This theoretical model simulates the diffusional transport of fatty acid from a constant source through two unstirred regions separated by a permeable membrane.
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.
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:
and at x=xmax
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.
We welcome comments and feedback for this model. Please use the button below to send comments:
Barta, Efrath; Sideman, Samuel; and Bassingthwaighte, James B.; Facilitated Diffusion and Membrane Permeation of Fatty Acid in Albumin Solutions, ABME 28: 331-345, 2000
Please cite https://www.imagwiki.nibib.nih.gov/physiome 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 https://www.imagwiki.nibib.nih.gov/physiome 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.