PHAR 4634 - Chapter 8 Page 2

## Differential equation

The differential equation for Xg is :-

**Equation VIII-1**

This is similar
to the equation for
after
an IV bolus administration.

The integrated equation is:-

Xg = Xg^{0} * e^{-ka * t} = F * Dose * e^{-ka * t}

**Equation VIII-2**

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
:-

**Equation VIII-3**

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**

Using a JAVA aware browser you can create your own version of Figure VIII-1.
**Plasma Concentration versus Time Plots**

This page was last modified: 12 February 2001
Copyright 2001 David W.A. Bourne