Models a tissue cylinder consisting of four regions: interstitial fluid, endothelial cells, and parenchymal cells.
Further reading:
Description
These partial differential equations model a "tissue cylinder" consisting of four regions. The four regions are capillary plasma, p; endothelial cell, ec; interstitial fluid, isf; and parenchymal cell, pc; and are separated by three barriers--the luminal or plasma surface and endothelial cell layer; the albuminal surface of the endothelial cell facing the interstitium; andthe membrane between the interstitial fluid and parenchymal cell. In addition, there is a diffusional path from plasma to ISF bypassing endothelial cells via intercellular clefts.
Equations
Differential Equations
Left Boundary Conditions
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Right Boundary Conditions
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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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W.C. Sangren and C.W. Sheppard. A mathematical derivation of the exchange of a labelled substance between a liquid flowing in a vessel and an external compartment. Bull Math BioPhys, 15, 387-394, 1953. C.A. Goresky, W.H. Ziegler, and G.G. Bach. Capillary exchange modeling: Barrier-limited and flow-limited distribution. Circ Res 27: 739-764, 1970. J.B. Bassingthwaighte. A concurrent flow model for extraction during transcapillary passage. Circ Res 35:483-503, 1974. B. Guller, T. Yipintsoi, A.L. Orvis, and J.B. Bassingthwaighte. Myocardial sodium extraction at varied coronary flows in the dog: Estimation of capillary permeability by residue and outflow detection. Circ Res 37: 359-378, 1975. C.P. Rose, C.A. Goresky, and G.G. Bach. The capillary and sarcolemmal barriers in the heart--an exploration of labelled water permeability. Circ Res 41: 515, 1977. J.B. Bassingthwaighte, C.Y. Wang, and I.S. Chan. Blood-tissue exchange via transport and transformation by endothelial cells. Circ. Res. 65:997-1020, 1989. Poulain CA, Finlayson BA, Bassingthwaighte JB.,Efficient numerical methods for nonlinear-facilitated transport and exchange in a blood-tissue exchange unit, Ann Biomed Eng. 1997 May-Jun;25(3):547-64.
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.