A two region model of capillary and cell with cell subdivided into 20 subregions with axial and radial diffusion. Time-dependent plots of contours and center-of-mass of material are calculated using MATLAB.
Model number: 0327
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This is a modification of the BTEX20 model. Radial diffusion has been included by subdividing the tissue region into 20 layers and solving the 2-D time dependent problem. The model includes a java interface to Matlab(TM) to make a movie (avi file) of the concentration contours in the capillary and tissue as a function of time. In order to use this feature, the user must have the Matlab(TM) routines and this JSim project file in the user's directory, along with the Matlab(TM) path set to that directory. The two lines of code at the end of this model which call the java interface to Matlab(TM) have been commented out (see code above). The Matlab routines are contained in a tar file which can be downloaded from this page along with the project file.
The following graphs are a snapshot at the end of the model run of contours of the concentration in the capillary and surrounding tissue.
Top panel shows the center of Mass of the
substance (red tissue only, blue tissue+capillary).
Panel Bottom Left shows the outflow on a log(Time)-linear(Concentration) plot. Panel Bottom Right shows the outflow on a linear(Time)-log(Concentration) plot. Parameters for this run are indicated in the middle of the Bottom Panel.
The equations for this model may be viewed by running the 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). To make the avi Movies, you must have Matlab installed, and the path set to the directory where the JSim project and Matlab files are stored. 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.
Blue-white curve is the center of mass including the capillary.
Red-white curve is the center of mass excluding the capillary.
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.
Modular Program Constructor (MPC)
- BTEX20radialDiffusion : BTEX20 with radial diffusion in parenchymal cell: A 2-d PDE in (x,r,t) with Java interface to Matlab(TM) ,
- Heat equation: A 2-d PDE in (x,y,t) ,
- How the Modular Program Constructor (MPC) tool generated the BTEX20radialDiffusion model (contains documentation and code for MPC)
- Recirculating O2-CO2 BTEX model built using MPC.
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[This page was last modified 14Mar18, 3:17 pm.]
Model development and archiving support at physiome.org 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.