Two compartments, plasma and interstitial fluid (ISF), with flow and exchange using physiological names and units for parameters and variables. The model is
A flow, Fp, carries an inflow concentration, Cin, into a plasma compartment with volume Vp. The substance is instantaneously well mixed. The material undergoes a passive exchange with an interstitial fluid (ISF) space with volume Visf. No reactions occur in this system. For a constant concentration of inflowing material the analytic steady state solution is Cp=Cin and Cisf=Cin if Psc is positive. 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. The model parameters are optimized to fit a data set.
Ordinary Differential Equations
Analytic Steady State Solutions when Cin 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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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.