One compartment with decay of substance, a first order process.
(See Comp1DecayPlus for more detailed treatment.)
A compartment model has a volume and a concentration of a substance. The product of the volume and the concentration is a quantity of material. The change in the quantity is described by mass balance equations.
The volume is usually designated as V, the concentration as C, and the amount of material 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 = -G*C
which is usually rewritten as
dC/dt = -(G/V)*C,
after dividing both sides by the volume. The term on the right hand side is a sink term. It is negative and removes material from the compartment.
Ordinary Differential Equation
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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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.