Instantaneous absorption models

Instantaneous Absorption) Model 221 Bolus IV (Instantaneous Absorption)... 

One-Compartment Bolus IV Injection (Instantaneous Absorption) Model... 

ONE COMPARTMENT BOLUS IV INJECTION (INSTANTANEOUS ABSORPTION) MODEL... 

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. 

The standard one-compartment bolus IV (or instantaneous absorption) model makes three inherent assumptions about the ADME processes that occur after drug delivery. The specific nature and implications of each of these assumptions are described in this section. 

As in all instantaneous absorption models, the entire absorbed dose of drug is taken to enter the systemic circulation instandy at time zero (< = 0). This provides an excellent approximation of the rapid drug delivery direcdy into the systemic circulation provided by a bolus IV injection, which truly occurs over a very short period of time (typically several seconds). However, this assumption does not actually require a strict interpretation of the word instantaneous. Even if an absorption process takes a substantial period of time (minutes or hours), it can still be approximated as instantaneous as long as absorption occurs quickly relative to other ADME processes. Thus, other routes of drug delivery besides a bolus IV injection can be approximated by instantaneous absorption if the time it takes for the absorption process to be essentially complete is very small compared to the half-life of elimination. The equations throughout most of this section are written specifically for a bolus IV injection, but modifications that can be employed to apply the equations to other drug delivery methods are described in Section 10.7.5. 

Itwas previously discussed in Section 10.7.5.1 that under certain circumstances, a zero-order drug delivery process of short duration 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 keeping the total absorbed dose FD = F- ko- T) the same in each simulation. As illustrated in Figure 10.39, the instantaneous absorption model provides a reasonable approximation when T < This criteria can be employed as a... 

Figure 10.39 Graphical illustration of how closely a one-compartment instantaneous absorption model approximates one-compartment zero-order absorption plasma concentrations for different values of T relative to...

This assumption is the same for all instantaneous absorption models. See Section 10.7.1.1 for the details regarding this assumption. 

These then represent all the parameters that have been introduced so far for the two-compartment bolus IV (instantaneous absorption) model. Several additional parameters will be introduced in the following sections. 

There are several common special case situations in which the two-compartment bolus IV model can be applied as a reasonable approximation for administration routes other than bolus IV injection. The means by which the two-compartment bolus IV model can be employed in these situations is described in this section. The criteria under which a drug following two-compartment instantaneous absorption can be approximated by a one-compartment instantaneous absorption model are also provided. 

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. 

Deviation between the one- and two-compartment instantaneous absorption models is related primarily to the relative values of the two-compartment constants Bi and defined earlier. When B = 0, the two-compartment model is identical to the one-compartment model. As the value of B1 becomes higher relative to the value of B2, the two-compartment model deviates more and more from the one-compartment model. Most marketed drugs have a B value of zero up to about bO B. Figure 10.66 illustrates the model deviation at relative values of B from zero (no deviation) up to 30 B. Note that even with = 30 B, the deviation is only significant at early times and quickly dwindles to an insignificant difference. Thus it is not surprising that the one-compartment model is often used even for large values of B. ... 

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