Lung morphometry with hyperpolarized ¹²⁹Xe: Theoretical background

The ³He lung morphometry technique, based on MRI measurements of hyperpolarized ³He gas diffusion in lung airspaces, provides unique information on the lung microstructure at the alveolar level. In vivo 3D tomographic images of standard morphological parameters (airspace chord length, lung parenchyma surface-to-volume ratio, and number of alveoli per unit volume) can be generated from a rather short (several seconds) MRI scan. The technique is based on a theory of gas diffusion in lung acinar airways and experimental measurements of diffusion-attenuated MRI signal. The present work aims at developing the theoretical background of a similar technique based on hyperpolarized ¹²⁹Xe gas. As the diffusion coefficient and gyromagnetic ratio of ¹²⁹Xe gas are substantially different from those of ³He gas, the specific details of the theory and experimental measurements with ¹²⁹Xe should be amended. We establish phenomenological relationships between acinar airway geometrical parameters and the diffusion-attenuated MR signal for human and small animal lungs, both normal lungs and lungs with mild emphysema. Optimal diffusion times are shown to be about 5 ms for human and 1.3 ms for small animals. The expected uncertainties in measuring main morphometrical parameters of the lungs are estimated in the framework of Bayesian probability theory.