# Half Life

The tm is the time it takes for the plasma concentration or the amount of drug in the body to be reduced by 50%. For the simplest case, the one-compartment model (Figure 1-3A), t1/2 may be determined readily by inspection and used to make decisions about drug dosage. However, drug concentrations in plasma often follow a multi-exponential pattern of decline (see Figure 1-3B); two or more t1/2 terms thus may be calculated. Such prolonged half times can represent drug elimination from storage sites or poorly perfused tissue spaces and can be linked to drug toxicity.

A useful approximate relationship between the clinically relevant t1/2, clearance, and volume of distribution at steady state is given by t1/2 = 0.693 • VJCL (1-9)

As clearance of a drug decreases, owing to a disease process, for example, t1/2 would be expected to increase as long as volume of distribution remains unchanged. However, increases in t1/2 can result from changes in volume of distribution, e.g., when changes in protein binding of a drug affect its clearance and lead to unpredictable changes in t1/2. The tm provides a good indication of the time required to reach steady state after a dosage regimen is initiated or changed (i.e., four half-lives to reach ~94% of a new steady state), the time for a drug to be removed from the body, and a means to estimate the appropriate dosing interval (see below).

STEADY STATE Equation (1-2) indicates that a steady-state concentration eventually will be achieved when a drug is administered at a constant rate (Dosing rate = CL • Css). At this point, drug elimination will equal the rate of drug availability. This concept also extends to regular intermittent dosage (e.g., 250 mg of drug every 8 hours). During each interdose interval, the concentration of drug rises with absorption and falls by elimination. At steady state, the entire cycle is repeated identically in each interval (see Figure 1-4). Equation (1-2) still applies for intermittent dosing, but it now describes the average steady-state drug concentration (Css) during an interdose interval.