One compartment with constant elimination rate of a drug, a first order process, and instantaneous injection of drug dose.

## Description

A one compartment model with intravenous (i.v.) injection is the simplest description of a drug time course through the body. It assumes that the concentration of the drug within the blood stream is representative of that throughout the body and that drug concentration within the tissue is instantaneously in equilibrium with blood concentration. With an i.v. injection the concentration at time t.min is equal to the amount injected into the vein. A compartment model has a volume and a concentration of a substance. Here the volume is equal to the dose (total quantity of drug) injected divided by the measured concentration in the blood stream. The change in the quantity of drug in the compartment is described by mass balance equations. The apparent volume of distribution is designated as V, the concentration as C, and the amount of material or drug as Q. The change in concentration, dQ/dt is governed by sources (which add material to Q) and sinks which subtract material from Q. A source will be a positive quantity. A sink will be a negative quantity. The change in Q can be written as: dQ/dt = d(V*C)/dt = C*dV/dt+V*dC/dt. Assuming V is constant, dQ/dt = V*dC/dt. The ODE equation describing the first order decay process is given as: V*dC/dt = -Clearance*C, where Clearance is the amount of drug removed from the compartment. This equation is usually rewritten as: dC/dt = -(Kelim)*C, after dividing both sides by the volume, where Kelim (Elimination rate const) = Clearance/V The term on the right hand side is a sink term. It is negative and removes material from the compartment. A note on V, the apparent volume of distribution: This is not a physiological volume but rather a ratio that measures the extent of drug distribution within a compartment. If the compartment represented blood volume and the drug distributed only in the plasma and not the red blood cells (RBCs), then the volume of distribution for the drug would be less than the volume of distribution of another drug that distributed into the RBCs as well as plasma. The volume of distribution is drug dependent.

## Equations

The equations for this model may be viewed by running the JSim model applet and clicking on the Source tab at the bottom left of JSim's Run Time graphical user interface. The equations are written in JSim's Mathematical Modeling Language (MML). See the Introduction to MML and the MML Reference Manual. Additional documentation for MML can be found by using the search option at the Physiome home page.

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Niazi S., Textbook of Biopharmaceutics and Clinical Pharmacokinetics, Appleton-Century-Crofts, NewYork, 1979, ISBN 0-8385-8868-9 Rosenbaum S.E., Basic Pharmacokinetics and Pharmacodynamics: An Integrated Textbook and Computer Simulations, Wiley, Hoboken NJ, 2011, ISBN: 978-0-470-56906-1

Please cite https://www.imagwiki.nibib.nih.gov/physiome in any publication for which this software is used and send one reprint to the address given below:

The National Simulation Resource, Director J. B. Bassingthwaighte, Department of Bioengineering, University of Washington, Seattle WA 98195-5061.

**Model development and archiving support at https://www.imagwiki.nibib.nih.gov/physiome provided by the following grants:** NIH U01HL122199 Analyzing the Cardiac Power Grid, 09/15/2015 - 05/31/2020, NIH/NIBIB BE08407 Software Integration, JSim and SBW 6/1/09-5/31/13; NIH/NHLBI T15 HL88516-01 Modeling for Heart, Lung and Blood: From Cell to Organ, 4/1/07-3/31/11; NSF BES-0506477 Adaptive Multi-Scale Model Simulation, 8/15/05-7/31/08; NIH/NHLBI R01 HL073598 Core 3: 3D Imaging and Computer Modeling of the Respiratory Tract, 9/1/04-8/31/09; as well as prior support from NIH/NCRR P41 RR01243 Simulation Resource in Circulatory Mass Transport and Exchange, 12/1/1980-11/30/01 and NIH/NIBIB R01 EB001973 JSim: A Simulation Analysis Platform, 3/1/02-2/28/07.