Functional magnetic resonance imaging of the lungs with hyperpolarized Helium provides an index of apparent diffusion measured over several seconds (ADC_sec) which is only 2% of its free diffusion in air (0.88cm²/s). The potential of ADC_sec to non-invasively assess in vivo lung structure of diseased lungs at the length scales corresponding to several seconds is critically dependent on the exact link between ADC_sec and lung peripheral structure. In order to understand the intruigingly small ADC_sec, numerical simulations of gas transport were performed in 1) a trumpet model, 2) a symmetrical and 3) an asymmetrical multiple branch point model of the human acinus. For initial gas boluses in different locations of the acinar models, ADC_sec was quantified as follows. At different time intervals, we computed a coefficient of variation (CoV) of the concentration distributions within each acinar model. The slope in the semi-log plot of log(CoV) vs time was proportional to the ADC_sec generated by the internal model structure, provided that the outer model boundaries were similar across all models (i.e.,similar cumulative cross section vs average path length). The simulations revealed an ADC_sec which amounted to approximately 1% of free diffusion in the trumpet model of the acinus, i. e., corresponding to free diffusion within the acinar geometrical boundaries. Our simulations show that for initial conditions corresponding to those used in magnetic resonance imaging experiments, intra-acinar branching introduces a dramatic diffusion delay, comparable to what is observed experimentally.