The oxygen‐air equation

Abstract

is derived from first principles. Readings of oxygen concentration were obtained using oxygen sensors when different flows of oxygen and air were mixed in an anaesthetic gas delivery system. Oxygen concentrations, calculated from the oxygen-air equation, were compared with the oxygen sensor readings. The calculated values of oxygen concentration correlated with the measured values, validating the equation. My colleagues and I have found this equation very useful in our clinical practice of anaesthesia. It is easy for the anaesthetist to set oxygen and nitrous oxide flows on the anaesthetic machine to deliver a predetermined oxygen concentration but it is not so straightforward when using oxygen and air. In the latter case one may have to make frequent adjustments using an oxygen monitor as a guide to deliver the desired inspired oxygen concentration. I use a simple formula to pre-set oxygen and air flows to deliver my predetermined oxygen concentration right from the outset. The calculation is easy and it is widely used in our anaesthetic department. Richardson et al, in determining the performance of the Quantiflex air/oxygen mixer, used a mathematical method to compare the acceptability, ease and accuracy of use.1 Some oxygen monitors are affected by the presence of volatile anaesthetic agents,2 such as desflurane.3 Using this formula when in doubt will be of further help to the anaesthetist. To test the accuracy of this formula, a Boyle Series 2000 anaesthetic machine with piped oxygen and medical air supply at 400 kPa was used together with a Datex AS/3 O2 monitor attached to the common gas outlet. The O2 sensor was calibrated in air and in 100% O2. In another series of independent measurements, the Ohmeda Modulus CD anaesthetic system with piped oxygen and medical air was used. The Ohmeda Modulus O2 sensor was attached to the common gas outlet after due calibrations. Before measurements, preliminary readings were taken to determine the longest time it takes for the monitors to settle to final readings after every gas flow setting. This was three minutes, so all further readings were obtained after three minutes. FiO2 values obtained from the above oxygen-air equation were collated with the different measurements. O2 flow was arbitrarily kept constant at 4 l/min and various readings obtained. Air flow was also kept constant at 4 l/min and various readings obtained. The results are presented in Tables 1 and 2 and Figures 1 and 2, respectively. From the above equation it can be seen that the oxygen concentration delivered by venturi oxygen masks theoretically depends not on O2 flow but on the entrainment ratio of the device. In deriving the O2-air equation it was assumed that air contains 20% oxygen rather than 20.98%. This assumption yields the factor 0.2 and finally 5 in the equation. This simplifies for clinical purposes. FiO2 calculated using 0.2 were compared with those calculated using factor 0.2098 and found to be lower by a range of 0.2–0.78%. This difference is within a clinically acceptable limit. The slightly lower calculated value is not clinically relevant. This difference is of an order that could have resulted from the human error inherent in adjusting and reading the rotameter precisely. Inadequate mixing of the gases may contribute. O2 sensors are themselves not 100% accurate and ±3% error is clinically acceptable. Although this formula is not a replacement for monitoring O2 levels, it is nonetheless a useful equation in clinical practice as one can easily set O2 and air flows at the rotameter to achieve a desired FiO2 right at the onset. I am grateful to Dr M O'Connor and Dr S O'Kelly for their assistance in preparing this paper.