Model of Intestinal Passive Absorption

Drug penetration from intestinum into blood can be divided into two processes: the drug diffusion to apical membrane of enterocytes and the drug diffusion through the membrane. Let C₀, C₁ are drug concentrations in the intestinal lumen and in close to intestinal wall, correspondingly;

h_d and h_m – are thickness of the diffusion layer adjacent to the intestinal wall and the enterocyte’s membrane;

D_w and D_L are diffusion coefficients of the drug in the intestinal lumen (can be approximately described by the diffusion coefficient in water), and in the drug membrane. D – distribution coefficient of the drug.

The drug diffusion to apical membrane of enterocytes and through it is described by Fick’s law:

dJ₁/dt = -D_w gradC = -D_w (C₁-C₀)/h_d

dJ₂/dt = -D_L gradC = -D_L C₁D/h_m.

(here we supposed the the blood flow is high that the drug concentration in the blood is zero)

In the steady-state
dJ₁/dt = dJ₂/dt = dJ/dt,
and

C₁ = (D_w/h_D)/ (D_LD/h_m + D_w/h_d) * C₀

Therefore apparent permeability of the drug is:

P_app = [dJ/dt] / ΔC = [dJ/dt] / C₀ = (D_w/h_d)/(1 + D_wh_m/(h_dD_LD)) (*)

The Figure represents experimental LogP_app plotted against LogD for drugs that are reported not to be subjected to active transport, active efflux, and paracellular diffusion (blue points); and model predictions (solid line). RMSD = 0.34 log units.