Application of Laplace Transforms to Pharmacokinetics

Just as there are tables of logarithms/ there are tables to aid the mathematical process of obtaining Laplace transforms (X) and inverse Laplace transforms ( ). Laplace transforms can also be calculated directly from the integral  

We can illustrate the application of Laplace transforms by using them to solve the simple differential equation that we have used to describe the singlecompartment model (Equation 2.7). Starting with this equation/ 

Since F(0) represents the initial condition, in this case the amount of drug in the model compartment at time zero, Xq, the subsidiary equation can be written 

In other wordS/ the Laplace operation transforms the differential equation from the time domain to another functional domain represented by the subsidiary equation. After algebraic simplification of this subsidiary equation/ the inverse transformation is used to return the solved equation to the time domain. 

We have selected a simple example to illustrate the use of Laplace transform methods. A more advanced application is given in the next chapter, in which equations are derived for a two-compartment model. It will be shown subsequently that Laplace transform methods also are helpful in pharmacokinetics when convolution/deconvolution methods are used to characterize drug absorption processes. 

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