# Elimination half-life

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The elimination half-life of a drug (or any xenobiotic agent) refers to the timecourse necessary for the quantity of the xenobiotic agent in the body (or plasma concentration) to be reduced to half of its original level through various elimination processes.

Half-life is an important pharmacokinetic parameter and is usually denoted by the abbreviation t1/2.

## Half-life in first-order eliminationEdit

This process is usually a first-order logarithmic process - that is, a constant proportion of the agent is eliminated per unit time (Birkett, 2002). Thus the fall in plasma concentration after the administration of a single dose is described by the following equation:

$C_{t} = C_{0} e^{-kt} \,$
• Ct is concentration after time t
• C0 is the initial concentration (t=0)
• k is the elimination rate constant

The relationship between the elimination rate constant and half-life is given by the following equation:

$k = \frac{\ln 2}{t_{1/2}} \,$

Half-life is determined by clearance (CL) and volume of distribution (VD) and the relationship is described by the following equation:

$t_{1/2} = \frac{{\ln 2}.{V_D}}{CL} \,$

## Half-life in zero-order eliminationEdit

There are circumstances where the half-life varies with the concentration of the drug. For example, ethanol may be consumed in sufficient quantity to saturate the metabolic enzymes in the liver, and so is eliminated from the body at an approximately constant rate (zero-order elimination). Thus the half-life, under these circumstances, is proportional to the initial concentration of the drug A0 and inversely proportional to the zero-order rate constant k0 where:

$t_{1/2} = \frac{0.5 A_{0}}{k_{0}} \,$