# Chapter 8

# Pharmacokinetics of Oral Administration

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## Scheme or diagram

This model can be represented as:-

**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.

## Differential Equations

### Drug Amount Remaining to be Absorbed, Xg

The differential equation for Xg is shown in Equation 8.2.1

**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

### Drug Amount in the Body, Xp

For Xp (= V • Cp) the amount of drug in the body, the differential equation is shown in Equation 8.2.3

**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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