Improving hyperpolarized ¹²⁹ Xe ADC mapping in pediatric and adult lungs with uncertainty propagation

Hyperpolarized (HP) ¹²⁹ Xe-MRI provides non-invasive methods to quantify lung function and structure, with the ¹²⁹ Xe apparent diffusion coefficient (ADC) being a well validated measure of alveolar airspace size. However, the experimental factors that impact the precision and accuracy of HP ¹²⁹ Xe ADC measurements have not been rigorously investigated. Here, we introduce an analytical model to predict the experimental uncertainty of ¹²⁹ Xe ADC estimates. Additionally, we report ADC dependence on age in healthy pediatric volunteers.

An analytical expression for ADC uncertainty was derived from the Stejskal-Tanner equation and simplified Bloch equations appropriate for HP media. Parameters in the model were maximum b-value (b_max ), number of b-values (N_b ), number of phase encoding lines (N_ph ), flip angle and the ADC itself. This model was validated by simulations and phantom experiments, and five fitting methods for calculating ADC were investigated. To examine the lower range for ¹²⁹ Xe ADC, 32 healthy subjects (age 6-40 years) underwent diffusion-weighted ¹²⁹ Xe MRI.

The analytical model provides a lower bound on ADC uncertainty and predicts that decreased signal-to-noise ratio yields increases in relative uncertainty $$ . As such, experimental parameters that impact non-equilibrium ¹²⁹ Xe magnetization necessarily impact the resulting $$ . The values of diffusion encoding parameters (N_b and b_max ) that minimize $$ strongly depend on the underlying ADC value, resulting in a global minimum for $$ . Bayesian fitting outperformed other methods (error < 5%) for estimating ADC. The whole-lung mean ¹²⁹ Xe ADC of healthy subjects increased with age at a rate of 1.75 × 10^-4  cm² /s/yr (p = 0.001).

HP ¹²⁹ Xe diffusion MRI can be improved by minimizing the uncertainty of ADC measurements via uncertainty propagation. Doing so will improve experimental accuracy when measuring lung microstructure in vivo and should allow improved monitoring of regional disease progression and assessment of therapy response in a range of lung diseases.