Consider the effect of an angiotensin-converting enzyme (ACE) inhibitor, such as enalapril, on ACE. After an oral dose of 20 mg, the peak plasma concentration at 2.5 hours is about 64 ng/mL. The half-life that explains ACE inhibition is about 4 hours. Enalapril is usually given once a day, so more than five of these half-lives will elapse from the time of peak concentration to the end of the dosing interval. The concentration of enalapril explaining the effect and the corresponding extent of ACE inhibition are shown in Figure 3–5. The extent of inhibition of ACE is calculated using the Emax model, where Emax, the maximum
CHAPTER 3 Pharmacokinetics & Pharmacodynamics: Rational Dosing & the Time Course of Drug Action
FIGURE 3–5 Time course (hours) of angiotensin-converting enzyme (ACE) inhibitor concentrations and effects. The blue line shows the plasma enalapril concentrations in nanograms per milliliter after a single oral dose. The red line indicates the percentage inhibition of its target, ACE. Note the different shapes of the concentration-time course (exponentially decreasing) and the effect-time course (linearly decreasing in its central portion).
extent of inhibition, is 100% and the C50, the concentration of enalapril associated with 50% of maximum effect, is 5 ng/mL.
Note that plasma concentrations of enalapril change by a factor of eight over the first 12 hours (three half-lives) after the peak, but ACE inhibition has only decreased by about 30%. Because the concentrations over this time are so high in relation to the C50, the effect on ACE is almost constant. After 24 hours, ACE is still about 25% inhibited. This explains why a drug with a short half-life can be given once a day and still maintain its effect throughout the day. The key factor is a high initial concentration in relation to the C50. Even though the plasma concentration at 24 hours is only about 1% of its peak, this low concentration is still around half the C50. Once-a-day dosing is common for drugs with minimal adverse effects related to peak concentrations that act on enzymes (eg, ACE inhibitors) or compete at receptors (eg, propranolol).
When concentrations are in the range between four times and one fourth of the C50, the time course of effect is essentially a linear function of time. It takes four half-lives for concentrations to drop from an effect of 80% to 20% of Emax—15% of the effect is lost every half-life over this concentration range. At concentrations below one fourth the C50, the effect becomes almost directly proportional to concentration, and the time course of drug effect will follow the exponential decline of concentration. It is only when the concentration is low in relation to the C50 that the concept of a “half-life of drug effect” has any meaning.
Changes in drug effects are often delayed in relation to changes in plasma concentration. This delay may reflect the time required for the drug to distribute from plasma to the site of action. This will be the case for almost all drugs. The delay due to distribution is a pharmacokinetic phenomenon that can account for delays of a few minutes. This distributional process can account for the short delay of effects after rapid intravenous injection of central nervous system (CNS)–active agents such as thiopental.
Some drugs bind tightly to receptors, and it is the half-life of dissociation that determines the delay in effect, eg, for digoxin. Note that it is the dissociation process that controls the time to receptor equilibrium. This is exactly the same principle as the elimination process controlling the time to accumulate to steady state with a constant rate infusion (see Figure 3–3).