Functional MRI of the lungs with hyperpolarized helium provides an index of apparent diffusion measured over several seconds (ADCsec) that is only 2% of its free diffusion in air (0.88 cm2/s). The potential of ADCsec to noninvasively assess in vivo lung structure of diseased lungs at the length scales corresponding to several seconds is critically dependent on the exact link between ADCsec and lung peripheral structure. To understand the intruigingly small ADCsec, 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, ADCsec 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 semilog plot of log(CoV) vs. time was proportional to the ADCsec 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 ADCsec that amounted to approximately 1% of free diffusion in the trumpet model of the acinus, i.e., corresponding to free diffusion within the acinar geometric boundaries. Our simulations show that for initial conditions corresponding to those used in MRI experiments, intra-acinar branching introduces a dramatic diffusion delay, comparable to what is observed experimentally.