Computer simulation of ternary diffusion in distal airways of the human lung

Abstract

Gaseous diffusion plays a fundamental role in the terminal generations of airways for respiratory physiology. It has been proposed as a prime mechanism underlying stratified inhomogeneity in the alveolar space. Nevertheless, the diffusion phenomenon in the lung has often been studied using Fick's law which is only valid for binary diffusion. Under conditions of more than two gases in a mixture, the appropriate equations for diffusion are those of Stefan. In respiration, diffusion involves at least three gases (O2, CO2 and N2), and in physiological experiments complex mixtures including heavy or light gases (SF6, He) are often added to enhance the effect of diffusion. We present in this paper the features of ternary diffusion and solve the appropriate equations for the non-steady state by a finite difference method. The simulation was performed using two models derived from the anatomical data of Weibel and Hansen-Ampaya. Moreover, four initial conditions most often encountered during current respiratory physiology tests, were used for the computations. Therefore in these four situations, O2-N2-He, O2-N2-Ar, O2-N2-SF6 and O2-N2-CO2 combinations were used. Our results showed that for each case mentioned above the oxygen acted differently in ternary diffusion owing to the specific nature of the components of each mixture. Moreover, the behaviour of each component in ternary diffusion was very different from that of binary diffusion. However, this difference may be negligible when the subject breathed normal air.