Total energy expenditure (TEE) of
rats during simulated microgravity is unknown. The doubly labeled water
method (DLW) reliably measures TEE, but the results depend on the
methods of calculation. These methods were validated and appraised by
indirect calorimetry in eight rats during isolation (7 days) and
simulated microgravity (10 days). There were no effects on
CO2 production in the method used to derive constant
flux rates as in the regression models. rCO2
estimates were dependent on the assumed fractionation processes, the
derivation of constant flux rate methods, and the selected pool models.
Use of respiratory or food quotients did not influence TEE estimations,
which were similar during isolation and simulation. During either
isolation with growth or simulation with a stabilized mass, the
one-pool model of Speakman (Speakman JR. Doubly Labelled Water. Theory and Practice. London: Chapman and Hall, 1997)
resulted in the more reliable validation (0.8 ± 2.2 and 2.2 ± 3.4% vs. calorimetry, respectively). However, during simulation,
agreement was also observed with the single pool model of Lifson
(Lifson N, Gordon GB, and McClintock R. J Appl Physiol
7: 704-710, 1955) (
2.5 ± 2.5%), and two two-pool
models [Schoeller (Schoeller DA. J Nutr 118:
1278-1289, 1988) (0.5 ± 3.1%) and Speakman (Speakman, JR.
Doubly Labelled Water. Theory and Practice. London: Chapman and Hall, 1997) (1.9 ± 2.7%)]. This latter finding seems
linked to the stable body mass and to fractionation consideration close to the single-pool model of Speakman. During isolation or
simulated microgravity, the other equations underestimated TEE by
10-20%.
deuterium; 18-oxygen; energy expenditure; isolation; indirect
calorimetry; microgravity
 |
INTRODUCTION |
THE HINDLIMB
TAIL-SUSPENDED rat was developed as a ground-based model for
simulations of physiological responses to weightlessness (25). This model reproduces, through the hypokinesia,
hypodynamia, and headward shift of body fluids the cardiovascular,
muscular, and bone adaptations to space. As far as we are aware, no
studies have investigated the energy metabolism adaptations to
simulated or actual microgravity in rats. Such determination is
essential, because weightlessness has been shown recently to
induce fuel perturbations that are implicated in body mass and
composition changes (45). Moreover, accurate estimates of
energy requirements are a prerequisite for any long-term spaceflights,
as they are foreseen in the International Space Station
(19).
The doubly labeled water method (DLW) is currently the most relevant
method for measuring free living energy expenditure (18). This method is based on the exponential disappearance from the body of the stable isotopes 2H and 18O after a
bolus dose of water labeled with both isotopes. The 2H is
lost as water, whereas the 18O is lost as both water and
CO2. Thus the excess disappearance rate of 18O
relative to 2H, after correction for isotopic
fractionation, is a measure of the CO2 production rate
(rCO2). This result can be converted to an estimate of
energy expenditure using a known or estimated respiratory quotient (RQ)
and the classical principle of indirect calorimetry. However,
several assumptions should be considered with the technique: 1) the rates of carbon dioxide production and water
loss/gains are constant, 2) the isotopic species leave the
animal body at equal abundance, 3) the body water pool size
is constant throughout the measurement period, 4) the
isotopes turnover in the same pool equal to the body water pool, and
5) all substances entering the animal are labeled at the
background level and there is no entry of unlabeled carbon dioxide and
water via the skin. All these assumptions are invalid to a
certain extent, because a number of complicated processes in mammals
impinge on the accuracy of the calculated metabolic rate
(36).
The favored method for assessing the accuracy of the DLW method has
been to compare isotopically derived rCO2 with
indirect calorimetry measurements. However, the assumptions may be
violated and constants are only known within certain limits. Not all
researchers apply the same assumptions, constants, or methods of
calculation: the determination of the isotope pool spaces, the
calculation of the constants elimination rate, the fractionation
factors, and the mode of rCO2 conversion to energy
expenditure all vary in approach (Fig.
1). Indeed, a number of variants of one
calculation are used and the authors decide that the one that gives the
best agreement between the indirect calorimetry and the DLW method is
the appropriate choice. Thus, even if the validation is ascertained, it
is tacitly assumed that the equation and constants used and the balance
of errors that may cancel in the respiration chamber will do so in all
physiological states and environmental conditions in which the method
will be applied.
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Fig. 1.
Summary of the different methods for assessing the doubly
labeled water (DLW) raw variables. The italic sentences refer to the
methods that are not tackled in this study.
|
|
Taking into account the above considerations, selection of one typical
way of calculation is not clear-cut, especially when environmental
conditions and physiological adaptations are atypical, such as during
simulated microgravity. This is why a longitudinal study was carried
out to validate and appraise the published theoretical methods of DLW
calculations during both a control period and hindlimb tail suspension
in rats. This is a different approach than the classical validation
studies that generally investigate the specific errors introduced in
the DLW-derived rCO2 when one assumption is violated.
The objective was to determine the most accurate method to apply during
simulated microgravity that could potentially be used during spaceflight.
| |
METHODS |
Animals
A group of 50 male Wistar rats weighing 290 ± 27 g
(mean ± SD) (Iffa Credo, les Oncins, France) were housed in
controlled conditions of 21 ± 1°C at humidity of 60 ± 10% with a 12:12-h light-dark cycle. They were fed chow comprised of
23.5% protein, 5% lipid, 49.8% carbohydrate, 12% moisture, 4%
fibers, 5.7% minerals with an energy equivalent of 13.4 MJ/kg (UAR,
Epinay sur Orge, France). Food and tap water were given ad libitum. All
procedures were conducted in accordance with the guiding principles of
the American Physiological Society and the Veterinary Board of the French Space Agency.
Experimental Protocol
The 50 rats were divided into three groups. The first group
(n = 8) was used to determine the 2H
plateau of equilibration, and the second (n = 34) was
required to fit a scaling relationship between body water pool size and body mass. The last group (n = 8) was devoted to the
validation study. The experimental procedures relative to each group
will be chronologically detailed in the relevant parts of
METHODS.
The experimental schedule of the validation study ran for 29 days and
was broken down in four successive periods: 5 days of surgery recovery,
7 days of isolation, 7 days of attachment, and 10 days of simulated
microgravity. The DLW method was tested twice against indirect
calorimetry in each rat during isolation and during simulated
microgravity. Weightlessness was simulated using the tail-suspension
model of Morey et al. (24) modified in the laboratory. The
attachment period allowed us to minimize the stress during the first
days of suspension and wash out isotopes; the rats were kept in a
horizontal position with their tails attached to the suspension device.
Surgical Procedures
Five days before the beginning of the experiments, the 50 rats
were anesthetized with halothane (2% with oxygen) and were chronically
cannulated using an aseptic technique. A polyethylene arterial catheter
(ID 0.28 mm; OD 0.61 mm) was inserted into the abdominal aorta via the
left femoral artery. After insertion, all cannulas were routed
subcutaneously to the top of the head and exteriorized. The catheters
were filled with a solution of polyvinylpyrrolidone in heparinized
saline. During 5 days of recovery, the rats were housed in individual
cages and were accustomed to human presence and handling.
DLW Procedures
Determination of the deuterium equilibration time.
After a 200-µl blood sample (for background enrichment), 0.05-g/kg
2H2O 99.9% (Isotec, St. Quentin en Yvelines,
France) was intraperitoneally injected into eight rats. The plateau of
equilibration was determined in 30-min blood samples taken during the
first 3 h. Other daily samples were taken over the 5 subsequent
days. The 18-oxygen plateau is considered the same as deuterium. Blood
was centrifuged 10 min at 3,500 rpm, and plasma was stored at 20°C
until analysis.
Validation study.
The first day of isolation, a 1-ml blood sample provided baseline
2H2O and H218O
enrichments. The rats were then intraperitoneally injected with H218O 10% (Isotec) mixed with
2H2O 99.9%. Each rat received 0.05 g/kg
2H2O and 1.5 g/kg
H218O. A second 1-ml blood sample was collected
at the plateau of equilibration. Plasma was separated and stored as
mentioned above. Daily urine samples were collected, centrifuged 5 min
at 5,000 rpm, and stored at 20°C. A second DLW dose was injected
the last day of the attachment period after the same procedure. After
equilibration, the rats were hindlimb tail suspended.
Mass Spectrometry
Isotope analyses were performed in triplicate at Centre de
Recherche en Nutrition Humaine de Lyon. Samples were analyzed in an
isotope ratio mass spectrometer (OPTIMA, Fisons, UK) by the zinc
reduction reaction for deuterium and the CO2 equilibration method for 18-oxygen, as previously described (4). In
these conditions, the sensitivity is ±0.04 parts/million (ppm) for
18O and ±0.31 ppm for 2H.
Estimation of the Constant Turnover Rates of
2H2O and H218O
Two-samples methodology.
The mean isotope turnover rates (Ko and
Kd in day
1) were
calculated by the mean values of isotope enrichments expressed in ppm
and the time between the two samples. For oxygen
|
(1)
|
For hydrogen
|
(2)
|
The proportion of the oxygen turnover linked to the hydrogen
turnover is represented by the ratio
Ko/Kd.
Multisamples methodology.
The Ko and Kd
were calculated from the curves fitted to data collected along the
isotope elimination track each day of the experimental period. This
data item along the time course is expressed above isotope background
enrichment, and the resulting difference is then converted to
loge. Ko and
Kd were derived by the slope of the
log-transformed line by linear regression. Two regression models were
compared, making different hypotheses about the error's structure of
the measured components (time and isotope enrichments) (29).
LEAST-SQUARES FIT MODEL.
These curves are fitted to pass through the mean of the time values and
minimize the sum of the squares residual deviations for the isotopic
enrichment. Thus with least-squares (LS) the relative magnitudes of the
error in time are not taken into account.
REDUCED MAJOR AXIS MODEL.
This regression assumes that the errors in the two variables are equal.
The reduced major axis (RMA) is calculated as the LS gradient divided
by the correlation coefficient.
Residuals were plotted to the fitted relationships for both isotopes.
This was performed only with the LS approach, because residuals,
equivalent to the vertical distances from data to the fitted curve,
have no meaning when the curve has been derived minimizing a different variable.
Estimation of the Isotope Dilution Spaces
Initial isotope spaces.
The dilution spaces for H218O and
2H2O (mole) were calculated using the
following equation (9, 34)
|
(3)
|
where N is the pool space; W is the amount of water used
to dilute the dose injected; A is the amount of dose administered; a is
the dose diluted for analysis, and 
is enrichment of dose (a),
dilution water (t), equilibrium enrichment of the isotopes in
the body (s), and background levels of isotopes (p). Two procedures well described in the literature (9) were compared to
determine s.
PLATEAU.
This approach takes s as the initial isotope estimated
after equilibration of isotopes.
INTERCEPT.
Given the gradient of the isotope elimination curves
Ko and Kd, the
No and Nd were reevaluated by calculating the
expected enrichment at the point of injection. The time elapsed between injecting the rats and the first urine sample was estimated. The isotope change over the equilibration period was then calculated along
the same gradient and added to the log-converted initial excess
enrichments to obtain the intercept value for s.
Final pool sizes.
Two potential methods for establishing the size of the 18O
and 2H dilution spaces at the end of the experiment were evaluated.
PERCENTAGE MASS (49).
The values for the initial pool sizes as percentages of the initial
body mass are applied to the final body mass to estimate the final pool size.
SCALED RELATIONSHIP (36).
The 34 remaining rats were intraperitoneally injected with
2H218O following the same
procedures as detailed above, and urine samples were taken on 2 consecutive days. The pool spaces were derived from estimates resulting
from either the plateau or intercept approaches. A scaling relationship
between the initial isotope spaces for each isotope and the initial
body mass was derived using the LS regression. Using the observed final
body mass and interpolating on these equations, we predicted the sizes
of the final body water pools.
Average pool sizes throughout the experiment.
The average N of the experiment can be calculated from
Ninitial and Nfinal by assuming a linear or
exponential increase (18). In fact, the consequences of
selecting one particular increase are very slight and the errors in
doing so are negligible because an unrealistic 50% increase in N
during the experiment will not introduce a difference >1.5% between
the two estimates. The average pool size was assumed to be
Naverage = (Ninitial + Nfinal)/2. Using the intercept or plateau approach for the
initial pool spaces and the percent mass approach or the scaled
relationship for the final ones, we calculated four estimates of the
average pool sizes for both oxygen and hydrogen. The pool size ratio
(R) was calculated as Nd/No.
Correction Factors For Fractionation
Three fractionation factors (f) are defined
depending on the temperature. These are first and second, the
fractionation of hydrogen and oxygen in gaseous water relative to
liquid water, respectively, and third, the fractionation factor of
oxygen in carbon dioxide relative to oxygen in liquid water. The
initial equation derived by Lifson et al. (18) for
estimation of CO2 output ignoring fractionation is
|
(4)
|
Completely derived, taking into account f1,
f2, and f3, the equation results in
|
(5)
|
where rH2Of is
the rate of water leaving the system that is fractionated.
Estimation of CO2 Production Rates
Ten different published techniques for estimating the
CO2 production by combination of the above-calculated
parameters were compared.
Single-pool model using 18O isotope space.
equation of lifson et al. (18).
The oxygen dilution space is used as an estimate of the body
water pool (N). Only the equilibrium fractionation factors, derived at
24°C, are taken into account: f1 = 0.93, f2 = 0.99, f3 = 1.04. The
fractionated water loss
(rH2Of) is assumed to
be half the total water loss. The final equation simplified
from Eq. 5 is
|
(6)
|
EQUATION OF SPEAKMAN 1997 (36).
The in vivo kinetic and equilibrium fractionation factors at
37°C are combined and assumed to contribute in a ratio of 3:1 to the
fractionated losses. It is assumed that 25% of the water loss is
fractionated. In these conditions, the ratios of Eq. 5 are
(f1 f2)/2f3 = 0.025 and f3 = 1.039 (15, and reviewed in Ref.
36). This is a single pool approach, only the 18-oxygen dilution space is considered as the water pool size.
|
(7)
|
Two-pool models using individual isotope spaces or a population
ratio.
equation of coward and prentice 1985 (10).
The observed isotope pool sizes Nd and No are
used in the estimate of CO2 production. This is the
simplest two-pool model. The fractionation factors are the same as
those assumed in Eq. 6
|
(8)
|
EQUATION OF SCHOELLER ET AL. 1986 (32), MODIFIED
1988 (30).
The author uses a fixed average pool size for oxygen and hydrogen pools
relative to the body water pool. The oxygen pool is assumed to be 1.01 times and the deuterium pool 1.04 times the actual water space.
Therefore, the isotope ratio is assumed to be 1.03. The fractionation
factors are taken for equilibrium processes at 37°C with fractionated
water loss (31) equal 2.3 rCO2.
|
(9)
|
where
|
(10)
|
Two-pool models using isotope spaces of the group studied.
equation of speakman 1993 (38).
This approach is related to the fact that there is no a priori reason
to consider the fixed ratio derived from studies in humans to be valid
in animal studies. Whatever the group, the mean dilution space ratio
(Rgroup), should be substituted in the equation. The
fractionation factors are the same as in Eq. 9
|
(11)
|
where
|
(12)
|
EQUATION OF SPEAKMAN 1997 (36).
This is the two-pool equivalent of Eq. 7 but taking into
account the data of the group dilution spaces. Thus
|
(13)
|
where N is calculated from Eq. 12.
Two-pool models using isotope spaces of the population and group
studied.
equation of speakman et al. 1993 (40).
This is the same approach as Schoeller et al. (32), but
using an alternative estimate of the constants derived from 211 measurements of the dilution space ratio in humans. This average ratio
was 1.0427 for the pool size ratio and thus 1.01 and 1.0532 for the
equation constants. A group mean dilution space ratio should be
evaluated for the group of animals under investigation, and the
statistical significance of the observed ratio should be tested against
the observed population level values for the constants. Thus
|
(14)
|
where
|
(15)
|
EQUATIONS OF RACETTE ET AL. 1994 (28) AND SCHOELLER
ET AL. 1995 (33).
Another population dilution space ratio (1.034) is derived from the
population, and further ways of combining the observed group and
population dilution spaces are proposed.
AVERAGE APPROACH. The average dilution space of
the group and the population is adopted
|
(16)
|
leading to
|
(17)
|
where
|
(18)
|
WEIGHTED APPROACH. An average weighting
of the group and population space ratio is used. Given a sample size of
ns for the Rgroup and a sample of 99 for the derived average dilution space for the population
|
(19)
|
This estimate for R' can be then substituted in Eqs.
17 and 18 to obtain the rCO2 estimation.
EQUATION OF COWARD ET AL. 1994 (11).
This approach is a weighted calculation considering the relative
variances of the sample and population means as the weights. The mean
population estimate is suggested to be 1.034 [as Racette et al.
(28)], with a standard deviation of 0.003. The estimated weighted dilution space ratio Rw is calculated as
|
(20)
|
where Rs and Rp and vars and
varp represent the sample and population mean dilution
space ratios and variances. The Rw is then substituted in
Eqs. 17 and 18 to yield rCO2 and N.
Estimation of the rCO2 Precision
The CO2 production using average values of the
isotope enrichment at the start and end points of the experiments was
derived with a precision error. These individual precision errors are combined to yield an overall precision error for the final estimate of
CO2 production. We use the empirical method described by
Speakman (37) called the Jackknife calculation. The
precision errors are made using the means of enrichment estimates.
However, each time the calculation is done, one of the measurements is
omitted. In each case, the means should be used to generate the final
CO2 production values. The Jackknife calculation proceeds
using the means so that the distribution estimate is a distribution of
means. Thus the standard deviation of the distribution is the standard error, and the 99% confidence limits are calculated as ±2.034 multiplied by the standard deviation of the resultant distribution.
Conversion of CO2 Production Into Energy Demands
Two methods were compared. The first one uses RQ values obtained
from indirect calorimetry, which are converted into an energy equivalent of CO2 (EeqCO2) calculated by
the Wier equation (47)
|
(21)
|
Then TEE (kJ/day) is calculated as
|
(22)
|
where 22.4 is the conversion factor for moles of
CO2.
The second method consists of the estimation of the RQ from the food
composition, so-called food quotient (FQ), calculated as follows
|
(23)
|
where P, F, C are protein, fat, and carbohydrate intakes,
respectively, expressed as grams per day (3).
Indirect Calorimetry
The rates of O2 consumption and CO2
production were assessed by an indirect calorimeter consisting of an
open-flow gas analysis system using gas analyzers. Oxygen and carbon
dioxide concentrations in downstream exhaust gases were successively
measured in five different cages. To avoid errors resulting from
sequential changes from one cage to another, common parts of the system
were rinsed for 90 s, after which gas exchanges were measured for
40 s. The final value is a mean of 10 values obtained
every 4 s. A computer-controlled system of three-way valves
allowed for the sequential analysis of the five cages every 11 min. One
cage was left vacant and served as reference for measuring ambient
O2 and CO2. Air samples were pumped at a
constant flow rate, controlled within strict limit by a mass flowmeter
(precision <1%; Tylan, FM 380), and directed to a paramagnetic oxygen
analyzer (range 0-100%, time delay <3 s; Klogor, Lannion,
France) and an infrared carbon dioxide analyzer (range 0-1%, time
delay <3 s; Gascard I, Edinburgh Sensors) after being dried through a
Permapure system and calcium chloride, which were changed twice daily.
The system was calibrated daily with pure nitrogen to set up the zero
of the analyzers and with a standard gas mixture (CFPO) containing
20.5% O2 (accuracy 20.44-20.56%), 0.5%
CO2 (accuracy 0.495-0.505%), and 79% nitrogen to set
up the sensitivity. The measuring system was found to be accurate to within ±1% by bleeding known rates of CO2 and
N2 as known rates O2 and CO2.
Analog signals from the analyzers and mass flowmeter were digitized
with an interface card and stored in a desktop computer. O2
and CO2 concentrations were measured continuously over
~23 h 30 min per day. Thirty minutes were required to calibrate the
system, clean the cages, change food and water, weigh the animals, and
collect urine samples for isotope measurements. Total quantities of
O2 consumed and CO2 produced in occupied cages
minus O2 and CO2 concentrations in the empty
reference cage, multiplied by the air flow through the cages, yielded
the respiratory gas exchanges of animals. The energy expenditure is
calculated from the Wier formula (47).
Software
The rCO2 estimations from the different
approaches were calculated using Microsoft Excel 98. The precision of
the DLW-derived rCO2 was assessed using the software
DLW version 1.0 developed by Professor Speakman and Dr. Lemen
(Aberdeen, UK).
Statistical Analysis
Because of the small number of rats and the inherent loss in
statistical power, a Student's paired t-test was used to
compare 1) the raw variables obtained from the different
methods, 2) the DLW-derived
rCO2 against the
indirect calorimetry results, and 3) the isolation against
the simulated microgravity periods. The impacts of the different
methods of deriving rCO2 at the different levels of
DLW calculations (pool sizes, constant elimination rates, fractionation
processes, and equations) during the two environmental conditions
(isolation and suspension) were evaluated by a multiway factorial ANOVA
(F-ANOVA). When a significant difference (P < 0.05)
was noted, post hoc tests were performed using Fisher's protected
least-significant difference (PLSD) test. A Bland and Altman test
(6) examined the agreement of the DLW method with indirect
calorimetry. The differences between the indirect calorimetry and the
DLW method were plotted against the average of the two methods. Bias
and precision were evaluated using the mean and standard deviation of
the differences between calorimetry and DLW. Bias measures systematic
error between the methods, and precision quantifies the random error or
variability. The limits of agreement were defined as the mean
difference ±2 SD. The biases were compared through a Student's paired
t-test. To simplify the results, the Bland and Altman test
was used on five of the ten equations described above selected for
representing a typical way of calculation. All analyses were performed
with STATVIEW 4.5 (Abacus Concepts, Berkeley, CA, 1992), and values are
expressed as means ± SD, with P < 0.05 considered to be statistically significant.
| |
RESULTS |
Energy Intake and Body Mass
Energy intake (Fig. 2) has to be
considered carefully, because we estimate an accuracy of ±10% in the
measurements due to losses. Therefore, the results are more qualitative
than quantitative. During isolation, rats grew normally, with an
average increase of ~9.1 ± 1.0% at the end of the period,
associated with a constant daily energy intake varying between 323 ± 14 (isolation day 3) to 363 ± 19 kJ/day (isolation
day 6). During suspension, body mass was stabilized (from
15.4 ± 1.3% on suspension day 1 to 15.7 ± 2.4%
on day 10). The energy intake throughout this period varied between 256 ± 34 and 295 ± 16 kJ/day on suspension
days 5 and 10.
Kinetic of Deuterium Equilibration
The deuterium equilibration in the rat body fluids was determined
from the plateau observed on the curve of isotope enrichment as a
function of time elapsed from dose administration (Fig.
3). It was observed at 120 min
(284.12 ± 9.91 ppm).
Scaled Relationship Between Isotope Dilution Spaces and Body Masses
One of thirty-four rats was excluded from the study because of a
sealed catheter. From the plots, four equations were derived and used
predictively (Fig. 4). The population
isotope space ratio resulting from this analysis was 1.04391 ± 0.03212 from plateau and 1.04396 ± 0.03118 from intercept.
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Fig. 4.
Scaled relationship between the 2H and 18O
isotope pool sizes determined from either plateau or intercept and the
body mass (n = 33).
|
|
Indirect Calorimetry
The produced CO2, consumed O2, and RQ are
presented in Table 1; there were no
differences between the periods of isolation and suspension.
Isotope Backgrounds, 2-h Equilibration, and Total Sampling Times
The isotope enrichments of daily tap water measurements throughout
the experiment were unchanged (H218O:
1,980.34 ± 0.54; 2H2O:
145.24 ± 0.36 ppm). The data for isotope backgrounds and equilibration are presented in Table 2.
During the simulated microgravity period, two rats were withdrawn from
the study at, respectively, 7 and 9 days due to tail injury from the
suspension device. The rCO2 was calculated until the
rats were removed.
Initial Isotope Dilution Spaces
During isolation, the H218O and
2H2O dilution spaces estimated from the plateau
were higher than from the intercept, whereas the dilution space ratios
were similar (Table 3). During simulated microgravity, the H218O and
2H2O dilution spaces were also statistically
distinct without differences between the ratios. The suspension did not
modify the isotope spaces of 18O and 2H from
either plateau or intercept. Conversely, higher ratios were observed
during suspension for both the intercept estimates and the plateau.
Isotope Constant Elimination Rates
To simplify the results (Table 4),
we focus on the Ko-Kd
differences, which pass directly into
rCO2. The differences calculated by
RMA and LS were similar during both isolation and suspension. This lack
of difference was also observed between the LS and two-point method
during both experimental periods. The
Ko/Kd ratios were comparable to the LS during isolation but were lower during suspension. The residual standard deviations were within the range of published values and therefore acceptable. For the above variables, no difference was noted between isolation and simulated microgravity.
Appraisal of the Different Methods of Calculations
Constant flux rates.
We did not observe any global effect of the constant flux rate
calculations, i.e., two- or multipoint methods (F = 1.664, P = 0.197). This was also noted when the
analysis was split by groups: during isolation (F = 0.235, P = 0.628) and during suspension (F = 2.192, P = 0.139). Therefore, we
will focus the following statistical results of the F-ANOVA on the
multipoint methodology.
Pool models.
The choice of the pool model is an important determinant of the
rCO2 estimations (F = 20.625, P < 0.0001). Overall, from the PLSD Fisher's test it
appears that the results of rCO2 were higher when a
single pool (No) was used than when two-pool models using individual N (P < 0.0001) or two-pool models using
either an R estimate from the population (P < 0.0001),
from the group (P = 0.001), or from the group and the
population studied (P < 0.0001) was used. Among the
two-pool models, R estimated from the population gave higher
rCO2 results than R from the group (P < 0.0001) or the group and population (P < 0.0001).
Splitting the analysis by period, these results were unchanged during
the suspension period (F = 9.797, P < 0.0001). Conversely, within the isolation period (F = 2.555, P = 0.0389), the Fisher's test showed only significant differences between the one-pool model and the two-pool models using individual N estimates (P = 0.006) or R
from the group and the population (P = 0.002).
Proportion of fractionated water loss and fractionated processes.
Regardless of the calculation used, assuming a fractionated water
loss of 25% the total water loss yielded a higher
rCO2 than an assumption of 50% (F = 9.883, P = 0.002). An overall effect of the
fractionation processes used has been demonstrated, i.e., kinetic
and/or equilibrium processes at 24 or 37°C (F = 26.991, P < 0.0001). Assuming kinetic and equilibrium
fractionation processes at 37°C resulted in a higher estimate of the
DLW-derived rCO2 than both equilibrium processes at
37°C (P < 0.0001) or at 24°C (P < 0.0001). These results are similar during either isolation (F = 4.629, P = 0.010) or suspension
(F = 11.902, P < 0.0001).
Average N throughout the study.
The Naverage estimation method, either intercept or plateau
assuming a scaled relationship or an inferred final mass evaluation, did not significantly influence the rCO2 estimates
(F = 1.714, P = 0.162). This lack of
significant effect was also noted during isolation (F = 0.820, P = 0.484) and simulated microgravity
(F = 1.587, P = 0.192).
Estimation of rCO2.
global effects of the different equations.
The association of the above-derived variables into the published
equations had an overall significant impact on the
rCO2 (F = 13.088, P < 0.0001) (Table 5, Fig.
5). More precisely, during isolation, this effect was maintained (F = 1.910, P = 0.049). The PLSD Fisher's test showed that
Eq. 8, using the individual N, gave the lower
rCO2 estimation.
These estimates were significantly different from the one-pool models
in Eqs. 6 and 7. We noted also that the different
ways of combining R obtained from group or population or both
(Eqs. 11, 14, 16,
17) result in significantly lower rCO2
production than the one-pool model (Eq. 7), although not in
the two-pool model (Eq. 13). During the suspension period,
the impact of the equation was also significant (F = 5.681, P < 0.0001). Between the equations, we observed
the same differences as noted during isolation, but other patterns can
be dissociated from the results. Effectively, the
rCO2 derived from Eq. 8
(the basic 2-pool model) was significantly lower than all the other
equations. On the other hand, Eq. 9, which is also a
two-pool model but using an R fixed at 1.03, yields significantly
higher results than the other two-pool models using R from group and/or
population, although not in Eq 13. There was no difference
between these latter two. Interestingly, these equations used
fractionation processes similar to those of Eq. 7.
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Fig. 5.
Relative deviation (%) of the DLW measurement from indirect
calorimetry during isolation and suspension. Five equations are
presented characterizing a particular way of calculation. The
rH2Of
is the proportion of water loss
(rH2O) that is fractionated. Eq,
equilibrium; k, kinetic. *P < 0.05 and
**P < 0.001 vs. indirect calorimetry
(n = 8).
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COMPARISON WITH INDIRECT CALORIMETRY.
A paired t-test comparison of the DLW-derived
rCO2 with indirect calorimetry raised evidence that
most equations are statistically different (Table 5). The test was
performed with the rCO2 estimates from two
Naverage calculations: plateau (P) or intercept (I), assuming a scaled (s) or percentage mass (%) relationship. Within isolation, either with the multipoint or two-point methods, no difference from calorimetry was observed for Eq. 7 (P%,
I%, and Ps) and Eq. 13 (P%). During suspension using the
multipoint, we noticed nonstatistical results for Eq. 7
(P%, I%, and Is), Eq. 13 (P%, I%, Ps, and Is), Eq. 6 (P%, Ps, and Is), and Eq. 9 (Ps and Is). With some
exceptions, the results were similar with the two-point method.
PRECISION ERRORS FROM EQ. 7 [SPEAKMAN
(36)].
The precision estimates were compared with the deviation of the DLW
estimates (Fig. 6). These comparisons
were realized with either the two- or multipoint methods. To simplify
the results, the scaled relationships are not represented. Except for a
few animals, we observed that the two-sample method used during
isolation or simulated microgravity lay to the right line of identity.
Thus the deviations between the DLW and indirect calorimetry
measurements were less than the observed precision of the DLW, pointing
to precision as a key problem. For the multipoint method, results fit
near the line of identity and were below 5% for both deviation and
precision (1 rat did not fit within 5%). Therefore problems arising
with the DLW technique are approximately equal to the precision and are
highly acceptable.
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Fig. 6.
Comparison of the calculated precision (99% confidence interval)
of the DLW measurement from Eq. 7 and the absolute deviation
of the measurement from indirect calorimetry. The line displays the
line of identity (n = 8).
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Bland and Altman Test.
The agreement between the two methods tested by the Bland and Altman
test (4) is represented in Fig.
7. The results show that for the five
equations tested, the individual data are in the range of agreement
(mean difference ± 2SD), except for one rat. However, we can note
that apart from Eq. 7, the mean differences are not close to
the zero (the statistical significance of this deviation is equivalent
to the test represented in Fig. 6 and Table 5) and the higher biases
are observed by using individual N estimates (Eq. 8).
Compared with our single pool reference model (Eq. 7), the
paired t-test during either isolation or suspension, for
both multi- or two-point methods, indicated significant higher biases
by using individual N estimates (Eq. 8), a fixed ratio (Eq. 9), and the initial model Eq. 6. No effect
on the biases using either a single pool (Eq. 7) or two
pools with a group ratio (Eq. 13) was noted. However, the
biases were significantly increased from a two-pool model using a group
ratio (Eq. 13) to a two-pool using a fixed ratio (Eq. 9) and from this latter to the individual N estimates (Eq. 8), whatever the period or the flux calculations. On the other
hand, biases were higher using the two-point method either during
isolation or suspension. An exception is observed with Eq. 7
where the biases of the two- versus multipoint method were similar
during isolation.
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Fig. 7.
Results of the Bland and Altman (6) test
during isolation and suspension using both multi- and 2-point method.
The DLW-derived CO2 production rate (rCO2)
was calculated using an Naverage from plateau and an
inferred final mass assumption. *P < 0.05 vs.
Eq. 7; $P < 0.05 vs. Eq. 13;
°P < 0.05 vs. Eq. 9; £P < 0.05 vs. 2-point method.
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rCO2 Conversion to Energy Expenditure
The selection of an RQ or an assumed FQ from the diet did not
significantly modify the energy expenditure estimations that were
similar during isolation and suspension (Table
6).
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DISCUSSION |
Numerous methods have been published to determine the energy
expenditure from the DLW method, but the validation studies supporting these methods used constants and assumptions that may be valid only
within the environmental conditions of the experiment. Therefore, the
selection of one method is far from trivial. This appears to be
particularly important when considering the spaceflight environment,
where the experimental conditions are poorly controlled and unusual.
The energy requirements of spaceflight have been poorly investigated in
humans (19, 45) and are unknown in rats. Therefore, this
study was undertaken 1) to summarize and validate the
different methods of DLW-derived
rCO2 production using the hindlimb
tail suspended rat model and 2) to appraise the best method
to use during simulated microgravity that could be extrapolated to spaceflight.
General Considerations of the Study
A validation study relies on the measurements of the reference
method. The indirect calorimetry system used has proven reliability in
different environmental and physiological situations (1, 8,
23).
The hindlimb tail-suspended rat model is used to mimic the
physiological consequences of spaceflight, and there has been wide acceptance of its usefulness. Suspension experiments using the Morey et
al. model (24) generally result in a constant growth, as
observed in flight (5). During our study, the
body mass was unexpectedly stabilized and this may be due to the
duration of the study and the use of mature rats. However, we cannot
exclude a stress response due to both confinement in the small
calorimetric cages for 29 days and suspension. This is supported by the
decrease in energy intake observed during suspension, keeping in mind
our limitation in energy intake records. In the same way, the stress response may explain the lack of changes observed in TEE and the nonsignificant RQ decrease. Studies conducted in humans were unable to
demonstrate changes in TEE, and this was attributed either to the cost
of physical activity in space or to stress (20). Overall,
the unexpected lack of growth during suspension allows us to observe
unexpected results concerning the application of the DLW method in rats
during simulated weightlessness, leading to the conclusion that during
growth or simulated microgravity without growth, Eq. 7
[Speakman (36)] results in the more reliable estimate of
TEE. In the following discussion, the influence of each calculation
step of on the final rCO2 production is appraised.
Estimation of the Isotope Pool Space
The calculations of rCO2 from the isotope data
assumed that the initial dilution space estimate of the body water pool
is accurate and precise. The technique of choice for measuring the dilution space in animal studies is the plateau technique. We observed
that the intercept estimate of the pool size is smaller than the
estimate from the plateau approach (3.1% for No and 3.2% for Nd) and such differences have been widely discussed
(9, 36). There is clear indication, based on human
studies, that the plateau samples do not always result in overestimates
of the body water pool and, if they are appropriately timed, can result in an accurate estimate. We did not observe an effect of the way of
deriving Ninitial, but this may be due to the lack of
statistical power linked to the small number of animals. Overall, it
appears from our results that when one equation is validated,
the best agreement with calorimetry is observed using the plateau
estimate whether the rats are isolated or suspended.
In the above discussion, we assumed that Ninitial is
constant throughout the measurement period. This may be realistic
during suspension, but not during isolation, where growth results in a
progressively changing pool size. Consequently, the initial dilution
space does not adequately reflect the average pool size throughout the
experimental period. Even if the variations in CO2
production occur at random and even if the rate of CO2
production is constant, this is a significant problem. The best
methods to evaluate the final pool size are to kill and
desiccate the animals or to perform a second isotope injection, but the
blood sampling and fasting necessary would result in a stress response.
We have tested two other classical noninvasive approaches. The first
was to establish empirically a relationship between body mass and the
initial body pool size (36). An error in individual
estimates, however, is introduced by using this method because animals
of the same mass may also vary in composition and hence in body water as well. Consequently, the predictive equation will not be perfect. Speakman et al. (44) studied this effect on long-eared
bats and observed an r2 = 0.67. The data
from this study give a better agreement, with an
r2 ranging from 0.83 (for deuterium pool size
estimate from plateau) to 0.91 (for 18-oxygen from plateau). The second
more widely used approach (36, 41, 44) is to calculate the
initial body pool as a percentage of the body mass for the same
individual. Nevertheless, this latter approach represents a misuse of
ratios (27), because it assumes a scaling exponent of body
pool size on body mass to be 1.0. It also assumes that there are no
changes in body composition associated with the mass change, which is
an unrealistic situation during growth. This question is of
importance in our study, because rat growth is principally driven by
fat deposition (35) and the direct consequence is an
increase in the exchange pool of 2H with labile hydrogen of lipids.
We were unable to demonstrate statistically any superiority of the
scaled relationship or of the inferred percentage of final mass for
estimating the final pool size on the
rCO2 calculations. However, during isolation when a particular equation validates the DLW
method, we can observe that the percentage of final mass approach
results in the best agreement with the calorimetry. On the other hand,
with the stabilization of body mass occurring during suspension, this
difference is no longer observed. This point emphasizes the above
considerations on the body mass and composition changes, as suggested
in growing pigs (16), and suggests that the scaled
relationship should be considered cautiously when body mass changes
during an experiment. In addition, the results demonstrate that the
hydroelectrolytic adaptations to simulated microgravity are less
significant on the DLW procedures than growth.
Effects of Pool Models
In the original formulation of Lifson et al. (17, 18)
both isotopes are assumed to turn over only in the body water pool. Hence, flow rates are calculated as
Kd · N and
Ko · N. However, this is an obvious
contradiction, because the fundamental basis of the technique is that
the oxygen isotope is in exchange equilibrium with the oxygen in
dissolved CO2 and bicarbonate. Hence, oxygen must spread
not only into the body water pool but also into the carbonate and
dissolved CO2 pools. In humans, Schoeller et al. (34) suggested that the body water from oxygen dilution is
overestimated by ~0.7%. Because the dilution space technique has an
analytic sensitivity ranging from 0.2 to 1.3% for oxygen (9,
34), the correspondence between the oxygen isotope dilution
space and the body water estimated from desiccation is good. For the
deuterium dilution space, in 79 animal studies of 35 species (reviewed
in Ref. 36), it exceeds the oxygen space and the body
water by desiccation by 4.57% (5.6-20%), suggesting the
existence of a rapid exchange pool for hydrogen, apart from the
hydrogen in body water. It is generally assumed to represent a
reversible exchange with labile hydrogen on amino groups in protein and
lipids, as previously stated.
The first equation developed by Lifson et al. (18) ignores
this difference in pool sizes and assumes the body water pool (N) to be
equivalent to the oxygen dilution space. Later, Schoeller et al.
(32) and Coward and Prentice (10) suggested
that the different pool sizes should be taken into account in the
calculations. However, the theoretical superiority of the two-pool
models is not evident in all the conditions. Lifson et al.
(18) first evaluated these effects and observed that the
two-pool model yielded a difference of 2% (SD 11%) against 3%
(SD 10%) for the single pool. In the same way Speakman
(36) concluded that it would be better to use a single
pool because of a large variation in the accuracy of the individual
estimates (23%) that did not allow significant difference between the
pool models. Nowadays, such comparisons are not easy because there are
three different approaches that can be employed for the two-pool model.
In the first approach, the individual measure of dilution spaces for a
given animal are used in the Eq. 8 of Coward et al.
(10). From our results, there is clear evidence that this
is not the best procedure to apply in rats. Regardless of period and
body mass changes, this equation results in an underestimation of
~20% of rCO2. This suggests that in animals of such
body mass or at least in rats, such equations are inadequate
independent of growth. Schoeller et al. (30, 32)
introduced a second variation for the pool ratio based on large samples
of pool size measurements. During isolation when the pool size
increased, this equation results in an underestimation of
rCO2 between 5 and 10%, significantly different from
indirect calorimetry data. Conversely, the same equation is validated
during simulated microgravity. Thus when body weight is stable over the experimental period, a two-pool model with the use of a fixed R is
valid. The third approach calculates an average pool size ratio for the
group of animals under study and uses that ratio to derive a
group-specific modification to the individual equation. In the latter,
there are related methods that advocate using both population and group
means: a combination method is to calculate an unweighted average of
the group and population means (28, 33) and another method
is to calculate an average weighted by sample size (28,
33) or variance (11). Whatever the period studied,
all these equations yielded approximately the same underestimation of
the rCO2 (10-15%), except for Eq. 13
[Speakman (36)], which uses R estimated from the group
studied. This suggests that regardless of the R combination method
(from group and/or population), the impact on the energy requirement
calculations is equivalent. The reason Eq. 13 of Speakman
(36) differs from the other equations may be attributable
to the fractionation processes that are discussed later. We should
mention that validation studies covering a range of body sizes
[barnache geese (26), tufted duck (2), and sea lions (7)] indicated that some form of the two-pool
model is superior. Conversely, when Speakman recalculated
rCO2 from the original studies of McClintock and
Lifson (21, 22) to compare the single- and two-pool model,
he observed that the single pool is more reliable (36).
Thus the selection of a pool model to apply to small animals is not
clear-cut.
From our study it seems difficult to prove the superiority of the
single- or the two-pool models. As with Speakman (36), we
found that the single-pool model is more reliable in small animals. But
undoubtedly some two-pool models using R from the group data give good
agreement with calorimetry when the pool space is constant during the
DLW measurement. Therefore, in absence of clear indication from the
literature, we suggest that the one-pool model yields more reliable DLW
results during both isolation and simulated microgravity in rats.
Methods of Calculation of the Isotope Constant Elimination Rates
LS and RMA fitting approaches.
Given the impact of the different regression models on the derived
gradients, the choice of which model to employ depends on the relative
magnitudes of error in time and isotope abundance variables. Precision
estimates for both isotope measurements by ratio mass spectrometry vary
between 0.5 and 1.5%. The question that arises is the precision error
for the sample timing. Primarily, this precision is very good
especially for blood samples. The precision on timing is so great
relative to the error in mass spectrometry that it will always be
appropriate to use the LS fit procedure. In the case of urine sampling,
the timing precision is reduced because of the difficulty of ascribing
a time to samples that have been stored in the bladder over a variable
period of time. In addition, these samples may include different
proportions of sample from different times. Thus the decision to use LS
or RMA to derive the elimination rate is not clear-cut. During our study, the urine samples were taken within the half-hour devoted to
daily maintenance, so that special attention was paid to the 24-h
interval. Significantly higher Ko and
Kd from RMA related to LS were noted, but the
Ko and Kd differences
that pass directly into the CO2 production were not
modified and the effects on energy expenditure were <0.5% (data not
shown). This suggests that respecting the 24-h interval overcomes the
problem of urine storage in the bladder and that LS regression can be
used without any transformation to RMA during either isolation or
simulated microgravity in rats.
Multisampling versus two-sampling method.
By using the two-point approach, the intricacies of the patterns of
decline are absolutely irrelevant. The two-point technique measures the
average rate at which the isotopes decline throughout the measurement
period. The error in the elimination rate using the two-sample approach
depends on two things: the precision and accuracy of the initial and
final isotope estimates and the timing of these samples. The two-sample
techniques ignore the temporal variation in isotope abundance in the
time between the samples and this led Coward and Prentice
(10) to suggest that the true error is underestimated
because there is also some contribution of the variation in isotope
abundance during the measurement period. On the other hand, and we
agree with this opinion, Speakman et al. (39) concluded
that this is not possible because the calculation fo
TOP
ABSTRACT
INTRODUCTION
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