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Derivation of pharmacokinetic equations
Anesth Pain Med 2018;13(4):349-62
Published online October 31, 2018
© 2018 Korean Society of Neuroscience in Anesthesiology and Critical Care.

Gyu-Jeong Noh1,2
Departments of 1Anesthesiology and Pain Medicine, 2Clinical Pharmacology and Therapeutics, Asan Medical Center, University of Ulsan College of Medicine, Seoul, Korea
Correspondence to: Gyu-Jeong Noh, M.D., Ph.D.
Departments of Anesthesiology and Pain Medicine, Clinical Pharmacology and Therapeutics, Asan Medical Center, University of Ulsan College of Medicine, 88 Olympic-ro 43-gil, Songpa-gu, Seoul 05505, Korea,
Tel: 82-2-3010-3855
Fax: 82-2-3010-4624
Received May 29, 2018; Revised July 3, 2018; Accepted August 12, 2018.
cc This is an Open Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License ( which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited.
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.
Key Words : Drug therapy; Pharmacokinetics; Theoretical models.

October 2018, 13 (4)
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