PHAR 4634 - Chapter 14 Page 7

### Development of general equation

We can now consider a general equation which could describe the plasma concentration at any time after multiple IV. bolus drug administration.

Concentration at the end of the first dosing interval

Equation XIV-11 Cp after the First Dose

where

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

At the start of the second interval

then at the end of the second dose interval

and so on.

It will help if we define the parameter

which is the fraction of the initial plasma concentration remaining at the end of the dosing interval.

Then

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

Start

Equation XIV-12 Cp Immediately after the nth Doses

End

Equation XIV-13 Cp at the end of nth Dosing Interval

these two sums can be simplified to give

Start

Equation XIV-14 Cp at the Beginning on the nth Dosing Interval

and

End

Equation XIV-15 Cp at the End of the nth Dosing Interval

using the first equation (Equation XIV-14) we can calculate the concentration in plasma at any time following uniform multiple IV bolus administration.

where t = time since the last dose. Then

Equation XIV-16 Cp at any Time after n Doses

GENERAL EQUATION