Measuring a patients’ oxygen consumption ( \( {\dot{\text{V}}}{\text{O}}_{2} \)) is valuable in critical care and during anesthesia. Up to now, there has been no satisfactory equation describing the relation between the \( {\dot{\text{V}}}{\text{O}}_{2} \), the fresh gas, and FIO2 in a semi-closed circle breathing system. By adopting a “volume-weighted average concentration” approach and stepwise calculations, we have proposed an equation. We constructed a model with known simulated O2 consumption (\( _{{{\text{SIM}}}} {\dot{\text{V}}}{\text{O}}_{2} \)) to test our equation and two other previous methods (Biro’s and Azami’s). After 32 different laboratory scenarios, the %-error of the calculated \( {\dot{\text{V}}}{\text{O}}_{2} \) (\( _{{{\text{CAL}}}} {\dot{\text{V}}}{\text{O}}_{2} \)) from our method is −4.0 ± 2.9%, which is significantly better than those from Azami’s method (−8.8 ± 6.2%, p < 0.01) and from Biro’s method (−27.4 ± 5.1%, p < 0.01). We also produce a Bland–Altman analysis of our \( _{{{\text{CAL}}}} {\dot{\text{V}}}{\text{O}}_{2} \) and \( _{{{\text{SIM}}}} {\dot{\text{V}}}{\text{O}}_{2} . \) The 95% limits of agreement are −18.6–3.3 mL/min with a mean bias of −7.7 mL/min, which shows a good agreement. Our equation also explains the difference between FIO2 and the oxygen concentration of the fresh gas in a semi-closed circle breathing system.
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We thank Marvin Chou for technical supports of the AS/3 anesthesia machine. Support was provided solely from institutional and/or department sources.
Author information Authors and AffiliationsDepartment of Anesthesiology, Chung Shan Medical University and Hospital, No. 110, Sec. 1, Chien-Kuo N. Road, Taichung, 402, Taiwan, R.O.C
Tsai-Hsin Chen, Wen-Ru Ko, Cher-Ming Liou & Wei-Te Hung
Department of Otorhinolaryngology, Chung Shan Medical University and Hospital, Taichung, 402, Taiwan, R.O.C
Chung-Han Hsin
Correspondence to Wei-Te Hung.
Appendix AppendixIn order to monitor O2 concentration, the multigas analyzer continuously samples gas from the Y-connector. If the sampled gas is returned to the circle (as in Fig. 1), 30 mL/min of room air is also added to the returned gas in addition to 200 mL/min of sampled gas. Room air serves as a reference gas for O2 measurement. In our calculations, the effect of the multigas analyzer on \( {\dot{\text{V}}}{\text{O}}_{2} \) calculation is considered as the addition of a flushing gas, the entrained room air, into the ventilator bellow. Equation 4 can be rewritten as:
$$ {\text{F}}_{{{\text{VB}}}} {\text{O}}_{{\text{2}}} = \frac{{{\left( {V_{{{\text{Expand}}}} + {\dot{\text{V}}}_{{{\text{FG}}}} \times E_{{\text{S}}} } \right)} \times {\text{F}}_{{\text{I}}} {\text{O}}_{{\text{2}}} + {\text{(TV}} - {\text{O}}_{{{\text{2Uptake}}}} + {\text{CO}}_{{{\text{2Produce}}}} {\text{)}} \times {\text{F}}_{{{\text{Exhale}}}} {\text{O}}_{{\text{2}}} + {\text{(30/RR)}} \times {\text{0}}{\text{.21}}}} {{V_{{{\text{Expand}}}} + {\dot{\text{V}}}_{{{\text{FG}}}} \times E_{{\text{S}}} + {\left( {{\text{TV}} - {\text{O}}_{{{\text{2Uptake}}}} + {\text{CO}}_{{{\text{2Produce}}}} } \right)} + {\left( {{\text{30/RR}}} \right)}}} $$
(4′)
30/RR is the volume of the entrained air in one respiratory period, and 0.21 is the O2 concentration of room air.
Equations (5) and (6) change to:
$$ {\text{F}}_{{{\text{VB}}}} {\text{O}}_{{\text{2}}} = \frac{{{\text{(}}V_{{{\text{Expand}}}} + {\dot{\text{V}}}_{{{\text{FG}}}} \times E_{{\text{S}}} {\text{)}} \times {\text{F}}_{{\text{I}}} {\text{O}}_{{\text{2}}} + {\text{(TV}} \times {\text{F}}_{{\text{I}}} {\text{O}}_{{\text{2}}} - {\text{O}}_{{{\text{2Uptake}}}} {\text{)}} + {\text{(30/RR)}} \times {\text{0}}{\text{.21}}}} {{V_{{{\text{Expand}}}} + {\dot{\text{V}}}_{{{\text{FG}}}} \times E_{{\text{S}}} + {\text{(TV}} - {\text{O}}_{{{\text{2Uptake}}}} + {\text{CO}}_{{{\text{2Produce}}}} {\text{)}} + {\text{(30/RR)}}}} $$
(5′)
$$ {\text{F}}^{\prime }_{{{\text{VB}}}} {\text{O}}_{{\text{2}}} {\text{ = }}\frac{{{\text{(}}V_{{{\text{Expand}}}} + {\dot{\text{V}}}_{{{\text{FG}}}} \times E_{{\text{S}}} {\text{)}} \times {\text{F}}_{{\text{I}}} {\text{O}}_{{\text{2}}} + {\text{(TV}} \times {\text{F}}_{{\text{I}}} {\text{O}}_{{\text{2}}} - {\text{O}}_{{{\text{2Uptake}}}} {\text{)}} + {\text{(30/RR)}} \times {\text{0}}{\text{.21}}}} {{V_{{{\text{Expand}}}} + {\dot{\text{V}}}_{{{\text{FG}}}} \times E_{{\text{S}}} + {\text{(TV}} - {\text{O}}_{{{\text{2Uptake}}}} {\text{)}} + {\text{(30/RR)}}}} $$
(6′)
Solving Eq. (2), (6′), and (7) gives: \( {\text{O}}_{{{\text{2Uptake}}}} = \frac{{{\text{A}} + {\text{B}} + {\text{C}}}} {{{\text{D}} + {\text{E}} - {\text{F}}}} \), in which A, B, D, E, and F are the same as in Eq. (8), and C is the corrected term in Eq. (9).
Of course the volume of the entrained air is much smaller than that of the other three flushing gases, and its effect might be simply omitted. However, the effect of the entrained air would be appreciable when the fresh gas flow approaches \( {\dot{\text{V}}}{\text{O}}_{2} \) or in a closed system.
About this article Cite this articleChen, TH., Hsin, CH., Ko, WR. et al. The Relation Between Oxygen Consumption and the Equilibrated Inspired Oxygen Fraction in an Anesthetic Circle Breathing System: A Mathematic Formulation & Laboratory Simulations. Ann Biomed Eng 37, 246–254 (2009). https://doi.org/10.1007/s10439-008-9593-x
Received: 25 August 2008
Accepted: 27 October 2008
Published: 08 November 2008
Issue Date: January 2009
DOI: https://doi.org/10.1007/s10439-008-9593-x
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