Instantaneous absorption models approximation with

The one-compartment bolus IV injection model is mathematically the simplest of aU PK models. Drug is delivered directly into the systemic circulation by a rapid injection over a very short period of time. Thus the bolus rV injection offers a near perfect example of an instantaneous absorption process. Representation of the body as a single compartment implies that the distribution process is essentially instantaneous as well. The exact meaning of the assumptions inherent in this model are described in the next section. Model equations are then introduced that allow the prediction of plasma concentrations for drugs with known PK parameters, or the estimation of PK parameters from measured plasma concentrations. Situations in which the one-compartment instantaneous absorption model can be used to reasonably approximate other types of drug delivery are described later in Section 10.7.5. 

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... 

As shown previously for the one-compartment case, the two-compartment model for steady (zero-order) drug delivery can be approximated by a two-compartment instantaneous absorption model as long as the drug delivery period (T) is relatively short compared to the elimination half-life ty eUm)- As a general rule, the instantaneous model can be employed with reasonable accuracy as when T < tiy eUm- For cases where this simplification applies, the two-compartment bolus IV model equations can be used by simply replacing with F-h-T. 

The two-compartment instantaneous absorption model is significantly more complex and harder to work with than the one-compartment instantaneous absorption model. Thus the one-compartment model is often 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. Model simulations can be employed to evaluate under what conditions the one-compartment approximation is reasonable, and how much deviation occurs between the models under less ideal conditions. 

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. 

Therefore, from a comparison with Eq. (29), the three models give nearly comparable results in this case. Also, when = D, the instantaneous enhancement factor , has the same form for the film and the surface-renewal models (D2). Recently De Coursey (DIO) derived an approximate solution for the Danckwerts model, given in the next section, which can help considerably when this model is used for design. Therefore, even though analytical expressions for the average rate of absorption based on the three models look very different, nevertheless the three will give the same value of the enhancement factor to within a few percent for all values of Ha between 0.1 and >. 

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. 

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