(a)CoCpLogeCpLog 10 CoTime Time(b)Figure 8.5 Determination ofCoby extrapolation of the plots of (a) theCpagainsttcurve and (b)
logCpagainst time for the changes in plasma concentration of a drug with time
The rate of elimination is an important characteristic of a drug. Too rapid an
elimination necessitates frequentrepeated administrationof the drug if its concen-
tration is to reach its therapeutic window. Conversely, too slow an elimination
could result in the accumulation of the drug in the patient, which might give an
increased risk of toxic effects. Most drug eliminations followfirst order kinetics
(equations (8.1) and (8.2) ), no matter how the drug is administered, but there are
some notable exceptions, such as ethanol which exhibits zero order kinetics where:
rate¼kandC¼Cokt: (8:4)
However, the order of elimination processes may change depending on the
biological situation, for example, drug concentration increasing to a level that
saturates the elimination processes, in which case first order eliminations pro-
cesses will change to zero order.
The time taken for the concentration of a drug to fall to half its original value
is known as itsbiological half-life(t1/2). For eliminations that followfirst order
kineticsit may be shown that:
t 1 = 2 ¼ 0 : 693 =kel (8:5)
In other words, for elimination processes that follow first order kineticst1/2is
a constant, characteristic of the drug and the biological system. Consequently,
for drugs that exhibitfirst order elimination kineticsboth andkelandt1/2are
used as indicators of the rate of elimination of a drug from the system. Half-lives
are normally quoted in the literature andkelvalues are calculated as required
using equation (8.5).
Forfirst orderelimination processes the values ofkelandt1/2may be calculated
from the experimental data using a logarithmic form of equation (8.2), that is
INTRAVASCULAR ADMINISTRATION 165