Laplace Transform Examples

One Compartment Models

IV Bolus Dose 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 Body

Step 1. Write the differential equations

Differential equation for X1

Step 2. Transform into the Laplace domain

Equation in the Laplace domain

Step 3. Rearrange and solve for L(X1)

Equation for Laplace of X1

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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