Bayesian Tracking of a Nonlinear Model of the Capnogram

Capnography, the monitoring of expired carbon dioxide (CO₂ ) has been employed clinically as a non-invasive measure for the adequacy of ventilation of the alveoli of the lung. In combination with air flow measurements, the capnogram can be used to estimate the partial pressure of CO₂ in the alveolar sacs. In addition, physiologically relevant parameters, such as the extent of CO₂ rebreathing, the airway dead space, and the metabolic CO ₂ production can be predicted. To calculate these parameters, mathematical models have been previously formulated and applied to experimental data using off-line optimization procedures. Unfortunately, this does not permit online identification of the capnogram to detect changes in the physiological model parameters. In the present study, a Bayesian method for breath-by-breath identification of the volumetric capnogram is presented. The method integrates a model of CO₂ exchange in the lungs, which is nonlinear due to the nature of human tidal breathing, with a particle filtering algorithm for estimation of the model parameters and changes therein. In addition, this allowed for a dynamic prediction of the unmeasured alveolar CO₂ tension. The method is demonstrated using simulations of the capnogram. The proposed method could aid the clinician in the interpretation of the capnogram