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Superposition Principle

The superposition principle can be used when all the disposition processes are linear. That is when 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. Also, doubling the dose will result in the concentrations at each time doubling.

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. The apparent volume of distribution is 15 L and the elimination rate constant is 0.15 hr^-1.

This method involved calculating the contribution from each dose at 24 hours after the first dose.

This result is shown grahpically in Figure 26.4.1.

Figure 26.4.1 Drug Concentration after Three IV Bolus Doses

Another approach is to work through the dosing regimen dose by dose.

This answer can also be calculated using an Excel spreadsheet illustrating the superposition principle.

Click on the figure
to download and use this Excel spreadsheet

Figure 26.4.2 Excel^™ Spreadsheet Illustrating the Superposition Principle - Multiple IV Doses

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 26.4.3 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.

This regimen can be explored further using an Excel spreadsheet illustrating the superposition principle.

Click on the figure
to download and use this Excel spreadsheet

Figure 26.4.4 Excel^™ Spreadsheet Illustrating the Superposition Princple - Multiple Oral Doses

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

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This file was last modified: Monday 29 Sep 2003 at 02:21 PM