Instantaneous absorption models first-order elimination

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... 

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 rates of movement of foreign compound into and out of the central compartment are characterized by rate constants kab and kei (Fig. 3.23). When a compound is administered intravenously, the absorption is effectively instantaneous and is not a factor. The situation after a single, intravenous dose, with distribution into one compartment, is the most simple to analyze kinetically, as only distribution and elimination are involved. With a rapidly distributed compound then, this may be simplified further to a consideration of just elimination. When the plasma (blood) concentration is plotted against time, the profile normally encountered is an exponential decline (Fig. 3.24). This is because the rate of removal is proportional to the concentration remaining it is a first-order process, and so a constant fraction of the compound is excreted at any given time. When the plasma concentration is plotted on a logio scale, the profile will be a straight line for this simple, one compartment model (Fig. 3.25). The equation for this line is... 

A separate mass balance equation is written in the form of Section 10.6.2 for each compartment in the model. Thus a total of n mass balance equations must be written and solved for an n compartment model. The details of these equations and their solution are not provided in this chapter. However, it will be noted that absorption, distribution, and elimination rates are written in the same form as in the previous one- and two-compartment models. The absorption rate for instantaneous, zero-order, or first-order absorption is identical to the previous forms for one- and two-com-partment models. Distribution and elimination rates are written as first-order linear rate equations using micro rate constants. So the distribution rate from compartment 1 to compartment n is given by kj Aj, the distribution rate from compartment n back to compartment 1 equals k i A , and the elimination rate from any compartment is written k o A schematic diagram for the generalized n compartment model is illustrated in Figure 10.90. 

Linear (or first-order) kinetics refers to the situation where the rate of some process is proportional to the amount or concentration of drug raised to the power of one (the first power, hence the name first-order kinetics). This is equivalent to stating that the rate is equal to the amount or concentration of drug multiplied by a constant (a linear function, hence linear kinetics). All the PK models described in this chapter have assumed linear elimination (metabolism and excretion) kinetics. All distribution processes have been taken to follow linear kinetics or to be instantaneous (completed quickly). Absorption processes have been taken to be instantaneous (completed quickly), follow linear first-order kinetics, or follow zero-order kinetics. Thus out of these processes, only zero-order absorption represents a nonlinear process that is not completed in too short of a time period to matter. This lone example of nonlinear kinetics in the standard PK models represents a special case since nonlinear absorption is relatively easy to handle mathematically. Inclusion of any other type of nonlinear kinetic process in a PK model makes it impossible to write the... 

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