Concentration-time profile for a hypothetical drug administered extravascularly. Cmax, maximum concentration achieved. Tmax, time required to achieve maximum concentration. AUC = Area under the curve. Y-axis is on logarithmic scale.
nation rate will generally exhibit a longer Tmax and higher Cmax. Once administered, a drug begins undergoing absorption, distribution, metabolism, and excretion all at once, not in a sequential fashion, such that all of these processes are involved in determining the shape of a concentration-time profile.
One indicator of the overall exposure of a person to a drug is through the calculation of the area under the curve (AUC). As the name implies, AUC is the mathematically integrated area under the concentration-time curve and is most commonly calculated using the trapezoidal rule of mathematics. In Figure 5.2, the AUC is represented by the shaded area. Though the shape of the concentration-time profile may affect the AUC for a drug, two drugs with entirely different concentration-time profile shapes may have the same AUC. It is, in fact, this property that makes calculating the AUC useful, because it can be used to assess the person's overall exposure to a drug, even though the individual may have reached different Tmax and Cmax values from those of other individuals. Furthermore, as will be discussed shortly, AUC is also useful for calculating another pharmacokinetic parameter, clearance.
An additional parameter that can be determined from a concentration-time profile is the half-life of the drug, that is, the time it takes for half of the drug to be eliminated from the body. Half-life determination is very useful, since it can readily be used to evaluate how long a drug is expected to remain in the body after termination of dosing, the time required for a drug to reach steady state (when the rate of drug entering the body is equal to the rate of drug leaving the body), and often the frequency of dosing. The following equation is used to calculate the half-life of a drug:
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