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Comparison of Several Equations and Derivation of a New Equation for Calculating Basal Metabolic Rate in Obese Children

Maimonides Medical Center Department of Pediatrics, Nutrition & Body Composition Laboratory, Brooklyn, New York

Address reprint requests to: Russell Rising, PhD, Miami Children’s Hospital Research Institute, 3100 S.W. 62^nd Avenue, Miami, FL 33155

	ABSTRACT

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Objectives: To compare basal metabolic rate (BMR) calculated by the Harris-Benedict, Ravussin, Cunningham, World Health Organization (WHO) and Schofield equations to BMR determined in an obese pediatric population. The second objective is to derive a new equation, based on measured BMR in obese children, for calculating BMR in obese pediatric patients.

Methods: The study included 110 (50 male/60 female) healthy obese subjects (BMI>28) (11.7 ± 2.8 years, 73 ± 27 kg, 152 ± 14 cm and 38 ± 6% fat) who had preprandial BMR determined by indirect calorimetry. These results were compared to BMR calculated with the five above mentioned equations. Fat-free mass was determined by bioelectrical impedance and body composition was calculated using the appropriate equation. The age groups analyzed were as follows: males 3 to 10 and 11 to 18 years old; females 3 to 10 and 11 to 18 years old. A new equation was derived by stepwise multiple regression analysis using 100 randomly selected subjects from our test group and tested using the remaining 10 subjects.

Results: Basal metabolic rate calculated by the Ravussin and Cunningham equations in all subgroups was lower (p<0.05) than measured BMR. Basal metabolic rate calculated by the Harris-Benedict equation was lower (p<0.05) than measured BMR in male populations ages 3 to 10, 11 to 18, and in the entire cohort. Measured BMR was overestimated by the Harris-Benedict equation (p<0.05) in females 11 to 18 years old; by the WHO equation (p<0.05) in both male and females 3 to 10 years old and by the Schofield equation (p<0.05) in males 11 to 18 years old. In comparison to measured BMR, the WHO equation appeared to be the most accurate for estimating BMR in males and females 11 to 18 years old. However, BMR calculated using our new equation in the 10 test subjects was similar to measured BMR.

Conclusions: The WHO equation was the most accurate of the prediction equations studied. However, our new prediction equation may be more appropriate for calculating BMR in an obese pediatric population.

Key words: basal metabolic rate, obesity, body composition, prediction equations

	INTRODUCTION

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Recent studies have been conducted in an attempt to determine the most accurate prediction equation for calculating basal metabolic rate (BMR) in children. Kaplan and coworkers [1] found a significant difference between measured BMR and BMR calculated by the World Health Organization (WHO) equation in 19 obese children. However, these investigators also found no difference between the measured BMR and that predicted by the Harris-Benedict (HB) and Schofield (SCF) height weight equations. In contrast, Dietz and coworkers [2] found no significant difference between measured BMR and that estimated by the WHO equation in the mixed group of obese and non-obese children. However, these investigators found that BMR, calculated using the Cunningham equation, overestimated measured BMR. Furthermore, Molnar [3] stated that all but the Cunningham equation overestimated BMR in both obese and non-obese children in comparison with measured values.

In our analysis we determined the most accurate equation for use in the obese pediatric population by comparing BMR, measured by indirect calorimetry, to BMR calculated from the five equations. Furthermore, we derived a new BMR equation, based on accurate measurements of BMR in obese children, specific for calculating BMR in an obese pediatric population.

	METHODS

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Subjects
One hundred and ten obese (BMI>28) pediatric patients (50 male/60 female) who had measurements of preprandial BMR (BMR) between 1992–1996 were used for analysis (Table 1). Eighty-one percent of the patients were Caucasian, 11% Hispanic and 8% African-American. All subjects were healthy other than obesity.

To ensure a resting awake state, all subjects were instructed to avoid unnecessary movements and watch non-violent programs or videos. A technician monitored the patient during the entire test. Body composition was assessed by measuring resistance and reactance with a Xitron 4000B impedance analyzer (Xitron Technologies, San Diego, CA) set at 50 kHz and fat-free mass and percent fat were calculated using Weight Manager (RJL systems, version 2.05).

Statistics
Statistical analysis was performed with Microsoft Excel (version 4.0). The measured BMR of each of the following groups were compared separately to BMRs (kcal/d) estimated by each equation according to the age groups listed in Table 1. Paired t-test was used to determine differences between measured BMR and BMR calculated by each equation.

Derivation of a New Prediction Equation
The new prediction equation was derived using SPSS software (version 7.0, SPSS inc, Chicago, IL) utilizing 100 randomly selected obese subjects from our study group (11 ± 2.8 years, 72 ± 26 kg, 38 ± 5.4% fat). Ten obese subjects were reserved for testing of the equation (13 ± 2.9 years, 88 ± 32 kg, 39 ± 6.3% fat). Stepwise multiple regression analysis (forward selection technique) was used with measured BMR (kcal/day), as the dependent variable, and body weight (kg), fat-free mass (kg), fat mass (kg), age (years), and height (cm) entered as independent variables. Variables were selected if they met the 5% level of significance. All data were expressed as mean ± standard deviation.

	RESULTS

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The differences between measured BMR and BMR calculated from each equation for all of our groups is shown in Table 2. In comparison to measured BMR, both the Ravussin and Cunningham equations underestimated BMR (p<0.05) in all subgroups as well as in the entire cohort (p<0.05). The Harris-Benedict equation underestimated (p<0.05) BMR in 3 to 10 and 11 to 18 year old males and in the entire cohort, while it overestimated (p<0.05) BMR in the 11- to 18-year-old female group. The Schofield equation overestimated (p<0.05) BMR in males 3 to 10 and 11 to 18 years old while underestimating (p<0.05) BMR in females 11 to 18 years old. In comparison to measured BMR, the WHO equation showed no significant differences in both 11- to 18-year-old male and female groups as well as in the entire cohort. However, the WHO equation overestimated BMR in 3- to 10-year-old males and females.

where fat-free mass (FFM) is expressed in kg, age in years, fat mass (FM) in kg; and for SEX a value of 1 is given for males and 0 for females. This equation had an R-square of 0.84 and a standard error of 153.0 kcals.

Table 3 shows the results of the comparison between measured BMR (males) and BMR calculated using the Ravussin (R), Cunningham (C) and Harris-Benedict (HB) equations, along with our new equation (D), in the 10 test patients. No differences existed between BMR, calculated using our new equation, and BMR determined by indirect calorimetry. The summary of the derivation of the new equation is shown in Table 4. All of the variables used in the equation were significant predictors of BMR. This means they were kept if they met the exclusion criteria of the model.

	DISCUSSION

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The Harris-Benedict, Ravussin, Cunningham, World Health Organization and Schofield equations are used by many clinicians in the treatment of obesity [5–9]. However, the validity of these equations becomes questionable when used in the pediatric obese population [10]. Such findings are not surprising since many of these equations were not derived using measurements of BMR utilizing indirect calorimetry, or were specific for the pediatric population. For example, Harris and Benedict derived their equation using data from healthy, non-obese infants and other subjects in the age range 20 to 70 years old, thus excluding a large group including the pediatric obese population [8]. When BMR values were not available, the respiratory quotient was estimated to be 0.85 and BMR calculated [8]. Furthermore, the same data from Harris and Benedict were included in the derivation of the Cunningham equation [7]. Using lean body mass as a predictive variable, the Ravussin equation was derived based on the data from 249 Pima Indians between the ages of 18 and 41 years old [6]. Although indirect calorimetry was used, this equation did not include an ethnically heterogeneous, pediatric population. The Schofield equation used data from studies which were done at the turn of the century [11]. Not all of the subjects used for this derivation were preprandial prior to the measurement of BMR [11].

Since none of the tested equations were appropriate for an obese pediatric population, we derived a new prediction equation specific for an obese pediatric population between the ages of 6 and 18 years. This new equation was derived based on accurate measurements of preprandial BMR by a ventilated hood indirect calorimeter in obese children within our laboratory. In a random sample of test subjects, the new equation estimated BMR to within 4% of the measured BMR. For clinicians who have no access to indirect calorimetry equipment, the new equation will provide an accurate estimate of BMR in an obese pediatric population.

It is important to use prediction equations in populations from which they were derived. This is due to individuals not within a particular population falling outside the parameters set fourth in the equation. For example, using our new equation for calculating BMR for an unusually slender adult would yield an inaccurate result. This is due to this individual not being part of our population that was used to derive the equation. Statistically, this individual was not within the scope of the data. Due to our large influx of obese children from our weight reduction program, a new equation for calculating BMR was derived that was specific for an obese population. This equation will provide health care professionals, who have limited access to indirect calorimetry equipment, a means for calculating BMR accurately in obese children.

	ACKNOWLEDGMENTS

 
We thank the Maimonides Research and Development Foundation for their generous support for this research.

Received October 1, 1997. Accepted March 1, 1998.

	REFERENCES

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1. Kaplan A, Zemel B, Neiswender K, Stallings V: Resting energy expenditure in clinical pediatrics: Measured versus prediction equations. J Pediatr 127: 200–205, 1995.[Medline]
2. Dietz H, Bandini L, Dale A, Schoeller A: Estimates of metabolic rate in obese and non-obese adolescents. J Pediatr 118: 146–149, 1991.[Medline]
3. Molnar D: Estimates of metabolic rate in obese and non-obese adolescents. J Pediatr 120: 660–661, 1992.[Medline]
4. Kinney J, Tucker HN: Energy metabolism. In "Tissue Determinants and Cellular Corollaries" New York: Raven, pp 1–19, 1992.
5. FAO/WHO/UNU Expert Consultation: "Energy and protein requirements." Geneva: World Health Organization, 1985.
6. Ravussin E, Bogardus C: Relationship of genetics, age, and physical fitness to daily energy expenditure and fuel utilization. Am J Clin Nutr 49: 968–975, 1989.
7. Cunningham JJ: A reanalysis of the factors influencing basal metabolic rate in normal adults. Am J Clin Nutr 33: 2372–2374, 1980.[Abstract/Free Full Text]
8. Harris J, Benedict G: A biometric study of basal metabolism in man. Washington DC: Carnegue Institution, publ. 279, pp 1–226, 1919.
9. Schofield WN: Predicting basal metabolic rate, new standards and review of previous work. Hum Nutr: Clin Nutr 39C: 5–40, 1985.
10. Maffeis C, Schutz Y, Micciolo R, Zoccante L, Pinelli L: Resting metabolic rate in six to ten-year-old obese and non-obese children. J Pediatr 122: 556–562, 1993.[Medline]
11. Du Bois E: The metabolism of boys 12 and 13 years old compared with the metabolism at other ages. Arch Int Med 17: 887–901, 1916.

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