The formulation of basal metabolic standards has resulted in the development of an extensive literature; work pertinent to infants will be reviewed (BENEDICT and TALBOT, 1921; LEVINE and MARPLES, 1931; KARLBERG, 1952; LEE and ILIFF, 1956; SCHOFIELD, 1985).
Extensive observations on the basal metabolism of 77 normal infants (40 boys and 33 girls, ages 8 days to 25 months) were used to derive normal standards (BENEDICT and TALBOT, 1921). Observations of basal metabolism were made during sleep with minimal extraneous muscular activity and minimal influence of food (1 to 1.5 hour after the ingestion of a small meal). Total basal expenditure increased with body weight; the low expenditure (kcal/kg/d) after birth increased to a maximum at approximately 1 to 2 years, with a tendency to decrease thereafter. The values of 23 individuals studied longitudinally, however, did not consistently show the trend of the composite curves. A number of physiological factors were found to influence basal metabolism, such as weight, length, and age, although weight had by far the greatest influence. By means of partial correlation, independent effects of weight, height, and age on metabolism were establish ed. Benedict noted a profound physiological difference in the metabolism of infants who weighed 6 to 8 kg; this greater metabolic intensity per unit active protoplasmic tissue, however, was not substantiated by other investigators.
LEVINE and MARPLES (1931) revised prediction curves for basal metabolism based on the data of BENEDICT and TALBOT (1921). The standards were derived from 137 observations of infants, aged 8 days to 25 months. Benedict claimed that these infants were normal and typical of infants at large; by Levine's assessment the infants were underweight for age. High correlations were detected between basal metabolism and age (r = 0.91), weight (r = 0.95), length (r = 0.96), and body surface area (r = 0.96). Independent effects of age, weight, height, and body surface on heat production were demonstrated, but the influence of age was apparently trivial. A multiple regression equation using weight and height was derived from the data:
c = 28.12 WT +8.40 HT 362.18
where calories (c) are expressed in kcal/24 h, weight (WT) in kg, and height (HT) in cm.
In Scandinavia, KARLBERG (1952) performed extensive studies on 60 normal infants who ranged in age from 1 week to 1 year. Karlberg's measurements were made on fasted infants in the morning or early forenoon; a barbituric acid (Hexobarbital) preparation was used as a sedative. Among infants of the same weight, thin infants had higher metabolic rates than normal weight and overweight infants. Among infants of the same height, thin infants had lower expenditures than averagesized infants. Karlberg's standards were based on weight and height for infants 1 week to 1 year of age:
c = WT^{.611} * HT^{.951} * 0.0829
where calories (c) are expressed in kcal/h, weight (WT) in kg, and height (HT) in cm.
LEE and ILIFF (1956) measured the basal metabolism of 78 healthy infants (aged 1 through 37 months) in an opencircuit chamber within 3.5 hours of feeding. No significant trend in energy expenditure, standardized by body weight, was demonstrated with age. There was substantial individual variation in energy expenditure over time; many of the individual curves peaked somewhere between 5 to 16 months.
Schofield compiled data of basal metabolism from BENEDICT and TALBOT (1914, 1921), CLAGETT and HATHAWAY (1941), HARRIS and BENEDICT (1919), and KARLBERG (1952). Predictive models were developed and the relative contributions to basal metabolism of various independent variables i.e., age, sex, weight, height, and weight/height were assessed. As expected, there were strong relationships between all measures; height and weight predicted BMR, as did the more complicated variables. For the under3years age group, height contributed significantly to the prediction of BMR. The following equations were computed with which to predict the BMR of children under 3 years:
m BMR = 0.249 WT  0.127 
R = 0.95 SEE = 0.292 
f BMR = 0.244 WT  0.130 
R = 0.96 SEE = 0.245 
m BMR = 0.0007 WT + 6.349 HT  2.584 
R = 0.97 SEE = 0.242 
f BMR = 0.068 WT + 4.281 HT  1.730 
R = 0.97 SEE = 0.216 
where BMR is in MJ/24 h, weight (WT) in kg, and height (HT) in m. SEE is the standard error of the estimate.
There was fair conformance between the standard equations of BenedictLevine and Schofield, which was not surprising since Schofield incorporated Benedict's data. Karlberg's standard equation yielded generally lower values of basal metabolism. Application of the three standard equations to the 60 infants, ages 1 week to 1 year, described in Karlberg's publication, resulted in the following mean values for basal metabolism: 54.6(3.2), 50.8(1.6), and 53.8(4.3) kcal/kg/d for the BenedictLevine, Karlberg, and Schofield equations, respectively (Figure 5). The slope relating SMR (kcal/kg/d) and age was positive by BenedictLevine, negative by Karlberg, and insignificant by Schofield predictions. Differences may be explained, in part, by the dissimilarities in subjects and experimental design, i.e., fed vs fasted state, time of day, etc.
In our studies of energy requirements during infancy, we have measured the basal metabolism of infants at 1 and 4 months of age. For the purposes of this presentation, data from two publications have been compiled (BUTTE, SMITH, and GARZA, 1989; BUTTE et al., 1989). A description of the 105 infants studied is presented in Table 3. At the time of observation, these breastfed (BF) and formulafed (FF) infants were healthy and growing adequately. Energy expenditure was measured in an indirect calorimeter for 3 to 4 consecutive hours after an ad libitum feeding of human milk or formula. The sleeping metabolic rate (SMR) was defined operationally as the mean energy expenditure 2 to 3 or 3 to 4 hours postprandially, whichever was smaller and/or available. The minimal 5minute interval observed during the SMR period was identified and designated as minimal observable energy expenditure (MOEE).
Table 3. Infant description
Age (mo) 

1 
4 

Sample size (n) 
54 
51 
Sex (M/F) 
32/22 
23/28 
Weight (kg) 
4.6(0.5) * 
6.6(0.6) 
Length (cm) 
55.0(1.7) 
62.4(19) 
Weight gain (g/d) 
36.1(11.7) 
19.3(8.4) 
Weight gain (g/kg/d) 
8.4(2.7) 
3.0(1.3) 
Sum of skinfolds (mm) ^{+} 
34.0(6.0) 
44.6(8.2) 
* Mean (SD).
^{+} Sum of triceps, biceps, subscapular, quadriceps, and flank skinfold thicknesses.
The combined results of SMR and MOEE are shown in Table 4. The ratio of MOEE/SMR was 0.89(0.04). SMR and MOEE were highly correlated (r = 0.97; p < 0.001). Our results did not enable us to determine whether SMR or MOEE had reached minimum values; in our first study, energy expenditure steadily decreased throughout the four postprandial hours. In our second study, energy expenditure tended to plateau between the third and fourth hour of observation.
Table 4. Sleeping metabolic rate (SMR) and minimal observable energy expenditure (MOE) of 105 infants at 1 and 4 months of age
Age (mo) 

1 
4 

SMR (kcal/d) 
244(30) * 
337(38) 

(kcal/kg/d) 
53(5) 
51(5) 

MOE (kcal/d) 
216(27) 
301(36) 

(kcal/kg/d) 
47(5) 
46(5) 

MOEE/SMR 
0.89(0.05) 
0.89(0.04) 
* Mean (SD).
As expected, SMR (kcal/d) increased with body size, was positively correlated with weight (r = 0.86) (Figure 6), length (r = 0.86), weight/length^{2} (r = 0.62), sum of 5 skinfold thicknesses (r = 0.57), energy intake (kcal/d; r = 0.48), and was negatively correlated with weight gain (g/d; r = 0.41; p < 0.001). Standardized by body weight, SMR (kcal/kg/d) was inversely related to body size. SMR (kcal/kg/d) was negatively associated with weight (r = 0.29), weight/length^{2} (r = 0.41), sum of skinfolds (r = 0.33); SMR (kcal/kg/d) was positively associated with energy intake (kcal/kg/d; r = 0.22; p < 0.05), but not significantly correlated with weight gain (g/kg/d) or length.
SMR and MOEE (kcal/d) differed significantly by feeding mode (FF > BF; p < 0.05), age (1 < 4 mo; p < 0.001), and sex (M > F; p < 0.03). Standardized by weight, SMR and MOEE were statistically lower among the breastfed infants than among the formulafed infants (p < 0.01). Values did not differ statistically by age or sex.
The positive linear relationship between SMR and body weight was highly significant (Table 5A). Weight or length alone accounted for 74% of the variability in SMR; the combination of weight and length accounted for 77% of the variability. To identify the power of body weight most suitable for the standardization of SMR, the data were fitted to the equation:
ln(SMR) = ln(k) + In(WT)
(Table 5B; Figure 7). Using this equation, the most suitable power was 0.9 (R^{2} = 0.77). Controlling for age (Table 5C), the most suitable power was 0.7. This equation accounted for 78% of the variability in SMR. Addition of length to the model increased R^{2} by 1%.
Table 5. Regression analysis for predicting sleeping metabolic rate (SMR) from weight, length, and age *
Adjusted 

R^{2} 
SEE 

A. 
SMR = 43.9 +43.8 WT 
0.74 
29.2 
SMR = 411.0 +12.0 LN 
0.74 
29.5 

SMR = 194 +23.4 WT +6.0 LN 
0.77 
27.8 

B. 
ln SMR = 4.2 +0.9 ln WT 
0.77 
0.096 
ln SMR = 4.4 +2.5 ln LN 
0.76 
0.098 

ln SMR = 0.2 +0.5 ln WT +1.1 ln LN 
0.79 
0.091 

C. 
ln SMR = 4.4 +0.08 age +0.7 ln WT 
0.78 
0.094 
ln SMR = 3.0 +0.06 age +2.1 ln LN 
0.76 
0.098 

ln SMR = 0.7 +0.03 age +0.5 ln WT +1.0 ln LN 
0.79 
0.091 
* Sleeping metabolic rate (SMR) in kcal/d, weight (WT) in kg, length (LN) in cm, and age in months; n = 105.
Regression analysis was used to explore the predictability of SMR by feeding mode, age, sex, weight, length, weight/length^{2}, sum of skinfolds, and weight gain (Table 6). The best predictive model contained weight/length^{2}, feeding mode, and length, and explained 78% of the variability of SMR. Elimination of feeding mode from this model decreased R^{2} to 76%. The combination of weight, length, and feeding mode also resulted in an R^{2} of 78%. As expected, the anthropometric indices were highly correlated with weight and length, which were virtually exchangeable. Variables entered in these predictive equations were representative of body mass and body dimension. Feeding mode was not highly correlated with the other variables, and therefore made a small independent contribution.
Table 6. Multiple regression analysis to predict sleeping metabolic rate (SMR) from infant characteristics  feeding mode, age, sex, weight, length, weight/length^{2}, sum of skinfolds, and weight gain; n = 105
Variables in the model 
Adjusted 

R^{2} 
SEE 

1) Weight, length, feeding mode 
0.78 
26.9 
2) Weight, length * 
0.76 
27.8 
3) Weight/length^{2}, feeding mode, length 
0.78 
26.8 
4) Weight/length^{2}, length * 
0.76 
27.7 
* Feeding mode eliminated from analysis.
In a subset of 40 infants (BUTTE et al., 1989), estimations of fatfree body mass (FFBM) and total daily energy expenditure (TDEE) were available from doublylabelled water measurements. Mean SMR was 50.4 kcal/kg/d or 66.7 kcal/kg FFBM/d. SMR (kcal/d) was significantly correlated with FFBM (kg) (r = 0.82) (Figure 8) and TDEE (r = 0.90) (Figure 9), while negatively correlated with FFBM (%WT)(r = 0.69; p < 0.001). Multiple regression analysis was used to explore the additional contribution of FFBM derived from oxygen18 dilution (in absolute terms and as a percentage of body weight) to the prediction of SMR (Table 7A). The R^{2} from this procedure was 0.86; the addition of FFBM did not improve the predictive ability of the model.
Table 7. Multiple regression analysis to predict A. sleeping metabolic rate (SMR) and B. total daily energy expenditure (TDEE) from infant characteristics  feeding mode, age, sex, weight, length, weight/length^{2}, sum of skinfolds, weight gain, and fatfree body mass (FFBM); n = 40
Variables in the model 
Adjusted 

R^{2} 
SEE 

A. 
SMR 

Weight, feeding mode, lengths 
0.86 
21.7 

Feeding mode, weight/length, length 
0.86 
21.5 

B. 
TDEE 
0.84 
35.4 
SMR, FFBM (absolute) 
0.84 
35.4 
Since SMR has been used to predict total daily energy expenditure, and therefore the daily energy requirement of adults (FAO/WHO/UNU, 1985), we explored the predictability of TDEE from SMR (Table 7B). The equation describing SMR as a function of TDEE was:
TDEE (kcal/d) = 31 +1.4 SMR
(kcal/d);
R^{2} = 0.81, SEE = 39.3.
The ratio of TDEE/SMR increased from 1.27(0.14) at 1 month to 1.35(0.13) at 4 months of age, as a result of the increasing mobility of the infants. Regression analysis indicated that SMR and FFBM (absolute) were the best predictors of TDEE (R^{2} = 0.84; SEE = 35.4). However, the ability to predict the TDEE of an individual from SMR with or without FFBM is limited; the potential error in the prediction for an individual would be approximately ±70 to 80 kcal/d.
In conclusion, SMR has been used as
a proxy for the basal metabolism of infants. SMR, under most prevailing measurement
conditions, represents energetic processes necessary for the maintenance of life, but
also, to varying extents, represents the energy cost of growth, the thermic effect of
feeding, and subtle body movement. In infancy, basal metabolism is accounted for primarily
by the brain, liver, heart, and kidney. The decline in basal metabolism relative to body
weight is secondary to the differential growth rates of these vital organs relative to
muscle and fat. The basal metabolism of infants is roughly proportional to body weight,
rather than to the fractional power of 0.75 identified for adults. SMR (kcal/kg/d) appears
to decline slightly over the first year of life, although this finding remains
controversial. Our series of studies has shown that SMR (kcal/kg/d) is inversely related
to body weight and parameters of body fatness. SMR (kcal/kg/d) differed by feeding mode,
but not by age or sex. The parameters weight/length^{2}, feeding mode, and length,
or weight, length, and feeding mode accounted for 78% of the variability in SMR. In a
subset analysis, FFBM did not augment the predictability of SMR. SMR and FFBM were shown
to predict 84% of the variability of TDEE. The advances in measurements of SMR have yet to
account completely for the individual variability observed in the basal metabolism of
infants.
This work is a publication of the USDA/ARS Children's Nutrition Research Center, Department of Pediatrics, Baylor College of Medicine and Texas Children's Hospital, Houston, TX.
This project has been funded in part with federal funds from the U.S. Department of Agriculture, Agricultural Research Service under Cooperative Agreement number 587MN16100. The contents of this publication do not necessarily reflect the views or policies of the U.S. Department of Agriculture, nor does mention of trade names, commercial products, or organizations imply endorsement by the U.S. Government.