Model number

Models a tissue cylinder consisting of two regions: plasma, and interstitial fluid. Fit to Crone 1963 data.


These partial differential equations model a "tissue cylinder" consisting of two regions. The two regions are capillary plasma, p, and interstitial fluid, isf. There is a diffusional path from plasma to the isf. A consumption term is included but is set to zero here. Model is fit to Crone 1963 data for sucrose uptake into hind leg of a dog and inulin uptake into the kidney. This paper was one of the first attempts at characterizing capilliary permeability in various organs and regions of the body. Vascular reference is Evans' Blue Dye.

Crone1963hindlimb pic1
Figure: Sucrose (red) and Vascular reference (blue) outflow curves fitted to Crone 1963 figure 7 data for canine hind leg. The permeability of the vascular wall can be calculated from this data. The Crone 1963 paper calculates the permeability coefficients for different organs and regions revealing large differences in capillary permeability.



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,

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.

Christian Crone, The Permeability of Capillaries in Various Organs as 
Deterimined by Use of the 'Indicator Diffusion' Method, 
Acta physiol.scand. 58:292-305, 1963,
Key terms
interstitial fluid
Indicator dilution
vascular reference

Please cite 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 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.