# Pharmacokinetic two-compartment model

Pharmacokinetics refers to the rate and extent of distribution of a drug to different tissues, and the rate of elimination of the drug. Pharmacokinetics can be reduced to mathematical equations, which describe the transit of the drug throughout the body, a net balance sheet from absorption and distribution to metabolism and excretion.

Pharmacokinetic two-compartment model divided the body into *central* and
*peripheral* compartment. The central compartment (compartment 1) consists of
the plasma and tissues where the distribution of the drug is
practically instantaneous. The peripheral compartment (compartment 2) consists of tissues where the
distribution of the drug is slower.

**Figure 1.**Two-compartment model with first-order absorption and elimination. A

_{GI}, A

_{1}, and A

_{2}are the amounts of drug in gastrointestinal tract (GI), central compartment (including plasma), and peripheral compartment, respectively.

*k*,

_{a}*k*,

_{12}*k*, and

_{21}*k*represent the first-order fractional rate constants for absorption, distribution, redistribution, and elimination.

_{10}Drug concentrations in the compartments equal to the amounts divided by volumes:
*C _{1}=A_{1}/V_{1}* and

*C*. Drug concentration in the central compartment is equal to the concentration in the plasma:

_{2}=A_{2}/V_{2}*C*. Clearance (in units L/h) is often used instead of the fractional rate constants (in units h

_{P}=C_{1}^{-1}); in pharmacokinetics the distribution volume is given in volume units (L), and rate constants can be represented as the ratio of clearance and distribution volume,

*k=CL/V*.

In the case of oral administration of the drug, at time *t=0* the amount of drug in
the central and peripheral compartments is zero (A_{1}(0)=A_{2}(0)=0), and
the initial amount in gastrointestinal tract (effective dose) is:

, where D is the administered dose of the drug, S is the salt factor (fraction of administered dose that is made up of pure drug), and F is the bioavailability factor (fraction of dose that reaches the systemic circulation).

The amount of drug in GI decreases with time:

Drug concentrations in the central and peripheral compartments can be calculated with differential equations:

After integration of the equations from time zero:

In the case of intravenous (IV) administration of the drug, F=1.0, and at time *t=0*
the amount of drug in the peripheral compartment is zero (A_{2}(0)=0), and the amount in
the central compartment, A_{1}, is:

## See also:

- Plasma pharmacokinetics
- Receptor occupancy
- Enzyme inhibition
- Binding potential
- Compartmental model ODEs in PET

## References:

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*Progr Drug Res.* 2005; 62: 280-317.

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CRC Press, 1995. ISBN 1-56676-204-9.

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10.2165/00003088-200241080-00003.

Jann MW, Penzak SR, Cohen LJ (eds.): *Applied Clinical Pharmacokinetics and Pharmacodynamics
of Psychopharmacological Agents*. Adis, Springer, 2016.
doi: 10.1007/978-3-319-27883-4.

Kuepfer L, Niederalt C, Wendl T, Schlender JF, Willmann S, Lippert J, Block M, Eissing T,
Teutonico D. Applied concepts in PBPK modeling: how to build a PBPK/PD model.
*CPT Pharmacometrics Syst Pharmacol.* 2016; 5(10): 516-531.
doi: 10.1002/psp4.12134.

Rosenbaum S (ed.): *Basic Pharmacokinetics and Pharmacodynamics - An Integrated Textbook and
Computer Simulations.* 2nd ed., Wiley, 2017. ISBN 9781119143154.

Zamuner S, Di Iorio VL, Nyberg J, Gunn RN, Cunningham VJ, Gomeni R, Hooker AC. Adaptive-optimal
design in PET occupancy studies. *Clin Pharmacol Ther.* 2010; 87(5): 563-571.
doi: 10.1038/clpt.2010.9.

Tags: Pharmacokinetics, Drug development, Plasma, Clearance

Created at: 2016-12-16

Updated at: 2018-06-12

Written by: Vesa Oikonen