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Cardiac Physiome Society workshop: November 6-9, 2017 , Toronto


Models diffusion through one dimensional slab with a constant diffusion coefficient, D, with flux into recipient chamber on right used to estimate the diffusion coefficient. Model includes partition coefficient.

Model number: 0395

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    In this model we calculate the one dimensional diffusion across a region 
    with a single rate of diffusion, D. On the left hand side the concentration
    is held constant (mixed, large reservoir) and at the right hand side is set at 0 mM at t=0
    in VolR, the recipient mixing chamber.  The partition coefficient, lambda, is the
    ratio of the concentration immediately inside the slab or region of diffusion
    to that immediately outside the region. It has been set to 0.9 in the example.
    This model serves as the basis for all the other slab diffusion model in which 
    the diffusion domain may have heterogeneities in thickness, in internal binding,
    in paths through cells and around them.
                   OCEAN      |     SLAB        |  Recipient Chamber
                              |   Concn = C     |
                 CL0 = 10 mM  |                 |  CR0 = 0 mM
                              |  D = Diff Coeff |
                              |                 |  VolR
                              |                 |
                              |    C0 = 0 mM    |
                              |                 |
                             x=0  Thickness    x=L



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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Aitken A and Barrer RM.Transport and solubility of isomeric paraffins in rubber.
Trans Faraday Soc 51: 116-130, 1955.

Barrer RM. A new approach to gas flow in capillary systems. J Phys Chem 57: 35-40, 1953.

Bassingthwaighte JB; Transport in Biological Systems, Springer Verlag, New York, 2016??.

Safford RE and Bassingthwaighte JB. Calcium diffusion in transient and steady
states in muscle. Biophys J 20: 113-136, 1977.

Safford RE, Bassingthwaighte EA, and Bassingthwaighte JB. Diffusion of water
in cat ventricular myocardium. J Gen Physiol 72: 513-538, 1978.

Suenson M, Richmond DR, and Bassingthwaighte JB. Diffusion of sucrose, sodium,
and water in ventricular myocardium. Am J Physiol 227: 1116-1123, 1974.

Related Models

Key Terms

Diffusion, Constant diffusion coefficient, PDE, Concentration, One slab, Transport physiology RELATED MODELS: #202: Safford 1977 Dead end pore model for Calciium diffusion in muscle #205: Safford 1978 Water diffusion in heart #193: Suenson 1974 Diffusion in heart tissue, sucrose and water #135: Two slab model: Facil_Diffusion_2Region #184: RandomWalk1D #212: TwoSlab Diffusion: different diffusion coeffs in adjacent slabs require special boundary condition

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Please cite in any publication for which this software is used and send an email with the citation and, if possible, a PDF file of the paper to:
Or send a copy to:
The National Simulation Resource, Director J. B. Bassingthwaighte, Department of Bioengineering, University of Washington, Seattle WA 98195-5061.

[This page was last modified 02Nov16, 2:21 pm.]

Model development and archiving support at provided by the following grants: 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.