First-order absorption models approximation with

Wade et al. (1993) simulated concentration data for 100 subjects under a one-compartment steady-state model using either first-or zero-order absorption. Simulated data were then fit using FO-approximation with a first-order absorption model having ka fixed to 0.25-, 0.5-, 1-, 2-, 3-, and 4 times the true ka value. Whatever value ka was fixed equal to, clearance was consistently biased, but was relatively robust with underpredictions of the true value by less than 5% on average. In contrast, volume of distribution was very sensitive to absorption misspecification, but only when there were samples collected in the absorption phase. When there were no concentration data in the absorption phase, significant parameter bias was not observed for any parameter. The variance components were far more sensitive to model misspecification than the parameter estimates with some... 

Three special cases are considered for the one-compartment first-order absorption model. Eirst is a relatively rare situation known as a flip-flop situation. Second is the use of the one-compartment first-order absorption model to approximate the plasma concentrations of drugs that follow two-compartment kinetics. The last case considered is the identification of conditions when first-order drug delivery with rapid absorption can be modeled as an instantaneous absorption process. 

The two-compartment first-order absorption model is significantly harder to work with than the one-compartment first-order absorption model. Thus the one-compartment model often is used when it provides a reasonable approximation to the two-compartment values. In fact, the one-compartment model is often used even when a drug is known to significantly deviate from single compartment kinetics. Just as in the case of the two-compartment bolus IV injection model in Section 10.10.5.3, as a general rule of thumb the one-compartment model can be employed with reasonable accuracy for Li < 2 B. When this simplification is used, the one-compartment first-order absorption model equations can be used without modification. 

Figure A.l Plot of Taylor-series approximations at t — 0 up to 4th order for a 1 compartment model with first-order absorption up to 4 h post dose. Heavy black line is the function line given D = lOOmg, V = 100L, k10 = 0.2perh, and ka = 0.7 perh.

It was previously discussed in Section 10.7.5.2 that under certain circumstances, a first-order drug delivery process with rapid absorption rates can be approximated as an instantaneous absorption process. The conditions under which this approximation gives reasonable results can be investigated mathematically using model simulations. These simulations are made by varying the value of the absorption rate constant kg) relative to a fixed elimination rate constant k). As illustrated in Figure 10.54, the instantaneous absorption model provides a reasonable approximation when kg > 1 k, which can be expressed... 

Conceptual models of percutaneous absorption which are rigidly adherent to general solutions of Pick s equation are not always applicable to in vivo conditions, primarily because such models may not always be physiologically relevant. Linear kinetic models describing percutaneous absorption in terms of mathematical compartments that have approximate physical or anatomical correlates have been proposed. In these models, the various relevant events, including cutaneous metabolism, considered to be important in the overall process of skin absorption are characterized by first-order rate constants. The rate constants associated with diffusional events in the skin are assumed to be proportional to mass transfer parameters. Constants associated with the systemic distribution and elimination processes are estimated from pharmacokinetic parameters derived from plasma concentration-time profiles obtained following intravenous administration of the penetrant. 

The distribution transport rate (r is ) is a measure of how quickly drug molecules are exchanged between the plasma and the tissues. A rapid distribution transport rate causes the plasma and tissues to come quickly into equilibrium with each other, whereas a slower rate will cause a prolonged approach to equilibrium. As with the rate of absorption, different types of PK modeling approaches can be employed to approximate distribution rates. In the case of distribution there are essentially two types of models, instantaneous distribution and first-order distribution. The difference between the two types of models is in the number of compartments used to represent the drug disposition in the body. 

A graphical representation of these equations is given in Fig. 6.4-14. van Kievelen and Hoftijzer originally developed their correlation only for irreversible second-order reactions (first-order in each reactant) and for equal difiusivities of the two reactants. Danckwetts pointed out that the results also are applicable to the case where is not equal to Dg. Decoursey developed an approximate solution for absorption with irreversible second-order reaction based on the Danckwerts surface-renewal model. The resulting expression, which is somewhat easier to use than the van Krevelen-HofUJzer approach, is... 

While the above rigid band model seems to give a simple picture for understanding the metallic properties observed in A3C60 in the first order of approximation, many unconventional types of behavior, unexpected from alkali-metal Cgo fullerides, are also observed. Firstly, very differently from the simple picture described earlier, fee Na2C6o and bet phases with the stoichiometry of A4C60 are not metallic [117,118,124]. Secondly, both experimental facts of a broad absorption peak other than the conduction band peak observed at the Fermi level [125] and the unexpectedly large temperature dependence in shape of the ti conduction bands observed in photoemission experiments [126]... 

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