Simulations of Short-Time Diffusivity in Lung Airspaces and Implications for S/V Measurements Using Hyperpolarized-Gas MRI

We demonstrate a method for simulating restricted diffusion of hyperpolarized gases in lung airspaces that does not rely on an idealized analytic model of alveolar structure. Instead, the restricting geometry was generated from digital representations of histological sections of actual lung tissue obtained from a rabbit model of emphysema. Monte-Carlo simulations of restricted diffusion were performed in the short-time-scale regime, for which the time-dependent diffusivity is quantitatively related to the surface-to-volume ratio (S/V) of the pore space. In each of the eight samples studied, the S/V extracted from the simulated time-dependent diffusivity curves differed by less than 3% from direct assessment of S/V using image-processing methods. Simulated MRI measurements of apparent diffusion coefficients (ADCs) were performed in three representative lung sections to determine the effect of realistic gradient pulse shapes on the extracted S/V values. It was confirmed that ADCs measured at short diffusion times using either narrow or square gradient pulses yield accurate S/V values based on previously derived theoretical relationships. Simulations of triangular and sinusoidal diffusion-sensitizing gradients were then used to quantify the modifications required to extract accurate S/V values from ADC measurements obtained using more realistic gradient waveforms.