Acinar determinants of the apparent diffusion coefficient for helium-3

Abstract

The apparent diffusion coefficient (ADC) obtained by helium-3 magnetic resonance imaging over several seconds is thought to reflect diffusion impairment due to both intra- and interacinar structure. In this study, numerical simulations of intra-acinar gas mixing and effective diffusion were performed in a multiple-branch-point model of the human acinus. Using a previously described method, we computed the instantaneous effective diffusion resulting from the diffusive impairment imposed by intra-acinar branching for varying times up to 5 s. We also tested the influence on effective diffusion of intra-acinar collateral channels in the fully alveolated intra-acinar airways to mimic the effect of emphysema. Randomly connecting two or four pairs of airways per generation (in generations 19-25) led to a 40 and 142% increase, respectively, in effective diffusion coefficient cumulated over the time interval of 0.2-5 s. Finally, we also used a system of two coupled multiple branch-point models to simulate diffusive attenuation over a 50-s interval in cases of purely acinar tagging (i.e., the initial gas concentration = 1 in one acinus and 0 in the other) and of partial tagging astride on two acini. It is shown that, in the latter case, the decay rate cannot be approximated by a mono-exponential with a several-fold faster decay for times below 10 s due to intra-acinar diffusion. We conclude that both the characteristic biphasic time dependence of simulated effective diffusion and its sensitivity to intra-acinar structural change mimic experimental ADC behavior. Additional simulations of combined inter- and intra-acinar diffusion strongly suggest that neglecting intra-acinar branching would in fact lead to considerable error of simulated ADC.