Laplace Transform Examples

One Compartment Models

IV Infusion Administration

Derive the Integrated Equation for the Amount of Drug in the Body, X1

The Model

Model with X1 highlighted

Component of Interest - Drug in the Body

Step 1. Write the differential equations

Differential equation for X1

Step 2. Transform into the Laplace domain

Laplace equation for X1

Step 3. Rearrange and solve for L(X1)

X1 in the s domain

Step 4. Back transform to produce the integrated equation for X1

Integrated equation for X1

using Laplace tables for the back transform

Integrated equation for X1

using the Fingerprint method for the back transform

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