Chapter 26 Integrating Differential Equations using Laplace Transforms

return to the Course index
previous | next

Finger Print Method - Example 3

The differential equation for amount of drug in body according to the two compartment model after an IV bolus (Dose) can be written as:

Equation 26.8.1 Laplace Transform of Amount in the Body after an IV Bolus - Two Compartment model

Note that the denominator has a power of 2 in s and no repeating terms. The numerator has a power of 1 in s. Therefore the fingerprint method can be applied.

Setting the denominator to zero:

(s + α) * (s + β) = 0

gives the two roots -α and -β.

The finger print method can then be applied as illustrated in the video below.

Figure 26.8.1 Video illustrating the Finger Print Method - 3

The solution

Equation 26.8.2 Integrated Equation for Amount in the Body after an IV Bolus - Two Compartment

Dividing both sides by V₁ provides the more familiar values A and B in the equation for Cp versus time. A and B were defined earlier in Equation 19.2.4.

Equation 26.8.3 Integrated Equation for Amount in the Body after an IV Bolus - Two Compartment

This page was last modified: Sunday, 28th Jul 2024 at 5:08 pm

Privacy Statement - 25 May 2018

Material on this website should be used for Educational or Self-Study Purposes Only

Bird Count
An iPhone app that facilitates the geotagging of Bird Count stops
and the return to the same stops during the next
and subsequent Bird Count sessions