Figure 8.1.1 Representing Oral Administration, One Compartment Pharmacokinetic Model
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Figure 8.1.1 Representing Oral Administration, One Compartment Pharmacokinetic Model
Where Xg is the amount of drug to be absorbed, Xp is the amount of drug in the body, and ka is the first order absorption rate constant.
Equation 8.2.1 Differential Equation for Amount Remaining in the G-I Tract
This is similar to the equation for dCp/dt after an IV bolus administration.
Using Laplace transforms it is possible to derive the integrated equation.
Equation 8.2.2 Integrated Equation for Drug Amount Remaining in the G-I Tract available for Absorption
where F is the fraction of the dose which can be 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 representing ka, Figure 8.2.1.
Figure 8.2.1 Semi-log Plot of X(g) versus Time
And as a linear plot.
Figure 8.2.2 Linear Plot of X(g) versus Time
Equation 8.2.3 Differential Equation for Amount of Drug in the Body
The first term, ka • Xg, represents absorption and the second term, kel • V • Cp, represents elimination
Even without integrating this equation we can get an idea of the plasma concentration time curve.
Shortly after the dose is administered ka • Xg is much larger than kel • V • Cp and the value of dCp/dt is positive, therefore the slope is positive and Cp will increase. With increasing time after the dose is administered, as Xg decreases, Cp is initially increasing, therefore there will be a time when ka • Xg will equal kel • V • Cp. At this time dCp/dt will be zero and there will be a peak in the plasma concentration. At even later times Xg will approach zero, and dCp/dt will become negative and Cp will decrease. It could be expected that the plasma concentration time curve will look like Figure 8.2.3.
Figure 8.2.3 Linear Plot of Cp versus Time after Oral Administration Showing Rise, Peak, and Fall in Cp
Click on the figure to view the interactive graph
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