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2.1. Relationship between body weight and energy expenditure
2.2. Calculations of centiles
3.1. Relationship between total energy expenditure and body weight
3.2. Construction of centiles
Discussion summarized by J.V.G.A. Durnin
P.S.W. DAVIES, J.E. CAMERON and A. LUCAS*
* MRC Dunn Nutrition Unit, Downham's
Lane, Milton Road, Cambridge CB4 1XJ, U.K.
Knowledge of total energy expenditure is of major biological and clinical importance, particularly during infancy. Ethical and practical problems, however, have limited the acquisition of such data during early life. The doubly labelled water technique has been used to measure, non invasively, total energy expenditure in a cohort of 41 normal full-term infants, at or close to 1.5, 3 and 6 months of age. Mean total energy expenditure was 270, 280 and 330 kJ/kg body weight per day at these ages.
The most appropriate method of expressing energy expenditure relative to body weight was investigated in a slightly larger cohort of 50 full-term infants, which includes the previous 41 infants at the same age points. Regression analysis revealed that the relationship between body weight and energy expenditure at each age could be adjusted for by expressing energy expenditure per kg0.65 per kg0.43 and per kg0.55 body weight at the three age points studied. A pooled estimate obtained from parallel line regression analysis was per kg0.56. This is very close to per kg0.5 or square root of body weight.
Centile charts have been constructed using a parametric approach for total energy expenditure in the first 6 months of life. Total energy expenditure has been expressed as kJ/d, kJ/kg body weight per day, per day. These data provide a new reference for energy expenditure in early infancy. This reference may be used in future studies to assess abnormal energy metabolism in disease.
Knowledge of total energy expenditure is of major biological and clinical importance, particularly during infancy. This information is required for the estimation of recommended daily amounts of food energy (DHSS, 1979), and is essential for designing artificial infant feeds. Moreover, normal data on total energy expenditure are required as reference data for studies on lesions in energy metabolism in disease states such as cystic fibrosis (SHEPHERD et al., 1988), congenital heart disease, and obesity (ROBERTS et al., 1988b).
Such data are lacking due to the practical and ethical problems of measuring total energy expenditure in infants. Long-established techniques for measuring total energy expenditure using direct or indirect calorimetry are unacceptable in childhood since they require that the subject is isolated for long periods. Recently, the doubly labelled water technique for measuring total energy expenditure non-invasively in free-living subjects has been validated in infants (ROBERTS et al., 1986; JONES et al., 1987). We have used this technique to measure total energy expenditure in a cohort of healthy British children.
Using the LMS method (COLE, 1988), we have derived centiles for total energy expenditure in the first 6 months of life. Further we have examined the most appropriate way to express energy expenditure relative to body weight. Traditionally, measurements of energy expenditure and energy requirements have been expressed per kg body weight (BEAL, 1970; WHO, 1973; DAVIDSON, PASSMORE and BROCK, 1973; OWEN et al., 1987). It has been suggested, however, that energy expenditure and energy requirements should be expressed relative to other measures of 'metabolic size' such as body surface area (FLEISCH, 1951) or lean body mass (OWEN et al., 1987). However, since these latter methods of adjustment require additional measurements, they have not been universally adopted. Nevertheless, it is important that an appropriate adjustment is made for 'metabolic size' since this is strongly related to energy expenditure and intake, and without such an adjustment comparisons of energy metabolism between groups and individuals may be invalid.
The most appropriate method of adjusting energy expenditure for body size in infancy, however, has not been adequately investigated. Thus we have studied the relationship between total energy expenditure and body weight in a cohort of infants.
It is hoped that these data can
serve as a reference for further studies into energy metabolism in both health and
2.1. Relationship between body weight and energy expenditure
2.2. Calculations of centiles
Forty-one, full-term, healthy infants were recruited into the major study within 5 days of birth. In the first 3 months, approximately half the cohort (21 subjects) were exclusively breast-fed and the remaining infants were fed on a cow's milk formula. By 6 months of age all infants had been introduced to weaning foods. Measurements of total energy expenditure were made over a period of 7 days on three occasions, the study period ending at or close to 6 weeks, 3 months and 6 months of age; we shall refer to these as periods A, B and C, respectively.
Total energy expenditure was measured using the doubly labelled water technique. Two stable, non-toxic isotopes of water (H218O and 2H2O) were administered orally. In breast-fed infants the dose was most easily administered by allowing the infant to suck on a nasogastric tube attached to a syringe, containing the dose. Usually no pressure was required on the plunger of the syringe, the infant's sucking being sufficient to draw the dose from the syringe. In formula-fed infants the dose was added to approximately 10 mL of 'ready-to-feed' formula in a standard feeding bottle. In each case the weight of the dose given was determined to five decimal places. A dose consisting of 0.28 g per kg body weight of 14.6% H218O and 0.1 g per kg body weight of 99% 2H2O was used. A single urine sample was collected immediately before administration of the dose to determine natural concentrations of 2H2O and H218O in body fluids. Urine samples were then collected 5 hours postdose, and thereafter a timed sample was collected every 24 hours for 7 days. Isotopic enrichment of the urine samples was measured relative to a local standard by isotope ratio mass spectrometry (Aqua-Sira model, VG Isogas, Cheshire, England). Results were expressed as enrichment relative to a local standard:
where RS and RR are the isotope ratios of the sample and reference water, respectively.
In this laboratory linear regression equations are obtained from the log-transformed enrichments of 2H and 18O vs time. The regression coefficients are therefore the disappearance rates, Kd and kO of 2H (deuterium) and 18O, respectively.
The dilution space of each isotope at the beginning of the study period is calculated as:
N = dilution space (g)
A = dose of isotope given (g)
a = a portion of dose retained for mass spectrometer analysis (g)
T = tap water in which portion (a) is diluted (g)
Ea = enrichment of portion
Et = enrichment of tap water
Es = antilog of intercept of regression line
Ep = enrichment of predose urine sample
In fast growing infants it is necessary to account for the changing size of the isotope dilution spaces during the study period. Output rates of H2O and CO2 were calculated as follows:
r1H2O = Nd *
r1H2O + r1CO2 = No * ko - Qo
r1CO2 = (No * ko - Qo) - (Nd * kd - Qd)
where Qd and Qo are the changes in isotope dilution space (g/d) over the study period.
True output ratios of H2O and CO2 were calculated taking into account the proportion of water (x) fractionated in infancy, and the fractionation factors for 2H and 18O in water vapour and 18O in carbon dioxide known as f1, f2 and f3 respectively. The value of x used in the study was 0.13. True output rates were calculated thus:
Nd * kd = x * f1 r1H2O + r1H2O(1-x) = r1H2O(x * f1 +1-x) ... (1)
No * ko = 2 * f3 * r1CO2 + x * f2 * r1H2O + r1H2O(1-x) = 2 * f3 * r1CO2 + r1H2O(x * f2 +1-x) ... (2)
From (1) it can be seen that:
and substitution of this into (2) gives:
Assuming a respiratory quotient (RQ) of 0.87 at periods A and B and 0.855 at period C (BLACK et al., 1986) total energy expenditure can be calculated using Weir's formula (WEIR, 1949). Body weight was measured to the nearest gram at the beginning and end of the study period.
The relationship between body weight (Wt) and energy expenditure (EE) can be adjusted for by linear regression. Alternatively, an index of the form EE/Wtp can be used, where the value of p, the power of body weight, is chosen to make the index highly correlated with EE but uncorrelated with Wt.
The appeal of this latter approach is that it is already standard practice to work with the index EE/Wt, i.e., energy expenditure per kg body weight. This is a special case of the more general index, where the power of Wt is 1.
There are several different ways of determining the best value for p, involving slightly different assumptions, but they give very similar answers. The simplest approach, which has an obvious connection with linear regression adjustment, is to consider the correlation between the logarithm of the index EE/Wtp and the logarithm of Wt. The log index can be rearranged as follows:
log(EE/Wtp) = log(EE) - p * log(Wt)
which shows why logarithms are useful here. They allow the index to be expressed as a linear function of logEE and logWt, which is suitable for analysis by linear regression.
If the log index is to be uncorrelated with logWt, then p must be chosen to remove all the logWt information from logEE. This is equivalent to saying that p should be the slope of the regression line relating logEE to logWt. Thus p can be estimated as the regression coefficient from the regression of logEE on logWt. Natural logarithms, to base e, are used.
In general, the relationship between EE and Wt is likely to change with age, so that simultaneous age and Wt adjustment is required. As the data were collected at three distinct ages, the power p can be estimated for each age group separately. This also gives three distinct intercepts, these being the logs of the geometric mean EE/Wtp for each age group.
For this analysis the repeated measures or longitudinal nature of the data is ignored. The interest is in the cross-sectional or between-subjects relationship between EE and Wt at different ages, not the within-subject changes from one age to another.
In practice, the standard errors of p are large and there is a potential advantage in using an average figure for the slope, so long as the individual values are not too dissimilar. It is thus possible to repeat the regression analysis, fitting three intercepts as before, but a single regression slope, so that the three lines are parallel to each other.
A third analysis can also be carried out, involving one intercept and one slope, and this effectively ignores the age grouping entirely and treats all the data as a single group. This is found not to be appropriate here.
Centiles for total energy expenditure can be derived from the raw data in a number of ways. Firstly, the data could be analysed non-parametrically, by direct counting. This approach obviously makes no assumption about the shape of the distribution of the data. However, large numbers are required, if the centiles are to be accurate and reliable.
Secondly, centiles can be derived using a parametric approach. This method uses the mean and standard deviation of the data to derive centiles assuming the distribution of the data is Gaussian or can be transformed to a Gaussian distribution. The major, single advantage of this approach is that many fewer data points are required to achieve the same level of accuracy. For example, four times as many data points are required by the non-parametric approach to achieve the same level of accuracy as the parametric approach when defining the 3rd centile.
Thirdly, a new approach to calculating centiles has recently been published (COLE, 1988). This technique, known as the LMS method, has been successfully applied to data pertaining to height and weight. We have used this latter technique. The details of the method have been published elsewhere (COLE, 1988). Suffice it to say here that the data are summarized by three parameters, the L, M and S parameters.
Firstly, a generalized mean (M) is calculated by interpretation between the arithmetic mean, the harmonic mean and the geometric mean. Secondly, one then calculates the Box-Cox power (L) (BOX and COX, 1964) that normalizes the data. Finally, a generalized coefficient of variation (S) is calculated for the data. Once these three values are known, any centile can be calculated using the formula, centilez = M(1 + L * Sz)1/L, where z is the standard normal deviate associated with the required centile.
The values for L, M and S were calculated from the data at periods A, B and C. If these values are then smoothed, the centiles produced from them will also change smoothly with age.
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