Bioavailability first-order absorption models

Applying these results to this simulation, it can be assumed that bioavailability would be 100% and that a first-order absorption model would apply such that the time to maximal concentrations was 1 h (which corresponds to an absorption rate constant of 1.2 per hour). Under these assumptions, the simulated concentrationtime profile after repeated administration of 1 mg/kg every 8 h is shown in Fig. 9.22. Maximal concentrations were attained 1.1 h. after intramuscular administration and were about half the maximal concentration attained after intravenous administration. Trough concentrations at steady-state after intramuscular administration were very near trough concentrations after intravenous administration. Hence, based on this simulation, the physician could either keep the dose as is or increase the dose to more attain the concentrations seen after intravenous administration. 

The remaining model parameters still to be determined include the overall clearance (CL) and the two-compartment distribution volumes (Fi, V s, Vauc)-As in the one-compartment first-order absorption model, these remaining model parameters cannot be calculated until the bioavailability (F) has been evaluated. This will require AUC calculations and a comparison to IV drug delivery results, as described in the next two sections. 

Evaluation of the bioavailability for a drug following two-compartment kinetics is identical to the methods employed for the one-compartment first-order absorption model. The ratio of bioavailabiUty values F1/F2) for a drug delivered by two different routes is called the relative bioavailability. The relative bioavailability can be determined from the dose D and D2) and AUC values AUCi and AUC ) of each route by the relationship... 

First-order absorption processes require AUC values in order to evaluate the bioavailability (F). The AUC for the multicompartment extravascular first-order absorption model can be calculated by the simple equation... 

A one-compartment model with first-order elimination was used to simulate unbound VPA concentrations. The two formulations differ only in the input function the ER formulation was accounted for through a zero-order input over 22 hours with 89% bioavailability. The DR formulation absorption was characterized by a 2h lag time (flag = 2h) followed by first-order absorption rate ka = 0.1 h ). The bioavailability F) of the DR preparation was assumed to be complete F = 1). 

A necessary and sufficient condition for identifia-bility is the concept that with p-estimable parameters at least p-solvable relations can be generated. Traditionally, for linear compartment models this involves using Laplace transforms. For example, going back to the 1-compartment model after first-order absorption with complete bioavailability, the model can be written in state-space notation as... 

Jernigan, Hatch, and Wilson (1988) studied the pharmacokinetics of tobramycin after intramuscular administration in cats. Bioavailability was estimated at 102.5% with maximal concentrations occurring within about an hour. Hence, tobramycin absorption appears rapid and complete. There are few papers modeling the intramuscular absorption of drugs. Swabb et al. (1983) modeled the intramuscular administration of aztreonam, another antibiotic, in humans and found that a simple first-order absorption was adequate to explain the rapid (time to maximal concentrations was 0.88 h) and complete (101% bioavailability) absorption. Similarly, Krishna et al. (2001) also found that first-order absorption was sufficient to model the pharmacokinetics of quinine after intramuscular administration. In both cases, the drugs were formulated in water. 

Figure 9.22 Simulated concentration—time profile in a 50 kg patient after repeated intravenous administration (solid line) and intramuscular administration (dashed line) of 1 mg/kg every 8 h assuming the final model given in Eq. (9.17). Parameter values are given in Table 9.18. Absorption after intramuscular administration was modeled assuming first-order absorption with a rate constant of 1.2 per hour and complete bioavailability.

Separate mass balance equations are written in the form of Section 10.6.2 for each of the two compartments. Variables and A2 represent the amount of drug in compartment 1 and compartment 2, respectively, and the total amount of drug in the body is given by the sum of Ai and A2. The rate of drug absorption is a function of a first-order absorption rate constant kj, the bioavailability (F), and the administered dose (D). Distribution between the compartments follows first-order kinetics as described previously. Elimination occurs only from compartment 1 in the standard model form, with the elimination rate equal to the amount of drug remaining in compartment... 

D, dose F, bioavailability fr, fraction of dose undergoing first-order input in a dual absorption model K, zero-order input rate L and k, first-order absorption rate constants MAT, mean absorption time NV, normalized variance of Gaussian density function, t, nominal time ti g, duration of time-lag x, duration of rapid input in dual absorption model Ti f, duration of zero-order IV infusion T, modulus time. 

The parameter estimates were fixed from Model 1 and model development proceeded with the inhalational (si) route of administration. The initial model treated the inhaled dose as going directly into an absorption compartment with first-order transfer (ka) into the central compartment (Model 2 in Fig. 5.5). To account for the fact that some of the inhaled cocaine was exhaled and that there may have been first-pass metabolism prior to reaching the sampling site, a bioavailability term was included in the model (Fsj). 

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