## Intravenous administration

### Scheme or diagram

**Diagram XIX-1 Two Compartment Pharmacokinetic Model**

### Differential equation

The differential equation for drug in the central compartment following
intravenous bolus administration is:-

**Equation XIX-1 Differential Equation for the Central Compartment**

The kel * X1 term describes elimination of the drug from the central
compartment, while the k12 * X1 and k21 * X2 terms describe the distribution of
drug between the central and peripheral compartments.

### Integrated equation

Integration of this equation (using Laplace transforms) leads to a
biexponential equation for plasma concentration as a function of time.

Thus,

Cp = A * e^{-
* t} + B * e^{-
* t} with > .

The A, B, , and terms were derived from the microconstants
during the integration process. They are functions of the microconstant k12,
k21, kel and V1

+ = kel + k12 + k21

* = kel * k21