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

Facil_Diffusion_2Region

This theoretical model simulates the diffusional transport of fatty acid from a constant source through two unstirred regions separated by a permeable membrane.

Model number: 0135

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Description

 Model for albumin-facilitated diffusion of palmitate in plane slab from a plane 
 source (equilibrated) to a planar membrane which palmitate permeates. Same as the 
 1 region model except there are now 2 regions with spatial domains x and y, with 
 duplicated code, the second being suffixed “y” on variables and parameters so that 
 comparisons can be made. The 2 regions are not connected, but this code will serve 
 as the basis for code in which the regions are connected, which reproduces the full 
 model in Barta et al 2000. This model assumes only 1 binding site on albumin, and 
 has adjustable rates and kd. 	



Equations

For the full formulation see the paper by Barta et al. But briefly the set of partial differential equations in each of the regions is:

with boundary conditions:
at x=0



at x=xmembrane




and at x=xmax


The equations for this model may also 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.

Download JSim model project file

References

 Barta, Efrath; Sideman, Samuel; and Bassingthwaighte, James B.;
 Facilitated Diffusion and Membrane Permeation of Fatty Acid in Albumin Solutions, 
 ABME 28: 331-345, 2000	

Related Models

Key Terms

Facilitated diffusion, permeation, Fatty acid, Albumin, Albumin-fatty acid complex, Multiregion, PDE, Publication, Transport Physiology,

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Posted by: BEJ

Acknowledgements

Please cite www.physiome.org 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: staff@physiome.org.
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, 2:31 pm.]

Model development and archiving support at physiome.org 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.