Derivation of the effective air volume of indirect room calorimeters: An uncertainty-based approach

Whole-Room Indirect Calorimeters (WRIC), also known as metabolic chambers, provide remote measurement of physiological parameters such as energy expenditure, respiratory gas exchange, and nutrient utilization through non-invasive gas exchange modeling. The accuracy of WRIC systems depends on the accurate estimation of the effective chamber air volume, which is critical for calculating the oxygen consumption and carbon dioxide production rates of an individual inside the chamber for long-term monitoring. This study proposes a novel analytical procedure to derive the metabolic chamber volume and its uncertainty by analyzing data obtained during washout experiments using an ad hoc weighted least square fitting approach based on the uncertainty of gas concentration and air flow measurements. The influence of the initial gas concentration and the air inflow rate during the washout experiment on the estimation of the chamber volume is discussed, and general rules for determining the optimal duration of a washout experiment to obtain an accurate volume estimate are proposed. The theoretical results were validated with Monte Carlo simulations and by processing real data from a washout experiment, demonstrating substantial agreement in the estimation of the chamber volume and its uncertainty. The combined analysis of both O2 and CO2 time courses using our proposed approach helps to reduce the overall measurement uncertainty and leads to a more accurate estimate of chamber volume, thereby improving the accuracy of WRIC outcome measurements.