Simulation of Data

In any modeling of pharmacokinetic data, values of the dependent variables may need to be calculated at many different values of the independent variable. During the optimization or fitting process many calculations may be performed with various values of the parameters of the model. In most cases, the translation of the explicit equation to program code is straight forward if some consideration is given to the possible parameter values that may be used during the modeling process. Implicit equations include the dependent variable so that it is not readily separated from the other terms of the equation. Pharmacokinetics is the mathematical description of drug and metabolite absorption and distribution throughout the body. The Laplace transform is a method of converting ordinary differential equations into a form that allows them to be more easily integrated. Runge-Kutta methods were developed to improve the accuracy of the numerical integration process without the need for higher-order derivatives.