Numerical simulation of the transient transport of inert gases in lung tissue

Abstract

A numerical simulation of the transport of xenon gas into healthy and oedematous lung tissue is described. The lung is modelled as four parallel tissue layers: alveolar membrane, interstitial fluid, capillary membrane, and blood, surrounded by a uniform air space. Using a finite difference representation of the governing diffusion equations, the concentration distribution of Xe gas in each of the layers of tissue is obtained for a step change in the Xe concentration in the air space. The effect of a thickening of the interstitial fluid layer, found in pulmonary oedema, on the kinetics of Xe transport is also considered. Computational findings indicate that a good approximation to the steady state profiles for Xe in the layers of tissue can be obtained simply by assuming that instantaneous equilibrium exists (as described by Henry's Law) between the lung tissue and surrounding air space. This same finding is documented even when the thickness of the interstitial fluid layer is increased by a factor of 40 above baseline values. The results suggest that the reduction in gas exchange which occurs in pulmonary oedema is caused by fluid flow into the alveoli, rather than a true diffusion deficit caused by a thicker alveolar-capillary barrier. The relationship of the present findings to those which would be obtained for more physiological input functions of Xe gas into the air space is also discussed.