Understanding the pharmacokinetics of reversible metabolism.

This tutorial introduces the mathematical skills required to obtain exact and approximate solutions for reversible reactions and provides graphical insights to help understand the pharmacokinetics of reversible metabolism. The matrix method provides an easy way to derive the exact solution for the amount of each species as a function of time. The plots of the exact solutions reveal some characteristic features of the pharmacokinetic profiles of the reversible metabolism. We also describe two approximation approaches, steady-state approximation, and equilibrium approximation, to simplify the solutions. The skills and knowledge acquired through this tutorial will provide a basis for understanding more complex reversible reaction systems.