RESEARCH ARTICLE Estimation of Instantaneous Gas Exchange in Flow-Through Respirometry Systems: A Modern Revision of Bartholomew's Z- Transform Method

Flow-through respirometry systems provide accurate measurement of gas exchange over long periods of time. However, these systems have limitations in tracking rapid changes. When an animal infuses a metabolic gas into the respirometry chamber in a short burst, diffu-sion and airflow in the chamber gradually alter the original signal before it arrives at the gas analyzer. For single or multiple bursts, the recorded signal is smeared or mixed, which may result in dramatically altered recordings compared to the emitted signal. Recovering the origi-nal metabolic signal is a difficult task because of the inherent ill conditioning problem. Here, we present two newmethods to recover the fast dynamics of metabolic patterns from recorded data. We first re-derive the equations of the well-known Z-transformmethod (ZT method) to show the source of imprecision in this method. Then, we develop a newmodel of analysis for respirometry systems based on the experimentally determined impulse response, which is the response of the system to a very short unit input. As a result, we present a major modification of the ZTmethod (dubbed the ‘EZTmethod’) by using a newmodel for the impulse response, enhancing its precision to recover the true metabolic signals. The second method, the generalized Z-transform (GZT) method, was then developed by generalizing the EZTmethod; it can be applied to any flow-through respirometry systemwith any arbitrary impulse response. Experiments verified that the accuracy of recovering the truemetabolic signals is significantly improved by the newmethods. These newmethods can be usedmore broadly for input estimation in variety of physiological systems