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O₂, CO₂, and RQ in a respiratory chamber: accurate estimation based on a new mathematical model using the Kalman-Bucy method

¹Dipartimento di Informatica e Sistemistica "Antonio Ruberti," Facoltà di Ingegneria, Università di Roma "La Sapienza," 00184 Rome; and ²Istituto di Medicina Interna, Università Cattolica del Sacro Cuore, 00168 Rome, Italy

Submitted 28 July 2003 ; accepted in final form 31 October 2003

A respiratory chamber is used for monitoring O₂ consumption (O₂), CO₂ production (CO₂), and respiratory quotient (RQ) in humans, enabling long term (24-h) observation under free-living conditions. Computation of O₂ and CO₂ 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 O₂ and CO₂ 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 O₂ and CO₂ estimates. Consequently, the accuracy of the computed RQ is also highly improved (0.3 x 10^-4 vs. 800 x 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.

indirect calorimetry; respiratory gas exchange; energy expenditure; Kalman filter; stochastic model

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