Non-Steady-State Diffusion in a Multilayered Tissue Initiated by Manipulation of Chemical Activity at the Boundaries

Diffusion of ionic and nonionic species in multilayered tissues plays an important role in the metabolic processes that take place in these tissues. To create a mathematical model of these diffusion processes, we have chosen as an example hydrogen-bicarbonate ion pair diffusion within the mammalian cornea. This choice was based on the availability of experimental data on this system. The diffusion coefficient of the hydrogen-bicarbonate ion pair in corneal stroma and epithelium is calculated from the observed change in pH in the stroma when conditions at the corneal anterior epithelial surface are changed while the posterior surface is continually bathed with a Ringer’s solution in equilibrium with a CO 2-gas air mixture. Matching experimental results to a mathematical model of the cornea as a two-layer diffusion system yields, at 37°C, a diffusion coefficient of the hydrogen-bicarbonate ion pair of 2.5 × 10 −6 cm 2/s in the stroma and 0.4 × 10 −6 cm 2/s in the epithelium. Application of the Nernst-Einstein equation to these data gives the following diffusion coefficients in the two layers: 1) stroma, D(H +) = 11.8 × 10 −6 cm 2/s; D(HCO 3 −) = 1.5 × 10 −6 cm 2/s; and 2) epithelium, D(H +) = 1.9 × 10 −6 cm 2/s; D(HCO 3 −) = 0.22 × 10 −6 cm 2/s.