Improving the estimation of biological indices via Kalman filtering

Monitoring of respiratory gas exchange (oxygen consumption - VO2 and carbon dioxide production - VCO2) in humans practicing normal daily life activity is important in order to establish physical condition and metabolic indices (such as the respiratory quotient - RQ) of the patients. A respiratory chamber is used to this extent, enabling long term (24h) observation under free-living conditions. Computation of VO2 and VCO2 is currently done by inversion of a mass balance equation, with no consideration of measurement errors and other uncertainties. In order to improve the accuracy of the results, a new mathematical model is suggested, explicitly accounting for the presence of such errors and uncertainties, enabling the use of optimal filtering methods. Validation experiments have been realized, injecting known gas quantities and estimating them using the proposed mathematical model and applying the Kalman filtering (KF) methods. The estimates obtained reproduce the known production rates much better than standard methods. Experiments with eleven humans were carried out as well, where VO2, VCO2 and RQ were estimated. The error covariance matrix, produced by the KF method, appears relatively small and rapidly convergent spectral analysis is performed to assess the residual noise content in the estimates, revealing large improvement. The presented study demonstrates the validity of the proposed model and the improvement in the results when using a KF method to resolve it.