pilocarpine, as shown in Figure 5d, which combines precorneal loss with differentiation of cornea and anterior chamber (44). However, cornea is still treated as a homogeneous tissue, when the epithelium is known to be the major barrier to ocular uptake. The model in Figure 5e portrays epithelium as one compartment and stro-ma/endothelium/aqueous humor as a separate lumped compartment and incorporates elimination from each of the compartments (64). An example of one of the more sophisticated models is shown in Figure 6, which includes a conjunctival compartment, along with sclera, intraocular, and systemic circulation compartments, as well as redistribution to the contralateral eye (21).

b. Physiological Model. Beyond the classical compartmental modeling approach is one that incorporates more realistic physiological components. Physiological pharmacokinetic models are intuitively more predictive by their use of actual anatomical and physiological parameters, such as tissue blood flow and volume (65). Ocular pharma-cokinetics appears to be an ideal candidate for physiological modeling, since it is relatively simple to remove the tissue components of the eye for measurement of drug levels. For example, Himmelstein et al. developed

Figure 6 Schematic of an ocular pharmacokinetic model showing precorneal events, absorption into the eye via the cornea or conjunctive/sclera, distribution to the systemic circulation, and redistribution to the contralateral (undosed) eye. PC = Precorneal area; Conj = conjunctiva; C = cornea; S = sclera; AC = anterior chamber; IT = intraocular tissues; OC = ocular circulation; SC = systemic circulation; CE = contralateral eye. (Adapted from Ref. 21.)

Figure 6 Schematic of an ocular pharmacokinetic model showing precorneal events, absorption into the eye via the cornea or conjunctive/sclera, distribution to the systemic circulation, and redistribution to the contralateral (undosed) eye. PC = Precorneal area; Conj = conjunctiva; C = cornea; S = sclera; AC = anterior chamber; IT = intraocular tissues; OC = ocular circulation; SC = systemic circulation; CE = contralateral eye. (Adapted from Ref. 21.)

a simple physiological pharmacokinetic model, shown in Figure 7, for predicting aqueous humor pilocarpine concentration following topical application to rabbit eyes (66). The model takes into account instilled volume and drug concentration and can predict the effect of precorneal drainage.

Physiological modeling may not be the best approach in all cases. For example, Chiang and Schoenwald determined the concentrations of cloni-dine in seven different ocular tissues and plasma after a single topical ocular dose of clonidine was administered to rabbits (67). The data were fit to a physiological model and a classical diffusion model with seven ocular tissue compartments and a plasma reservoir. The complex classical model was subdivided into fragmental models. While predicted and observed concentrations profiles closely agreed with the physiological model, the classical model fit the data better than the physiological model.

c. Other Models. A few other modeling approaches have been proposed, including noncompartmental modeling and population pharmaco-kinetics. Eller et al. applied noncompartmental statistical moment theory to topical infusion data to describe the disposition of various compounds with a range of transcorneal permeabilities within the rabbit eye (48). Morlet et al. used population pharmacokinetics to evaluate pharmacokinetic data in plasma and vitreous of the human eye (68). Gillespie et al. applied principles and methods of linear system analysis to the analysis of ocular pharmacokinetics (69). Using convolution integral mathematics, a

Figure 7 Schematic of a two-compartment model consisting of the precorneal area and the aqueous humor. PC = precorneal; QT = normal tear production rate; VT = total volume in the precorneal area any given time; K = proportionality constant that is a function of instilled drop size; V0 = normal tear volume; VAH = normal aqueous humor volume A = corneal area; L = corneal thickness; Kel = lumped first-order clearance parameter from aqueous humor. (Adapted from Ref. 66.)

Figure 7 Schematic of a two-compartment model consisting of the precorneal area and the aqueous humor. PC = precorneal; QT = normal tear production rate; VT = total volume in the precorneal area any given time; K = proportionality constant that is a function of instilled drop size; V0 = normal tear volume; VAH = normal aqueous humor volume A = corneal area; L = corneal thickness; Kel = lumped first-order clearance parameter from aqueous humor. (Adapted from Ref. 66.)

mechanistic model of precorneal disposition was used to predict concentration. The authors adequately predicted betaxolol levels resulting from a multiple dose regimen and from single doses of prototype controlled-re-lease ocular inserts. This approach appears to require fewer, less restrictive assumptions than compartmental or physiological model methods.

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