Closed-Loop Control of Carbon Dioxide ...

Human and Clinical Nutrition

Closed-Loop Control of Carbon Dioxide Concentration and Pressure Improves Response of Room Respiration Calorimeters1'2 *

JON K. MOON,3 FIROZ A. VOHRA, OMAR S. VALERIO JIMENEZ, MAURICE R. PUYAU AND NANCY F. BÃœTTE USDA/ARS

Children's

Nutrition Research

Baylor College of Medicine, Houston,

Center, Department

of Pediatrics,

TX 77030

INDEXING KEY WORDS:

•indirect calorimeter •oxygen consumption •carbon dioxide production •humans

'This

Respiration (indirect) calorimetry is recognized as a standard for metabolic rate measurements in humans. Individuals find room calorimeters to be comfortable for extended periods. Behavioral changes caused by the discomfort of masks and mouthpieces can be minimized. Dramatic improvements in continuous-flow gas analyzers and thermal-mass flow controllers and in corporation of digital computers have significantly improved the response of large room calorimeters. Large room calorimeters designed for fast response can achieve 95% response for intervals of 2gas and 243 24-h studies of individuals. Our sub jects included children weighing 20 kg and adults en gaged in heavy exercise. Errors for 24-h infusion meas urements (n = 23) were -0.34 ±1.24% for oxygen consumption rate and 0.11: 0.98% for carbon dioxide production rate. Calorimeter 90% response times were 2 to 6 min over a range of oxygen consumption rates from 100 to -4000 mL/min. Closed-loop control of supply and exhaust air flows provided consistent 24-h mean CO2 levels (0.39 ±0.015%) and pressures (13.2 ±4.4 Pa). Room calorimeters operated with closed-loop control can be used for accurate measurement of energy expenditure rate dynamics for a wide range of in dividuals. J. Nutr. 125: 220-228, 1995.

CLOSED CONTROL

OF RESPIRATION

In this report we describe four room respiration calorimeters constructed to study the metabolic dy namics of children and adults over long periods. The reported performance required closed-loop control of air inflow and outflow rates, continuous gas sampling, rapid gas sample desiccation, data reprocessing with a centered difference algorithm to estimate gas accumu lation rate, and calibration of flow meters and gas analyzers that was traceable to international stan dards.

MATERIALS AND METHODS

221

needed from a steam generator (D200, Nortec, Ogdensburg, NY). The calorimeters were operated with closed-loop control of air inflow rate to maintain a constant room CÜ2 concentration (F£CO2). Tests began at a minimum air inflow rate of 13 L/min so that p£CO2 built up rapidly. As p£CO2approached the set-point value (usually 0.45%), air inflow rate increased. Maximum air inflow rate was 160 to 200 L/min. A pressure control loop was created between a differential pressure sensor (C-264, Setra Systems, Acton, MA) and the exhaust flow controller (0 to 140 L/min) for each room. Pressure control was usually set at 13.3 Pa (0.1 mm Hg). Thermal-mass flow controllers (740 and 840, Sierra, Monterrey, CA) were used for air inflow and exhaust flow rates. The flow controllers provided an internally linearized 0- to 5-volt output signal for mass flow rate. The published accuracy of the meters was ±2%of full scale. We calibrated the inflow con trollers every 6 mo from 7 L/min to full-scale flow at standard dry conditions of 0°Cand 101.3 kPa (760 mm Hg). A piece-wise linearization was calculated for each controller from the calibration data. Before every test the controllers were checked at 13 and 50 L/min. A linear gain and offset correction was made as needed to maintain accuracy at ±0.5% of reading. Four pairs of oxygen (paramagnetic, Oxymat 5E, Siemens, Karlsruhe, Germany) and carbon dioxide (nondispersive infrared, Ultramat 5E, Siemens) gas analyzers continuously monitored F£U2and F£CO2of the calorimeters. A fifth pair of analyzers monitored O2 and CO2 of supply air (FiO2 and FiCC^). All analyzers operated with 1% ranges (Û2: 20-21%, C02: 0-1%). We programmed the analyzers with 7-s first-order, low-pass digital filters. The filter time constant was chosen to keep the output noise level below -40 db for signal periods 2 analyzers are inherently linear. Air was sampled from the room exhaust outlet through insulated, 0.64-cm diameter stainless steel tubes. Sample flow was ~6 L/min. Sampled air from the most distant room (-15 m) reached the gas analyzers within 10 s. A perfluorosilicate membrane dryer (PD-625-48SS, Perma-Pure, Toms River, NJ) reduced the water con centration of the samples to -0.01%. Sample gas

4Abbreviations used: FgCO2 & ^£^2concentrations of CO2 and C>2, respectively, in calorimeter and exhaust air; FjCO2, FjC>2 & FjH2O concentrations of CO2, O2 and H2Û, respectively, in inlet air; AFCÜ2& AFO2, difference between exhaust and incoming CO2 and O2 concentrations, respectively.

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Calorimeter design. We constructed two large (3 x 3.9 m, 34 m3) and two small (2.7 x 3 m, 19 m3) room calorimeters. The shells were made of aluminumfaced polyurethane foam panels (Conviron, Winnipeg, Manitoba, Canada). Air-handling equipment and sensors were hung above a drop ceiling 2.3 m high. Hardwood floors were installed on a 3.8-cm base. The rooms were equipped with a bed, table, video and stereo equipment, a lavatory and flush commode. The doors swung outward and could easily be opened by the subject from the inside. A 1.2 x 0.3-m window in each door allowed an operator to see most of the room interior. The large rooms had a window of 0.9 x 1.2 m facing a building exterior window. A pair of air-lock passthroughs were in stalled to exchange meals and materials with the subject. The lower passthroughs were refrigerated for urine samples. A Doppler microwave sensor (D9/50, Microwave Sensors, Ann Arbor, MI), modified to increase reso lution, was installed in each chamber to record ac tivity. Each room contained photo-electric and ionization smoke detectors. An automatic sprinkler protected the calorimeter laboratory and the rooms from fire. Temperature and humidity in the calorimeter were maintained with a microprocessor controller (CMP 3244, Conviron). A direct-drive blower recirculated air through an evaporator coil, electric heaters and into a distribution box with a bypass damper. The damper mixed air in the ceiling space and could be adjusted to reduce air velocity from the ceiling diffusers if the subject was uncomfortable. A propor tioning valve adjusted the flow of liquid and hot gaseous freon to the evaporator in the room every few seconds. Dry air (0.1% FiH2O)4 supplied to the rooms kept the humidity in a comfortable range (30 to 40% relative humidity) when subjects were at rest. Excess water condensed during heavy exercise was removed from the room by an added heat load from the electric heaters. A deep trap (15 cm) and manual trap primer prevented air from leaking through the condensate drain. Water vapor was added to the rooms when

CALORIMETERS

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222

V02 = -[WFiC-2 - FE02-H) + VC-FE02}

(1)

VCC-2 = WFiCC-2 - FEC02-H) + VC-FEC02

(2)

where Vc = volume of calorimeter and V\ = air flow rate. Better estimates of VO2 and VCO2 were produced by reprocessing the data after the tests were complete to accommodate interruptions and to use estimates of accumulation rates of O2 and CO2 in the room (d[FEO2]/dt and d[FECO2]/dt) that could not be calculated at the time that the data were collected (Equations 3 and 4, where A is a sample index of 1 to 3 min). d(FE02)/dt = (FECV* - FE02-*)/2.ic

(3)

d(FECO2)/dt = (FECO2+i - FECO2-k)/2-A

(4)

The computer activated alarms if FECO2 exceeded 0.65%, FEO2 dropped to 20.1% or air inflow rate dropped below 10 L/min. Other alarms were set for room pressure, FiO2, FiCO2, heart rate and dryer per formance. Standards laboratory. A standards laboratory was constructed with the calorimeters to calibrate the flow meters, gas analyzers and other instruments. A piston prover (CalBench, Sierra) traceable to the Na tional Institute of Standards and Technology provided calibration of flow meters from 2 to 200 L/min with an accuracy of ±0.5%of reading. Two-component gas mixtures at any ratio and at total flow rates up to 5 L/ min were prepared by a computerized gas blender (Series 200, Environics, West Willington, CT) that was similar to the device described by Kwant and Oeseburg (1989). Analyte dilutions were accurate to ±0.002% by cross-calibration of the blender flows to the piston prover for each mixture. The gas blends were used to calibrate gas analyzers directly and to test the calorimeters by infusion of CO2 and N2 mix tures. Room environment and instrument evaluation. Sound levels were recorded in the center of the rooms at a height of l m with a laboratory-grade condenser microphone and amplifier (4144 and 2609, Bruel & Kjaer, Naerum, Denmark). Recirculated air flow was measured at each ceiling diffuser and summed (6461, Alnor, Skokie, IL). Temperature and air velocity were tested at the center and each corner of the rooms at heights of 0.5 and l m with a portable monitor (550e, Solomat, Stamford, CT). Temperature control provided a range of 10 to 35°Cwith an accuracy of ±0.3°C and stable to 2analyzers is inherent to Equation 1 because FEU2are calculated relative to either FjC^ or earlier measurements of FEO2. Long term drift was compensated by a daily infusion test. No nonlinearities were observed with any of the O2 analyzers. The CÛ2analyzers exhibited a maximum nonlinearity of 6.8% (as percentage of reading, mean = 2.5 ±1.8%). Linearization data entered into our com puter reduced the maximum nonlinearity for CC>2 analyzers to 1.7% (mean = 0.67 ±0.45%). Inflow controllers were calibrated at flow rates of -13, 25, 50, 75, 100, 120 and 160 L/min. Before cali bration, mean absolute error, expressed as a per centage of reading, was 0.7 ±0.7% (maximum = 3.1%). Mean post-calibration error was 0.3 ±0.2% (maximum = 0.6%). Steady-state accuracy and dynamic response. Mean volumes were 31,500 ±400 L for the large rooms (n = 13) and 18,800 ±300 L for the small rooms (n = 10). Measured volumes were not significantly different between the two large (P = 0.33) or two small rooms (P = 0.09). There was no effect of temperature, in the range 23 to 25°C,or humidity. Twenty-three infusions were performed, and the rooms were ventilated between tests. Overall mean error in VOi was -0.34 ±1.24% for the large rooms and 0.11 ±0.98% for the small rooms (Table 1). A second set of gas analyzers was used to measure FEO2and FECOi during several infusion tests. Physio logical QI consumption and CÛ2 production rates were calculated from the secondary FEU2 and FECU2 and primary air inflow rate. Paired differences be tween the primary and secondary measurements are summarized in Table 2. The similar or lower error standard deviations in Table 2 compared with Table 1 indicate that most of the variability in a test origi nated in the gas analyzers rather than the inflow controller. Room response time to step changes in infusion rate was equal to the span of the centered derivative

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Each room was subjected to continuous infusions of CC>2and N2 for 24 h to evaluate steady-state accuracy. Infusion rates of CC»2 and N2 were chosen to simulate the metabolic level of a 50-kg adult at rest (VO2 = 0.26 L/min; VCO2 = 0.22 L/min). Temper ature, pressure and humidity were the same as for the washout tests. To evaluate dynamic response of the calorimeters, the gas blender was programmed to produce simu lated rest and light exercise of a 50-kg adult (rest as above, exercise: VO2 = 0.85 L/min, VCO2 = 0.76 L/ min). Step changes were made between the two levels every 30 min for both large and small calorimeters. Human studies. To assess the performance of the air inflow and exhaust rate control systems, we ex amined FECO2 and pressure from minute-by-minute data in uninterrupted, 24-h subject records. Oxygen consumption and heart rate were examined to demon strate response to exercise in human subjects. Total daily energy expenditure and basal metabolic rates were compared with weight across a wide range of subjects as a check on both long-term (24 h) and short-term (30 min) measurements. The data were taken from several studies that used pre-adolescent and adolescent girls, pregnant and postpartum women, and adults of both sexes. All pro tocols were approved by the Baylor College of Medicine Institutional Review Board. Written consent was obtained from subjects or their parents. All the tests included morning and afternoon exercise periods. Pre-adolescent and adolescent girls (n = 81, 12 ±2 y, 48 ±15 kg) cycled on a stationary ergometer for 20 min at -50% of their maximal VOi- Pregnant and postpartum women (n = 122, 30 ±4 y, 69 ±12 kg) walked at 3.2 km/h for 13 min. Another group of adults (n = 40, 30 ±7 y, 67 ±10 kg) exercised in the morning on the bicycle and in the afternoon on the treadmill at -30, 50 and 85% of maximal VÛ2.Some subjects continued exercising to match the level of their daily workouts. Energy expenditure was calculated with the Weir nonprotein equation (Equation 6, Weir 1949).

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ET AL.

TABLE 1 Mean percentage

error and confidence intervals for O¿consumption (VO¿)and CO? production rates (VCOz) from 24-h infusion tests of NZ and COz into large (32 m3) and small (19 m3) calorimeters1 VO2

VCÛ2 interval-3.46

CalorimeterLarge

Small Alln14

9 23Error-0.22

interval-1

to 3.02 -0.53 -2.02 to 0.96 0.66 -0.34±±1.51 -2.91 to 2.23Error0.21 1.24Confidence

-0.05 ±1.36 0.11± 0.98Confidence ±0.68

'Values are means ±SDfor errors and mean ±t-SDfor confidence intervals (t is the two-tailed distribution freedom and a probability

to 1 -3-125 .13 to 3 .03,14 92 to 2.67

factor for the specified degrees of

of 0.05].

rized as a function of weight in Figure 4. Mean basal energy expenditure for all subjects was 99 ±10% of estimates calculated from equations based on age, sex, height and weight (Schofield 1985). Mean study duration for estimation of 24-h energy expenditure rates was 1438 ±20 min. Periods of sleep, exercise and meals were included. The ratio of mean 24-h to basal energy expenditure rates was 1.45 ± 0.18.

DISCUSSION Calorimeter model. Rates of oxygen consumption and carbon dioxide production were modeled with first-order differential equations (Equations 1 and 2). The first term in each equation describes steady-state conditions, the second (dynamic) term represents the rate of gas accumulation in the room. By incor porating the second term a calorimeter is considered to be operated with fast response (Brown et al. 1984, McLean and Watts 1976, Shetty et al. 1987). Optimal performance of the calorimeters is achieved only if several assumptions made in the

TABLE 2

TABLE 3

Mean percentage difference of O¡consumption (V(hi a"d ('(>2 production rate (V('O^) measurements from separate O% and 2after an initial period of low air inflow rate (Ravussin et al. 1986). Abrupt changes in air inflow rate can disturb calculations of Û2 consumption and CÜ2production rates. Manual adjustment requires that a trained operator be present to accommodate initial equilibration, exercise and reduced metabolic rates during sleep. Closed control of F£CO2maintained a nearly con stant mean FtCC^ of 0.39% for tests on subjects with total 24-h CÛ2 production of 215 to 605 L. The concentration of CÛ2 in the calorimeters remained 2consumption and CC>2 production rates. Active p£CO2control took best advantage of the 1% range of our gas analyzers by keeping the mean AFÜ2and AFCÛ2 between 0.3 and 0.5%. Without active control, either F£CO2would rise quite high

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volume of air contained in a calorimeter is given by the constant, Vc, in Equations 1 and 2. For VQ to be constant, the gas pressure in the room must be con trolled. Large variations in gas pressure can be caused by small changes in temperature or imbalances be tween air flow and exhaust rates. For example, a O.rC temperature change produces a pressure change of 34 Pa. A temperature fluctuation of O.rC/min generates a leak flow of 10 L/min in a 30 m3 calo rimeter. Earlier calorimeters required high-ventilation flow rates and low-resistance tubing to keep the room pressure close to atmospheric pressure. With an active pressure control system, we were able to seal the rooms tightly and maintain a pressure of only 13 Pa for any air inflow rate from 13 to 200 L/min. Delays. The only storage (delay) element described in Equations 1 and 2 is gas accumulation in the calorimeter. Delays in the gas sampling and meas urement system (desiccant, tubing, analyzer response) can be neglected if they are much smaller than the desired response time. Significant delays require com plicated models of Û2 consumption and CÛ2 production rates for alignment with independent events, such as heart rate. We limited delays in sam pling and analysis to 2consumption and CC>2production rates because of the speed of the calorimeter systems and because we reprocessed data with a centered difference formula (Equations 3 and 4). Accuracy. We have reported errors and error standard deviations in Ü2consumption and CÛ2 production rates (Table 1) that are similar to the performance of other room respiration calorimeters (Brown et al. 1976, Scale et al. 1991). When calculated as standard errors our results of 0.26 and 0.20% for Û2 consumption and CO?, production rates, respec tively, are similar to those of Dulloo et al. (1988). Two reports have described extremely precise respi ration calorimeters (error SD = 0.55%, Murgatroyd et al. 1987; error range = ±0.43%, Shetty et al. 1987). An uncertainty analysis of our instruments indicates the minimum theoretical range of errors for individual measurements to be 1 to 1.5%. We are not aware of any techniques that could further decrease error. Measurements in calorimeters are commonly reported as energy expenditure calculated from a linear combination of Û2 consumption and CÛ2 production rates (e.g., Equation 6). From the calcu lated 95% confidence intervals (Table 1), the error range for a single 24-h measurement of energy expen diture is ~±3%.Expected mean error for a group of measurements can be estimated from confidence in

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LITERATURE CITED Atwater, W. O. & Benedict, F. G. (1899) Metabolism of matter and energy in the human body. Bulletin 69. U.S. Department of Agriculture, Office of Experiment Stations, Washington, DC. Atwater, W. O, Woods, C. D. & Benedict, F. G. (1897) Report of preliminary investigations on the metabolism of nitrogen and carbon in the human organism with a respiration calorimeter of special construction. Bulletin 44. U.S. Department of Agriculture, Office of Experiment Stations, Washington, DC. Baker, B. B., Jr. (1974) Measuring trace impurities in air by infrared spectroscopy at 20 meters path and 10 atmospheres pressure. J. Am. Ind. Hyg. Assoc. Nov.: 735-740. Brown, D., Cole, T. J., Dauncey, M. J., Marrs, R. W. &. Murgatroyd, P. R. (1984) Analysis of gaseous exchange in open-circuit in direct calorimetry. Med. & Biol. Eng. & Comput. 22: 333-338. Brown, G. A., Bennetto, H. P., Miller, D. S., Rigby, M. & Stirling, J. L. (1976) A DIY human calorimeter for £100.Proc. Nutr. Soc. 36: ISA (abs.). Charbonnier, A., Jones, C.D.R., Schutz, Y., Murgatroyd, P. R., Whitehead, R. G., Jéquier,E. & Spinnler, G. (1990) A whole body transportable indirect calorimeter for human use in the tropics. Eur. J. Clin. Nutr. 44: 725-731. Dulloo, A. G., Ismail, M. N., Ryall, M., Mêlas,G., Geissler, C. A. &. Miller, D. S. |1988) A low-budget and easy-to-operate respirometer for measuring daily energy expenditure in man. Am. J. Clin. Nutr. 48: 1367-1374. Garby, L., Lammert, O. & Nielsen, E. (1986) Energy expenditure over 24 hours on low physical activity programmes in human subjects. Hum. Nutr. Clin. Nutr. 40C: 141-150. Jéquier,E. (1981) Long-term measurement of energy expenditure in man: direct or indirect calorimetry? Recent Adv. Obes. Res. IH: 130-135. Kwant, G. & Oeseburg, B. (1989) Gas mixing for biomedicai appli cation using mass flow controllers. Med. & Biol. Eng. & Comput. 27: 634-636. McLean, J. A. & Watts, P. R. (1976) Analytical refinements in animal calorimetry. J. Appi. Phys. 40: 827-831. Moon, J. K., Jensen, C. L. & Butte, N. F. (1993) Fast-response whole body indirect calorimeters for infants. J. Appi. Physiol. 74: 476-484. Murgatroyd, P. R., Davies, H. L. & Prentice, A. M. (1987) Intraindividual variability and measurement noise in estimates of energy expenditure by whole body indirect calorimetry. Br. J. Nutr. 58: 347-356. Prentice, A. M., Coward, W. A., Davies, H. L., Murgatroyd, P. R., Black, A. E., Goldberg, G. R., Ashford, J., Sawyer, M. & Whitehead, R. G. (1985) Unexpectedly low levels of energy expenditure in healthy women. Lancet (June 22): 1419-1422. Ravussin, E., Lillioja, S., Anderson, T. E., Christin, L. & Bogardus, C. (1986) Determinants of 24-hour energy expenditure in man. Methods and results using a respiratory chamber. J. Clin. Invest. 78: 1568-1578. Schofield, W. N. (1985) Predicting basal metabolic rate, new stan dards and review of previous work. Hum. Nutr. Clin. Nutr. 39C (Suppl. 1): 5^1. Scale, J. L., Rumpler, W. V. & Moe, P. W. (1991) Description of a direct-indirect room-sized calorimeter. Am. J. Physiol. 260 (Endocrinol. Metab. 23): E306-E320. Shetty, P. S., Sheela, M. L., Murgatroyd, P. R. &. Kurpad, A. V. (1987) An open-circuit indirect whole body calorimeter for the continuous measurement of energy expenditure of man in the tropics. Indian J. Med. Res. 85: 453-460. Weir, J. B. (1949) New methods for calculating metabolic rate with special reference to protein metabolism. J. Physiol. 109: 1-9.

APPENDIX Oxygen consumption and carbon di oxide production in respiration calorimeters can be

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during exercise or the air flow must be set so high that the mean p£CO2during rest and sleep would be near 0.1% and quite sensitive to errors (McLean and Watts 1976). Differences in mean FEO2 and FECO2 can be eliminated as potential sources of variation in calorimeter experiments by closed control of air intake and exhaust rates. Four fast-response calorimeters provided accurate measurements of metabolic rates over 24-h and during short-term exercise, rest and basal conditions in studies of children and adults. The calorimeters were constructed to perform optimally under a standard first-order model (Equations 1 and 2). Con straints in the model required good mixing, rapid gas analysis and constant pressure in the rooms. Air change periods of 1.5 and 2.7 min were provided by large blowers and diffusers while limiting noise levels to 46 db on the A-weight scale. Gas analysis was accelerated by 6 L/min sample flows, low-volume membrane desiccation and by plumbing the O2 and CO2 analyzers in parallel. Room volume was kept constant and leaks minimized by active control of exhaust flow to maintain constant room pressure of 13.3 Pa. Instrument accuracy was improved by regular cali bration and linearization to traceable standards (Na tional Institute of Standards and Technology). Active control of inflow rate provided the same mean 24-h CO2 for all subjects and optimized the CO2 levels for 1% range analyzers. Data intervals of 1 min and the use of a centered derivative estimate enabled measurement periods as short as 2 min. Overall ac curacy was ±3%for individual measurements of O2 consumption rates and energy expenditure and ±2% for CO2 production rates. Basal energy expenditures in 243 adults, adoles cents and children were 99 ±10% of the equations published by Schofield (1985). Infusion tests can simulate short-term energy expenditure rates, but do not guarantee the ability to make measurements in humans. Our measured mean 24-h energy to basal expenditure rate ratio of 1.45 ±0.18 was similar to other studies. Ravussin et al. (1986) reported a 24-h sleep ratio of 1.41 for a mixed population of adults in a room calorimeter without exercise. Healthy pregnant and postpartum women had a lower 24-h to basal metabolic rate ratio of 1.38 in a study that included exercise similar to ours (Prentice 1985). Mean 24-h to resting metabolic rate ratios were 1.38 for a protocol without exercise and 1.53 with exercise (Garby 1985). Closed-loop control of FgCOj, and pressure allowed us to accommodate a range of subjects for both long and short-term measurements of energy expenditure. Measurements of children have not been described for other room calorimeters.

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MOON ET AL.

accurately modeled with simple first-order differential equations. The derivation presented here is for calcu lation of O2 consumption (VO^}and CÛ2production rates (VCO^}in a respiration calorimeter operated in the "push," or inflow rate measured, configuration. These are exact analytic solutions to the calorimeter model given four assumptions: 1}complete mixing of the air in the chamber; 2} the mass of air in the chamber remains constant; 3) lag in the measurement system is less than the response time expected from the calorimeter; and 4) N2 (and other inert gases) is conserved in metabolic gas exchange. Equation 1 is the differential equation for mass accumulation within a control volume. d

-7-

dt

m an} dt

m Eoa

U)

If the mass of air in the calorimeter (Qç)is constant, then accumulation of gas m' can be written as the product of Qc and the fractional concentration fçj.If air in the calorimeter is also homogeneous then its composition will be the same as in exhaust air, FCJ= f^. Incorporating these assumptions into Equation 2 gives

If the net exchange of N2 (and other inert gases such as argon) within the control volume is zero, then the outflow rate, QE, can be calculated from Q¡and the measured gas fractions. Water vapor can be neglected if all gases are dried before analysis. QE = Qr

i1 - FSÌ

(4)

The ratio in Equation 4 is generally called the "Haldane" factor and is abbreviated as "H." H esti mates the unmeasured d(Q£)/dtfrom d(Qi)/dt and any net loss of gas (which occurs whenever respiration quotient * 1). Substituting Equation 4 into Equation 3 for QE gives -

i +

(5)

By convention, metabolic gas exchange is written as volume flow rather than mass flow, net oxygen con sumption is a positive value and derivatives are presented in dot notation. The conversion of mass flows to volume is achieved by multiplying through by a constant. No corrections for pressure, temper ature or humidity are required for mass flow meters. Chamber volume is determined empirically and ad justed for changes in temperature or pressure if necessary. V02 - -[V1(FI02

VC02

- FE02-H)

+ VC-FE02]

- FEC02-H)

(6) (7)

Equations 6 and 7 are identical to the Equations numbered 1 and 2 in the text.

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In Equation 1, m1 are the masses of O2, CO2 or other gases, dQ/dt are mass flow rates into the control volume (I = inflow, E = exhaust, S = subject respiratory exchange). The ratio mVErn* represents the fractional concentration of the gas species 'i' in the flow and can be written as F1.Rearranging (1) to solve for the subject's respiratory exchange gives Equation 2.

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