Model with two species A and B, with flow in a plasma compartment and exchange with an interstitial fluid compartment with A converting to B reversibly.
Description
This is a two compartment model (plasma and isf) exchange model with flow in the plasma compartment. Both spaces are instantaneously well mixed. A and B reversibly convert to each other in the isf space. The isf space can also be used as a cell space. Flow, Fp, and exchange rates, PSa and PSb, have the same units, ml/(g*min) (milliliters per minute per gram of tissue). These units are used in the physiological terminology to relate them to fluxes per gram of tissue.
The conversion rates have the same units, ml/(g*min). Ga2b is the conversion rate of A going to B, and Gb2a is the conversion rate of B becoming A.
The steady state solutions for constant inflow of A are solved implicitly, using the final value of the input concentration (assumed to have been constant).
Further reading:
Equations
Ordinary Differential Equations
Initial Conditions
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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.