Chapter 15 Multiple Oral Dose Administration

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Cp_min Equation

Starting with equation 15.2.3 we can derive an equation for Cp_min which can be more easily determined at t = 0 or t = t. Thus at t = 0 and n approaches ∞ as e^{-n • k • τ} approaches 0.

Equation 15.3.1 Cp_min after Many Oral Doses - Version 1

This can be further simplified if we assume that the subsequent doses are given after the plasma concentration has peaked and e^{-ka • τ} is close to zero. That is the next dose is given after the absorption phase is complete.

Figure 15.3.1 Plot Cp versus Time after a Single Dose showing Possible Time of Second Dose

Cp_min then becomes:

Equation 15.3.2 Cp_min after Many Oral Doses - Version 2

The relationship between loading dose and maintenance dose and thus drug accumulation during multiple dose administration can be studied by looking at the ratio between the minimum concentration at steady state and the concentration at the end of the first dosing interval,τ, after the first dose. [Assuming e^{-ka • τ} is close to zero].

Equation 15.3.3 Ratio Between Cp after First and Last Dose

Which can be simplified to give:

Equation 15.3.4 Ratio Between Cp after First and Last Dose

This turns out to be the same equation as for the multiple IV bolus doses. Therefore we can estimate a loading dose just as we did for an IV multiple dose regimen.

Equation 15.3.5 Loading Dose Equation

This equation holds if each dose is given after the absorption phase of the previous dose is complete.

We can further simplify Equation 15.3.2 when ka is high if we assume that ka >> kel then (ka - kel) is approximately equal to ka and ka/(ka - kel) is approximately equal to one.

Equation 15.3.6 Cp_min after Many Oral Doses - Version 3

Equation 15.3.6 is an even more extreme simplification. However, it can be very useful if we don't know the ka value but we can assume that absorption is reasonably fast. Equation 15.3.6 will tend to give concentrations that are lower than those obtained with the full equation (Equation 15.3.1). Thus any estimated fluctuation between Cp_min and Cp_max will be overestimated using the simplified equation.

Click on the figure
to download and use this Excel spreadsheet

Figure 15.3.2 Excel^™ Spreadsheet Illustrating the Use of Three Cp_min Equations

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Pharmacy Math Part Two
A selection of Pharmacy Math Problems

Chapter 15

Multiple Oral Dose Administration

Cpmin Equation

Cp_min Equation