Models single compartment with inflowing and outflowing concentration of a single substance.
A Flow carries an inflow concentration, Cin, into a one compartment model with a given Volume. Cin is constantly and instantaneously well mixed becoming C, the concentration in the compartment. C empties out of the compartment and is designated Cout. No reactions occur in this system. For a constant concentration of inflowing material the analytic solution is given. Various methods for checking the calculations in a model are illustrated: (1) comparison with an analytic solution, (2) two methods of calculating the amount of material in a compartment with flow, (3) comparison of the running integrals of inflow and outflow concentrations, and (4) calculation of the system transit time of a compartment model with flow by two different methods.
Further reading: Understanding the Comp1FlowPlus Model
Ordinary Differential Equation
Analytic Solution when Cin(t) is constant
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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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.