Development of General Equation

Concentration at the end of the first dosing interval

Equation 25.5.1 Cp after the First Dose

where

This gives the plasma concentrations at the end of first interval, where τ is the dosing interval in hours.

Concentration at the start of the second interval

Equation 25.5.2 Cp at the Start of the Second Interval

Concentration at the end of the second dose interval

Equation 25.5.3 Cp at the End of the Second Interval

and so on.

It will help if we define the parameter, R = e^{-kel • τ}, which is the fraction of the initial plasma concentration remaining at the end of the dosing interval.

Then

Equation 25.5.4 Cp at the End of the Second Interval

Equation 25.5.5 Cp at the Start of the Third Interval

this is a geometric series with each term R times the preceding term.

Equation 25.5.6 Cp at the Start of the nth Interval

Equation 25.5.7 Cp at the End of the nth Interval

these two sums are sums of geometric series they can be simplified to give

Equation 25.5.8 Cp at the Start of the nth Interval

Equation 25.5.9 Cp at the End of the nth Interval

Using the first equation (Equation 25.5.8) we can calculate drug concentration in blood or plasma at any time following uniform multiple IV bolus administration.

Equation 25.5.10 Cp at time,t, after the nth IV Bolus Dose

where here t = time since the last dose.

Equation 25.5.11 Cp at time,t, after the nth IV Bolus Dose
General Equation

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Copyright 2001-3 David W. A. Bourne (david@boomer.org)