It is also worth discussing the relationship between the percentage of drug eliminated and the number of half-lives. Įquation 3: t-half= 0.693*Vd/CL, where Vd is the volume of distribution and CL is clearance An alternative half-life equation exists that relates half-life to other pharmacokinetic parameters known as the volume of distribution and clearance (Equation 3). From this equation, one can quickly determine the half-life of a drug, given its predetermined rate constant k. Elimination curves are useful for determining if a drug indeed follows first-order kinetics, in which case the curve should follow a logarithmic decay according to the integrated rate law of first-order reactions (Equation 1). After solving the differential equation, one can obtain the half-life equation that is commonly tested on and used in clinical practice (Equation 2). Total drug exposure over time is represented in these graphs as the integral area under the curve (AUC).
Half-life elimination is graphically represented with elimination curves that track the amount of a drug in the body over time, typically with time on the independent axis and drug plasma concentration on the dependent axis, as shown in Figure 1. This article will focus on first-order half-life elimination as it is the most frequently encountered in clinical practice. In contrast, a few drugs follow zero-order elimination in which the drug amount decreases by a constant amount over time regardless of initial concentration (i.e., ethanol). Most clinically relevant drugs tend to follow first-order pharmacokinetics that is, their drug-elimination rates are proportional to plasma concentrations. The characteristic decreases of drugs over time have long been studied in a field known as pharmacokinetics and are depictable by basic differential equations.
Different drugs have different half-lives however, they all follow this rule: after one half-life has passed, 50% of the initial drug amount is removed from the body. Understanding the concept of half-life is useful for determining excretion rates as well as steady-state concentrations for any specific drug. Half-life in the context of medical science typically refers to the elimination half-life. The definition of elimination half-life is the length of time required for the concentration of a particular substance (typically a drug) to decrease to half of its starting dose in the body.
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