PHAR 4634 - Chapter 15 Page 3

##
Equation

Another very useful concentration term for the calculation of oral dosing
regimens is the average plasma concentration,
,
during the dosing interval at steady state.

This term is defined as the area under the plasma concentration versus time
curve during the dosing interval at steady state divided by the dosing
interval.

Thus:-

**Equation XV-9 Average Cp for a Dosing Interval at Steady State**

**Figure XV-3, Plot of Cp versus Time after Multiple Oral Administration showing AUC at Steady State**

By integrating the equation for plasma
concentration at the plateau, between t = 0 and t = t gives:-

**Equation XV-10 Average Cp for a Dosing Interval at Steady State**

An interesting result of
this equation is that we get the same average plasma concentration whether the
dose is given as a single dose every t dosing interval or is subdivided into
shorter dosing intervals.

For example 300 mg every 12 hours will give the same average plasma
concentration as 100 mg every 4 hours. Of course, the difference between the
maximum and minimum plasma concentration will be larger in the case of the less
frequent dosing.

For example F = 1.0; V = 30 liter; t_{1/2} = 6 hours or kel = 0.693/6 = 0.116 hr^{-1}.

We can now calculate the dose given every 12 hours required to achieve an
average plasma concentration of 15 mg/L.

=

We could now calculate the loading dose

R = e^{-kel * [[tau]]} = e^{-0.116 x 12} = 0.25

To get some idea of the fluctuations in plasma concentration we could calculate
the Cpmin value.

Assuming that ka >> kel and that e^{-ka * t} --> 0, using Equation XV-8.

Therefore the plasma concentration would probably fluctuate between 7 and 23
mg/L (very approximate) with an average concentration of about 15 mg/L. [23 = 15 + (15-7),
i.e. high = average + (average - low), very approximate!].

As an alternative we could give half the dose, 312 mg, every 6 hours give:-

The
would be the same

Thus the plasma concentration would fluctuate between about 10.4 to 20 with an
average of 15 mg/L.

Practice problems involving Cp_{average}, Cp_{max} and Cp_{min} at steady state after uniform multiple dose Oral doses.

This page was last modified: 22 July 2002
Copyright 2001 David W.A. Bourne