Compartmental Model Analysis

The pharmacokinetic processes of drug absorption, distribution, metabolism, and elimination determine the concentration-versus-time profile in a target organ. Ocular pharmacokinetic models for intraperitoneal (IP), intravenous (IV), and intraocular drug administration are described by three-, two-, or one-compartment models, respectively. These models are not representative of real tissue spaces. Physiologically based models using mass balances and blood-flow limited elimination are least useful for ocular pharmacokinetics because of the nonidentifiable nature of drug transfer by flow, blood diffusional exchange, and anterior-posterior drainage. Compartmental open models are depicted with elimination from the central compartment.

Drugs that distribute rapidly and homogeneously into the plasma and well-perfused, extracellular fluid follow a one-compartment model (and often show first-order kinetics). Drug elimination from the eye generally follows first-order kinetics. One-compartment models best describe mono-exponential (log-linear) elimination kinetics (Fig. 2). Two-compartment kinetic models demonstrate identifiable distribution and elimination phases where competing elimination rates govern both the distribution and elimination phases (Fig. 3).

Analysis of concentration-versus-time data optimally co-models plasma samples and ocular samples simultaneously for pharmacokinetic parameter estimation (16). Pharmacokinetic analyses of these data provide apparent volumes of distribution and areas under the concentration-versus-time curve of the serum and peripheral compartments as part of the phar-macokinetic parameter identification procedure. AUCs are determined by numerical integration (or trapezoidal approximation). The calculated

Figure 2 On-compartment open model. The figure depicted shows the pharmacokinetic model for changing drug concentrations in the eye, where drug is injected directly into the vitreous either as a bolus [d(t)] or rapid prolonged-bolus (infusion) [F(t)]. Infusion of drug into the eye is of fixed rate F(t) and known duration. ke1 is a first order removal rate constant from the eye. k'd is the rate of removal of drug due to active pumping. Amte is the drug amount in the eye compartment. Given most achievable concentrations, this behaves in a pseudo-linear fashion. Ce = Concentration in the eye; Ve = volume of distribution of the eye.

Figure 2 On-compartment open model. The figure depicted shows the pharmacokinetic model for changing drug concentrations in the eye, where drug is injected directly into the vitreous either as a bolus [d(t)] or rapid prolonged-bolus (infusion) [F(t)]. Infusion of drug into the eye is of fixed rate F(t) and known duration. ke1 is a first order removal rate constant from the eye. k'd is the rate of removal of drug due to active pumping. Amte is the drug amount in the eye compartment. Given most achievable concentrations, this behaves in a pseudo-linear fashion. Ce = Concentration in the eye; Ve = volume of distribution of the eye.

Figure 3 Two-compartment open model. Rates of change in drug concentrations in the eye can alternatively be described by a two-compartment open model, where ceep and Vc e p represent drug concentrations and apparent volumes of distributions in the central, eye, and peripheral compartments, respectively. F, k'ei are as defined previously. kcp, kpc, kce and kec are first-order transfer rate constants, and kd is a firstorder elimination rate constant. V' is as previously defined; Vc = volume of central compartment. Amtc = Drug amount in the central compartment; Amtp = drug amount in the peripheral compartment; Amte = drug amount in the eye compartment.

Figure 3 Two-compartment open model. Rates of change in drug concentrations in the eye can alternatively be described by a two-compartment open model, where ceep and Vc e p represent drug concentrations and apparent volumes of distributions in the central, eye, and peripheral compartments, respectively. F, k'ei are as defined previously. kcp, kpc, kce and kec are first-order transfer rate constants, and kd is a firstorder elimination rate constant. V' is as previously defined; Vc = volume of central compartment. Amtc = Drug amount in the central compartment; Amtp = drug amount in the peripheral compartment; Amte = drug amount in the eye compartment.

volumes of distribution do not necessarily correspond to real anatomical tissue space. They are proportionality constants, which relate observed drug concentrations to the amount given. Since ocular compartment volumes are much smaller than the central compartment, the volume of the ocular compartment can be fixed at the physiologically determined mean values to improve identification of the other parameters. The mean drug concentrations after a single dose (or at steady state) are inversely proportional to the AUC. Since the AUC is related to average observed concentrations, the ratio of serum (plasma) AUC to aqueous/vitreous humor AUC provides the most accurate determination of drug penetration into the eye (Fig. 4).

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