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 = Xg0 * 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.

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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