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

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=x_membrane

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.