| HOME | HELP | FEEDBACK | SUBSCRIPTIONS | ARCHIVE | SEARCH | TABLE OF CONTENTS |
|
|
|
|||||||
|
|||||||||
Vol. 83, Issue 6, 2064-2072, December 1997
Department of Human Biology, Maastricht University, 6200 MD Maastricht, The Netherlands
ABSTRACT
INTRODUCTION
METHODS
RESULTS
DISCUSSION
APPENDIX
ACKNOWLEDGEMENTS
FOOTNOTES
REFERENCES
ABSTRACT 
Schoffelen, Paul F. M., Klaas R. Westerterp, Wim H. M. Saris, and Foppe Ten Hoor. A dual-respiration chamber
system with automated calibration. J. Appl.
Physiol. 83(6): 2064-2072, 1997.
This study
characterizes respiration chambers with fully automated calibration.
The system consists of two 14-m3
pull-type chambers. Care was taken to provide a friendly environment for the subjects, with the possibility of social contact during the
experiment. Gas analysis was automated to correct for analyzer drift
and barometric pressure variations and to provide ease of use. Methods
used for checking the system's performance are described. The
gas-analysis repeatability was within 0.002%. Results of alcohol combustion (50-350 ml/min
CO2) show an accuracy of 0.5 ± 2.0 (SD) % for O2
consumption and 
0.3 ± 1.6% for
CO2 production for 2- to 24-h
experiments. It is concluded that response time is not the main factor
with respect to the smallest practical measurement interval (duration);
volume, mixing, gas-analysis accuracy, and levels of
O2 consumption and
CO2 production are at least
equally important. The smallest practical interval was 15-25 min,
as also found with most chamber systems described in the literature. We chose to standardize 0.5 h as the minimum measurement
interval.
indirect calorimetry; energy expenditure; oxygen consumption and
carbon dioxide production; measurement interval
INTRODUCTION ENERGY EXPENDITURE IN HUMANS can be determined by
direct measurement of heat loss (direct calorimetry) or by
calculation of heat production from
O2 consumption
( METHODS Subject Environment
The chambers are equipped with a deep-freeze toilet (Special Product,
Mulders) for collecting feces; urine is collected separately in
bottles. Three air locks provide passage for the exchange of food,
collection of feces and urine, and for sampling of blood. Safety
precautions include a fire alarm and extinguisher, emergency lighting,
and panic buttons. The door can be opened from both sides without
hindrance. The chambers are checked once a year for electrical safety
(S1 standard), and the climate is constantly regulated and monitored by
an automated information system. Physical activity can be performed by
using a cycle ergometer (Lode) or a treadmill (Quinton). The height of
the chamber also allows the use of a stepping platform. Activity of the
subject is measured by an analog ultrasound system (Advisor DU160).
Ventilation
O2; ml/min),
CO2 production (CO2; ml/min), and nitrogen
loss in urine. O2 and
CO2 may be determined
with a variety of methods usually involving a mouthpiece, face mask, or
ventilated hood (2, 9, 20), limiting the duration of the measurement to
a few hours. For the determination of
O2 and
CO2 during a longer time
interval (up to several days), a respiration chamber may be the method
of choice (1, 3-6, 8, 11-19). During the measurement, the
subject stays in an airtight room through which a stream of fresh air
is directed. Composition and volume of the inlet and outlet airstream
are measured. The respiration chambers described below feature a double
set of gas analyzers with continuous automated calibration and
automated data collection. This approach circumvents most problems due
to ambient variations in gas composition and pressure and due to operator errors. Independent checks of the automated calibration procedure are performed regularly by using alcohol combustion or
injection of gas with known composition. The chambers have been
operational for over 10 years and provide an easy-to-use and
labor-saving service with minimum downtime.
Fig. 1.
Layout of dual respiration chamber. 1, Television set; 2, chair; 3, sink with hot and cold running water; 4, deep-freeze toilet; 5, air
lock for blood samples; 6, cycle ergometer; 7, bed (folded down for
sleeping or sitting); 8, body-weight balance; 9, air locks, one for
food, one for feces; 10, folding chair, which may be stored under bed;
11, bed (folded up for more floor space).
[View Larger Version of this Image (31K GIF file)]
The fresh-air supply is routed directly into the air-conditioning for mixing and temperature control. The temperature variation is ±0.1°C during rest and ±0.4°C during exercise. The air leaves the chamber diagonally opposite the input at two levels. Volume and flow measurements are corrected to STPD by using data obtained from temperature (AD590, National Semiconductor), humidity (SA100c, Rotronic), and barometric pressure (4-801-1124, Bell & Howell) sensors that are calibrated on a yearly basis.
O2- and CO2-Measurement Systems
O2 is measured by using paramagnetic 0-22% oxygen analyzers (Magnos 6G, Hartmann & Braun; OA184A, Servomex), and CO2 is measured by using infrared 0-1% analyzers (Uras 3G, Hartmann & Braun). To improve the reliability of the measurement, each gas sample is analyzed in duplicate, reducing the risk of losing data because of hard-to-detect failures.Samples from the input and the output of the chamber are drawn into a
sample preparation unit by using membrane pumps (model 300, Wisa). When
a sample is not selected, the sample line is still flushed to reduce
dead time. Pressure and humidity variations are reduced through
utilization of needle valves and oil-filled overflow bubblers (constant
pressure to ambient) and by using membrane dryers (ME050-24-MFL,
Perma Pure). The membrane dryers have an enhanced drying capacity
obtained from using an outer hull with a counterflowing dry purge gas
at 50 KPa negative pressure; this provides a steady drying capacity.
The combination of fully flushed sample routes with identical delays
and a membrane-drying tube resulted in a 90% response of the
CO2 analyzers of 5 s after the
switch from N2 to calibration gas.
The system ensures that all samples are clean (1-µm filter) and are
of equal pressure (±10 Pa), temperature (±0.1°C), and
humidity (15°C dew point). The linearity error of each
CO2 analyzer was reduced by
constructing a linearization curve for each apparatus. The range of the
linearized curve is 0-0.8%; the
CO2 concentration inside the
chambers normally never exceeds 0.8%.
The difference in gas composition (dg) between incoming and outgoing
air and the ratio of dg to the difference in time
(dt) in the chamber
(derived from measurement of the outgoing air) have to be known for the
calculation of O2 and
CO2
(APPENDIX B). Air samples are
measured in sequence (10) and alternated with samples of calibration
and zero gases, thus eliminating errors because of differences in
analyzers or sample preparation. The measurement of each sample
requires 1 min. During each interval of 15 min, samples of fresh air
and zero and calibration gas are measured in addition to the 12 chamber
samples (Fig. 2). In this way, effects due
to baseline drift, barometric pressure (3, 18), and temperature
variation, factors that vary more slowly than in 15 min, are minimized.
Because of the full automatization, no operator action is required,
eliminating this source of error.
Calibration and fresh-air measurements account for 12 min
every hour. The remaining 48 min during the hour provide time for two
concentration measurements for both chambers during each of twelve
5-min intervals. O2 and
CO2 are
calculated for each 5-min interval, and the 5-min results are
integrated to 0.5-h values in the standard output file. Although it is
possible to calculate 5-min values for
O2 and
CO2, the accuracy
of these values will be low because the standard deviation (SD) in the measurement of the minute concentration changes is multiplied with the
large volume of the chamber (13). The standard procedure is the
calculation of O2 and
CO2 over 0.5 h or longer
time intervals.
The calibration gas contains 0.8% CO2-18% O2-remainder N2. The CO2 concentration of this gas can be obtained with a certified accuracy of 0.008%. The O2 concentration, however, has a certified accuracy of only 0.18%. For the O2 analysis, we therefore rely on the accuracy of the overall O2 concentration of the fresh air (4, 10, 14, 15) during a whole day, while using the 18% O2 content of the calibration gas as a stable, but at first unknown, O2 reference. The unknown O2 concentration of the calibration gas is calculated on the basis of measurement of fresh air, N2, and calibration gas O2 concentration by using mean values over the whole experiment. The calculated calibration gas O2 value is then used to determine momentary O2 concentrations during the experiment. Because the O2 concentration of the calibration gas is calculated during each experiment, monitoring the obtained calibration gas values over a 3-mo interval (lifespan of a single calibration gas bottle) provides data on the accuracy of the O2 measurement, including any drift in fresh-air O2 concentration over the 3-mo interval.
A microcomputer (Macintosh, Apple) is used to monitor the parameters
for determining O2 and
CO2. Each analyzer and
sensor has its own analog-to-digital converter (ADC;
voltage-to-frequency, VFC62, Burr-Brown) and is optically isolated from
the microcomputer, enabling optimal conversion of electrical signals by
reducing electrical noise from long cabling and earth loops.
Calibration of sensors is done in the software; the analog range of the
converters was individually chosen to handle any long-term drift.
Parameters used in the calculation of
O2 and
CO2 are temperature,
humidity, flow, barometric pressure, and a digital reading of
O2 and
CO2 concentrations in sample and
calibration gases.
On-line calculation enables continuous monitoring of the progress of
the experiment. Final calculation is done after the experiment is
completed, allowing the use of all data for calculation of calibration
constants (12), specifically the
O2 concentration in the
calibration gas bottle. The equations used in the calculation of gas
exchange are based on the assumption of
N2 conservation ["haldane" correction (3, 5, 7, 10-12,
15-17)] with incorporation of differentiated changes in the
chamber volume for the N2 equation [dFN2/dt;
determined at the outlet (3, 7, 12, 17)]. Water vapor is taken
into account (3, 10) by first calculating all flow and volumes
[including differentiated changes in the chamber volume
(dH2O/dt)]
to STPD. Energy expenditure is
calculated from O2 and
CO2 with the Weir formula
(21).
To achieve flexibility, the software for the system is modular; data acquisition is based on a graphical engineering program (Labview, National Instruments), and calculation is performed with a spreadsheet macro program (Excel, Microsoft). Additional parameters can be incorporated by using the flexibility of the software and the network capability of the computer (network-connected ADCs and serial ports). The audio capability of the computer (speech) was used to synchronize the subject's behavior to a protocol by providing an audio signal to the subject when it was time for a certain activity.
Validation
Each month, an independent check of the whole system is obtained by combusting alcohol inside the chamber or, in some instances, by injecting gas with a known composition into the chamber. The alcohol (99.8% methanol pro analyse; Merck) is combusted by using a gas burner (Fig. 3A). The burner is placed on a calibrated balance connected to a computer to measure the rate of combustion during the experiment. When alcohol is combusted, O2 is consumed and CO2 is produced, mimicking normal measurement. With the use of gas injection with CO2, N2, or a combination of both (Fig. 3B; Refs. 4, 11-14, 17, 18), the accuracy of CO2 and O2 measurement can be checked.
Calculating produced CO2 from
weight should take into account that at barometric pressure the
CO2 compressibility (3a) accounts for a 0.6% deviation between molar and volume fraction, valid for both alcohol combustion and
CO2 injection. In this context, it
should be pointed out that calibration gas certificates can therefore
be obtained on the basis of molar or volume fraction. In our setting,
all calculations were done by using volume (fractions) at
STPD.
The duration of validation experiments is 24 or 2 h; both time intervals are relevant to actual experiments.
RESULTS
During operation of the system for 10 yr, only 2 of >2,000 subjects felt isolated and finished the experiment prematurely. No safety hazards have occurred.
Ventilation
The perforated ceiling reduced the noise at ear level to 45 dbA at the lowest recirculation flow of 3,300 l/min. At the highest recirculation of 10,000 l/min, the noise increased to 54 dbA. At the lowest recirculation flow of 3,300 l/min and a flow through the chamber of 50 l/min, 99% of a 5-min continuous injection was measured within 15 min, and 63% was measured in 5 min.O2- and CO2-Measurement System
Key elements in the gas-analysis system are the sampling system and the reproducibility of the gas analyzers. The time needed to flush the sampling system after a change of sample was measured to be
5
s, leaving 55 s for stabilization {at least 10-fold; analyzer response time [reponse time to 90%
(t90) 3.5 s]} and measurement. The drying capacity of the sampling
system, particularly important for measuring
O2, showed a steady sample dew
point lower than 15°C. To check the reproducibility of the
O2 analyzers, the difference
between two analyzers was measured over the 0-18% O2 concentration range (Fig.
4) when identical gas samples were measured. The signal-to-noise levels had an SD < 0.002%
(n = 75), illustrating the
reproducibility of the O2 gas
analysis.
Validation
Alcohol-combustion experiments over the present year (n = 44) resulted in differences between "alcohol combustion" values and "chamber system" values of0.3 ± 1.6% for
CO2, 0.5 ± 2.0% for
O2 (Fig.
5) and a respiratory quotient of 0.663 ± 0.012. No difference was found between 2- and 24-h tests. The
results of calibration experiments using
CO2 injection over the past years were comparable with those found for alcohol combustion (0.6 ± 2.3%, n = 20).
The system compares the stable O2 concentration of the calibration gas with the mean 24-h fresh-air O2 concentration; the variation in these 24-h O2 concentration measurements can be determined. Maximum difference in 24-h measurements over the 3-mo lifespan of a calibration gas bottle was found to vary from 0.003 ± 0.002 to 0.006 ± 0.004% O2. This variation can be attributed to both variation in fresh air %O2 and variation in the measurement system; these factors cannot be separated. Because these variations are also both present in normal experiments, the maximum difference found is an indication of the performance and stability of the system with respect to calibration based on fresh air %O2. If calculated O2 concentration in the calibration gas was compared by using data of two O2 analyzers, the maximum difference and SD increased by 50%, showing the advantage of measuring input and output concentrations sequentially (10, 14) with one analyzer compared with measurement of input and output concentrations with separate analyzers.
Registration of energy expenditure and physical activity of a subject
is shown in Fig. 6. Energy expenditure data
are given for 0.5-h intervals. Physical activity was synchronized with
these 0.5-h intervals by using computer audio.
DISCUSSION
Subject Environment
After the creation of a friendly environment, only noise and draft due to air conditioning remain as the major factors compromising comfort. The rate of recirculation flow is therefore limited (12) and, because of its cooling effect, the room temperature is normally set a few degrees higher (3°C) than at home.
Ventilation
The recirculation flow range of ventilating the 14-m3 volume at a rate of 15-42 times per hour calculates to a mixing time constant (12) of 1.4-4.2 min, which is comparable to those calculated from the literature (4-6, 12, 14-16), ranging from 0.4 to 4 min. The result of observing 99% of a 5-min continuous injection within 15 min is slightly better than expected from the calculated 4.2-min time constant at the lowest recirculation rate. Extending the recirculation flow range will either compromise the mixing time constant (
4 min) or
the comfort of the subject. The negative pressure [pull type (5,
8, 13, 15)] ensures that airflow through leaks will only be from
outside to inside the chamber. If the room around the chamber is well
ventilated, this will have a negligible effect on the measurements. In
some settings, factors like environment (4) or control of inlet air
(11, 12) can necessitate the use of a positive pressure system. Such a
system [push type (4, 6, 11, 12, 14, 16-18)] requires
better sealing (12, 16) because it cannot be guaranteed that leaked air
was already completely mixed and sampled.
Wherever possible, care was taken to avoid confined spaces, which would act as buffer volumes. A confined space behaves as a volume in which gas concentrations will slowly follow the concentration in the chamber. If a subject's expired air is directed to a confined space, the mixing time will increase. For this reason, no closed cabinets were provided inside the chambers and the cabinets around equipment like the deep-freeze toilets and television sets were perforated.
O2- and CO2-Measurement System
The automated system operates continuously, and thus the system is calibrated 96 times/24 h. The SD < 0.004% in the daily calculated O2 concentration of the calibration gas over 3 mo shows the capability of the system for handling environmental variation and drift. As far as we know from the literature, this frequent automated calibration is a unique feature of the system, making it easy to use; to start an experiment, one has only to close the door of the chamber. Multiplexing samples in time on one analyzer (10, 14), rather than using multiple analyzers, combined with interleaved (frequent) calibration, eliminates the need for temperature and pressure correction (3, 18) when momentary concentration values are calculated, because the time of calibration is almost identical to the measurement time (15 min).
Validation
The results of the alcohol-combustion tests were0.3 ± 1.6% for CO2. One
factor determining the accuracy is the
CO2 concentration in the
calibration gas, which in our case was determined to be 0.8 ± 0.008%. Elimination of this possible source of deviation would require
a certificate with an accuracy of 0.8 ± 0.0008% for the
CO2 component and possibly further
improved linearization of the analyzers. However, neither was
available.
The 0.5 ± 2.0% result for O2 is only achievable with analyzers that perform well within the factory specification and requires meticulous sample preparation and stable laboratory conditions. The reason for this is the ~20% O2 background in all measured air because every type of analyzer has to deal with a 20% background in relation to a 1% measurement span, requiring a 21% physical measurement range for a 1% differential physiological range. This is easily understood for mass-spectrometer (17) and paramagnetic optical analyzers that measure one gas stream; they can only be differential in time (10, 14). However, it is also valid for dual-gas stream differential analyzers because these use dual compartments (magnetic wind principle) for comparison, and in each of these compartments the 20% background again largely determines the signal-to-noise ratio. Because the result of subtracting the background in differential analyzers is instantaneous, it is often erroneously assumed that the 20% background is eliminated from the physical measurement.
Alcohol combustion is normally used for checking experiments because it
tests O2 and
CO2 simultaneously and
experiments are easy to perform. However, for troubleshooting,
CO2 and
N2 infusion is the method of
choice because it is independent of a chemical reaction. The slightly
larger error margin in the
CO2-infusion experiments (over
several years) compared with the regular alcohol-combustion experiments
(over 1 yr) is attributable to the fact that gas infusion was mostly
used for troubleshooting when a problem was detected.
Response Time and Measurement Interval
In the literature, two types of system responses are given. One is actually the time constant (therefore, not referred to as response time in this study) of the mixing process (8, 12, 15), and the other is the (90-99%) response time of the complete system to a change in energy expenditure (4, 6, 11, 12, 14). The response time incorporates the mixing time constant (because all air should first be well mixed) and will therefore be larger than the mixing time constant. The response time is only important, in part, when measurement protocol is decided on, i.e., rate of change of energy expenditure to be measured. The volume of the chamber, the rate of gas flow through the chamber, and the accuracy of the gas measurement determine the interval (duration) needed to reach 95% of accuracy. Normally, this interval is at least 1 h, as can be seen from calibration experiments (Table 1, Refs. 4, 6, 8, 11, 12, 15-17, 19), even if the response time is much smaller (4, 6, 11, 12, 14, 15, 17). Furthermore, it is not proven that subjects will behave in the same way as the testing methods, specifically with respect to the mixing and leaking (push-type chamber) of the subject's expired air, because the subject can direct his breath and move in any direction inside the chamber in an unpredictable manner. This may be the reason that virtually all publications refer to a minimum measurement interval (duration) of 15-30 min, as illustrated in Table 1.
|
||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
Today's line of research is often a combination of long-term
observations with short-term changes in energy expenditure. If, for
example, the O2 concentration SD
of 0.002%, which is the SD we found for our calibration gas
O2 concentration check over 3 mo,
is applied to a subject with a
O2 of 350 ml/min for a 0.5-h interval, the resulting SD in
O2 will be ~3%. In
reality, the shorter intervals have a slightly lower SD because the
short-term stability of the O2
measurement is better than 0.002%. In addition, the change in
concentration of the chamber volume is smaller, which decreases
eventual errors due to nonlinearity of
CO2 analyzers.
Although the results of "ideal" injection experiments (good mixing, predictable injection flow) show that shorter interval measurements are feasible, we chose the standard of 0.5-h results as the smallest practical time interval with subjects. The smallest experiment duration allowed (limited in software) is 2 h, to provide at least eight automatic calibrations for the off-line calculation, although a minimum of 12 h is preferred (for instance, one night). The 2-h interval is also used in our standard checking experiments because it illustrates the accuracy for measuring sleeping metabolic rate, which is done over a 2- to 3-h interval (mostly over 3 h). Whenever possible, the experiment duration with subjects was chosen to be at least 24 h.
Conclusions
The automated system with its intermittent calibration showed stable performance and can effectively be used on a 24-h/day, 7-day/wk basis. The system has a low risk of operating errors. Variations in ambient temperature and pressure have little effect because of the intermittent-calibration method.The accuracy of the respiration chambers is dependent on the
measurement interval (duration) and the level of
O2 and
CO2 to be measured. In our
setting, the accuracy, described as a mean error ± SD, is 2.1 ± 7.4 and 1.3 ± 3.7 ml/min for
O2 and
CO2, respectively, for intervals
2 h. Calculated energy expenditure has an accuracy of
0.7 ± 2.3% for an adult consuming 300 ml/min O2.
On the basis of our experiments, the smallest time interval needed to
measure a subject was 15-25 min. When measuring plateau values
(constant metabolic rate), one should wait a few minutes (5 min)
after changing the plateau to accommodate the mixing time constant. The
smallest time constant possible was determined, for the most part, by
the mixing properties of the chamber, but the smallest practical
measurement interval (duration 0.5 h) was determined by volume and
gas-analysis accuracy.
ACKNOWLEDGEMENTS
The authors acknowledge Dr. P. Webb for many valuable comments in the field of calorimetry during the past 10 years.
FOOTNOTES
Deceased 1 October 1997.
Address for reprint requests: P. F. M. Schoffelen, Dept. of Human Biology, Universiteit Maastricht, PO Box 616, 6200 MD Maastricht, The Netherlands (E-mail: P.Schoffelen{at}HB.UNIMAAS.NL).
Received 12 March 1997; accepted in final form 23 July 1997.
APPENDIX A
Glossary
| A | Analyzer-output uncalibrated value |
| c | Chamber |
| cal | Calibration |
| F | Volumetric fraction of gas (STPD) |
| g | Any gas |
| i | Incoming |
| o | Outgoing |
| P | Pressure |
| r | Recirculation |
| Rh | Relative humidity |
| s | Time-derivative operator, d/dt |
| sat | Saturated with water vapor |
| T | Temperature |
| t | Time |
| t90 | Response time to 90% |
 |
Time constant |
| d |
Delay time |
| V | Volume (STPD) |
| |
Volumetric flow rate (STPD) |
| w | Water vapor |
Mixing Process
Response time is understood, in general, to be the time needed for the outlet of a process to reach at least 90% of final value after a step change at the inlet. Percentages used to define the response time vary: 90% (t90), 95% (t95), and 99% (t99) are often used. A response time may be the result of complex higher-order terms. In contrast, the time constant () associated with a
first-order process of type
Y(t) = X · [1e
] or, better, in process notation H = 1/(s+1), is well defined; e.g., it
takes 3 to reach 95% and 10 to reach 99.995% (14.5-bit resolution) of final value.
The first-order system
1/(c1s+1)
normally associated with a respiration chamber is only valid for a
completely mixed volume; in reality, there will always be a small
initial mixing interval before a subject's air is well mixed. With the
use of recent fast-response respiration chambers, the measurement
interval approaches the mixing interval, raising the question of how
the mixing interval fits into the equation and which factors affect it.
The recirculation flow through the chamber (if evenly distributed) can
be thought to be the sum of several
(n) partial flows or pathways (Fig.
7), each behaving as a tube reactor.
Because diffusion in a tube reactor (backward or axial mixing) is
beneficial to mixing and we are interested only in the problematic
dominant factors, we chose to consider each flow as an ideal tube
reactor with a delay time
(
). If a partial flow m passes a confined
space, an additional time constant
[1/(
)]
is added for that pathway. The subject's expired air enters one or
more of the pathways. Leakage will also affect one or more of the
pathways, possibly where the subject respires. In a negative-pressure
chamber, the direction of the leakage flow prevents loss of subject air
and has the same effect as fresh air normally entering the chamber.
c1s+1)
normally associated with a respiration chamber augmented with
higher-order terms (c2 and
dc) for mixing. Recirculation
flow through chamber can be thought to be sum of several
(n) partial pathways, each of which has its own delay time
dn and,
where confined space is present, a time constant
n
(dc and
c2 are a complex composite of
values
d1~n
and
1~n). Subject's respiration and possibly leakage take place in some of
pathways, depending on subject's position in chamber. For clarity, subject's respiration and confined
volume influence have been drawn
only in a single pathway. O2
and CO2,
O2 uptake and CO2 production, respectively.
Determination of each parameter involved (including position and level
of energy expenditure) is difficult; however, most higher-order natural
proccesses can be simplified to the form Ke
ds/[(1s+1) · (2s+1)].
This is usually also the maximum number of parameters that can be
determined from measurement of standard input signals (pulse and step).
When the simplified higher-order system
Ke
/[(c1s+1) · (c2s+1)] with a
respiration chamber K = 1 (response at
t = 
) is used, dc and
c2 are a complex composite of
values
d1~n and 1~n
from the n partial flows, and the
dominant time constant c1 is
determined by volume and flow
(o/Vc).
In the case of evenly distributed flow,
dc will be mostly determined by
volume and recirculation flow
(Vc/r)
and by the position of the subject in the chamber (i.e., at midpoint
0.5 · Vc/r). c2 is the result of backward
and axial mixing and exchange with confined spaces. If confined spaces
are avoided, c2 will be very small. Determining chamber characteristics from standard input signals
(pulse and step) should take into account possible variation of
dc and
c2.
APPENDIX B
Calculation of O2 and
CO2
t1 5 min, the
smallest usable interval with our sample sequence. A value at
t1,
t2, or
t1+2 (average over interval t1
to t2)
represents the best value calculated from multiple samples for that
point in time. Algorithms used ensure that summing values calculated
over small intervals are mathematically identical to calculation over
one long interval.
The frequent calibration technique allows pressure- and temperature-independent calculations of momentary gas concentration
![F<SUB>g</SUB>(<IT>t</IT>) = F<SUB>cal</SUB> ⋅ [A<SUB>g</SUB>(<IT>t</IT>) − A<SUB>0</SUB>(<IT>t</IT>)]/[A<SUB>cal</SUB>(<IT>t</IT>) − A<SUB>0</SUB>(<IT>t</IT>)]](/content/vol83/issue6/fulltext/2064/img005.gif)
|
O2 and
CO2, the following
parameters can be derived directly
|
|
|
![<A><AC>V</AC><AC>˙</AC></A><SUB>o</SUB>(<IT>t</IT>) = <A><AC>V</AC><AC>˙</AC></A><SUB>o</SUB><SC>atp</SC>(<IT>t</IT>) ⋅ [P<SUB>o</SUB>(<IT>t</IT>) − P<SUB>w</SUB>(<IT>t</IT>)]/[1013.25 ⋅ (1 + 0.00367 ⋅ T<SUB>o</SUB>(<IT>t</IT>)]](/content/vol83/issue6/fulltext/2064/img009.gif)
|
![V<SUB>c</SUB>(<IT>t</IT>) = V<SUB>c</SUB><SC>atp</SC> ⋅ [P<SUB>c</SUB>(<IT>t</IT>) − P<SUB>w</SUB>(<IT>t</IT>)]/[1013.25 ⋅ (1 + 0.00367 ⋅ T<SUB>c</SUB>(<IT>t</IT>)]](/content/vol83/issue6/fulltext/2064/img010.gif)
|
|
|
|
i(t),
the flow of the input in STPD.
i(t)
may be calculated by using the "haldane" correction. The formula
used must incorporate changing N2
fractions and STPD correction of the
chamber volume as a function of time
|
![− V<SUB>c</SUB>(<IT>t</IT><SUB>1</SUB>) ⋅ F<SUB>o</SUB><SC>n</SC><SUB>2</SUB>(<IT>t</IT><SUB>1</SUB>)]/F<SUB>i</SUB><SC>n</SC><SUB>2</SUB>(<IT>t</IT><SUB>1+2</SUB>)](/content/vol83/issue6/fulltext/2064/img015.gif)
|
Now that
i(t)
is known, the following parameters are derived
|
|
![<A><AC>V</AC><AC>˙</AC></A><SUB>c</SUB><SC>o</SC><SUB>2</SUB>(<IT>t</IT><SUB>1+2</SUB>) = [V<SUB>c</SUB>(<IT>t</IT><SUB>2</SUB>) ⋅ F<SUB>oc</SUB><SC>o</SC><SUB>2</SUB>(<IT>t</IT><SUB>2</SUB>) − V<SUB>c</SUB>(<IT>t</IT><SUB>1</SUB>) ⋅ F<SUB>oc</SUB><SC>o</SC><SUB>2</SUB>(<IT>t</IT><SUB>1</SUB>)]/[100 ⋅ (<IT>t</IT><SUB>2</SUB> − <IT>t</IT><SUB>1</SUB>)]](/content/vol83/issue6/fulltext/2064/img018.gif)
|
|
![− V<SUB>c</SUB>(<IT>t</IT><SUB>1</SUB>) ⋅ F<SUB>oc</SUB><SC>co</SC><SUB>2</SUB>(<IT>t</IT><SUB>1</SUB>)]/[100 ⋅ (<IT>t</IT><SUB>2</SUB> − <IT>t</IT><SUB>1</SUB>)]](/content/vol83/issue6/fulltext/2064/img020.gif)
|
O2
and CO2 to be calculated
|
|
REFERENCES
| 1. | Atwater, W. O., and F. G. Benedict. Experiments on the Metabolism of Matter and Energy in the Human Body. Washington, DC: US Government Printing Office, 1903. (USDA Office of Experiment Stations Bull. No. 136) |
| 2. | Benedict, F. G. A helmet for use in clinical studies of gaseous metabolism. N. Engl. J. Med. 203: 150-158, 1930. |
| 3. | Brown, D., T. J. Cole, M. J. Dauncey, R. W. Marrs, and P. R. Murgatroyd. Analysis of gaseous exchange in open-circuit indirect calorimetry. Med. Biol. Eng. Comput. 22: 333-338, 1984[Medline]. |
| 3a. | Centre de Recherche Claud-Delorme de L'Air Liquid.. Encyclopedie des Gaz. Amsterdam: Elsevier, 1976. |
| 4. | Charbonnier, A., C. D. R. Jones, Y. Schutz, P. R. Murgatroyd, R. G. Whitehead, E. Jéquier, and G. Spinnler. A whole body transportable indirect calorimeter for human use in the tropics. Eur. J. Clin. Nutr. 44: 725-731, 1990[Medline]. |
| 5. | Dauncey, M. J., P. R. Murgatroyd, and T. J. Cole. A human calorimeter for the direct and indirect measurement of 24 h energy expenditure. Br. J. Nutr. 39: 557-566, 1978[Medline]. |
| 6. | Henning, B., R. Löfgren, and L. Sjöström. Chamber for indirect calorimetry with improved transient response. Med. Biol. Eng. Comput. 34: 207-212, 1996[Medline]. |
| 7. | Heymsfield, S. B., D. B. Allison, F. X. Pi-Sunyer, and Y. Sun. Columbia respiratory-chamber indirect calorimeter: a new approach to air-flow modelling. Med. Biol. Eng. Comput. 32: 406-410, 1994[Medline]. |
| 8. |
Jéquier, E.,
and
Y. Schutz.
Long-term measurements of energy expenditure in humans using a respiration chamber.
Am. J. Clin. Nutr.
38:
989-998,
1983 |
| 9. | Kinney, J. M., A. P. Morgan, F. J. Domingues, and K. J. Gildner. A method for the continuous measurement of gas exchange and expired radioactivity in acutely ill patients. Metabolism 13: 205-211, 1964[Medline]. |
| 10. |
McLean, J. A.,
and
P. R. Watts.
Analytical refinements in animal calorimetry.
J. Appl. Physiol.
40:
827-831,
1976 |
| 11. |
Moon, J. K.,
C. L. Jensen,
and
N. F. Butte.
Fast-response whole body indirect calorimeter for infants.
J. Appl. Physiol.
74:
476-484,
1993 |
| 12. | Moon, J. K., F. A. Vohra, O. S. Valerio Jimenez, M. R. Puyau, and N. F. Butte. Closed-loop control of carbon dioxide concentration and pressure improves response of room respiration calorimeters. J. Appl. Physiol. 125: 220-228, 1995. |
| 13. | Murgatroyd, P. R., H. L. Davies, and A. M. Prentice. Intra-individual variability and measurement noise in estimates of energy expenditure by whole body indirect calorimetry. Br. J. Nutr. 58: 347-356, 1987[Medline]. |
| 14. | Prentice, A. M., G. R. Goldberg, H. L. Davies, P. R. Murgatroyd, and W. Scott. Energy-sparing adaptations in human pregnancy assessed by whole-body calorimetry. Br. J. Nutr. 62: 5-22, 1989[Medline]. |
| 15. | Ravussin, E., S. Lillioja, T. Anderson, L. Christin, and C. Bogardus. Determinants of 24-hour energy expenditure in man: methods and results using a respiratory chamber. J. Clin. Invest. 78: 1568-1578, 1986. |
| 16. |
Rumpler, W. V.,
J. L. Seale,
J. M. Conway,
and
P. W. Moe.
Repeatability of 24-h energy expenditure measurements in humans by indirect calorimetry.
Am. J. Clin. Nutr.
51:
147-152,
1990 |
| 17. |
Seale, J. L.,
W. V. Rumpler,
and
P. W. Moe.
Description of a direct-indirect room-sized calorimeter.
Am. J. Physiol.
260 ((Endocrinol. Metab. 23):
E306-E320,
1991 |
| 18. | Shetty, P. S., M. L. Sheela, P. R. Murgatroyd, and A. V. Kurpad. 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, 1987[Medline]. |
| 19. |
Treuth, S. M.,
G. R. Hunter,
R. L. Weinsier,
and
S. H. Kell.
Energy expenditure and substrate utilization in older women after strength training: 24-h calorimeter results.
J. Appl. Physiol.
78:
2140-2146,
1995 |
| 20. |
Webb, P.,
and
S. J. Troutman, Jr.
An instrument for continuous measurement of oxygen consumption.
J. Appl. Physiol.
28:
867-871,
1970 |
| 21. | Weir, J. B. New methods for calculating metabolic rate with special reference to predicting protein metabolism. J. Physiol. (Lond.) 109: 1-9, 1949. |
This article has been cited by other articles:
|
|
 |
|
  A. J. Smeets, S. Soenen, N. D. Luscombe-Marsh, O. Ueland, and M. S. Westerterp-Plantenga Energy Expenditure, Satiety, and Plasma Ghrelin, Glucagon-Like Peptide 1, and Peptide Tyrosine-Tyrosine Concentrations following a Single High-Protein Lunch J. Nutr., April 1, 2008; 138(4): 698 - 702. [Abstract] [Full Text] [PDF]
|
|
|
|
 |
|
 K. R Westerterp, A. Smeets, M. P Lejeune, M. P. Wouters-Adriaens, and M. S Westerterp-Plantenga Dietary fat oxidation as a function of body fat Am. J. Clinical Nutrition, January 1, 2008; 87(1): 132 - 135. [Abstract] [Full Text] [PDF]
|
|
|
|
 |
|
 S. L. J. Wijers, W. H. M. Saris, and W. D. van Marken Lichtenbelt Individual Thermogenic Responses to Mild Cold and Overfeeding Are Closely Related J. Clin. Endocrinol. Metab., November 1, 2007; 92(11): 4299 - 4305. [Abstract] [Full Text] [PDF]
|
|
|
|
|
|
E. G. A. H. Van Mil, K. R. Westerterp, A. D. M. Kester, H. A. Delemarre-van de Waal, W. J. M. Gerver, and W. H. M. Saris The Effect of Sibutramine on Energy Expenditure and Body Composition in Obese Adolescents J. Clin. Endocrinol. Metab., April 1, 2007; 92(4): 1409 - 1414. [Abstract] [Full Text] [PDF]
|
|
|
|
|
|
K. C Hansen, Z. Zhang, T. Gomez, A. K Adams, and D. A Schoeller Exercise increases the proportion of fat utilization during short-term consumption of a high-fat diet Am. J. Clinical Nutrition, January 1, 2007; 85(1): 109 - 116. [Abstract] [Full Text] [PDF]
|
|
|
|
|
|
M. P. Lejeune, K. R Westerterp, T. C. Adam, N. D Luscombe-Marsh, and M. S Westerterp-Plantenga Ghrelin and glucagon-like peptide 1 concentrations, 24-h satiety, and energy and substrate metabolism during a high-protein diet and measured in a respiration chamber Am. J. Clinical Nutrition, January 1, 2006; 83(1): 89 - 94. [Abstract] [Full Text] [PDF]
|
|
|
|
|
|
N. Boon, G. B. Hul, N. Viguerie, A. Sicard, D. Langin, and W. H. Saris Effects of 3 diets with various calcium contents on 24-h energy expenditure, fat oxidation, and adipose tissue message RNA expression of lipid metabolism-related proteins Am. J. Clinical Nutrition, December 1, 2005; 82(6): 1244 - 1252. [Abstract] [Full Text] [PDF]
|
|
|
|
|
|
A. M. Joosen, M. Gielen, R. Vlietinck, and K. R Westerterp Genetic analysis of physical activity in twins Am. J. Clinical Nutrition, December 1, 2005; 82(6): 1253 - 1259. [Abstract] [Full Text] [PDF]
|
|
|
|
|
|
J. M. Oomen, C. T. M. van Rossum, B. Hoebee, W. H. M. Saris, and M. A. van Baak {beta}2-Adrenergic Receptor Polymorphisms and Salbutamol-Stimulated Energy Expenditure J. Clin. Endocrinol. Metab., April 1, 2005; 90(4): 2301 - 2307. [Abstract] [Full Text] [PDF]
|
|
|
|
 |
|
 G. Plasqui, A. D. M. Kester, and K. R. Westerterp Seasonal variation in sleeping metabolic rate, thyroid activity, and leptin Am J Physiol Endocrinol Metab, August 1, 200 |
O2, %