Concentration profiles in capillary and tissue when exchange is diffusion limited. Includes axial and radial diffusion in a 2-D (x,r,t) partial differential equation problem.
Model number: 0325
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This is a modified version of a BTEX20 model where the cell has been divided into 20 sub-compartments. The exchange coefficients between the sub-compartments are calculated to solve the radial diffusion equation. This is a two-dimensional partial differential equation. Solutions are displayed in 3 formats: Contours, Wire Mesh (RUN LOOPS), and Vertically Exaggerated Wire Mesh (RUN LOOPS). NOTA BENE: To construct the wire mesh plots requires 21*21=441 solutions. The program takes significant time to run. The vertically exaggerated wire mesh shows that the low tissue diffusion coefficient results in a "trailing wave" of concentration in the tissue. This model was generated by MPC (the Modular Program Constructor).
The wire mesh concentration profiles in capillary and tissue when exchange is diffusion limited.
Advection-diffusion partial differential equation in cylindrical coordinates without angular dependence
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.
Bassingthwaighte JB, Knopp TJ, and Hazelrig JB. A concurrent flow model for capillary-tissue exchanges. In: Capillary Permeability (Alfred Benzon Symp. II), edited by Crone C and Lassen NA. Copenhagen: Munksgaard, 1970, pp 60-80.
Blood Tissue Exchange (BTEX) models
- BTEX10 : Single region (Capillary) model,
- BTEX10 model with Terminology plots,
- BTEX10stat : BTEX10 with inflow and outflow concentration statistics,
- BTEX10x2CircularFlow : Two BTEX10s used as a pipes for circular flow illustrating right and left flows,
- BTEX10_OscillatingFlow : BTEX10 used as a pipe for oscillating flow,
- BTEX20 : Two region (Capillary and ISF) model,
- BTEX20_Augmented : BTEX20 with visual interface and additional calculations,
- NestedPlots : BTEX20 used to illustrate "Nested Plots",
- DiffusionLimitedProfiles : BTEX20 with radial diffusion in parenchymal cell: A 2-d PDE in (x,r,t) ,
- BTEX20radialDiffusion : BTEX20 with radial diffusion in parenchymal cell: A 2-d PDE in (x,r,t) with Java interface to Matlab(TM) ,
- How the Modular Program Constructor (MPC) tool generated the BTEX20radialDiffusion model (contains documentation and code for MPC)
- BTEX30 : Three region (Capillary, ISF, and parenchymal cell) model,
- BTEX40 : Four region (Capillary, endothelial cell, ISF, and parenchymal cell) model,
- BTEX40_Augmented : BTEX40 with visual interface,
- BTEX50 : Five region (Capillary, endothelial cell, ISF, parenchymal cell, and mitochondria)) model,
- MID4pde : Multiple indicator dilution model for vascular (BTEX10), extravascular (BTEX20) and permeant (BTEX40) tracers,
MPC: This model was initially created using the Modular Program Constructor (MPC). For more information:
- Detailed MPC information.
- MPC text file that generated initial model.
- Download zip file containing MPC file and MPC library files used to build this model.
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Posted by: G.M. Raymond
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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.