This is similar to the equation for after an IV bolus administration.
The integrated equation is:-
Xg = Xg0 * e-ka * t = F * Dose * e-ka * t
where F is the fraction of the dose which is absorbed, the bioavailability.
We could therefore plot Xg (the amount remaining to be absorbed) versus time on semi-log graph paper and get a straight line with a slope of -ka.
For Xp ( = V * Cp) the amount of drug in the body, the differential equation is :-
The first term --> ka * Xg absorption
The second term --> kel * V * Cp elimination
Even without integrating this equation we can get an idea of the plasma concentration time curve.
At the start Xg >> V * Cp therefore the value of is positive, the slope will be positive and Cp will increase. With increasing time Xg will decrease, while initially Cp is increasing, therefore there will be a time when ka * Xg = kel * V * Cp. At this time will be zero and there will be a peak in the plasma concentration. At even later times Xg --> 0, and will become negative and Cp will decrease. The plasma concentration time curve will look like Figure VIII-1:-
Figure VIII-1, Linear Plot of Cp versus Time after Oral Administration Showing Rise, Peak, and Fall in Cp
Plasma Concentration versus Time Plots
Copyright 2001 David W.A. Bourne