Calculation of the Aqueous Diffusion Layer Resistance for Absorption in a Tube: Application to Intestinal Membrane Permeability Determination

Abstract

The single-pass intestinal perfusion technique has been used extensively to estimate the wall permeability in rats. The unbiased membrane parameters can be obtained only when the aqueous resistance is properly accounted for. This aqueous resistance was calculated numerically from a convective diffusive mass transfer model, including both passive and carrier-mediated transport at the intestinal wall. The aqueous diffusion layer resistance was shown to be best described by a function of the form,$\overline {P_{aq}^* } ^{ - 1} = AG_z ^{1/3} + BG_Z ^C \left[ {P_c^* \left( {\frac{{K_m }}{{C_o }}} \right)^D + P_m^* } \right]^E$ where G _z , P* _m P* _c K _m and C o are, respectively, Graetz number, passive permeability, carrier-mediated permeability, Michaelis constant, and the drug concentration entering the tube. Asterisked are dimensionless quantities obtained by multiplying the permeability constants with R/D, where R and D being radius and drug diffusivity, respectively. A, B, C, D and E were obtained by a least-squares nonlinear regression method, giving values of 1.05, 1.74, 1.27, 0.0659, and 0.377, respectively, over the range of 0.001 ≤ G _z ≤ 0.5, 0.01 ≤ P* _m ≤ 10, 0.01 ≤ P* _c ≤ 10, and 0.01 ≤ K _m /C _o ≤ 100. This aqueous resistance was found to converge to those calculated from Levich's boundary layer solution in low Graetz range, indicating the correct theoretical limit. Using an iteration method, the equation was shown to be useful in extracting the intrinsic membrane permeability from the experimental data.