3.1. Relationship between total energy expenditure and body weight
3.2. Construction of centiles
Table 1 shows a number of the demographic characteristics of the infants recruited for the major study. The means and standard deviations of age, length and weight are shown in Table 2 and the means and standard deviations for total energy expenditure are shown in Table 3. Dose loss, caused by posseting or vomiting during or immediately following the administration of the dose resulted in a loss of 2,1 and 4 data points at periods A, B and C, respectively. The mean and standard deviation of the isotopic enrichments in the predose urine samples, the disappearance rate constants Ko and Kd and the intercepts of the regression lines of log enrichment versus time are shown in Table 4.
Table 1. Some demographic characteristics of the infants recruited into the study
Gestational age (wks) 
Mean 
39.9 

SD 
1.34 

Birth weight (g) 
Mean 
3513 

SD 
419 

Percentage of infants 

Standard vaginal delivery 
68 

Caesarian section 
17 

Male 
39 

Breastfed 
51 

Social classes 1 and 2 
63 

Social class 3 
27 
Table 2. Means and standard deviations of age, weight and length of the infants studied
Period 
n 
AGE (d) 
WEIGHT (g) 
LENGTH (mm) 

Mean 
SD 
Mean 
SD 
Mean 
SD 

A 
39 
36 
3.2 
4653 
397 
551 
16 
B 
40 
77 
4.0 
5792 
468 
592 
17 
C 
37 
181 
5.1 
7704 
773 
667 
21 
Table 3. Means and standard deviation of total energy expenditure expressed kJ/d and kJ/kg per day
TOTAL ENERGY EXPENDITURE 

kJ/d 
kJ/kg per day 

Period 
Mean 
SD 
Mean 
SD 
A 
1280 
390 
270 
70 
B 
1640 
400 
280 
60 
C 
2530 
420 
330 
50 
Table 4. Predose isotope enrichments, rate constants (kd, ko) and intercepts of the regression lines for the cohort of fullterm infants studied
PERIOD 
A 
B 
C 

Mean 
SD 
Mean 
SD 
Mean 
SD 

^{2}H enrichment in predose urine (‰) 
21.5 
7.2 
21.1 
7.8 
21.9 
7.0 
^{18}O enrichment in predose urine (‰) 
3.4 
1.5 
3.6 
1.7 
3.7 
1.3 
kd 
0.251 
0.032 
0.239 
0.030 
0.221 
0.034 
ko 
0.292 
0.035 
0.282 
0.032 
0.268 
0.037 
^{2}H intercept 
1065.2 
170.9 
1090.2 
160.4 
1461.8 
169.0 
^{18}O intercept 
215.0 
34.8 
223.7 
28.5 
230.6 
27.5 
The regression coefficients and intercept obtained from the regressions of logEE and logWt are given in Table 5. In the first analysis, the individual regression coefficients at each period were not significantly different (variance ratio = 0.2 on 2 and 130 df). This led to the second analysis, where the regression coefficients for each period were constrained to be the same, but with different intercepts. The intercepts were significantly different (variance ratio = 5.6 on 2 and 132 df), showing that after adjustment of weight, there remained an important age effect.
Table 5. Intercepts, regression coefficients and standard errors from the regression of logEE on logWt at three periods of age. In Analysis 1 the periods are treated separately, while in Analysis 2 the regression coefficients for each period are constrained to be the same
Period 
Intercept 
Regression coefficient 
Standard error 

Analysis 1 
A 
4.72 
0.65 
0.40 
B 
5.24 
0.43 
0.42 

C 
5.27 
0.55 
0.26 

Analysis 2 
A 
4.85 
0.56 
0.22 
B 
5.02 
0.56 
0.22 

C 
5.26 
0.56 
0.22 
The average regression coefficient for the relationship between log body weight and log energy expenditure of 0.56 (SE = 0.22) is significantly different both from 0 and from 1. A regression coefficient of 0 would have indicated that energy expenditure was not related to body weight at all, whilst a regression coefficient of 1 would indicate that an adjustment to kcal or kJ/kg body weight was appropriate to remove the body weight effect upon energy expenditure. Conversely, the average regression coefficient of 0.56 is very close to 0.50, which indicates that a numerically convenient and statistically valid adjustment of energy expenditure in early infancy would be to express energy expenditure as kcal/kg^{0.5} or kJ/kg^{0.5}, that is per square root of body weight.
Centiles were calculated by the LMS method for total energy expenditure expressed as kJ/d, kJ/kg per day and _{} per day. The centile charts are shown in Figures 1 to 3, respectively.
We have used the doubly labelled water technique to measure noninvasively total energy expenditure over a period of 7 days, to provide the first centiles for total energy expenditure for infants up to 6 months of age.
There are a number of potential sources of error in the doubly labelled water technique that need careful consideration. These include the choice of the respiratory quotient (RQ), and the proportion of water output fractionated, the possible sequestration of isotope into body tissue, and the effect of weaning, or major changes in diet during an isotope study period.
In adult studies, using the doubly labelled water technique, an RQ of 0.85 is usually applied. Although RQ may vary throughout a study, over a period of 1014 days, the length of most adult studies, RQ will tend towards 0.85 and the use of this figure will not introduce a large error. However, an RQ value used in infants must take into account growth. BLACK et al. (1986) list unadjusted and adjusted food quotients (FQ) for infants, and conclude that the FQ and RQ can be used interchangeably in the doubly labelled water technique, due to the length of study period (7 days in our study). The value for RQ we have used at periods A and B (i.e., 0.87) is the mean of some 143 individual calculations of FQ, adjusted to allow for growth using the body composition data reported by FOMON (1974). At period C an adjusted FQ of 0.855 is used; this is based on 253 individual measurements of FQ between the ages of 4 and 12 months. Consequently, we feel that our choice of RQ is appropriate and justified.
Another source of potential error in the doubly labelled water technique is the use of an inappropriate value for the proportion of total water output that is subject to isotopic fractionation (fractionation factor). The magnitude of error produced in the final estimation of total energy expenditure due to an inappropriate choice of fractionation factor depends strongly on the kd:ko ratio. The closer this ratio is to 1 the greater the final error. In adults, the kd:ko ratio is usually about 0.75. In young infants, as water turnover is high in relation to carbon dioxide production rate, the ratio is higher (0.86, 0.85, and 0.82 at periods A, B and C, respectively, in this study). COWARD (1988) recently showed that with a kd:ko ratio of 0.90 as much as an 8% error in carbon dioxide production rate will be induced by an error of 0.1 in the value of fractionation factor used. The factor assumed in this present study (0.13) is based upon an unpublished water balance study (LUCAS, unpublished results), in a subset of infants in the present cohort.
In the validation study reported by JONES et al. (1987) a higher value (0.18) was used. This value was based upon the assumptions that breath is saturated with water and contains 3.5% carbon dioxide. Thus, breath water losses can be related to carbon dioxide production rate. Skin losses (nonsweat) were estimated using a value of 0.18 g/min/m2 insensible skin water loss, and assuming that 75% of the infants' skin was exposed to the air. While appropriate for the infants studied by JONES et al. (1987), their assumed value for the proportion of exposed skin was undoubtedly too high for the infants in our study. We estimate that a figure of about 30% would be more appropriate. Using this, and the approach of JONES et al. (1987), the mean proportion of water output fractionated in our study would have been 0.15; close to our value of 0.13.
The sequestration of isotope into tissues during the rapid growth experienced in early infancy could lead to error in the calculation of total energy expenditure. Labelled hydrogen exchanges with nonaqueous hydrogen in proteins and other tissues. In contrast, there is little nonaqueous oxygen in the body with which ^{18}O could exchange, and in any case such an exchange does not occur readily at physiological temperature and pH, JONES et al. (1987) addressed the potential problem of label sequestration in rapidly growing infants. They hypothesised that if there was significant isotope sequestration, notably of labelled hydrogen, the difference in energy expenditure (calculated by doubly labelled water) and respiratory gas exchange would be correlated with the change in body weight during the study period. No such relationship was found and these workers concluded that sequestration rates were insignificant.
Finally, changes in the enrichment of ^{2}H and ^{18}O in dietary water during a study period can produce major error in the calculation of energy expenditure with doubly labelled water (ROBERTS et al., 1988a; JONES et al., 1988). During infancy the principal factor in the change in dietary water ^{2}H and ^{18}O content is weaning. At periods A and B. the infants studied here were exclusively being breast or formulafed, while at period C, care was taken that no major change in diet occurred during the study period.
We have attempted to define the most appropriate way that an infant's energy expenditure should be expressed in relation to body weight in order to minimize the correlation between body weight and energy expenditure. We have found that a statistically valid and numerically convenient adjustment of energy expenditure would be to express energy expenditure as kcal/kg^{0.5} or kJ/kg^{0.5}, that is, per square root of body weight. We suggest that in studies on energy metabolism in early infancy this expression should be used.
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It was doubted that the reference Wt^{0.5} (i.e., body weight to the power of 0.5 = square root of body weight) had any usefulness in human infancy and childhood. It was pointed out that this power of Wt is affected by the growth of bone, fat, etc., and the influence of these tissues would alter at different growth periods.
Also, there are problems about the use of the same factor of Wt (e.g., energy per kg body weight) or of fatfree mass for wellnourished or undernourished infants, since both body composition and growth rates differ in these groups.
Davies et al. suggested that the data collected using the doublylabelled water technique on Cambridge populations might be useful as reference data. This may not be appropriate since data from upperclass Cambridge women and children may not be representative of other population groups.
The doublylabelled water method of measuring energy expenditure does not permit any breakdown of activity patterns but nevertheless is a way of measuring total energy expenditure of freeliving infants and children. It might be possible to combine this with heartrate measures to allow some qualitative assessment of physical activity patterns.