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A number of other important pharmacokinetic principles can be appreciated by considering the concentrations that result following a single intravenous bolus dose (see Figure 1.4) and through a number of complex equations the time at which steady state will be achieved after starting a regular treatment schedule or after any change in dose can be predicted.

As a rule, in the absence of a loading dose, steady state is attained after four to five half‐lives (Figure 1.5).

Furthermore, when toxic drug levels have been inadvertently produced, it is very useful to estimate how long it will take for such levels to reach the therapeutic range, or how long it will take for the entire drug to be eliminated once the drug has been stopped. Usually, elimination is effectively complete after four to five half‐lives (Figure 1.6).

Figure 1.4 Plot of concentration versus time after a bolus intravenous injection. The intercept on the y‐ (concentration) axis, C₀, is the concentration resulting from the instantaneous injection of the bolus dose.

The elimination half‐life can also be used to determine dosage intervals to achieve a target concentration–time profile. For example, in order to obtain a gentamicin peak of 8 mg/L and a trough of 0.5 mg/L in a patient with an elimination half‐life of 3 hours, the dosage interval should be 12 hours. (The concentration will fall from 8 to 4 mg/L in 3 hours, to 2 mg/L in 6 hours, to 1 mg/L in 9 hours and to 0.5 mg/L in 12 hours.) However, for many drugs, dosage regimens should be designed to maintain concentrations within a range that avoids high (potentially toxic) peaks or low, ineffective troughs. Excessive fluctuations in the concentration–time profile can be prevented by giving the drug at intervals of less than one half‐life or by using a slow‐release formulation.

Figure 1.5 Plot of concentration versus time illustrating the accumulation to steady state when a drug is administered by regular oral doses.

Figure 1.6 Semi‐logarithmic plot of concentration versus time after a bolus intravenous injection. The slope of this line is −k; the elimination rate constant and the elimination half‐life of the drug can be determined from such a plot by noting the time at which the concentration has fallen to half its original value.