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Pain Medicine  |   June 2004
Measurement of Oxygen Uptake and Carbon Dioxide Elimination Using the Bymixer: Validation in a Metabolic Lung Simulator
Author Affiliations & Notes
  • Abraham Rosenbaum, M.D.
    *
  • Christopher Kirby, B.Sc.
  • Peter H. Breen, M.D., F.R.C.P.C.
  • * Postgraduate Researcher, Department of Anesthesiology, University of California–Irvine. Currently on leave from the Department of Anesthesiology, The Technion-Israel Institute of Technology, Haifa, Israel. † Staff Research Associate, ‡ Associate Professor and Chair, Department of Anesthesiology, University of California-Irvine.
Article Information
Pain Medicine
Pain Medicine   |   June 2004
Measurement of Oxygen Uptake and Carbon Dioxide Elimination Using the Bymixer: Validation in a Metabolic Lung Simulator
Anesthesiology 6 2004, Vol.100, 1427-1437. doi:
Anesthesiology 6 2004, Vol.100, 1427-1437. doi:
INDIRECT calorimetry, the measurement of airway carbon dioxide elimination (V̇CO2), airway oxygen uptake V̇O2), and the respiratory quotient (RQ =V̇CO2/V̇O2), is used for cardiopulmonary exercise testing 1 and the determination of noninvasive metabolic gas exchange in the intensive care unit. 2,3 Indirect calorimetry has a wide range of clinical applications in critical care medicine, including the assessment of metabolic expenditure (resting energy expenditure) and the titration of nutritional support. 2 In the normal condition, where carbon dioxide is absent from inspired gas, EQUATION
where V̇E is the expired ventilation and FĒCO2is the mixed expired carbon dioxide fraction. Oxygen uptake is given by:EQUATION
where I denotes inspiration. Standard indirect calorimetry methodology invokes the principle of conservation of the inert gas nitrogen during the steady state condition (Haldane transformation),4,5 where V̇I·FIN2=V̇E·FĒ2. Substitution into equation 2yields: EQUATION
Accordingly, V̇CO2and V̇O2can be determined from measurements of minute ventilation (V̇E) and mixed inspired and expired gas fractions. Hence, the Haldane transformation compensates for flow measurement inaccuracies between inspiration and expiration.
Mixed expired gas fractions are classically measured in a collection bag (Douglas bag) attached to the expiratory exhaust port of the ventilator, 1,6 but the apparatus is bulky, and the procedure is time consuming and cannot be quickly repeated. In critical care medicine, commercial metabolic monitors 4 attach directly onto the exhaust gas port of the ventilator (e.g.  , Datex Deltatrac II Metabolic Monitor; Datex Instrumentarium, Helsinki, Finland). 7,8 
We have developed a new clinical bymixer 9 (fig. 1), an inline, compact, disposable mixing device that is interposed in the expiratory and inspiratory limbs of the ventilator circuit. The bymixer bypasses a constant fraction of gas flow through a mixing arm. A gas monitor continuously samples gas from the bymixer to measure mixed gas fractions. Accordingly, the clinical bymixer allows the determination of indirect calorimetry whenever basic expired flow and gas monitoring measurements are in use for the patient, 10 without the need for expensive, dedicated, and complex equipment. Furthermore, in contrast to the gas collection bag or metabolic monitor, the bymixer is also able to measure gas fractions in the inspired limb of the ventilation circuit. Thus, the bymixer can measure mixed gas concentrations in both limbs of the anesthesia circle circuit. Several authors 4,11 have indicated the need for an inspiratory limb bymixer because of an unstable inspired oxygen fraction, especially in a semiclosed system with low input of fresh gas flow. Despite the fact we used an open-circuit ventilator in this study, we decided to use an inspiratory limb bymixer to eliminate any chance of error originating from unstable fractional inspired oxygen (FIO2) and to validate its use in the V̇O2measurement.
Fig. 1. New clinical bymixer. 9 The resistor determines the constant fraction of total flow that bypasses through the mixing chamber (V̇BYPASS). The volume of the mixing chamber (VBYPASS) can be adjusted by changing the length of corrugated tube. The mixing chamber tube is coiled (not shown) to reduce total length of the bymixer. A sidestream gas analysis monitor aspirates flow-averaged (mixed) gas from the sampling port. The time constant or responsiveness of the bymixer to a change in input gas oncentration is given by τ (= VBYPASS/V̇BYPASS). Hence, decreasing VBYPASSimproves bymixer response but with potential for incomplete gas mixing. In this study, the volume of the mixing arm was 200 ml.
Fig. 1. New clinical bymixer. 9The resistor determines the constant fraction of total flow that bypasses through the mixing chamber (V̇BYPASS). The volume of the mixing chamber (VBYPASS) can be adjusted by changing the length of corrugated tube. The mixing chamber tube is coiled (not shown) to reduce total length of the bymixer. A sidestream gas analysis monitor aspirates flow-averaged (mixed) gas from the sampling port. The time constant or responsiveness of the bymixer to a change in input gas oncentration is given by τ (= VBYPASS/V̇BYPASS). Hence, decreasing VBYPASSimproves bymixer response but with potential for incomplete gas mixing. In this study, the volume of the mixing arm was 200 ml.
Fig. 1. New clinical bymixer. 9 The resistor determines the constant fraction of total flow that bypasses through the mixing chamber (V̇BYPASS). The volume of the mixing chamber (VBYPASS) can be adjusted by changing the length of corrugated tube. The mixing chamber tube is coiled (not shown) to reduce total length of the bymixer. A sidestream gas analysis monitor aspirates flow-averaged (mixed) gas from the sampling port. The time constant or responsiveness of the bymixer to a change in input gas oncentration is given by τ (= VBYPASS/V̇BYPASS). Hence, decreasing VBYPASSimproves bymixer response but with potential for incomplete gas mixing. In this study, the volume of the mixing arm was 200 ml.
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In this study, we tested how the new clinical bymixer, along with a standard clinical flowmeter and gas monitor, can measure V̇CO2and V̇O2. We invoked a specially designed metabolic lung simulator (fig. 2), which was an extension from previous work. 12 Complete combustion of metered ethanol provided accurate reference carbon dioxide production and oxygen consumption. A rapid response airway sensor of relative humidity (RH) and temperature (T) 13 was required and used to convert gas volumes to standard temperature and pressure, dry (STPD) condition.
Fig. 2. Metabolic lung simulator. The mechanical lung was connected to the rigid wall metabolic chamber through a circular circuit. An occlusive roller pump drove gas flow through the circuit at 5 l/min. A second roller pump (not shown) helped to return gas from the metabolic chamber to the mechanical lung. This dual-pump design protected the metabolic chamber from ventilatory pressure fluctuation to ensure stable alcohol combustion. A gauge sensed pressure in the metabolic chamber to facilitate flow equilibration of the two pumps. A precision syringe pump delivered an adjustable, metered flow of ethanol to the burner assembly inside the metabolic chamber. The metabolic chamber was maintained at constant temperature in a cooling water bath. The open circuit ventilator inspired and expired limbs joined at the Y junction. A bymixer was interposed in each limb of the ventilation circuit. In order, the Y junction was connected to the pneumotachometer adapter, the humidity and temperature sensor, and the mechanical lung. The ventilator is depicted during inspiration.
Fig. 2. Metabolic lung simulator. The mechanical lung was connected to the rigid wall metabolic chamber through a circular circuit. An occlusive roller pump drove gas flow through the circuit at 5 l/min. A second roller pump (not shown) helped to return gas from the metabolic chamber to the mechanical lung. This dual-pump design protected the metabolic chamber from ventilatory pressure fluctuation to ensure stable alcohol combustion. A gauge sensed pressure in the metabolic chamber to facilitate flow equilibration of the two pumps. A precision syringe pump delivered an adjustable, metered flow of ethanol to the burner assembly inside the metabolic chamber. The metabolic chamber was maintained at constant temperature in a cooling water bath. The open circuit ventilator inspired and expired limbs joined at the Y junction. A bymixer was interposed in each limb of the ventilation circuit. In order, the Y junction was connected to the pneumotachometer adapter, the humidity and temperature sensor, and the mechanical lung. The ventilator is depicted during inspiration.
Fig. 2. Metabolic lung simulator. The mechanical lung was connected to the rigid wall metabolic chamber through a circular circuit. An occlusive roller pump drove gas flow through the circuit at 5 l/min. A second roller pump (not shown) helped to return gas from the metabolic chamber to the mechanical lung. This dual-pump design protected the metabolic chamber from ventilatory pressure fluctuation to ensure stable alcohol combustion. A gauge sensed pressure in the metabolic chamber to facilitate flow equilibration of the two pumps. A precision syringe pump delivered an adjustable, metered flow of ethanol to the burner assembly inside the metabolic chamber. The metabolic chamber was maintained at constant temperature in a cooling water bath. The open circuit ventilator inspired and expired limbs joined at the Y junction. A bymixer was interposed in each limb of the ventilation circuit. In order, the Y junction was connected to the pneumotachometer adapter, the humidity and temperature sensor, and the mechanical lung. The ventilator is depicted during inspiration.
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Materials and Methods
New Clinical Bymixer
To measure mixed gas fractions, 14 we developed a mechanical clinical bymixer 9 (patent pending, applied for by Peter H. Breen) (fig. 1), which by  passes a constant portion of the main flow through the mix  ing chamber. The main flow channel was constructed of a 24-cm length of standard ¾-in polyvinyl chloride pipe (22 mm ID). The bypass channel was composed of a length of expandable–collapsible pediatric anesthesia circuit tubing (15 mm ID, Expandoflex; Cleveland Tubing Inc., Cleveland, TN). The adjustable tubing was connected, in series, to a sampling port adapter (Datex-Engstrom Division, Instrumentarium Corp., Helsinki, Finland), a flow resistor, and a 12-cm length of standard ¾-in polyvinyl chloride tubing. The flow resistor was constructed by placing a plastic cap with a 4-mm hole (NAS-820-10; Niagra Plastics, Erie, PA) inside a connector (Multi Adapter; Hudson RCI, Temecula, CA; 15 mm ID, 22 mm OD). In this study, the mixing arm length was set to 121 cm, which generated a mixing chamber volume (measured up to the sampling port) of 200 ml. The volume of the bypass channel from the sampling port to the downstream Y connector was 53 ml. The main flow and bypass flow channels were connected at each end by identical Y connectors (supplied with standard anesthesia circle circuits). With coiling of the mixing arm, the bymixer length was 37 cm. The average width was 8 cm, and the weight was 149 g. The ratio of bypass flow to total flow was 1:9. 9 
Experimental Setup of Metabolic Lung Simulator
Experimental setup of the metabolic lung simulator is shown in figure 2. The mechanical lung (Dual Adult TTL, model 1600; Michigan Instruments, Inc., Grand Rapids, MI) was connected by a circular circuit to an airtight, rigid chamber (5.7 l pressure cooker). Both the pressure-relief valve and the emergency valve of the cooker were sealed. The pressure cooker was glued to the bottom of a large, flat, open container. Tap water constantly flowed through a port into this container and flowed out of a second port into a sink drain, forming a constant temperature water jacket around the pressure cooker. An occlusive roller pump (15-mm-ID tubing; Precision Blood Pump; COBE Perfusion System, Lakewood, CO) generated constant gas flow (5 l/min) between the metabolic chamber and the lung simulator. A second roller pump (not shown) helped to return gas from the metabolic chamber to the mechanical lung. This dual-pump design protected the metabolic chamber from ventilatory pressure fluctuation to ensure stable alcohol combustion. A pressure gauge, connected to the metabolic chamber, facilitated flow equilibration between the two pumps.
The inspired and expired limbs of the open circuit ventilator (Servo Ventilator 900C; Siemens AB, Solna, Sweden) joined at the Y junction. A bymixer was interposed in each limb of the ventilation circuit. In order, the Y junction was connected to the pneumotachometer adapter (Capnomac Ultima; Datex Medical Instruments, Instrumentarium Corp.), the humidity and temperature sensor, and a 50-cm tube leading to the mechanical lung. These latter three components composed the anatomical dead space of the mechanical lung, determined by the Bohr calculation to be 150 ml. The end-expiratory volume of the mechanical lung was 920 ml. The ventilator is depicted during inspiration. The lung simulator was ventilated with 60% dry oxygen in nitrogen. At each level of alcohol combustion rate (and, hence, resultant carbon dioxide production and oxygen consumption), tidal volume (200 –1,080 ml) and respiratory frequency (8–12 min−1) were adjusted to maintain end-tidal partial pressure of carbon dioxide near 40 mmHg. Before each study, the entire system was pressurized to 40 cm H2O to check for leaks. A leak was signaled by descent of the mechanical lung or decrease in system pressure over 10 min or both. All leaks were sealed before proceeding with any experiment. A leak source was detected by the presence of bubbles, after spraying system components with soapy water.
Alcohol Combustion System to Generate CO2Production and O2Consumption
A 60-ml syringe (Becton Dickinson & Co., Franklin Lakes, NJ) installed in a precision syringe pump (Syringe pump A-99; Razel Scientific Instruments Inc., Stamford, CT) delivered an adjustable, metered flow of ethanol to a custom-made burner assembly inside the metabolic chamber. The alcohol was pure ethanol (100% Gold Shield Alcohol, Hayward, CA). The combustion of ethanol 15 is given by:EQUATION
so that the RQ (V̇CO2/V̇O2) is 2/3 (0.667).
For a given minute volume delivery (ml/min) of liquid ethanol (Q), EQUATION
where ρ is the density of ethanol (0.7893 g/cm3) at syringe T (25°C) and MW is the molecular weight of ethanol (46.069 g/mole).
The law of Avogadro states that 1 mole of a gas has a volume of 22,414 ml STPD. Then, EQUATION
Table 1displays the six infusion rates of alcohol into the combustion metabolic chamber and the corresponding stoichiometric generation of V̇CO2and V̇O2. The ethanol volumetric infusion rates for combustion in the metabolic chamber were chosen so that resultant V̇CO2and V̇O2would span the physiologic range of adults and children (> 12 kg body weight).
Table 1. Precise Generation of Carbon Dioxide Production (V̇CO2) and Oxygen Consumption (V̇O2) at Six Infusion Rates of Liquid Ethanol (C2H5OH) into the Combustion Metabolic Chamber
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Table 1. Precise Generation of Carbon Dioxide Production (V̇CO2) and Oxygen Consumption (V̇O2) at Six Infusion Rates of Liquid Ethanol (C2H5OH) into the Combustion Metabolic Chamber
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Airway Humidity and Temperature Sensor
To allow conversion of airway gas flows to STPD values, 5 we have developed a fast-response humidity and temperature (T) sensor 13 (U.S. Patent No. 6,014,890, owned by Peter H. Breen, January 18, 2000), which is attached to the airway opening of the mechanical lung (fig. 2). Two tiny thermometers (copper and constantan type T thermocouples, Omega Engineering, Inc., Stamford, CT) were mounted in a standard anesthesia adapter (T adapter; Datex-Ohmeda, Milwaukee, WI). A thermocouple is formed at the junction of two dissimilar metals, which generates a small voltage potential as a function of junction T. One thermocouple was constantly wetted by a special wicking system 13 (wet T). Airway gas T was measured by dry T. Humidity was measured by psychrometry, 16 where dry gas causes evaporative cooling to decrease wet T below dry T. Each thermocouple was connected to a separate isolated linearized thermocouple amplifier equipped with cold-junction compensation (model 5B47 amplifier, energized in a 5B08 eight-channel back-plane; Analog Devices, Norwood, MA). The thermocouple voltage potentials were amplified approximately 5,000 times.
Data Collection
The anesthesia monitor (Capnomac Ultima) was connected to the pneumotachometer cuvette through dual-lumen pressure tubing. The monitor sampling line was connected to the bymixer sampling port (200 ml/min) (fig. 2). Oxygen fraction (FO2) and carbon dioxide fraction were measured by paramagnetic (2.0 vol% accuracy) and infrared (0.2 vol% accuracy) technologies, respectively. The Capnomac monitor routes the gas sample through water-permeable tubing (Nafion®; Dupont Fluoroproducts, Fayetteville, NC) before entering the measurement cuvettes (carbon dioxide and oxygen). Thus, the gas samples are always measured at ambient room humidity. Performance of the water-permeable tubing was tested by sampling dry room air compared with gas over open boiling water; there was no change in measured gas fractions. Temperature in the measurement cuvettes was not considered because gas fractions do not change with T.
Calibration of the anesthesia monitor followed the manufacturer's published procedures. Airway flow was calibrated with a 700-ml precision syringe. Gas fractions were calibrated with a precision gas mixture (5.00% CO2, 54.5% O2calibration cylinder). The calibration procedure was conducted at the beginning of each experimental day, 30 min after powering up the monitor.
All signals were continuously captured (100 Hz) by an analog-to-digital acquisition PC card (DAQcard 700; National Instruments, Austin, TX) installed in a notebook computer. The digital data acquisition system was driven by a custom program (Delphi Pascal; Borland International, Scotts Valley, CA) written by our computer support specialist (David Chien, B.Sc., Department of Anesthesiology, University of California-Irvine Medical Center, Orange, California) and one author (P. H. B.).
Experimental Protocol
After initial combustion of the ethanol infusion, we waited approximately 45 min for steady state, signaled by steady values of end-tidal partial pressure of carbon dioxide (PFETCO2) and the FIO2− ETO2(end-tidal oxygen fraction) relation. Thereafter, after adjusting the rate of ethanol infusion, a new equilibrium was achieved in approximately 15 min. Then, the measurement sequence was conducted, consisting of the digital sampling of the following parameters for 1 min: airway flow, pressure, dry T, wet T, and bymixer FĒCO2,FĒO2, FICO2, and FIO2. At each ethanol infusion rate, each measurement was consecutively repeated five times, 1 min apart, for the determination of reproducibility. For each experiment, this procedure was repeated at each of the six infusion rates of ethanol (table 1). The entire experiment was repeated on 4 different days.
Data Analysis
Airway V̇CO2and V̇O2were calculated by equations 1 and 3, respectively. Because the gas monitor does not measure nitrogen concentration directly, FN2was given by:EQUATION
Exhaled ventilation was calculated by:EQUATION
where BE and EE are begin-expiration and end-expiration, respectively, of each n  th breath, dt  is the digital sampling period (1/100 Hz = 0.01 s), and f  is the respiratory frequency.
Conversion to STPD conditions proceeded by:EQUATION
where V̇ is the airway flow measured at ambient temperature, pressure, and saturation (ATPS) conditions, PTOT is the ambient barometric pressure plus airway pressure, and PH2O is the water vapor partial pressure determined by psychrometry 16 from the airway humidity and T sensor. Equation 10converts ATPS to STPD 5 by removing volume expansion due to water vapor (second term on right side of equation), by removing volume expansion due to thermal change above 0°C (third term), and by removing volume change due to a pressure variation from 760 mmHg (fourth term).
We developed a computer program to automate data analysis (Excel spreadsheet; Microsoft Corp., Redmond, WA). If required, airway flow was processed by moving average filter. The algorithms defined negative values of flow as inspiration and positive values as expiration. The computer routines also identified the begin time of the first inspiration and the end time of the last expiration. Then, expired volume was determined by the integration of expired flow with respect to time. Using simultaneous measurements of airway temperature and RH and inspired and expired gas fraction measurements from the bymixers, the program automatically converted gas volumes to STPD conditions and then calculated V̇CO2and V̇O2.
Statistical Analysis
Airway V̇CO2and V̇O2were compared to the stoichiometric values generated by ethanol combustion by least squares linear regression (slope, y-intercept, and coefficient of determination, R  2) and by the limits of agreement technique described by Bland and Altman. 17–19 Computer programs were used for data analysis (Excel spreadsheet), statistical testing (Medcalc 20; Medcalc Software, Mariakerke, Belgium), and graphical presentation (SigmaPlot 8.0; SPSS, Chicago, IL).
Results
Figure 3displays airway opening flow, pressure, FO2, and PCO2amid two typical respiratory cycles, during ventilation of the metabolic lung simulator. Relative to the flow signal, PCO2and FO2were shifted ahead in time by 1.24 and 2.84 s, respectively, to account for transport delay during sidestream sampling. Relative to the flow signal, pressure was advanced in time by 0.04 s to account for measurement delay in the monitor. The range of inspired RH was 3–8%, and inspired temperature was 22.7–23.4°T. The range of expired RH was 39–64% (inversely proportional to minute ventilation) and expired temperature was 23.0–23.5°T. Over the range of tidal volume (200 –1,080 ml), SD was nearly constant at 5.3 ml.
Fig. 3. Typical, actual data of two respiratory cycles. (Top  ) Airway opening pressure (thick line  ) and flow (thin line  ) versus  time. Negative and positive flow represent inspiration and expiration, respectively. (Bottom  ) Oxygen fraction (FO2) and partial pressure of carbon dioxide (PCO2). Note the physiologic FO2waveform (normal oxygram) and PCO2waveform (normal capnogram), generated from ventilation of the respiratory dead space and the alveolar compartment of the metabolic lung simulator (fig. 2). Relative to flow, FO2and PCO2were advanced in time (1.24 and 2.84 s, respectively) to compensate for transport delay through the sidestream sampling tube. Similarly, pressure was advanced in time by 0.04 s to compensate for the measurement delay in the monitor. For graph clarity, every tenth data point was plotted for pressure, FO2, and PCO2(every fifth point for flow).
Fig. 3. Typical, actual data of two respiratory cycles. (Top 
	) Airway opening pressure (thick line 
	) and flow (thin line 
	) versus 
	time. Negative and positive flow represent inspiration and expiration, respectively. (Bottom 
	) Oxygen fraction (FO2) and partial pressure of carbon dioxide (PCO2). Note the physiologic FO2waveform (normal oxygram) and PCO2waveform (normal capnogram), generated from ventilation of the respiratory dead space and the alveolar compartment of the metabolic lung simulator (fig. 2). Relative to flow, FO2and PCO2were advanced in time (1.24 and 2.84 s, respectively) to compensate for transport delay through the sidestream sampling tube. Similarly, pressure was advanced in time by 0.04 s to compensate for the measurement delay in the monitor. For graph clarity, every tenth data point was plotted for pressure, FO2, and PCO2(every fifth point for flow).
Fig. 3. Typical, actual data of two respiratory cycles. (Top  ) Airway opening pressure (thick line  ) and flow (thin line  ) versus  time. Negative and positive flow represent inspiration and expiration, respectively. (Bottom  ) Oxygen fraction (FO2) and partial pressure of carbon dioxide (PCO2). Note the physiologic FO2waveform (normal oxygram) and PCO2waveform (normal capnogram), generated from ventilation of the respiratory dead space and the alveolar compartment of the metabolic lung simulator (fig. 2). Relative to flow, FO2and PCO2were advanced in time (1.24 and 2.84 s, respectively) to compensate for transport delay through the sidestream sampling tube. Similarly, pressure was advanced in time by 0.04 s to compensate for the measurement delay in the monitor. For graph clarity, every tenth data point was plotted for pressure, FO2, and PCO2(every fifth point for flow).
×
For each experiment, figure 4displays the linear regression of the airway measurements of V̇CO2(open circles and dotted lines) and V̇O2(solid circles and lines) versus  the stoichiometric values generated by metered ethanol combustion. Each point was the average of five consecutive replicate measurements conducted 1 min apart. When all data points were analyzed together by linear regression, for V̇CO2, the slope was 0.984, the y-intercept was 2.03, and R  2was 0.999. For V̇O2, the slope was 1.00, the y-intercept was 1.31, and R  2was 0.998. Therefore, the correlation between airway and stoichiometric values for both V̇CO2and V̇O2were excellent in all experiments.
Fig. 4. Linear regression of airway measurements of carbon dioxide elimination (V̇CO2; open circles  and dotted lines  ) and oxygen uptake (V̇O2; solid circles  and lines  ) versus  the stoichiometric values generated by metered ethanol combustion. Five consecutive replicate measurements are shown at each constant ethanol combustion level. Each panel was a separate experiment. b =y  intercept; m = slope; R  2= coefficient of determination.
Fig. 4. Linear regression of airway measurements of carbon dioxide elimination (V̇CO2; open circles 
	and dotted lines 
	) and oxygen uptake (V̇O2; solid circles 
	and lines 
	) versus 
	the stoichiometric values generated by metered ethanol combustion. Five consecutive replicate measurements are shown at each constant ethanol combustion level. Each panel was a separate experiment. b =y 
	intercept; m = slope; R  2= coefficient of determination.
Fig. 4. Linear regression of airway measurements of carbon dioxide elimination (V̇CO2; open circles  and dotted lines  ) and oxygen uptake (V̇O2; solid circles  and lines  ) versus  the stoichiometric values generated by metered ethanol combustion. Five consecutive replicate measurements are shown at each constant ethanol combustion level. Each panel was a separate experiment. b =y  intercept; m = slope; R  2= coefficient of determination.
×
The limits of agreement (LOA) analysis 17,19 (fig. 5) demonstrated good agreement between the airway measured values and the stoichiometric values generated by ethanol combustion. The LOA (mean ± 1.96 SD) for V̇CO2were −0.76 ± 8.68 ml/min, where 95% of the points (19 of 20 trials) were bounded by those limits (fig. 5, top panel, open symbols). However, as average V̇CO2increased along the x-axis, the scatter of the differences around the mean increased along the y-axis. Thus, the LOA poorly reflected the accuracy of the smaller values of V̇CO2. In a similar analysis for V̇O2(fig. 5, bottom panel, closed symbols), the LOA were 2.85 ± 14.73 ml/min. As the average value of V̇O2increased along the x-axis, there was an increase in the scatter of differences around the mean along the y-axis. Again, the LOA poorly reflected the smaller values of V̇O2.
Fig. 5. Bland-Altman limits of agreement (LOA) analysis. 18,19 (Top  ) The difference between the airway measurement of V̇CO2and the stoichiometric value was plotted against the average of both values. At each ethanol infusion level, V̇CO2was the average of five replicate consecutive measurements. The LOA (mean ± 1.96 SD) for V̇CO2were −0.8 ± 8.7 ml/min, where 95% of all points were bounded by those limits. As the average value of V̇CO2increased along the x  axis, the scatter of the differences around the mean increased along the y  axis. Thus, greater scatter at higher values levels of V̇CO2increased LOA, which then poorly reflected the accuracy of lower V̇CO2. (Bottom  ) The LOA for V̇O2were 2.9 ± 14.7 ml/min. Similar to the top panel  , as the average value of V̇O2increased along the x  axis, the scatter of the differences around the mean increased along the y  axis. Again, LOA poorly reflected the smaller values of V̇O2.
Fig. 5. Bland-Altman limits of agreement (LOA) analysis. 18,19(Top 
	) The difference between the airway measurement of V̇CO2and the stoichiometric value was plotted against the average of both values. At each ethanol infusion level, V̇CO2was the average of five replicate consecutive measurements. The LOA (mean ± 1.96 SD) for V̇CO2were −0.8 ± 8.7 ml/min, where 95% of all points were bounded by those limits. As the average value of V̇CO2increased along the x 
	axis, the scatter of the differences around the mean increased along the y 
	axis. Thus, greater scatter at higher values levels of V̇CO2increased LOA, which then poorly reflected the accuracy of lower V̇CO2. (Bottom 
	) The LOA for V̇O2were 2.9 ± 14.7 ml/min. Similar to the top panel 
	, as the average value of V̇O2increased along the x 
	axis, the scatter of the differences around the mean increased along the y 
	axis. Again, LOA poorly reflected the smaller values of V̇O2.
Fig. 5. Bland-Altman limits of agreement (LOA) analysis. 18,19 (Top  ) The difference between the airway measurement of V̇CO2and the stoichiometric value was plotted against the average of both values. At each ethanol infusion level, V̇CO2was the average of five replicate consecutive measurements. The LOA (mean ± 1.96 SD) for V̇CO2were −0.8 ± 8.7 ml/min, where 95% of all points were bounded by those limits. As the average value of V̇CO2increased along the x  axis, the scatter of the differences around the mean increased along the y  axis. Thus, greater scatter at higher values levels of V̇CO2increased LOA, which then poorly reflected the accuracy of lower V̇CO2. (Bottom  ) The LOA for V̇O2were 2.9 ± 14.7 ml/min. Similar to the top panel  , as the average value of V̇O2increased along the x  axis, the scatter of the differences around the mean increased along the y  axis. Again, LOA poorly reflected the smaller values of V̇O2.
×
To account for these increases in the spread of the differences as the average value increased, the top panel of figure 6plotted the ratio 18,20 of the airway measurement of V̇CO2to the stoichiometric value versus  the average of both values. The LOA (mean ± 1.96 SD) for V̇CO2were 1.001 ± 0.047 or, expressed as a percentage, 0.1 ± 4.7%, where 95% of all points lay within these limits. In a similar analysis for V̇O2(fig. 6, bottom panel), the LOA were 1.1 ± 5.7%.
Fig. 6. Bland-Altman limits of agreement (LOA) analysis using a ratio transformation. 17,18 (Top  ) The ratio of the airway measurement of V̇CO2to the stoichiometric value was plotted against the average of both values. At each ethanol infusion level, V̇CO2was the average of five replicate consecutive measurements. The LOA (mean ± 1.96 SD) for V̇CO2were 0.1 ± 4.7%, where 95% of all points lay within these limits. (Bottom  ) In the same analysis for V̇O2, the LOA were 1.1 ± 5.7%. Compared with figure 5, where LOA were calculated by plotting the difference between the airway measurement of V̇CO2(or V̇O2) and the stoichiometric value versus  the average of both values, the ratio plot corrected for the greater scatter of the differences at higher values of either V̇CO2or V̇O2and provided a better reflection of the accuracy of the data.
Fig. 6. Bland-Altman limits of agreement (LOA) analysis using a ratio transformation. 17,18(Top 
	) The ratio of the airway measurement of V̇CO2to the stoichiometric value was plotted against the average of both values. At each ethanol infusion level, V̇CO2was the average of five replicate consecutive measurements. The LOA (mean ± 1.96 SD) for V̇CO2were 0.1 ± 4.7%, where 95% of all points lay within these limits. (Bottom 
	) In the same analysis for V̇O2, the LOA were 1.1 ± 5.7%. Compared with figure 5, where LOA were calculated by plotting the difference between the airway measurement of V̇CO2(or V̇O2) and the stoichiometric value versus 
	the average of both values, the ratio plot corrected for the greater scatter of the differences at higher values of either V̇CO2or V̇O2and provided a better reflection of the accuracy of the data.
Fig. 6. Bland-Altman limits of agreement (LOA) analysis using a ratio transformation. 17,18 (Top  ) The ratio of the airway measurement of V̇CO2to the stoichiometric value was plotted against the average of both values. At each ethanol infusion level, V̇CO2was the average of five replicate consecutive measurements. The LOA (mean ± 1.96 SD) for V̇CO2were 0.1 ± 4.7%, where 95% of all points lay within these limits. (Bottom  ) In the same analysis for V̇O2, the LOA were 1.1 ± 5.7%. Compared with figure 5, where LOA were calculated by plotting the difference between the airway measurement of V̇CO2(or V̇O2) and the stoichiometric value versus  the average of both values, the ratio plot corrected for the greater scatter of the differences at higher values of either V̇CO2or V̇O2and provided a better reflection of the accuracy of the data.
×
The average (± SD) percent error for airway V̇CO2(compared with the stoichiometric value) was 0.1 ± 2.4% (table 2). The average (± SD) percent error for airway V̇O2was 1.1 ± 2.9%. The average RQ was 0.660 ± 0.013. If inspired and expired gas flows were not converted to STPD conditions, the average percent error (mean ± SD) in airway measurements of V̇CO2and V̇O2significantly increased (6.1 ± 5.1 and 6.8 ± 6.9%, respectively). The coefficient of variation between the consecutive measurements was 3.3% for the measurement of V̇O2and 3.2% for the measurement of V̇CO2, which supports good reproducibility (precision) of the measurements.
Table 2. Measurements of Airway Carbon Dioxide Elimination (V̇CO2) and Oxygen Uptake (V̇O2), Using Exhaled Flow and Bymixer Gas Fractions, Compared to the Stoichiometric Reference Values of V̇CO2and V̇O2, Generated by Six Infusion Rates of Ethanol into the Combustion Metabolic Chamber
Image not available
Table 2. Measurements of Airway Carbon Dioxide Elimination (V̇CO2) and Oxygen Uptake (V̇O2), Using Exhaled Flow and Bymixer Gas Fractions, Compared to the Stoichiometric Reference Values of V̇CO2and V̇O2, Generated by Six Infusion Rates of Ethanol into the Combustion Metabolic Chamber
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Discussion
This study demonstrates for the first time that the bymixer can measure mixed expired gas fractions in an open ventilatory circuit to generate, along with a measurement of exhaled ventilation, accurate determinations of airway V̇CO2and V̇O2. Compared with the reference standard values in the metabolic lung simulator (combustion of metered ethanol), the average (± SD) percent error of V̇CO2was 0.1 ± 2.4%, and the percent error of V̇O2was 1.1 ± 2.9%. Inspection of the linear regression analysis (fig. 4) demonstrates excellent correlation of airway V̇CO2and V̇O2versus  the stoichiometric values. Similarly, the LOA analysis put forth by Bland-Altman 17,19 (figs. 5 and 6) demonstrated excellent agreement between the airway and stoichiometric values (especially when the ratios plot, fig. 6, accounted for the increase in differences as the average value of V̇CO2or V̇O2increased) and is considered acceptable for clinical measurements.
In particular, note the precise determinations of the respiratory quotient, RQ (0.660 ± 0.013). RQ is a sensitive parameter because it is the ratio of two airway measurements (V̇CO2/V̇O2). This high precision of measured airway RQ presents a reliable indicator for metabolic monitoring and clinical decisions. 2 
The LOA for V̇CO2(difference between airway and stoichiometric value vs.  the mean value) were −0.76 ± 8.68 ml/min (fig. 5, top panel), which encompasses 95% of the points. However, as V̇CO2increased along the x-axis to its maximum value of approximately 300 ml/min, the difference between the airway and stoichiometric measurements progressively increased. Thus, the high values of V̇CO2increased the LOA, generating limits that poorly represented the accuracy of smaller values of V̇CO2. For example, for a given V̇CO2of 300 ml/min, the LOA place the maximum error at 9.4 ml/min below the real value (290.6 ml/min), which is a percent error of 3.1%, within the expected error range (table 2; mean ± 1.96 SD). However, for a given V̇CO2of 33.3 ml/min, the LOA place the maximum error for the measurement at 9.4 ml/min below the real value (23.9 ml/min), which is an error of 28.3%, far in excess of the expected error range.
Accordingly, to provide a more accurate reflection of the difference between the airway and stoichiometric measurements, the data were plotted as a ratio of the two values versus  the mean value (fig. 6, top panel). The LOA for the ratio plot were 0.1 ± 4.7%. Although the error limit for the larger values of V̇CO2increased slightly from 3.1 to 4.8%, the limit for the lesser values decreased significantly from 28.3% to 4.8%. These limits for V̇CO2compare well with the expected error range (table 2; mean ± 1.96 SD) and support the overall accuracy of the measurement.
A similar analysis was performed for V̇O2. For the plot of the difference of the airway and stoichiometric value versus  the mean of the two values (fig. 5, bottom panel), the LOA were 2.9 ± 14.7 ml/min. Inspection of the graph reveals that, as the values of V̇O2increased along the x-axis, the differences between the airway and stoichiometric measurements increased, which was also evident in the linear regression analysis (fig. 4, solid symbols). Thus, the LOA were increased by high values of V̇O2, with poor reflection of the accuracy of low values of V̇O2. For example, for a given V̇O2of 49.9 ml/min, the LOA place the maximum error at 17.6 ml/min above the actual value (error of 35.2%), well in excess of the expected error range (table 2). To better represent the data, the plot of the airway/stoichiometric measurement ratio versus  the average value of V̇O2(fig. 6, bottom panel) generated LOA of 1.1 ± 5.7%, for a maximum error of 6.8%, similar to the expected error range (table 2; mean ± 1.96 SD).
Although the above LOA analysis is the most accepted method to assess the accuracy of the bymixer-flow airway measurements of indirect calorimetry, additional information can be gleaned by inspection of the individual linear regression plots for each experiment (fig. 4). Undetected, tiny leaks in the metabolic lung simulator can cause small systematic effects on the slope and y-intercept of the plots of airway measurements versus  the stoichiometric values of V̇CO2and V̇O2generated by the metered combustion of ethanol.
To explore the repeatability or precision of the measurements of V̇CO2and V̇O2, at a given ethanol combustion level, we examined how five consecutive, replicate measurements agreed with one another. The raw data revealed that the variability of the measurements increased at higher values of V̇CO2or V̇O2. To account for this phenomenon, the coefficient of variation (SD divided by the mean) was used to quantify the precision of the measurement. For the measurement of V̇CO2and V̇O2, the coefficient of variations were 3.2 and 3.3%, respectively, supporting good precision of the measurements.
We chose to perform this study using a FIO2of 60% (FIN2[inspired nitrogen fraction]= 40%) because most patients in the critical care environment are ventilated with oxygen fractions at or below this level. The accuracy of our bymixer-airway flow measurements of V̇CO2and V̇O2should even be better at lower FIO2because the fraction of nitrogen increases in the respiratory gas (equation 3). Similar to commercial monitors, our indirect calorimetry system does not directly measure FN2(nitrogen fraction). Instead, FN2is calculated by subtracting the other gas fractions from unity (equation 8). If available, a mass spectrometer 21 can directly measure FN2and potentially improve accuracy of the measurements of V̇CO2and V̇O2.
Conservation of the inert gas nitrogen (Haldane transformation) allows determination of the volume difference between inspiration and expiration due to differences in inspired and expired T and humidity. 5 Classic respiratory physiology emphasizes that steady state (including stable inspired gas concentration and lung end-expired volume) is mandatory for the nitrogen conservation principle. 22 Values of ventilation, gas circulation between the metabolic chamber and the mechanical lung, and ethanol combustion in the metabolic chamber must also be in steady state to allow comparisons of indirect calorimetry versus  values of V̇O2and V̇CO2generated by the metabolic chamber. We took care in the experiments to ensure equilibrium before conducting the measurement sequences. A limitation of the Haldane transformation in the anesthesia environment is the inability to use inspired nitrous oxide. The Haldane transformation is defined for nitrogen, an insoluble inert gas, where nitrogen balance during steady state can be harnessed to express inspired volume in terms of nitrogen fractions and expired volume (equations 2 and 3). For these purposes, nitrous oxide is too soluble in the body, rarely reaches true equilibrium, and cannot be used in the Haldane transformation.
In this study, the bymixer mixing chamber volume (fig. 1) was set to 200 ml, which generated a bymixer response of approximately 90 s. 9 For faster response, the mixing chamber volume could be decreased to 100 ml, which would allow bymixer measurements to update every 30 s. The adjustment of mixing chamber volume can proceed during actual clinical ventilation without disconnection of any circuit component. The bymixer added only negligible resistance to gas flow because the internal diameter of the main flow channel was similar to standard ventilation circuit tubes. 9 The resistor in the bypass flow tube resulted in a bypass:total flow ratio of approximately 1:9. However, because of the behavior of parallel resistors (1/RBYMIXER= 1/RMAIN+1/RBYPASS), the bypass flow actually slightly reduced the total resistance of the bymixer below the value of the main flow channel.
The metabolic lung simulator added warmth and water vapor to exhaled airway gas flow. If gas flow was not corrected to the STPD condition, the error of V̇CO2and V̇O2, compared with the reference standard of alcohol combustion, significantly increased. That ventilated patients have higher exhaled gas temperature and RH (compared to the metabolic lung simulator) makes the correction of V̇O2and V̇CO2to STPD conditions even more important. We have developed a fast-response airway sensor of humidity and temperature, 13 suitable for the clinical ventilation, which provided continuous airway opening measurements of T and RH to allow STPD correction of gas flow.
Development of an accurate and stable metabolic lung simulator required considerable effort. This bench apparatus was an absolute requirement to perform the validation of the bymixer-airway flow measurements of V̇CO2, V̇O2, and RQ for several reasons. First, there are no available, accurate reference standard measurements of V̇CO2and V̇O2in critical care medicine or during anesthesia care. Second, in patients, it is difficult to both maintain and confirm presence of steady state, which is mandatory for validation data collections. Third, the metabolic lung simulator can quickly and accurately generate a wide range of V̇CO2and V̇O2, which would be impossible in patient studies. The mechanical lung closely simulates the resistance, compliance, and dead space characteristics of the human respiratory system. Figure 3depicts normal airway opening flow and pressure waveforms (top panel) during mechanical ventilation of the metabolic lung simulator, generating a physiologic oxygram and capnogram. Presence of anatomical dead space was mandatory; otherwise, the alveolar gas fractions would have been similar to the values in the expired limb of the ventilation circuit.
In conclusion, the new clinical bymixer allows measurements of indirect calorimetry (V̇CO2, V̇O2, and RQ) whenever basic expired flow and gas monitoring measurements are in use for the patient, without the need for expensive, dedicated, and complex equipment. In contrast to the gas collection bag or metabolic monitor, the bymixer can also measure gas fractions in the inspired limb of the ventilation circuit, for conditions in which inspired gas fractions are not stable. Also, the bymixer offers the first opportunity, we believe, to measure mixed gas concentrations in the inspired and expired limb of the common anesthesia circle ventilation circuit, which will be the subject of a future investigation. The accuracy of the bymixer-airway flow measurements of indirect calorimetry compare favorably with the accuracy of commercial monitors. 3,7,23 
The authors thank David Chien, B.Sc. (Computer Support Specialist, Department of Anesthesiology, University of California-Irvine Medical Center, Orange, California), for assistance in the development of the metabolic lung simulator and the digital data acquisition program. The authors also thank Jeffrey C. Milliken, M.D. (Clinical Professor), W. Lane Parker, C.C.P. (Senior Perfusionist), and Berend J. Ages, C.C.P. (Perfusionist, Division of Cardio-Thoracic Surgery, University of California-Irvine Medical Center), for assistance using the precision occlusion roller pump.
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Fig. 1. New clinical bymixer. 9 The resistor determines the constant fraction of total flow that bypasses through the mixing chamber (V̇BYPASS). The volume of the mixing chamber (VBYPASS) can be adjusted by changing the length of corrugated tube. The mixing chamber tube is coiled (not shown) to reduce total length of the bymixer. A sidestream gas analysis monitor aspirates flow-averaged (mixed) gas from the sampling port. The time constant or responsiveness of the bymixer to a change in input gas oncentration is given by τ (= VBYPASS/V̇BYPASS). Hence, decreasing VBYPASSimproves bymixer response but with potential for incomplete gas mixing. In this study, the volume of the mixing arm was 200 ml.
Fig. 1. New clinical bymixer. 9The resistor determines the constant fraction of total flow that bypasses through the mixing chamber (V̇BYPASS). The volume of the mixing chamber (VBYPASS) can be adjusted by changing the length of corrugated tube. The mixing chamber tube is coiled (not shown) to reduce total length of the bymixer. A sidestream gas analysis monitor aspirates flow-averaged (mixed) gas from the sampling port. The time constant or responsiveness of the bymixer to a change in input gas oncentration is given by τ (= VBYPASS/V̇BYPASS). Hence, decreasing VBYPASSimproves bymixer response but with potential for incomplete gas mixing. In this study, the volume of the mixing arm was 200 ml.
Fig. 1. New clinical bymixer. 9 The resistor determines the constant fraction of total flow that bypasses through the mixing chamber (V̇BYPASS). The volume of the mixing chamber (VBYPASS) can be adjusted by changing the length of corrugated tube. The mixing chamber tube is coiled (not shown) to reduce total length of the bymixer. A sidestream gas analysis monitor aspirates flow-averaged (mixed) gas from the sampling port. The time constant or responsiveness of the bymixer to a change in input gas oncentration is given by τ (= VBYPASS/V̇BYPASS). Hence, decreasing VBYPASSimproves bymixer response but with potential for incomplete gas mixing. In this study, the volume of the mixing arm was 200 ml.
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Fig. 2. Metabolic lung simulator. The mechanical lung was connected to the rigid wall metabolic chamber through a circular circuit. An occlusive roller pump drove gas flow through the circuit at 5 l/min. A second roller pump (not shown) helped to return gas from the metabolic chamber to the mechanical lung. This dual-pump design protected the metabolic chamber from ventilatory pressure fluctuation to ensure stable alcohol combustion. A gauge sensed pressure in the metabolic chamber to facilitate flow equilibration of the two pumps. A precision syringe pump delivered an adjustable, metered flow of ethanol to the burner assembly inside the metabolic chamber. The metabolic chamber was maintained at constant temperature in a cooling water bath. The open circuit ventilator inspired and expired limbs joined at the Y junction. A bymixer was interposed in each limb of the ventilation circuit. In order, the Y junction was connected to the pneumotachometer adapter, the humidity and temperature sensor, and the mechanical lung. The ventilator is depicted during inspiration.
Fig. 2. Metabolic lung simulator. The mechanical lung was connected to the rigid wall metabolic chamber through a circular circuit. An occlusive roller pump drove gas flow through the circuit at 5 l/min. A second roller pump (not shown) helped to return gas from the metabolic chamber to the mechanical lung. This dual-pump design protected the metabolic chamber from ventilatory pressure fluctuation to ensure stable alcohol combustion. A gauge sensed pressure in the metabolic chamber to facilitate flow equilibration of the two pumps. A precision syringe pump delivered an adjustable, metered flow of ethanol to the burner assembly inside the metabolic chamber. The metabolic chamber was maintained at constant temperature in a cooling water bath. The open circuit ventilator inspired and expired limbs joined at the Y junction. A bymixer was interposed in each limb of the ventilation circuit. In order, the Y junction was connected to the pneumotachometer adapter, the humidity and temperature sensor, and the mechanical lung. The ventilator is depicted during inspiration.
Fig. 2. Metabolic lung simulator. The mechanical lung was connected to the rigid wall metabolic chamber through a circular circuit. An occlusive roller pump drove gas flow through the circuit at 5 l/min. A second roller pump (not shown) helped to return gas from the metabolic chamber to the mechanical lung. This dual-pump design protected the metabolic chamber from ventilatory pressure fluctuation to ensure stable alcohol combustion. A gauge sensed pressure in the metabolic chamber to facilitate flow equilibration of the two pumps. A precision syringe pump delivered an adjustable, metered flow of ethanol to the burner assembly inside the metabolic chamber. The metabolic chamber was maintained at constant temperature in a cooling water bath. The open circuit ventilator inspired and expired limbs joined at the Y junction. A bymixer was interposed in each limb of the ventilation circuit. In order, the Y junction was connected to the pneumotachometer adapter, the humidity and temperature sensor, and the mechanical lung. The ventilator is depicted during inspiration.
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Fig. 3. Typical, actual data of two respiratory cycles. (Top  ) Airway opening pressure (thick line  ) and flow (thin line  ) versus  time. Negative and positive flow represent inspiration and expiration, respectively. (Bottom  ) Oxygen fraction (FO2) and partial pressure of carbon dioxide (PCO2). Note the physiologic FO2waveform (normal oxygram) and PCO2waveform (normal capnogram), generated from ventilation of the respiratory dead space and the alveolar compartment of the metabolic lung simulator (fig. 2). Relative to flow, FO2and PCO2were advanced in time (1.24 and 2.84 s, respectively) to compensate for transport delay through the sidestream sampling tube. Similarly, pressure was advanced in time by 0.04 s to compensate for the measurement delay in the monitor. For graph clarity, every tenth data point was plotted for pressure, FO2, and PCO2(every fifth point for flow).
Fig. 3. Typical, actual data of two respiratory cycles. (Top 
	) Airway opening pressure (thick line 
	) and flow (thin line 
	) versus 
	time. Negative and positive flow represent inspiration and expiration, respectively. (Bottom 
	) Oxygen fraction (FO2) and partial pressure of carbon dioxide (PCO2). Note the physiologic FO2waveform (normal oxygram) and PCO2waveform (normal capnogram), generated from ventilation of the respiratory dead space and the alveolar compartment of the metabolic lung simulator (fig. 2). Relative to flow, FO2and PCO2were advanced in time (1.24 and 2.84 s, respectively) to compensate for transport delay through the sidestream sampling tube. Similarly, pressure was advanced in time by 0.04 s to compensate for the measurement delay in the monitor. For graph clarity, every tenth data point was plotted for pressure, FO2, and PCO2(every fifth point for flow).
Fig. 3. Typical, actual data of two respiratory cycles. (Top  ) Airway opening pressure (thick line  ) and flow (thin line  ) versus  time. Negative and positive flow represent inspiration and expiration, respectively. (Bottom  ) Oxygen fraction (FO2) and partial pressure of carbon dioxide (PCO2). Note the physiologic FO2waveform (normal oxygram) and PCO2waveform (normal capnogram), generated from ventilation of the respiratory dead space and the alveolar compartment of the metabolic lung simulator (fig. 2). Relative to flow, FO2and PCO2were advanced in time (1.24 and 2.84 s, respectively) to compensate for transport delay through the sidestream sampling tube. Similarly, pressure was advanced in time by 0.04 s to compensate for the measurement delay in the monitor. For graph clarity, every tenth data point was plotted for pressure, FO2, and PCO2(every fifth point for flow).
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Fig. 4. Linear regression of airway measurements of carbon dioxide elimination (V̇CO2; open circles  and dotted lines  ) and oxygen uptake (V̇O2; solid circles  and lines  ) versus  the stoichiometric values generated by metered ethanol combustion. Five consecutive replicate measurements are shown at each constant ethanol combustion level. Each panel was a separate experiment. b =y  intercept; m = slope; R  2= coefficient of determination.
Fig. 4. Linear regression of airway measurements of carbon dioxide elimination (V̇CO2; open circles 
	and dotted lines 
	) and oxygen uptake (V̇O2; solid circles 
	and lines 
	) versus 
	the stoichiometric values generated by metered ethanol combustion. Five consecutive replicate measurements are shown at each constant ethanol combustion level. Each panel was a separate experiment. b =y 
	intercept; m = slope; R  2= coefficient of determination.
Fig. 4. Linear regression of airway measurements of carbon dioxide elimination (V̇CO2; open circles  and dotted lines  ) and oxygen uptake (V̇O2; solid circles  and lines  ) versus  the stoichiometric values generated by metered ethanol combustion. Five consecutive replicate measurements are shown at each constant ethanol combustion level. Each panel was a separate experiment. b =y  intercept; m = slope; R  2= coefficient of determination.
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Fig. 5. Bland-Altman limits of agreement (LOA) analysis. 18,19 (Top  ) The difference between the airway measurement of V̇CO2and the stoichiometric value was plotted against the average of both values. At each ethanol infusion level, V̇CO2was the average of five replicate consecutive measurements. The LOA (mean ± 1.96 SD) for V̇CO2were −0.8 ± 8.7 ml/min, where 95% of all points were bounded by those limits. As the average value of V̇CO2increased along the x  axis, the scatter of the differences around the mean increased along the y  axis. Thus, greater scatter at higher values levels of V̇CO2increased LOA, which then poorly reflected the accuracy of lower V̇CO2. (Bottom  ) The LOA for V̇O2were 2.9 ± 14.7 ml/min. Similar to the top panel  , as the average value of V̇O2increased along the x  axis, the scatter of the differences around the mean increased along the y  axis. Again, LOA poorly reflected the smaller values of V̇O2.
Fig. 5. Bland-Altman limits of agreement (LOA) analysis. 18,19(Top 
	) The difference between the airway measurement of V̇CO2and the stoichiometric value was plotted against the average of both values. At each ethanol infusion level, V̇CO2was the average of five replicate consecutive measurements. The LOA (mean ± 1.96 SD) for V̇CO2were −0.8 ± 8.7 ml/min, where 95% of all points were bounded by those limits. As the average value of V̇CO2increased along the x 
	axis, the scatter of the differences around the mean increased along the y 
	axis. Thus, greater scatter at higher values levels of V̇CO2increased LOA, which then poorly reflected the accuracy of lower V̇CO2. (Bottom 
	) The LOA for V̇O2were 2.9 ± 14.7 ml/min. Similar to the top panel 
	, as the average value of V̇O2increased along the x 
	axis, the scatter of the differences around the mean increased along the y 
	axis. Again, LOA poorly reflected the smaller values of V̇O2.
Fig. 5. Bland-Altman limits of agreement (LOA) analysis. 18,19 (Top  ) The difference between the airway measurement of V̇CO2and the stoichiometric value was plotted against the average of both values. At each ethanol infusion level, V̇CO2was the average of five replicate consecutive measurements. The LOA (mean ± 1.96 SD) for V̇CO2were −0.8 ± 8.7 ml/min, where 95% of all points were bounded by those limits. As the average value of V̇CO2increased along the x  axis, the scatter of the differences around the mean increased along the y  axis. Thus, greater scatter at higher values levels of V̇CO2increased LOA, which then poorly reflected the accuracy of lower V̇CO2. (Bottom  ) The LOA for V̇O2were 2.9 ± 14.7 ml/min. Similar to the top panel  , as the average value of V̇O2increased along the x  axis, the scatter of the differences around the mean increased along the y  axis. Again, LOA poorly reflected the smaller values of V̇O2.
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Fig. 6. Bland-Altman limits of agreement (LOA) analysis using a ratio transformation. 17,18 (Top  ) The ratio of the airway measurement of V̇CO2to the stoichiometric value was plotted against the average of both values. At each ethanol infusion level, V̇CO2was the average of five replicate consecutive measurements. The LOA (mean ± 1.96 SD) for V̇CO2were 0.1 ± 4.7%, where 95% of all points lay within these limits. (Bottom  ) In the same analysis for V̇O2, the LOA were 1.1 ± 5.7%. Compared with figure 5, where LOA were calculated by plotting the difference between the airway measurement of V̇CO2(or V̇O2) and the stoichiometric value versus  the average of both values, the ratio plot corrected for the greater scatter of the differences at higher values of either V̇CO2or V̇O2and provided a better reflection of the accuracy of the data.
Fig. 6. Bland-Altman limits of agreement (LOA) analysis using a ratio transformation. 17,18(Top 
	) The ratio of the airway measurement of V̇CO2to the stoichiometric value was plotted against the average of both values. At each ethanol infusion level, V̇CO2was the average of five replicate consecutive measurements. The LOA (mean ± 1.96 SD) for V̇CO2were 0.1 ± 4.7%, where 95% of all points lay within these limits. (Bottom 
	) In the same analysis for V̇O2, the LOA were 1.1 ± 5.7%. Compared with figure 5, where LOA were calculated by plotting the difference between the airway measurement of V̇CO2(or V̇O2) and the stoichiometric value versus 
	the average of both values, the ratio plot corrected for the greater scatter of the differences at higher values of either V̇CO2or V̇O2and provided a better reflection of the accuracy of the data.
Fig. 6. Bland-Altman limits of agreement (LOA) analysis using a ratio transformation. 17,18 (Top  ) The ratio of the airway measurement of V̇CO2to the stoichiometric value was plotted against the average of both values. At each ethanol infusion level, V̇CO2was the average of five replicate consecutive measurements. The LOA (mean ± 1.96 SD) for V̇CO2were 0.1 ± 4.7%, where 95% of all points lay within these limits. (Bottom  ) In the same analysis for V̇O2, the LOA were 1.1 ± 5.7%. Compared with figure 5, where LOA were calculated by plotting the difference between the airway measurement of V̇CO2(or V̇O2) and the stoichiometric value versus  the average of both values, the ratio plot corrected for the greater scatter of the differences at higher values of either V̇CO2or V̇O2and provided a better reflection of the accuracy of the data.
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Table 1. Precise Generation of Carbon Dioxide Production (V̇CO2) and Oxygen Consumption (V̇O2) at Six Infusion Rates of Liquid Ethanol (C2H5OH) into the Combustion Metabolic Chamber
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Table 1. Precise Generation of Carbon Dioxide Production (V̇CO2) and Oxygen Consumption (V̇O2) at Six Infusion Rates of Liquid Ethanol (C2H5OH) into the Combustion Metabolic Chamber
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Table 2. Measurements of Airway Carbon Dioxide Elimination (V̇CO2) and Oxygen Uptake (V̇O2), Using Exhaled Flow and Bymixer Gas Fractions, Compared to the Stoichiometric Reference Values of V̇CO2and V̇O2, Generated by Six Infusion Rates of Ethanol into the Combustion Metabolic Chamber
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Table 2. Measurements of Airway Carbon Dioxide Elimination (V̇CO2) and Oxygen Uptake (V̇O2), Using Exhaled Flow and Bymixer Gas Fractions, Compared to the Stoichiometric Reference Values of V̇CO2and V̇O2, Generated by Six Infusion Rates of Ethanol into the Combustion Metabolic Chamber
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