Laplace Transform Examples

One Compartment Model

Oral Dose Administration with Metabolism to Active Drug

Derive the Integrated Equation for the Amount of Drug in the Body, X4

The Model

Model with X3 highlighted

Component of Interest - Drug in the Body

Step 1. Write the differential equations

Step 2. Transform into the Laplace domain

Step 3. Rearrange and solve for L(X4)

Step 4. Back transform to produce the integrated equation for X4

with roots -ka, -kel and -kmu

using the Fingerprint method for the back transform

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