FIGURE 3–2 Models of drug distribution and elimination. The effect of adding drug to the blood by rapid intravenous injection is represented by expelling a known amount of the agent into a beaker. The time course of the amount of drug in the beaker is shown in the graphs at the right. In the first example (A), there is no movement of drug out of the beaker, so the graph shows only a steep rise to a maximum followed by a plateau. In the second example (B), a route of elimination is present, and the graph shows a slow decay after a sharp rise to a maximum. Because the amount of agent in the beaker falls, the “pressure” driving the elimination process also falls, and the slope of the curve decreases. This is an exponential decay curve. In the third model (C), drug placed in the first compartment (“blood”) equilibrates rapidly with the second compartment (“extravascular volume”) and the amount of drug in “blood” declines exponentially to a new steady state. The fourth model (D) illustrates a more realistic combination of elimination mechanism and extravascular equilibration. The resulting graph shows an early distribution phase followed by the slower elimination phase. Note that the volume of fluid remains constant because of a fluid input at the same rate as elimination in (B) and (D).
concentration of drug that is achieved (Table 3–1). Capacity-limited elimination is also known as mixed-order, saturable, doseor concentration-dependent, nonlinear, and Michaelis-Menten elimination.
Most drug elimination pathways will become saturated if the dose and therefore the concentration are high enough. When blood flow to an organ does not limit elimination (see below), the relation between elimination rate and concentration (C) is expressed mathematically in equation (5):
The maximum elimination capacity is Vmax, and Km is the drug concentration at which the rate of elimination is 50% of Vmax. At concentrations that are high relative to the Km, the elimination rate is almost independent of concentration—a state of “pseudozero order” elimination. If dosing rate exceeds elimination capacity, steady state cannot be achieved: The concentration will keep on rising as long as dosing continues. This pattern of capacity-limited elimination is important for three drugs in common use: ethanol, phenytoin, and aspirin. Clearance has no real meaning for drugs with capacity-limited elimination, and AUC should not be used to calculate clearance of such drugs.
B. Flow-Dependent Elimination
In contrast to capacity-limited drug elimination, some drugs are cleared very readily by the organ of elimination, so that at any clinically realistic concentration of the drug, most of the drug in the blood perfusing the organ is eliminated on the first pass of the drug through it. The elimination of these drugs will thus depend primarily on the rate of drug delivery to the organ of elimination. Such drugs (see Table 4–7) can be called “high-extraction” drugs since they are almost completely extracted from the blood by the organ. Blood flow to the organ is the main determinant of drug delivery, but plasma protein binding and blood cell partitioning may also be important for extensively bound drugs that are highly extracted.
Half-life (t1/2) is the time required to change the amount of drug in the body by one-half during elimination (or during a constant infusion). In the simplest case—and the most useful in designing drug dosage regimens—the body may be considered as a single compartment (as illustrated in Figure 3–2B) of a size equal to the volume of distribution (V). The time course of drug in the body will depend on both the volume of distribution and the clearance:
Because drug elimination can be described by an exponential process, the time taken for a twofold decrease can be shown to be proportional to the natural logarithm of 2. The constant 0.7 in equation (6) is an approximation to the natural logarithm of 2.