Derivation of pharmacokinetic equations

ABSTRACT

A variety of drugs are continuously or intermittently administered to patients during general or regional anesthesia. Pharmacotherapy should also receive priority compared with several treatment modalities including nerve blocks for chronic pain control. Therefore, pharmacology may be fundamental to anesthesia as well as pain medicine. Pharmacokinetic equations quantitatively evaluating drug transfer in the body are essential to understanding pharmacological principles. In mammillary compartmental models, pharmacokinetic equations are easily derived from a few simple principles. The kinetics of drug transfer between compartments is determined initially. Ordinary, linear differential equations are constructed based on the kinetics. The Laplace transforms of these differential equations are used to derive functions for the calculation of drug amounts in the central or effect compartments in the Laplace domain. The inverse Laplace transforms of these functions are used to obtain pharmacokinetic equations in time domain. In this review, a two-compartment mammillary pharmacokinetic model is used to derive pharmacokinetic equations using the aforementioned principles.