V̇o2, V̇co2, 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 O2 consumption (V̇o2), CO2 production (V̇co2), and respiratory quotient (RQ) in humans, enabling long term (24-h) observation under free-living conditions. Computation of V̇o2 and V̇co2 is currently done by inversion of a mass balance equation, with no consideration of measurement errors and other uncertainties. 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 vs. 186 ± 36 ml/min obtained using a conventional method. Experiments with 11 humans were carried out as well, where V̇o2 and V̇co2 were estimated. The variance of the estimation errors, produced by the KB method, appears 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 vs. 3,440 ± 824 (ml/min)2 and 1.8 ± 0.5 vs. 2,057 ± 532 (ml/min)2, respectively, for V̇o2 and V̇co2 estimates. Consequently, the accuracy of the computed RQ is also highly improved (0.3 × 10-4 vs. 800 × 10-4). 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.