Superposition Principle

Applies when all disposition processes are linear. That is, distribution, metabolism, and excretion (DME) processes are linear or first order. Thus, concentrations after multiple doses can be calculated by adding together the concentrations from each dose.

For example, calculate drug concentration at 24 hours after the first dose of 200 mg. The second dose of 300 mg was given at 6 hours and the third dose of 100 mg at 18 hours.

Graphically, this will look like the results in the figure below:

Figure XV-4 Drug Concentration after Three IV Bolus Doses

A small Excel spreadsheet illustrating the superposition principle

Non-uniform dosing intervals

The calculations we have looked at consider that the dosing intervals are quite uniform, however, commonly this ideal situation is not adhered to completely.

Dosing three times a day may be interpreted as with meals, the plasma concentration may then look like the plot in Figure 60. The ratio between Cpmax and Cpmin is seven fold (8.2/1.1 = 7.45) in this example.

Figure XV-5 Cp versus Time during Dosing at 8 am, 1 pm, and 7 pm

However this regimen may be acceptable if

1) the drug has a wide therapeutic index

2) there is no therapeutic disadvantage to low overnight plasma concentrations, e.g., analgesic of patient stays asleep.

Other practice problems involving the calculation of Cp at three times during a uniform dosing interval with Linear or Semi-log graphical answers or calculation of Cp at three times during a non-uniform dosing interval with Linear or Semi-log graphical answers
Fifth Homework Set 1995