VO2, VCO2 and RQ in a respiratory chamber: accurate estimation based on a new mathematical model using the Kalman-Bucy method

A respiratory chamber is used for monitoring VO2, VCO2 and RQ in humans, 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 in the present study explicitly accounting for the presence of such uncertainties and error sources, and enabling the use of Optimal Filtering methods. Experiments have been realized, injecting known gas quantities and estimating them using the proposed mathematical model and the Kalman-Bucy (KB) estimation method. The estimates obtained reproduce the known production rates much better than standard methods; in particular the mean error when fitting the known production rates is 15.6±0.9 ml/min, vs 186±36 ml/min obtained using a conventional method. Experiments with eleven humans were carried out as well, where VO2, VCO2 were estimated. The variance of the estimation errors, produced by the KB method, appear relatively small and rapidly convergent. Spectral analysis is performed to assess the residual noise content in the estimates, revealing large improvement: 2.9±0.8 (ml/min) vs 3440±824 (ml/min) and 1.8±0.5 (ml/min) vs 2057±532 (ml/min) respectively for VO2 and VCO2 estimates. Consequently the accuracy of the computed RQ is also highly improved (0.3·10 vs 800·10). The presented study demonstrates the validity of the proposed model and the improvement in the results when using a KB estimation method to resolve it.