Half-life first-order absorption model

A two-compartment open linear model has been described for the pharmacokinetic profile of cocaine after intravenous administration.14 The distribution phase after cocaine administration is rapid and the elimination half-life estimated as 31 to 82 min.14 Cone9 fitted data to a two-compartment model with bolus input and first-order elimination for the intravenous and smoked routes. For the intranasal route, data were fitted to a two-compartment model with first-order absorption and first-order elimination. The average elimination half-life (tx 2 3) was 244 min after intravenous administration, 272 min after smoked administration, and 299 min after intranasal administration. 

Again similar to the one-compartment case, two-compartment first-order absorption of drug can be approximated by the two-compartment instantaneous absorption model as long as the absorption phase is completed at a very short time relative to the elimination half-life As a general rule of thumb, the... 

The advantages of using non-compartmental methods for calculating pharmacokinetic parameters, such as systemic clearance (CZg), volume of distribution (Vd(area))/ systemic availability (F) and mean residence time (MRT), are that they can be applied to any route of administration and do not entail the selection of a compartmental pharmacokinetic model. The important assumption made, however, is that the absorption and disposition processes for the drug being studied obey first-order (linear) pharmacokinetic behaviour. The first-order elimination rate constant (and half-life) of the drug can be calculated by regression analysis of the terminal four to six measured plasma... 

It should be noted that as in absorption, first-order distribution represents linear kinetics, as the net rate of distribution is a linear function of the amount of drug remaining in compartment 1 (Ai) and the amount of drug remaining in compartment 2( 2). Also as in the absorption case, a half-life of distrihution tvz,dist) be defined in terms of the distrihution rate constants. However, because distribution occurs in more than one direction, and due to other model complications that will be explained later, the distribution half-life cannot be written as a simple function of ki2 and 1. It turns out that the distribution half-life is defined in terms of a hybrid rate constant (/Ij) by the equation... 

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