Optimal strategy for b-values selection for lung morphometry with hyperpolarized 3He diffusion MRI

Introduction: The lung morphometry technique [1] allows the evaluation of lung microstructure based on an MRI measurement of hyperpolarized He gas diffusion. In this approach, acinar lung airways are considered as cylinders covered by alveolar sleeves [2]. Diffusion of He gas in each airway is anisotropic and described by distinct longitudinal and transverse diffusion coefficients, DL and DT. An analytical expression for the diffusion MR signal as a function of b-value was derived taking into account the fact that airways with a flat distribution across all orientations are present in each imaging voxel. In [3], the relationships between DL and DT and geometrical parameters of alveolar airways – external, R, and internal, r, radii were found. This approach allows estimation of R and r from multi b-value MR experiments [1,3]. An important practical question is how to optimize experimental sequence parameters for a given restricted imaging time (usually about 10-second breathhold). Herein we provide estimates of the values of the optimal b-values that allow evaluation of lung geometrical parameters with minimal errors. Theory: Previously we have developed a theory of parameters optimization assuming an equidistant data sampling [4]. Here we generalize this theory for non-equidistant sampling. We use Bayesian analysis [4-6] to analyze how the estimated geometrical parameters R and r depend on their “true values”, signal-to-noise ratio, data sampling and total number of data values N. The basic quantity in Bayesian analysis is a joint posterior