Laplace Transform Examples

One Compartment Models

Oral Dose Administration

Derive the Integrated Equation for the Amount of Drug in the GI Tract, X5

The Model

Model with X5 highlighted

Component of Interest - Drug in the GI Tract

Step 1. Write the differential equations

Differential equation for X5

Step 2. Transform into the Laplace domain

X5 in the Laplace domain

Step 3. Rearrange and solve for L(X5)

X5 in the s domain

Step 4. Back transform to produce the integrated equation for X5

Integrated equation for X5

using Laplace tables for the back transform

Integrated equation for X5

using the Fingerprint method for the back transform

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