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Scientist: Examples: Laplace Transforms

Laplace Transforms

The use of Laplace transforms can greatly simplify the solution of models representing very complicated physical systems. Scientist has the ability to calculate inverse Laplace transforms numerically which makes this elegant technique easily accessible. Scientist can be used to simulate systems expressed in terms of Laplace transforms, or fit data to models expressed as Laplace transforms. This is especially useful when inverse Laplace transformation is difficult or even impossible analytically. This example is from the study of pharmacokinetics, this technique is equally useful in electrical engineering and other fields.

In this example we use Scientist to study administration of a drug by infusion for a finite time. The model can be expressed in terms of the Laplace transform as follows, where K0 is the infusion rate and TAU is the time at which infusion is stopped.

Micromath Scientist Model Infusion for a Finite Time Laplace Transforms

In order to solve the equations and calculate the results we run a simulation from time T = 0 to time T = 24 with 48 intervals by setting the independant parameter range and number of intervals in the variable and parameter interface as shown.

Micromath Scientist Infusion for a Finite Time Variable and Parameter Interface

Scientist runs the simulation and places the calculated values in a spreadsheet. Using the quick chart function we can quickly graph the results of the calculation.

Micromath Scientist Infusion for a Finite Time Chart