Bayesian estimation of physiological parameters governing a dynamic two-compartment model of exhaled nitric oxide

The fractional concentration of nitric oxide in exhaled breath (fe_NO) is a biomarker of airway inflammation with applications in clinical asthma management and environmental epidemiology. fe_NO concentration depends on the expiratory flow rate. Standard fe_NO is assessed at 50 mL/sec, but "extended NO analysis" uses fe_NO measured at multiple different flow rates to estimate parameters quantifying proximal and distal sources of NO in the lower respiratory tract. Most approaches to modeling multiple flow fe_NO assume the concentration of NO throughout the airway has achieved a "steady-state." In practice, this assumption demands that subjects maintain sustained flow rate exhalations, during which both fe_NO and expiratory flow rate must remain constant, and the fe_NO maneuver is summarized by the average fe_NO concentration and average flow during a small interval. In this work, we drop the steady-state assumption in the classic two-compartment model. Instead, we have developed a new parameter estimation approach based on measuring and adjusting for a continuously varying flow rate over the entire fe_NO maneuver. We have developed a Bayesian inference framework for the parameters of the partial differential equation underlying this model. Based on multiple flow fe_NO data from the Southern California Children's Health Study, we use observed and simulated NO concentrations to demonstrate that our approach has reasonable computation time and is consistent with existing steady-state approaches, while our inferences consistently offer greater precision than current methods.