Figure 4.2. Fick's first law of diffusion intestinal epithelium. The passive diffusion of the molecules is governed by Fick's first law (Lennernas, 1998; Yoon and Burgess, 1998; Chidambaram and Burgess, 2000).
Fick's first law of diffusion (Fig. 4.2)
where J is the flux (amount of material flowing through a unit cross section); M, the drug mass (g, mol); A, the surface area (cm2); t, the time (s); D, the diffusion coefficient (diffusivity, cm2 s ); Ci, the drug concentration at membrane wall in intestinal lumen (mol l-1); C2, the drug concentration at membrane wall in blood side (mol l-1); and h is the membrane thickness (cm).
The assumptions made by this model are the following: (1) steady state flux. The transfer of drugs reaches to steady state very fast and (2) the steady state follows sink conditions: both sides of the membrane are well stirred and homogenous.
Define partition coefficient K as K = Ci/Cd = C2/Cr (Cd as drug concentration in the gastric intestinal (Gi) lumen, and Cr is the drug concentration in the blood), we can get (4.2)
Define permeability coefficient P as P = DK/h (unit cm s-1), then
Consider the absorptive surface area, we can get the final (4.4)