Sensitivity analysis of models of gas exchange for lung hyperpolarised ¹²⁹Xe MR

Sensitivity analysis enables the identification of influential parameters and the optimisation of model composition. Such methods have not previously been applied systematically to models describing hyperpolarised ¹²⁹Xe gas exchange in the lung. Here, we evaluate the current ¹²⁹Xe gas exchange models to assess their precision for identifying alterations in pulmonary vascular function and lung microstructure. We assess sensitivity using established univariate methods and scatter plots for parameter interactions. We apply them to the model described by Patz et al and the Model of Xenon Exchange (MOXE), examining their ability to measure: i) importance (rank), ii) temporal dependence and iii) interaction effects of each parameter across healthy and diseased ranges. The univariate methods and scatter plot analyses demonstrate consistently similar results for the importance of parameters common to both models evaluated. Alveolar surface area to volume ratio is identified as the parameter to which model signals are most sensitive. The alveolar-capillary barrier thickness is identified as a low-sensitivity parameter for the MOXE model. An acquisition window of at least 200 ms effectively demonstrates model sensitivity to most parameters. Scatter plots reveal interaction effects in both models, impacting output variability and sensitivity. Our sensitivity analysis ranks the parameters within the model described by Patz et al and within the MOXE model. The MOXE model shows low sensitivity to alveolar-capillary barrier thickness, highlighting the need for designing acquisition protocols optimised for the measurement of this parameter. The presence of parameter interaction effects highlights the requirement for care in interpreting model outputs.