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.
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; t1/2 = 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.
Copyright 2001 David W.A. Bourne