Finite‐difference simulations of ³He diffusion in 3D alveolar ducts: Comparison with the “cylinder model”

Time-dependent measurements of 3He diffusion in the lung could provide an accurate method to quantify alveolar length scales and the progression of diseases such as emphysema. However, the apparent diffusion coefficient (ADC) presents a complex problem to model and solve analytically. Here, finite-difference methods were used to simulate diffusion in 3D alveolar ducts. The results were compared to the only available analytical model--the "cylinder model"--from which it is possible to estimate the average radii of the alveolar ducts from in vivo data. The trend in data observed from simulations was found to agree well with the cylinder model. However, the cylinder model always overestimated the average radii of the simulated alveolar ducts. The simulations also demonstrated that the measurement of the longitudinal ADC (along the alveolar ducts) should be sensitive to early emphysematous changes, whereas the measured radii should be far less sensitive.