Determinants of the long-range apparent diffusion coefficient in the human lung: collateral channels or intra-acinar branching?

TO THE EDITOR: We have given considerable thought to the study by Bartel and colleagues (1) in an attempt to reconcile their simulation of the long-range apparent diffusion coefficient (LRADC) obtained from hyperpolarized helium-3 experiments in human lungs, with our own simulation using totally different models (3). Bartel et al. (1) use a branching network, where airways are treated as line segments, but with a three-dimensional (3D) spatial orientation of subsequent branching generations between generation 5 and 14 mimicking that of a real lung. Any internal branching structure peripheral to generation 14 is suppressed, and each acinus, covering generations 15–23, is lumped to one point object occupying a typical acinar volume of 185 mm at total lung capacity. Considering the lungs to be initially filled with a uniform spin magnetization and applying a magnetization modulation in a randomly selected spatial direction across this 3D model, they obtain a simulated LRADC of 0.001 cm/s, which is an order of magnitude smaller than the experimental LRADC value (1, 4). From this discrepancy, the authors propose that the model should incorporate collateral paths to better mimic experimental LRADC values. In our work (3), we use an acinar model, branching through several generations down to the alveolar sacs, with an average longitudinal pathway along its airway axes of 7.7 mm at functional residual capacity. Using a one-dimensional (1D) diffusing equation and imposing an initial concentration 1 in randomly selected locations of the acinus, the time course of equilibration of concentration differences within the acinus can then be related to that which considers free diffusion inside an acinus devoid of internal branching, to obtain an effective dispersion coefficient. Averaged over the time interval 0.5–5 s, this coefficient amounted to 0.0085 cm/s. The choice of considering branching inside the acinar space (which makes up over 90% of lung volume) and no branching generations proximal to the acinar entrance was based on He wash-in studies (e.g., Ref. 2). These had shown that structural intraacinar branching asymmetry can induce considerable intraacinar concentration differences, which take at least 5 s to equilibrate. The above simulation methods, be it by imposing a magnetic spin 1 or a concentration 1 on random locations in the lung periphery led to us to wonder to what extent either mechanism (intra-acinar branching or bronchial branching with collateral channels between them) underlies actual LRADC measurement. An interesting clue stems from a study by Wang et al. (4) showing the dependence of apparent diffusion coefficient (ADC) on acquisition time between 0.2 and 10 s. The main result was a rapid initial ADC decrease from values ranging from 0.04 to 0.10 cm/s for 0.2 s (depending on subject and/or tag length) and a slower ADC decrease beyond 2 s. Typically, the ADC decrease was six to eight times slower between 2 and 5 s than between 0.5 and 2 s, and at 5 s, ADC was 0.01 cm/s. From our simulation curves (Fig. 5 in Ref. 3), ADC values can also be extracted for each point in time, showing a rapid initial ADC decrease from 0.064 cm/s for 0.2 s, and a simulated ADC decrease that was nine times slower between 2 and 5 s than between 0.5 and 2 s. The major difference between the experimental and our simulated values is for 5 s, where we simulated an ADC of only 0.005 cm/s. This could indicate that for times exceeding 5 s, inter-acinar diffusion needs to be taken into account as well. In the future, we should probably consider including airways proximal to the acinus and see how connecting several neighboring acini affects the ADC vs. time curve. Possibly, Bartel et al. (1) could also retrieve ADC dependence on time from their existing simulations and venture in the peripheral direction to verify the potential role of intra-acinar branching using their independent simulation method.