Laplace Transform Examples

One Compartment Models

The Model

Model with X3 highlighted

Component of Interest - Metabolite in the Body

Step 1. Write the differential equations

Differential equation for X3

Step 2. Transform into the Laplace domain

and

Equation for X3 in the Laplace domain

Step 3. Rearrange and solve for L(X3)

and

Equation for Laplace of X3

substituting the first term (L(X1)) into the second equation gives

Equation for Laplace of X3

Step 4. Back transform to produce the integrated equation for X3

using Laplace tables for the back transform

using the Fingerprint method for the back transform

This page was last modified: Sunday, 28th Jul 2024 at 4:43 pm